The Collapse of Mechanism and the Rise of Sensibility: Science and the Shaping of Modernity, 1680-1760

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T HE C OL LAP SE OF MEC HAN IS M AND THE RISE OF SENSIBILITY

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The Collapse of Mechanism and the Rise of Sensibility Science and the Shaping of Modernity, 1680–1760 STEPHEN GAUKROGER

CLARENDON PRESS

3

Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With ofﬁces in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York # Stephen Gaukroger 2010 The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2010 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available Typeset by SPI Publisher Services, Pondicherry, India Printed in Great Britain on acid-free paper by CPI Antony Rowe, Chippenham, Wiltshire ISBN 978–0–19–959493–1 1 3 5 7 9 10 8 6 4 2

Preface Nec miremur tam tarde erui quae tam alte iacent (‘no wonder that it has taken me so long to uncover something that lies so deep’). Seneca, Quaestiones Naturales

This book is the sequel to The Emergence of a Scientiﬁc Culture: Science and the Shaping of Modernity, 1210–1685. Although it follows on naturally from the story told in the earlier volume, it can nevertheless be read in its own right as an account of the development of a scientiﬁc culture in early Enlightenment Europe. I take such a development to be a distinctive and unique feature of Western culture. In many respects it is the characteristic that marks the West out decisively from other cultures, and it is in the period between 1680 and 1760 that the distinctive credentials of this new development began to be established. I have set out to build a detailed historical picture of how the modern image of science emerged, my aim being to provide us with a lever by which to prise open questions which would otherwise remain hidden and unexplored. Some might wonder why I have gone to such trouble, for surely—it might be thought—the question of why a scientiﬁc culture emerged in the West has a simple answer: namely, it emerged because, in the aftermath of the Scientiﬁc Revolution, science itself was so successful that it carried all in its wake, providing a model to which all other cognitive disciplines could aspire. Here we would do well to heed the advice of H. L. Mencken, who pointed out that for every complex problem there is always a simple solution, and it is always wrong. I have not confused clarity with simplicity, and in aiming at the former, I have tried to see complex questions for what they are, and for what in many cases they will remain. This book is the second in a planned series of six volumes. It is now ﬁfteen years since I began the project in earnest, and something on this scale incurs many intellectual debts. In working on the present volume, I would particularly like to thank: Fre´de´rique Aı¨t-Touati, Peter Anstey, Guido Bacciagaluppi, Mark Colyvan, Conal Condren, Lisa Downing, Larrie Ferreiro, Ofer Gal, Dan Garber, Cressida Gaukroger, Peter Harrison, John Henry, Rod Home, Ian Hunter, Helen Irving, Dana Jalobeanu, Mogens Laerke, Alex Marr, Julia Mihai, Paul Redding, Dean Rickles, Jessica Riskin, John Rogers, Eric Schliesser, John Schuster, Jeffrey Schwegman, J. B. Shank, Bill Shea, Julia´n Simo´n Calero, Sandy Stewart, Aidan Sudbury, Theo Verbeek, Anik Waldow, Catherine Wilson, Charles Wolfe, and Richard Yeo. Work on the book has been pursued at the University of Sydney—where, from the mid-1990s, I have received very generous support from the Australian Research Council—and more recently also at the University of Aberdeen. Recent research has been supported by two

vi

Preface

Australian Research Council Professorial Fellowships, which have completely freed up my time for research since the beginning of 2004, thereby enabling me to commit myself to a long-term project. Material from the book has been presented at talks at the University of Aberdeen, Freie Universita¨t Berlin, Birkbeck College London, University of British Columbia, University of Bucharest, University of Cambridge, University of Dundee, Edinburgh University, University of Otago, Oxford University, University of Padua, University of Pisa, University of Reading, University of St Andrews, University of Singapore, the Sorbonne, Stanford University, University of Stirling, University of Sussex, University of Sydney, University of Verona, and University of Western Australia. I am particularly grateful for the opportunity for detailed discussions of work in progress at New York University in 2009, and at the University of Ghent in 2010. I have drawn freely on earlier writings in some sections of the book. In particular, an early version of parts of Chapter 4 appeared in British Journal for the History of Philosophy (2009), and an early version of parts of Chapter 6 appeared in Intellectual History Review (2008).

Contents Introduction

1 PART I

1. The Construction of a New World Picture The Completeness of Natural Philosophy A New Metaphysics Physico-Theology The Rationalization of Religion

11 13 17 30 40

2. The Mathematical Principles of Natural Philosophy From Principia Philosophiae to Principia Mathematica The Structure of Newton’s Principia Gravitation: Matter Theory versus Mechanics

55 57 64 83

PART II 3. The Metaphysical Unity of Natural Philosophy Leibniz and the Unity of Knowledge The Role of Metaphysics Leibnizian Dynamics Demonstration: Geometry versus Analysis Phenomenalism and the Rise of Rational Mechanics

97 98 104 115 125 145

4. From Experimental Philosophy to Empiricism The Vindication of Experimental Philosophy The Origins of Locke’s Essay Natural Philosophy and Primary Qualities Locke and the Defence of Newton

150 157 163 170 184

5. Explaining the Phenomena The ‘Nature’ of Species The ‘Nature’ of Electricity The ‘Nature’ of Metals Causation and Explanation

187 188 196 206 217

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Contents PART III

6. Natural Philosophy and the Republic of Letters The Acade´mie des Sciences and the Republic of Letters Vortices, Attraction, and the Shape of the Earth

229 232 247

7. The Realm of Reason The Birth of the Philosophe The Encyclope´die Reason and the Unity of Knowledge

257 257 269 283

PART IV 8. The Fortunes of a Mechanical Model for Natural Philosophy Explanatory Models and the Unity of Natural Philosophy Mechanics as an A Priori Discipline The Limits of Mechanics

293 294 304 317

9. Material Activity The Resurgence of an Autonomous Matter Theory Electriﬁed Matter The Chemistry of Fluids and Sympathies

328 330 336 350

10. Living and Dead Matter Matter and Activity A Developmental History of the World

355 356 365

PART V 11. The Realm of Sensibility From Sensibility to Sensibilism Physiological Sensitivity Moral Sensibility The Unity of Sensibility

387 389 394 402 409

Contents

ix

12. Historical Understanding and the Human Condition The History of Manners From Myth to Reason Reason and Sensibility The Varieties of Understanding

421 423 427 438 444

Conclusion

453

Bibliography of Works Cited Index

454 493

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Introduction In what follows, I have set out to trace, in the period between the 1680s and the middle of the eighteenth century, the emergence of scientiﬁc values, considered both as a cognitive norm—a model for all cognitive claims—and as a development that explicitly goes beyond technical expertise and articulates a world-view that was designed to displace others, whether humanist or Christian. The signiﬁcance of the emergence of such scientiﬁc values lies above all in their ability to provide the criteria by which we come to appraise cognitive enquiry, and which shape our understanding of what it can achieve. This concern with scientiﬁc values is not an essentially new one. In his Essai sur l’E´tude de la Literature (1761), Gibbon writes: In every country in every age, we witness some discipline being given preference which is too often unmerited, while other studies suffer from an equally unmerited contempt. Metaphysics and dialectic in the successors of Alexander, politics and eloquence in the Roman Republic, history and poetry in the Augustan age, grammar and jurisprudence in the later Empire, scholastic philosophy in the thirteenth century, humane letters up to the age of our fathers: each of these has enjoyed by turn the admiration and scorn of men. Physics and mathematics presently occupy the throne. We witness their sisters prostrate before them, chained to their chariot wheels, or otherwise devoted to the adornment of their triumph. Perhaps their fall is not far off. The time of a skilful writer would be well spent dealing with this revolution in religion, government, and manners, whose successive phases have misled, devastated, and corrupted humanity.1

Between 1680 and 1760, Western culture underwent a profound transformation, one in which natural philosophy—particularly the physics and mathematics of which Gibbon speaks—played a leading part, and from which it emerged with a new standing. The questions that Gibbon raises have become progressively more profound and central since he wrote. Understanding the emergence of a scientiﬁc culture—one in which cognitive values generally are modelled on, or subordinated to, scientiﬁc ones—is, I believe, one of the foremost historical and philosophical problems with which we are now confronted in understanding our own culture.

1

Edward Gibbon, Essai sur l’E´tude de la Literature (Dublin, 1777), 2–4.

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Introduction

If such an understanding is to be fruitful, we need to consider science both as a particular kind of cognitive practice, and as a particular kind of cultural product, with a view to exploring the connections between these two. The developments with which we shall be concerned are, I shall argue, quite different from the way in which they have commonly been portrayed, and may at ﬁrst seem in many respects surprising or even paradoxical, especially if one assumes that there is more or less linear progress in the establishment of scientiﬁc authority between the seventeenth and the twentieth centuries. It is true that, from the perspective of science as a cultural practice, the developments at ﬁrst sight seem to follow a path leading to increasing scientiﬁc authority, but we shall see that there is not one but a number of such paths, which do not all end up in the same place, and which each tend to culminate in programmes somewhat different from those initially envisaged. There are three main developments with which we shall be concerned. The ﬁrst comprised an attempt to subject all areas with cognitive aspirations, including natural philosophy and theology, to metaphysical foundations which embodied canons of rationality that, as we shall see, were very close to those which had been generated in efforts to regulate natural philosophy. As a result, what were in effect natural-philosophical precepts took over the role of cognitive standards, albeit not by a direct route but via the intermediary of metaphysics. For reasons that we shall be exploring in some detail, this path—pioneered by Malebranche, Spinoza, and especially Leibniz—effectively proved a dead end in the ﬁrst half of the eighteenth century. The second is physico-theology, in which a concerted effort was made to combine the resources of natural philosophy and theology. The thinking behind this was that, although these were deemed independent sources of truth, the truths they yielded could not contradict one another and still remain truths. Consequently a form of what can best be described as ‘triangulation’ was envisaged, in which the resources of both disciplines were combined, with a view to devising a powerful means of converging on fundamental truths. Physicotheology was a largely English phenomenon, and it was devised as a way of reconciling natural-philosophical enquiry with Christian natural theology and revelation. Its primary application was in the history of the formation of the earth, stimulated by Thomas Burnet’s 1680 attempt to supplement the wholly naturalistic and hypothetical Cartesian theory of how the earth might have been formed, with the historical details supplied in Genesis, revising both so as to provide something more satisfactory than either alone could hope to offer. But what was at issue could never have been just a question of bringing the full resources of both disciplines into play. These resources had to be tailored so that they were doing the same thing, preferably doing it in much the same way, otherwise one would be stuck with the problems of incompatibility that the exercise was designed to resolve. Moreover this tailoring could only take one form: a reduction of the various disciplines to their cognitive content. This

Introduction

3

turned out to be a problematic move on the theological side. The problem was not, as one might initially expect, that the move was unprecedented or imposed from outside. A new understanding of ‘religion’ arose in the seventeenth century whereby—contrary to earlier notions that effectively identiﬁed Christianity and religion so that Judaism and Islam, for example, were simply forms of heresy— there were now different religions: Christianity was now a religion, a new meaning for the term ‘religion’. The importance of the idea of different religions, from the point of view of our present concerns, was that they were distinguished by their cognitive contents, by contrast with different traditions, forms of worship, etc. In other words, thinking of Christianity in terms of its cognitive content was in many respects internally generated. The problem was not so much that Christianity had come to be characterized in terms of its cognitive content but that, considered purely in terms of cognitive content, natural philosophy was far more secure in its cognitive values than was Christianity, and these values leant themselves easily to generalization, so that it was consequently these that came to predominate. In this way, the project of combining the resources of natural philosophy with Christian natural theology and revelation pushed the cognitive standards of natural philosophy to the fore of any form of intellectual enquiry. Even more signiﬁcantly, however, what resulted was an incorporation of natural philosophy into a world-view as part of the core of a Christian understanding of the world and our place in it, thereby endowing it with a greatly enhanced signiﬁcance, a signiﬁcance which, once locked into place, it would continue to have independently of—and, from the mid-nineteenth century, at the expense of—the fortunes of Christianity. The third development was completely different from these and was conﬁned to the Francophone world. On the face of it, its upshot was the idea, associated with Voltaire and the philosophes, that natural philosophy embodied ultimate cognitive standards, but what occurred took place in a peculiar and overdetermined fashion, and closer scrutiny of the history of what happened indicates that the outcome was not the triumph of ‘reason’, as has commonly been supposed, but rather a simultaneous elevation of the standing of natural philosophy and the beginnings of a serious questioning of the connection between natural philosophy and reason. Three developments in this connection will concern us: the attempt by the French Crown to act as absolute arbiter and guardian of standards by means of the institution of various Acade´mies; the gradual appearance of a Republic of Letters in which any claim to a monopoly of judgements of cognitive worth was quickly undermined; and ﬁnally the way in which the rise of Newtonianism in the 1730s threatened the prevalent understanding of natural philosophy and opened up the question of its standing. The combination of these circumstances provided the context in which natural philosophy emerged as the paradigm bearer of, and the standard for, cognitive values. It was Fontenelle who, from the 1680s onwards, had positioned natural philosophy within the Republic of Letters, in a successful attempt to generate public support for the

4

Introduction

natural philosophy of the Acade´mie des Sciences, establishing its standing as a worthy and useful form of enquiry; and it was Voltaire who had elevated its standing further by making it into the model for cognitive grasp per se. Fontenelle’s idea of natural philosophy was that of a highly abstract and rariﬁed form of mechanics, but a rather different Lockean-inspired form of Newtonianism had been introduced into the Acade´mie in the 1730s by Maupertuis, and it was this latter that Voltaire was concerned to defend, associating it with liberal political notions, an association continued in the Encyclope´die, the ﬁrst volumes of which began to appear in 1751. In d’Alembert’s preliminary Discours to the Encyclope´die, a more elaborate statement of the archetypal role of natural philosophy in cognitive enquiry was set out, together with a genealogy showing how the search for knowledge, from its very beginnings, converged on a natural-philosophical model that dominated and provided focus for the Encyclope´die. But here a problem arose for, in tandem with these developments, there was a radical rethinking of the Lockeanism which Voltaire had used to draw the general cultural consequences of accepting a Newtonian natural philosophy. For Voltaire, the defence of Locke had been a defence of reason against prejudice (dressed up in the form of supposedly innate ideas), but the new generation of French Lockeans of the 1740s were exploring the sensory basis of knowledge as a way of developing a notion of sensibility, which became in some ways a competitor to reason, not as an antidote to prejudice (although the idea of exclusive reliance on sensation was subsequently put to work in this regard), but as what it was that underlay and regulated our cognitive states. What emerged was a new conception of natural philosophy, one in which, to a signiﬁcant extent, sensibility took over the role previously occupied by reason. This conception answered to the needs of a general model for cognition in a more satisfactory way that did its predecessor, not least in that the notion of sensibility tied together developments in natural philosophy, philosophical psychology, literary culture, and moral and political theory. Diderot and others argued that sensibility actually underlay cognition, and this had fundamental implications for our understanding of our relation to the world. In particular, whereas the conception of natural philosophy as an embodiment of reason suggested that there might be a single cognitive account of the world and our place in it, taking sensibility seriously opened up the possibility, latent in the Lockean understanding of natural philosophy that dominated mid-century thought, that there may need to be many different forms of understanding of the world. In particular, it suggested that the propositional form represented by ‘reason’ may need to be supplemented by various non-propositional forms of understanding, forms which captured the kinds of relation we have to the world not in terms of knowledge that something is the case, as with propositional understanding, but in terms of our fears, anxieties, aspirations, desires, etc. With this development, a number of questions that had traditionally been dealt with either in humanist or ‘civic’ terms, or in terms of Christian teaching, but in

Introduction

5

which considerations of sensibility had played an increasing role, now began to fall under the new expanded cognitive model, especially to the extent to which this embodied and sanctioned a form of secular anthropology. In considering natural philosophy as a cultural practice, one thing that will emerge clearly is that the idea of science as the arbiter for all cognitive values was arrived at in a variety of different ways in response to different kinds of problems and needs, over a period of at least a century. It is not a question of some cultures being backward or slower to respond in some great struggle between science and religion, for example, but rather a question of the development of different kinds of response to speciﬁc worries about cognitive authority and the satisfactoriness of particular aspirations to provide a world-view. Just how signiﬁcant the differences were is evident in the two cases that I shall be looking at in detail, namely British physico-theology and Parisian philosophe culture. When we turn to consider natural philosophy as a cognitive practice, we can begin to appreciate the extent to which exploring the connections between a cognitive practice and a cultural product teaches us something important about the concerns and values of modern thought. The question that goes to the heart of late seventeenth- and eighteenth-century natural philosophy as a cognitive practice, I shall argue, is that of the relationship between mechanics and matter theory. A natural philosophy that uniﬁed mechanics and matter theory was the aim of seventeenth-century natural philosophers, receiving a canonical systematic formulation in the mechanism set out in Descartes’ Principia. The Principia offered a vision of a comprehensive, uniﬁed understanding of the world whose very success enabled it to present itself as a model for all forms of understanding. Its demise came with a parting of the ways for mechanics and matter theory, and the emergence of very different, effectively non-overlapping understandings of what natural philosophy consisted in, what its aims were, and how these aims were to be realized. Both the dominant natural-philosophical system in the Middle Ages and Renaissance—Aristotelianism—and the dominant system in the mid to late seventeenth century—Cartesian mechanism—had assumed that the way to pursue natural philosophy was via systematic matter theory. These systems were designed to be comprehensive. In the ﬁrst case, what was offered was an account of everything that had an explanation, which was considered to be everything that followed from the essential nature of the object of study. Excluded as non-natural processes that were thereby not capable of explanation were those that occurred as a result of mechanical devices, and so caused a body to behave against its nature. By the late sixteenth century, however, the exclusion of mechanics from the domain of natural philosophy was beginning to be considered highly problematic, and Cartesian mechanism offered a systematic account which was designed to include all physical phenomena. The core of the account was a particular form of mechanized matter theory, and this required fundamental reconsideration of a number of recalcitrant areas if the claims to

6

Introduction

comprehensiveness were to stand up. Vital or organic phenomena had been at the core of the Aristotelian account, but these now became problematic, and a thoroughgoing reduction, rendering such phenomena describable in purely mechanical terms, was put into play. At the same time, a vast range of qualitative phenomena—colour being that to which Descartes himself devoted the most attention—were redescribed as not genuine physical phenomena at all but secondary qualities, that is, responses of the perceiving mind to genuine physical phenomena. The aim was to provide a single, uniﬁed, comprehensive account of natural phenomena in terms of their underlying corpuscular micro-structure: all macroscopic physical processes were to be accounted for in terms of mechanically described interactions between micro-corpuscles. With this conception came a model of physical explanation in terms of clarity and distinctness, which its proponents insisted must be adhered to by any viable account of the phenomena. An important factor in the success of mechanism was the way in which it uniﬁed the various disparate physical disciplines under a general conception of the ultimate material constituents of all bodies, insisting that everything must be accounted for in terms of these constituents, so that there was, in the ﬁnal analysis, a single physical master-discipline: the mechanics of micro-corpuscles, which offered explanatory unity and eschewed notions like force that could not be accounted for in an uncompromisingly transparent and self-evident way. In the 1660s, however, principally in the work of Boyle on pneumatics and Newton on the production of the optical spectrum, the imposition of such a grand aim was shown to be counter-productive, and the possibility began to be raised that, as well as explanation in terms of micro-structure, there was also a legitimate non-reductive form of explanation of phenomena in terms of their relationships to other phenomena. From the 1680s onwards, it became increasingly difﬁcult to see how the mechanist project might be realized, and mechanical explanation degenerated into promissory notes when it came to recalcitrant phenomena such as gravitation, electricity, magnetism, and chemical reactions. Indeed, there emerged a broadly Lockean stream of thought that insisted that the uniﬁcatory project to which mechanism subscribed was based on a fundamental and egregious misunderstanding of the nature of physical enquiry. The mechanist tradition had assumed that the success of physical enquiry was a product of structural features of the new mathematically inspired microcorpuscularian natural philosophy, features that conferred on it an explanatory unity, in that everything had the same ultimate constituents, which were to be explained in the same way, meeting the same rigorous criteria for satisfactory explanation. For mechanists, it was precisely these criteria for satisfactory explanation that marked out the new natural philosophy from Aristotelian natural philosophy, whose purported explanations were now deemed empty, and that motivated it to offer a new conception of matter which replaced that of the Aristotelian tradition, and provided a new principle of uniﬁcation. But the new generation of natural philosophers that emerged in the wake of

Introduction

7

Newton’s Principia, particularly after the 1730s, rejected this conception of their enterprise. Mechanists such as Descartes had in effect thought of what they were doing as a successful realization of a project that at the most basic level was much the same as that of Aristotle, namely the provision of an account of the nature and behaviour of matter. Because of a new appreciation of the role of mechanics in physical explanation, however, they believed they were able to redirect this project in a novel and fruitful direction. By contrast, the new generation of natural philosophers conceived of what they were doing as something completely different from the aims and aspirations of the Aristotelian project. Amongst other things, they did not automatically associate the physical and the material. In the process, the efforts to replace the old Aristotelian principle of the unity of physical enquiry with a new one were abandoned. Indeed, as Locke’s ideas—treated by many as a philosophical mirroring and clariﬁcation of the methodological rationale behind Newton’s physical theory—were taken up in various forms, it became increasingly clear that the structural features of natural-philosophical enquiry that issued in its explanatory success had nothing to do with any assumed explanatory unity. Quite the contrary, they were due in many cases to a refusal to conﬁne physical explanation to reduction to some fundamental microscopic level of matter. What emerged was a form of explanatory pluralism, which had indeed been a feature of Newton’s own work, and which came to a head in the late 1740s and 1750s. The most signiﬁcant feature of this new explanatory pluralism was that the various forms of physical enquiry had only a loose, indirect, and changing relationship with one another. Here a question of fundamental importance arises. If natural philosophy is not a single uniﬁed structure but simply a loose grouping of disciplines with different subject matters and different methods, tied in various ways each of which work for some purposes but not for others, then there can be no modelling of cognitive values generally on scientiﬁc ones. In fact, not only can we identify a number of cases where appeal to more fundamental principles is manifestly counterproductive, but, when we look in detail at the two most comprehensive eighteenth-century attempts at reduction—the attempt to reduce physics generally to mechanics, and the attempt to reduce chemistry to corpuscular matter theory— we ﬁnd that not only are they failures, but they artiﬁcially impose a wholly inappropriate conception of the unity of the discipline. It will be clear that what is at issue here is not the explanatory success of the various natural-philosophical disciplines, but the question of whether there is something about natural philosophy as such that generates, and perhaps guarantees, this success. The mechanist idea that there was such a thing was gradually abandoned after the 1680s, and the upshot of this was that the ability of natural philosophy to present itself as a model for all cognitive endeavours could no longer plausibly have been argued for in terms of the explanatory unity of natural philosophy, for after the 1680s such unity was no longer in

8

Introduction

evidence. In comparison with developments between the 1640s and the 1680s, the period we shall be looking at is one of turmoil on these important issues. Turmoil brings to the surface fundamental questions that may lie safely hidden when there is widespread agreement, however, and it is precisely such fundamental questions that we shall be concerned to identify.

PART I

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1 The Construction of a New World Picture In 1715, in the ﬁrst letter of what was to become a series of exchanges with Samuel Clarke, Leibniz wrote: Sir Isaac Newton, and his Followers, have also a very odd Opinion concerning the work of God. According to their Doctrine, God Almighty wants to wind up his Watch from Time to Time: Otherwise it would cease to move. He had not, it seems, sufﬁcient Foresight to make it a perpetual Motion. Nay, the Machine of God’s making, is so imperfect, according to these Gentlemen; that he is obliged to clean it now and then by an extraordinary Concourse, and even to mend it, as a Clockmaker mends his Work; who must consequently be so much the more unskilful a Workman, as he is oftner obliged to mend his Work and to set it right.1

He goes on to accuse Newton and Locke of being responsible for ‘a decline in natural religion’ in England, opening up in a polemical way the general question of what the relationship is between the kind of understanding of the world that natural philosophy provides, and that provided by Christian revelation and natural theology. This had been a pressing question since the beginning of the thirteenth century, with the introduction of Aristotelianism into Western medieval intellectual culture. Interest in it peaked between the 1680s and the ﬁrst decade of the eighteenth century, when it was closely associated with competing natural-philosophical models. It peaked again, albeit in a different form, between the late 1730s and the 1750s, as attempts were made to sever the tie between the two completely. The relation between natural philosophy and Christianity was a fundamental issue, because it was on this question, more than any other, that the ability of natural philosophy to establish itself—in the late seventeenth and early eighteenth centuries—as a permanent and integral feature of Western intellectual life depended. More particularly, what was at stake was the transformation of natural philosophy from a set of theories, and experimental and observational practices, of widely varying levels of abstraction and no less widely differing degrees of success, dealing with various aspects of natural processes, into something that 1 The translation is by Samuel Clarke, from the full version of his exchange with Leibniz, ‘A Collection of Papers, which passed between the late Learned Mr. Leibnitz, and Dr. Clarke’: The Works of Samuel Clarke (4 vols., London, 1738), iv. 587–8. The Leibniz/Clarke exchange is analysed in detail in Ezio Vailati, Leibniz and Clarke: A Study of Their Correspondence (New York, 1997).

12

The Construction of a New World Picture

uniﬁed knowledge and was not only fundamental to, but in some ways constitutive of, our understanding of our place in the world. In the course of this book, we shall be examining the complex reshapings of the kinds of understanding provided by natural philosophy, Christianity, and the traditional humanistic disciplines. I shall be especially concerned with the extent to which, and the way in which, natural philosophy comes to dislodge the other two in certain crucial respects. As an introduction to these questions, the attempts of the 1680s to link Christianity and natural philosophy are a good starting point. Starting from these issues, I want to explore the broader cultural context within which natural philosophy was pursued at the turn of the century, focusing on metaphysics and physico-theology, with a view to showing the extent to which these were novel developments. In particular, I want to identify any extraneous expectations that were placed on natural philosophy which might have shaped how it was received and assessed, and which had implications for what the broader relevance and standing of natural philosophy was taken to be. Inseparably tied up with these questions is that of the expectations placed on the natural philosopher, for natural philosophy had been shaped as a particular kind of calling in the seventeenth century,2 a calling whose value had to be established in the face of criticism that natural philosophy was useless, for example, and not on a par with the traditional professions.3 What distinguishes natural-philosophical claims, and natural-philosophical systems more generally, from one another is their cognitive content. But natural philosophy can also be considered as a profession or calling, and a number of questions turn on this characterization, or, more speciﬁcally, on how the goals manifested in the standing and speciﬁcally conceived role of the natural philosopher bear upon the content of natural-philosophical practice. In the early-modern period, natural philosophy was beginning to be construed as a calling of a problematic kind which was vindicated in large part by being associated with a particular persona. It was an activity carried out by a particular type of investigator who manifested distinctive intellectual and quasi-moral qualities such as objectivity and impartiality which marked him out, for example, from the theologian, whose intellectual motivations were different from these. The distinctive qualities of the natural philosopher conferred on him a particular kind of standing, one which entitled him to make certain kinds of claims, but also placed on him particular responsibilities. Compatibility with, or reconciliation with, religious orthodoxy was an important responsibility, and it was not conceived as alien to the natural-philosophical enterprise, as an account that construed this 2 See e.g. Stephen Gaukroger, The Emergence of a Scientiﬁc Culture: Science and the Shaping of Modernity, 1210–1685 (Oxford, 2006), ch. 6; and Mordechai Feingold, ‘Science as a Calling: The Early Modern Dilemma’, Science in Context 15 (2002), 79–120. More generally, see Conal Condren, Argument and Authority in Early-Modern England: The Presupposition of Oaths and Ofﬁces (Cambridge, 2006). 3 See Gaukroger, Emergence, ch. 1.

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enterprise purely in terms of theoretical content might suggest. While there were signiﬁcant differences in just what this responsibility entailed in England and continental Europe in the late seventeenth and early eighteenth centuries, there were constraints of a general nature to which Leibniz and Newton, qua natural philosophers, were subject, and the Leibniz/Clarke correspondence directly raises the question of the standing of the participants as responsible natural philosophers, able to articulate an account of the structure of the world that did not violate shared assumptions about our place in this world which were deemed fundamental to morality and the values of civilization more generally. This was by contrast with a widely disparaged ‘Epicurean’ conception whereby the cosmos had come about by chance, our place in it reﬂecting the necessity that subsequently governed all its constituents, so that (its critics claimed) the values of morality and civilization had no place in it. The prevailing view was that if this latter was indeed the picture of the cosmos that natural philosophy had to offer, then so much the worse for natural philosophy, for its proponents were, for all intents and purposes, advocates of atheism, of a world devoid of meaning and purpose. THE COMPLETENESS OF NATURAL PHILOSOPHY One central question that was at stake was that of the explanatory ambitions of natural philosophy. In particular, the question arose whether natural philosophy, in the form of the Cartesian mechanism prevalent up to the 1680s, was sufﬁciently complete in itself to offer a full understanding of basic physical processes, without need of supplementation. And if Cartesian mechanism failed in this regard, did this mean that it had to be revised, or to be replaced by something that met this requirement? Or was it rather that the requirement was misconceived, that nothing could make natural philosophy into a single theory of all physical phenomena, and that there were considerable costs in attempting to force it into such a mould? It is of signiﬁcance here that such disputes were mirrored in conﬂicts over whether there was a single form of Christianity which should or could be acceptable to all Christians. What this suggests is that there was a broad issue of the wisdom of seeking single general forms of understanding, and if this is the case, as I shall show it is, then what we are witnessing is a very signiﬁcant break with those forms of understanding inherited from medieval and Renaissance cultures, in the natural-philosophical, religious, political, and other realms. Let us begin by brieﬂy considering Newtonianism, which offers the most immediately fruitful context in which to examine the issues that underlie the disputes over the nature and standing of natural philosophy in this period. In the wake of the publication of the Principia in 1687, Newtonianism in effect provided the ground on which many natural-philosophical battles were

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fought. In the ﬁrst two decades after its publication, the credentials of the cosmological theory it replaced, Cartesian vortex theory, were crucial. In dealing with the motions of planets in terms of bodies moving in empty space attracted to a central sun, Newton faced the problem of accounting for the nature of the physical mechanism by which such attraction was communicated to the planet. There was a level of description at which the nature of gravitational attraction could be ignored, but proponents of the vortex theory, and mechanists more generally, denied any autonomy to such a level of description. Mechanists had seen mechanics as providing the basis for a full theory of the physical world: it described the fundamental physical processes, and the task was to move out from these to everyday macroscopic physical processes. In the mechanist view, Newton, by refusing to engage the question of the nature of gravity in mechanical terms, had drawn mechanics back into a more restricted domain. It could no longer act as a basis for a mechanist reconstruction of the world. At the same time, in abandoning vortices, Newton had abandoned an intrinsically balanced universe. Vortex theory had its origins in a hydrostatic model of the cosmos, in which the planets were carried along by a rotating celestial ﬂuid, their orbits balanced by centrifugal forces acting outwards from the centre and by rapidly moving vortical matter pressing inwards towards the centre, so that the orbit was simply a question of the planets being in equilibrium in relation to the surrounding ﬂuid matter. Newton realized that if a planetary orbit was composed of a uniform rectilinear motion and a (reciprocal) uniformly accelerated motion not just towards the sun but also towards other celestial bodies, which in turn also exercised (reciprocal) gravitational attraction, then there was nothing intrinsically balanced about the solar system. His calculations led him to conclude that the processes were so complex that talk of intrinsic balance and equilibrium were now out of the question. God was needed to ensure the stability of planetary orbits, for, given the new understanding of the potentially inﬁnite complexity of the forces acting on an orbiting body, no purely natural processes could secure the remarkable stability involved.4 It is ‘unphilosophical’, he tells us in Query 31 to the Opticks, to suggest that the world ‘might arise out of chaos by the mere laws of Nature; though being once formed, it may continue by those laws for many ages. For while comets move in very excentrick orbs in all manner of positions, blind Fate could never make all the planets move one and the same way in orbs concentrick, some inconsiderable irregularities excepted, which may

4 Newton’s calculations were based on mathematical approximations employing the ﬁrst few terms of their inﬁnite series representations. At the end of the eighteenth century, Laplace was able to show that, on his far more detailed but still idealized mathematical solar system model, any deviations in the eccentricities and inclinations of planetary orbits occurred within well-deﬁned limits, being small, constant, and self-correcting. In other words, as Laplace himself put it, he did not need God as a hypothesis to account for planetary stability.

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have risen from the mutual actions of comets and planets upon one another, and which will be apt to increase, till this system wants a reformation.’5 Such a claim was in direct conﬂict with the mechanist assumption that the cosmos that God had created worked in terms of wholly self-regulating processes. Moreover, the problem was not conﬁned to planetary orbits, for there was also the difﬁculty of the dissipation of motion in non-elastic collisions: For bodies, which are either absolutely hard, or so soft as to be void of elasticity, will not rebound from one another. Impenetrability makes them only stop. If two equal bodies meet directly in Vacuo, they will, by the laws of motion, stop where they meet, and lose all their motion, and remain in rest: unless they be Elastick, and received new motion from their spring. If they have so much elasticity as sufﬁces to make them rebound with a quarter, or half, or three-quarters of the force with which they come together, they will lose three-quarters, or half, or a quarter of their motion.6

Consequently, if the quantity of motion in the universe were to remain constant, ‘some other principle is necessary for conserving the motion’. What is raised here is a dilemma that was uppermost in the minds of late seventeenth-century natural philosophers, namely that of the mode of God’s activity in nature: whether he intervened directly or whether this activity was mediated.7 This question takes us to the issue of the relation between Christianity and natural philosophy. What is at stake here is not straightforward. Note, for example, that Leibniz’s complaint was not that the association of natural philosophy with Christian theology was misguided. In 1686, he writes that ‘since the wisdom of God has always been recognized in the detail of the mechanical structure of some particular bodies, it ought also to show itself in the general economy of the world and in the constitution of the laws of nature. And this is so true that one notices the counsels of this wisdom in the laws of motion in 5 Newton, Opera quae exstant omnia commentariis illustrabat Samuel Horsley (5 vols., London, 1779–85), iv. 261–2. Compare the report by William Derham of a conversation with Newton: ‘peculiar sort of Proof of God wch Sr Is: mentioned in some discourse wch he & I had soon after I published my Astro-Theology [1715]. He said there were 3 things in the Motions of the Heavenly Bodies, that were plain evidences of Omnipotence & wise Counsel. 1. That the Motion imprest upon those Globes was lateral, or in a Direction perpendicular to their Radii, not along them or parallel with them. 2. That the Motions of them tend the same way. 3. That their Orbits have all the same inclination.’ Quoted in Frank E. Manuel, A Portrait of Isaac Newton (Cambridge, Mass., 1968), 127. 6 Newton, Opera, iv. 258. 7 In fact, it is a little obscure whether primary or secondary causes are required in these cases. Newton talks of ‘active principles’ renewing motion in the case of collision, and there is no reason in principle why secondary causes should not be at work in stabilizing planetary orbits, but, like Leibniz, Newton and his followers take it that it is a case of primary causes, that is, direct divine intervention. The invocation of direct intervention is part of a more general argument against deism on the part of Newtonians, and it is not the mechanics but physico-theology that requires the introduction of primary causes. See Herbert H. Odom, ‘The Estrangement of Celestial Mechanics and Religion’, Journal of the History of Ideas 27 (1966), 533–48; and David Kubrin, ‘Newton and the Cyclical Cosmos: Providence and the Mechanical Philosophy’, Journal of the History of Ideas 28 (1967), 325–46.

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general.’8 For Leibniz, as for most natural philosophers of his time, the world embodied God’s intentions for his creation, and natural enquiry, suitably pursued, could reveal these intentions to the diligent natural philosopher. It was a shared assumption between the parties to the debates that the link was an intimate and unbreakable one. There was agreement that, construed correctly, the association would beneﬁt both Christianity and natural philosophy. Indeed, the general view was that the future development of both of them depended on their being combined in a satisfactory manner: they were complementary. Yet while there was deep disagreement on just what the relation was, there can be no doubt that, for many, Newton’s Principia provided the model. In 1699, Newton’s friend John Craig had attempted to provide algebraic proofs of the truths of Christianity in his Theologiae Christianae Principia Mathematica. In 1715, the year that Leibniz wrote his letter criticizing the Newtonian conception of God’s activity, at the same time accusing Newton and Locke of being responsible for a decline in ‘natural religion’ in England, George Cheyne, in his Philosophical Principles of Religion,9 was offering a new expanded edition of his recasting of Christian theology on the lines of Newtonian natural philosophy—replete with deﬁnitions, axioms, theorems, lemmas, and corollaries—in which motion was dependent upon God’s will. The aim was a synthesis of an orthodox Protestant understanding of God and an accurate understanding of his creation, building a comprehensive picture of the world and our place in it. Cheyne was certainly not an isolated voice. In his History of the Royal Society (1667), Thomas Sprat had noted that ‘The universal Disposition of this Age is bent upon a rational Religion,’10 and far from being in decline in early eighteenth-century England, natural religion was in fact thriving under the inﬂuence of Newtonianism. And Newton himself certainly encouraged this. At the end of Query 31 of the Opticks, he writes that ‘if Natural Philosophy in all its parts, by pursuing this method, shall at length be perfected; the bounds of Moral Philosophy will also be enlarged. For so far as we can know by natural Philosophy what is the First cause, what power he has over us, and what beneﬁts we receive from him; so far our duty towards him, as well as that towards one another, will appear to us by the light of Nature.’11 Such an approach was quite different from that followed by continental metaphysicians, however, and the difference is reﬂected in different conceptions of what was appropriate and acceptable in explanations in a natural-philosophical system. 8 Leibniz, ‘Discours de metaphysique’, Die philosophischen Schriften, ed. C. I. Gerhardt (7 vols., Berlin, 1875–90), iv. 446. 9 George Cheyne, Philosophical Principles of Religion: Natural and Revealed (London, 1715). The original part was published as Philosophical Principles of Natural Religion: Containing the Elements of Natural Religion, Arising from Them (London, 1705). 10 Thomas Sprat, The History of the Royal-Society of London for the Improving of Natural Knowledge (London, 1657), 374 (mispaginated as 366). 11 Newton, Opera, iv. 264.

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A N EW META PHY SI CS From the 1660s onwards, natural philosophy and Christianity entered into a number of new and distinctive kinds of relationship in an attempt to offer a comprehensive uniﬁed understanding of the natural world. This meant incorporating natural philosophy into a larger picture, and I have distinguished metaphysical and physico-theological ways of achieving this as the main contenders. Each of these involved a reassessment of the disciplines involved, and the metaphysical route required a rethinking of the tasks of metaphysics. It will be helpful to begin by identifying some of the dominant types of metaphysical enquiry that existed before this process of reassessment, which effectively starts with Descartes’ Principia philosophiae. We can distinguish three broad forms of metaphysics that ﬂourished between the thirteenth and the seventeenth centuries: two scholastic forms, Thomism and Scotism, and a non-scholastic form, Neoplatonism.12 These each offered fundamentally different understandings of the relation between metaphysics and natural philosophy, and consideration of them will help us identify what is distinctive about the seventeenth-century project of attempting to provide metaphysical foundations for natural philosophy. On the Thomist understanding, natural philosophy and theology were autonomous disciplines, employing legitimately different procedures of enquiry, the ﬁrst being premissed on the reliability of sense perception, the second on the reliability of revelation. Natural philosophy was basically Aristotelian, revelation was Christian revelation, and the combination of the two yielded a Christianized Aristotelianism. However, there were discrepancies between Aristotelian natural philosophy and revelation on a number of fundamental questions, such as whether the world had been created, and whether the soul could enjoy personal immortality after the death and corruption of the body. Theology could not simply override natural philosophy on this conception, for that would be to deny the latter autonomy and legitimacy in its own domain. What had to be provided was some way of bridging the two disciplines in order that corrections could be made, and for this some discipline that was neutral with respect to theology and natural philosophy was needed, that is, something which was dependent neither on revelation nor sense perception but rather on reason alone. On Aquinas’ conception, it was metaphysics that was ﬁtted to this role, just as it was the very neutrality of metaphysics, as Aquinas conceived of it, that enabled it to provide defences of the Christian understanding of God that met the demands of those (pagans, Muslims, Jews) who did not recognize the sacred texts of Christianity. 12

See Gaukroger, Emergence, chs. 2 and 3, for a full account of these developments.

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The Scotist understanding of metaphysics was different from this in a number of crucial respects, not least in that it did not conceive of metaphysics to be a neutral discourse, but rather to be one which could be intimately connected with theology. It had the advantage that it was closer to Aristotle’s own conception in some respects. Aristotle had conceived of metaphysics as a general science of being, and Duns Scotus had offered this as an alternative to the Thomist conception, on the grounds that there must be some uniﬁed notion of being, provided by metaphysics. It was a discipline whose subject matter was beingqua-being, and consequently our understanding of inﬁnite being—theology— and our understanding of ﬁnite being—natural philosophy—were grounded in a discipline which was not neutral with respect to them but uniﬁed the two as part of a general cognitive enterprise. On the Scotist conception, metaphysics was integrally bound in with Christian theology. With the revival of Scotist notions, in the scholastic textbook tradition that emerged in the second half of the sixteenth century, there is an overriding concern with questions of systematic derivation from general principles. These textbooks, among which those of Sua´rez have a central place, had as their explicit aim the systematic reconstruction of Aristotle’s metaphysics and natural philosophy from ﬁrst principles, rearranging material in Aristotle as necessary. They recast the whole Aristotelian tradition with two main aims: to show how the truths of a Christianized Aristotelianism could be derived from ﬁrst principles, and to show how this was a single, coherent, comprehensive system. The guiding idea behind the project was one at the core of Aristotelianism, namely that understanding ultimately took the form of scientia, which consisted in the derivation of true and certain conclusions from ﬁrst principles that were both evident and indemonstrable. Scientia was built up and consolidated as more and more conclusions were drawn from the basic principles, and the ultimate aim was a wholly exhaustive and encyclopedic account of theoretical knowledge.13 Neoplatonist metaphysics was very different from both these. As represented by the work of Ficino in the ﬁfteenth century, and in that of Patrizi in the late sixteenth century, it was driven by a theological metaphysics, conceived as a wholly comprehensive system, in which natural philosophy was really little more than a materialization of basic metaphysical principles. Its content was dictated by these principles, and it had no autonomy. Consider the case of optics. Ficino’s treatise De sole et lumine (1493) was devoted to a distinctive Neoplatonist topic: the question of the relation between corporeal and incorporeal light. A central concern of the Neoplatonist tradition was a light cosmogony deriving from the doctrine of emanation, where light is construed as the ‘ﬁrst corporeal form’, with the material universe itself evolving from a 13 See the comprehensive account in Charles Lohr, ‘Metaphysics’, in Charles B. Schmitt, Quentin Skinner, and Eckhard Kessler, eds., The Cambridge History of Renaissance Philosophy (Cambridge, 1988), 537–638.

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primordial point of light. On this conception, the study of ‘physical’ light is a prerequisite to the understanding of the origins and structure of the material universe. In the Neoplatonic view all causation in the material universe operates on the analogy of the radiation of light. A crucial source for Christian Neoplatonists here was pseudo-Dionysius the Aeropagite, who set out an elaborate hierarchy of heavenly and terrestrial beings, which worked via degrees of illumination deriving from God himself. Physical illumination and spiritual enlightenment are effectively identiﬁed on this conception: the creation of the world is explicitly identiﬁed with the appearance of light in the darkness, and with the emergence of a spatial universe from a purely spiritual one. The basic distinction is between the intelligible realm and the visible realm, and one of Dionysius’ aims was to show how the intelligible is veiled in the visible and how it can be unveiled through illumination. To study light on this view, was to study the emanations of God. This approach is reﬂected in Patrizi’s Nova de universis philosophia (1591), the only comprehensive statement of a Neoplatonist natural philosophy. The full title of the book gives a good indication of its structure. It rises to the ﬁrst cause, we are told, not by the standard naturalphilosophical route of motion or change, but by means of lux (light) and lumen (brightness). It does this, Patrizi claims, by a ‘new and special method’ whereby all of divinity comes into view, and his aim is to ‘derive’ the universe by the Platonic method from God. Thomism and Neoplatonism occupy the two ends of the spectrum. On the Thomist view, natural philosophy and Christian teaching are autonomous disciplines, bridged, where they appear to conﬂict, by the neutral discipline of metaphysics. By contrast, on the Neoplatonic conception, metaphysics is in effect identiﬁed with theology, and this metaphysico-theology provides all the basic principles for all forms of enquiry, so that natural philosophy is explicitly not an autonomous discipline but simply a ﬂeshing out of these principles in the material domain. Both Thomism and Neoplatonism came under severe pressure in the late sixteenth century. The Thomist aim of a reconciliatory metaphysics had begun to unravel in the course of the sixteenth century, beginning with the problem of the immortality of the soul early in the century—where it became clear that there was no metaphysics that could reconcile the Aristotelian view that the soul could not survive the corruption and decay of the body with the Christian doctrine of personal immortality—and coming to a head with the disputes over heliocentrism at the end of the century. The problem for Neoplatonism was that its metaphysico-theology was not, and indeed had never been, reconcilable with Christian teaching. Its association with extreme heterodoxy meant that it was under suspicion throughout the sixteenth century, and, although it continued to play some role in eclectic metaphysical projects such as those of the Cambridge Platonists and Leibniz, it had a comparatively

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marginal standing by the next century. It was its nemesis, scholastic metaphysics, that dominated seventeenth-century discussions.14 Scotism seemed to avoid some of the difﬁculties of these conceptions of metaphysics. At ﬁrst sight, the Scotist project looks as if it might provide a metaphysical basis for natural philosophy while avoiding heterodoxy. Certainly, in its early seventeenth-century versions, its aim was very explicitly to secure orthodoxy. It sought to achieve this through systematic understanding, but metaphysics did not play a foundational role. At issue here is the question of the position of metaphysics in the ordering of knowledge: whether it was the starting point for enquiry or its culmination. The late-scholastic textbooks set out to present a scientia, a systematic and encyclopedic form of presentation of knowledge in which known facts were grasped deﬁnitively in terms of their underlying principles and causes. In accord with this, seventeenth-century scholastic textbooks adopted a standard order: logic, ethics, physics, and metaphysics.15 Logic came ﬁrst because logic provides the language for building one’s system, supplying the basic categories and techniques by which we must proceed if we are to progress scientiﬁcally. It is the method by which the basic principles of the various scientiae are discovered, and from which one then demonstrates conclusions. Ethics follows because the aim of philosophy is human happiness, and, as Eustachius—author of one of the principal early seventeenth-century textbooks—points out, ‘this happiness has been taken to consist partly in the contemplation of truth, and partly in action in accordance with virtue’.16 Consideration of ethics at this stage shows us the point of the exercise. Finally, the placing of metaphysics after natural philosophy follows a traditional hierarchical ordering of subject matters, working from the most concrete to the most abstract forms of knowledge: knowledge is a pyramid, as it were, with metaphysics, as the highest science, at its apex. On the Scotist understanding of 14

On scholasticism in the early modern period, see Christia Mercer, ‘The Vitality and Importance of Early Modern Aristotelianism’, in Tom Sorell, ed., The Rise of Modern Philosophy (Oxford, 1993), 33–67; Jacob Schmutz, ‘Bulletin de scolastique (I)’, Revue thomiste 100 (2000), 270–341; P. J. Fitzgerald and John Haldane, ‘Medieval Philosophy in Later Thought’, in A. S. McGrade, ed., The Cambridge Companion to Medieval Philosophy (Cambridge, 2003), 300–27; M. W. F. Stone, ‘Scholastic Schools and Early Modern Philosophy’, in Donald Rutherford, ed., The Cambridge Companion to Early Modern Philosophy (Cambridge, 2006), 299–327; and, on speciﬁc national varieties: Paul R. Blum, Philosophenphilosophie und Schulphilosophie: Typen des Philosophierens in der Neuzeit (Stuttgart, 1999); Laurence Brockliss, French Higher Education in the Seventeenth and Eighteenth Centuries (Oxford, 1987); Franc¸ois de Danville, ‘L’Enseignement scientiﬁque dans les colle`ges des Je´suites’, in Rene´ Taton, ed., Enseignement et diffusion des sciences en France au dix-huitie`me sie`cle (Paris, 1986), 27–65; Marcus Hellyer, Catholic Physics: Jesuit Natural Philosophy in Early-Modern Germany (Notre Dame, Ind., 2005). 15 This is, for example, the order adopted in the three standard early seventeenth-century textbooks: Scipion Dupleix, Corps de philosophie, contenant la logique, l’ethique, la physique, et la metaphysique (Geneva, 1623); Eustachius a Sancto Paulo, Summa philosophae quadripartita, de rebus Dialecticis, Ethicis, Physicis, & Metaphysicis (Cologne, 1629); Charles Franc¸ois d’Abra de Raconis, Totius philosophae, hoc est logicae, moralis, physicae, et metaphysicae (2 vols., Paris, 1633). 16 Eustachius, Summa, Part II, Praefatio.

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metaphysics as a science of being-qua-being, as represented in writers like Sua´rez, there is no reason in principle why metaphysics could not have come at the beginning of the process of systematic understanding, for it provided the basic categories by which to distinguish the natures of the different kinds of things that existed. But in fact it comes at the end: metaphysics is the culmination of systematic understanding, not its starting point. In the new seventeenth-century natural philosophies, metaphysics tends to shift to the starting point of systematic understanding, although the question is complicated, and there is not only signiﬁcant disagreement but signiﬁcant uncertainty. Gassendi, in his Syntagma, collapsed metaphysics into natural philosophy, rejecting the idea of metaphysics as a discipline separate from the latter, a separation he traces back to Plato, and he followed the Hellenistic division of philosophy into logic, natural philosophy, and ethics, which he takes to be the natural ordering.17 Descartes, by contrast, keeps metaphysics and natural philosophy separate, and in both of his accounts of the ordering of knowledge, the Discours and the Principia, he deals with metaphysics before natural philosophy. A metaphysical grounding of natural philosophy would seem central to the Principia as far as Descartes himself was concerned, but many of his followers found it easier to ignore its metaphysics. His erstwhile follower Henricus Regius dispensed with metaphysics in Fundamenta physices (1646), which was in effect an alternative textbook of Cartesian natural philosophy to Descartes’ own Principia, as did Rohault in what became the deﬁnitive textbook of Cartesian natural philosophy, his Traite´ de physique (1671).18 Descartes disowned Regius’ textbook, and its author,19 principally because he saw the metaphysical foundations that he had provided as crucial to his project. Descartes’ own commitment to metaphysics was not at all straightforward however. His natural-philosophical work of the 1620s and early 1630s, culminating in Le Monde, was not pursued via metaphysics, but via an explicitly autonomous natural philosophy whose basic ingredients were a micro-corpuscularian matter theory and mechanics. In the wake of the condemnation of Galileo, however, 17

Gassendi, Opera Omnia (6 vols., Lyon, 1658), i. 27 col. 1. On this aspect of Gassendi’s approach, see Olivier Bloch, La philosophie de Gassendi (The Hague, 1971); and Barry Brundell, Pierre Gassendi (Dordrecht, 1987). 18 On Cartesian natural philosophy from the 1640s to the end of the century, see Eric J. Aiton, The Vortex Theory of the Planetary Motions (London, 1972); Desmond M. Clarke, Occult Powers and Hypotheses: Cartesian Natural Philosophy under Louis XIV (Oxford, 1989); Paul Mouy, Le de´veloppement de la physique carte´sienne 1646–1712 (Paris, 1934); Ge´raud Tournadre, L’Orientation de la science carte´sienne (Paris, 1982); and Trevor McClaughlin, ‘Descartes, Experiments, and a First Generation Cartesian, Jacques Rohault’, in S. Gaukroger, J. Schuster, and J. Sutton, eds., Descartes’ Natural Philosophy (London, 2000), 330–46. 19 See Gaukroger, Descartes, An Intellectual Biography (Oxford, 1995), 408–10; Theo Verbeek, ‘Le contexte historique des Notae in Programma Quoddam’, in Theo Verbeek, ed., Descartes et Regius (Amsterdam, 1993), 1–34; idem, ‘The Invention of Nature: Descartes and Regius’, in Stephen Gaukroger, John Schuster, and John Sutton, eds., Descartes’ Natural Philosophy (London, 2000), 149–67.

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Descartes rethought his natural philosophy, not in terms of its basic content, which remained intact, but in terms of how that natural philosophy might be defended against the kinds of criticism that had been directed against Galileo’s establishment of heliocentrism. Paramount among these was the charge that purely natural-philosophical arguments could not carry sufﬁcient conviction to establish a theory that was not in accord with accepted tradition. The basis of the charge lay in large part in a widely held view among sixteenth- and seventeenthcentury scholastic philosophers that natural-philosophical argument was not able to establish unique truths, as the correct interpretation of revelation was for example, but was able only to assess the respective merits of different theories and hypotheses on the basis of evidence and arguments: it was able to establish matters relative to the best evidence and argument, but not in absolute terms. The situation was complicated by the use of astronomical arguments, for astronomy, as a practical-mathematical discipline, was deemed even less able to establish anything conclusively than was natural philosophy: it was designed merely to save the appearances, and the fact that a system saved the appearances better than others had no bearing on any claims it might make to represent physical reality.20 Descartes’ response was to supply his already developed natural philosophy with a set of new credentials, which had two features. First, these credentials would establish the legitimacy of his natural philosophy: they would transcend particular natural-philosophical and confessional differences by appealing, at the most fundamental level, to truths so basic, and presented in such a transparent way, that reﬂection on their content would compel assent. What is at issue here is the criterion of clarity and distinctness that was to play a crucial role in the subsequent development of the Cartesian programme, broadly construed, even in those, such as Huygens, who had no interest in metaphysical questions and proceeded as if such questions had no bearing on the natural-philosophical issues with which they were concerned. Second, these credentials would establish the orthodoxy of Cartesian natural philosophy, even if they effectively worked by attempting to forge a new orthodoxy. This is why Descartes’ original plan for his Principia (subsequently abandoned because it was too unwieldy) was to publish a scholastic natural-philosophy textbook alongside his own account, comparing the results where possible point by point.21 In this way, he had hoped that the Principia would be taken up as a teaching text in Jesuit colleges. In order to facilitate such a critical comparison, however, he had to translate his own account into a terminology that would enable comparison. This was 20 See in particular the discussion of Pereira, who presents a clear version of the reasoning behind this, in Nicholas Jardine, The Birth of History and Philosophy of Science: Kepler’s A Defence of Tycho against Ursus with Essays on its Provenance and Signiﬁcance (Cambridge, 1988). 21 See Descartes to Mersenne, 30 December 1640, and Descartes to [Charlet], [December 1640]: Œuvres de Descartes, ed. Charles Adam and Paul Tannery (2nd edn., 11 vols. in 13 parts, Paris, 1974–86), iii. 233 and 270 respectively.

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problematic because the Aristotelian terminology deployed by scholastic metaphysicians was shared with that used in their natural philosophy, to which it was closely related: indeed, in many respects they were integral parts of the same exercise. Descartes adapted scholastic terminology to his legitimating language of clarity and distinctness, attempting to forge a new metaphysics. Of the two procedures involved, translating his natural philosophy into the language of clarity and distinctness—despite criticism from Gassendi and others that clarity and distinctness were relative, so that what was clear and distinct for one person might not be for another—turned out be immensely successful, and it would become part of the armoury not just of supporters of Descartes but of many of his critics also. The second procedure, namely the translation from the language of clarity and distinctness into the terminology of substances, modes, and attributes, was not such a success however, either from the point of view of Cartesian natural philosophy or from the point of view of scholastic metaphysics.22 Yet without this, the orthodoxy of the Cartesian system could not be established. Why, it might be asked, should orthodoxy be of such concern? In the second half of the seventeenth century, one reason is the ofﬁcial condemnation of Cartesianism by the Roman Catholic Church, which placed Descartes’ works on the Index of Prohibited Books in 1663, and by the French state—Louis XIV issued an ofﬁcial condemnation of Cartesianism in 1671, and renewed a ban on the teaching of Cartesian philosophy in 1685—as well as the resistance to Cartesianism from Theology Faculties in the French universities,23 and in German ones.24 There were moves to rehabilitate Cartesianism, of course, and Antoine Le Grand’s popular Cartesian textbook of 1672 put Descartes into scholastic form a little more thoroughly than Descartes himself had done. But Le Grand’s eclectic assimilation of Cartesian and Aristotelian positions was superﬁcial and could have achieved little by way of establishing orthodoxy.25 22

See Stephen Gaukroger, Descartes’ System of Natural Philosophy (Cambridge, 2002), ch. 3. See Brockliss, French Higher Education; idem, ‘Rapports de structure et de contenu entre les Principia et les cours de philosophie des colle`ges’, in Jean-Robert Armogathe and Giulia Belgioiso, eds., Descartes: Principia Philosophiae, 1644–1994 (Naples, 1996), 491–516. More generally, see Gaston Sortais, Le carte´sianisme chez les Je´suites franc¸ais au XVIIe et au XVIIIe sie`cle (Paris, 1929). There is a very useful account of the issues in Tad Schmaltz, Radical Cartesianism: The French Reception of Descartes (Cambridge, 2002), who notes that the ﬁrst wave of condemnations, beginning in 1671, focused on the Cartesian doctrine of the Eucharist (it was prompted by the publication of Desgabets’ Conside´rations sur l’e´tat pre´sent de la controverse touchant le Tre`s SantSacrament de l’autel (Paris, 1671)), whereas the second wave, beginning with the 1691 condemnation at the University of Paris, was much broader, raising questions about the compatibility of Cartesian doubt and the demands of faith. 24 Any teacher defending Cartesianism in the German universities in the second half of the seventeenth century was subject to immediate dismissal: see Wilhelm Hestermayer, Paedagogia Mathematica (Paderborn, 1969), 51. 25 Antoine Le Grand, Institutio Philosophiae, secundum principia Domini Renati Descartes: Nova methodo adornata et explicata (London, 1672). Le Grand extended Cartesian natural philosophy into the arena of natural history in a more comprehensive way than Descartes had attempted in Book IV of the Principia, and—reﬂecting the prevalent understanding of Descartes by the late 23

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During the 1660s and early 1670s, two projects of a more substantial nature were under way, those of Spinoza and Malebranche, each of them directly engaging Descartes’ natural philosophy but offering different if related metaphysical systems.26 Both took their initial bearings from Cartesianism, and each could be seen as a logical development of Cartesianism. Indeed, each aimed to develop a broad metaphysics adequate to Cartesian natural philosophy, one which integrated the criterion of clarity and distinctness into a metaphysics that was not a mere appendage, as it had in effect been in Descartes’ own work, but was consistent, complete, and had an autonomy that genuinely enabled it to ground all other areas of cognitive endeavour. It is in the work of Spinoza and especially Malebranche, whose writings were particularly inﬂuential,27 that we ﬁnd the beginnings of the project of providing metaphysical foundations for knowledge. Because Spinoza was associated to a signiﬁcant extent with Cartesianism, Spinozean metaphysics had the potential to be taken as the true development of Cartesianism. He had displayed his Cartesian credentials with his attempt to present the ﬁrst two Books of Descartes’ Principia in an axiomatic form in his Renati Des Cartes Principiorum Philosophiae (1663).28 Seven years later, he published, anonymously and under a false imprint, his Tractatus TheologicoPoliticus, a tightly argued and devastating critique of the claims of religion to offer cognitive judgements. On the basis of a detailed argument as to how one might assess revelation and prophecy, Spinoza concluded that cognitive judgements fell outside the realm of religious authority, and a religion such as seventeenth century—he emphasized a potentially occasionalist element in Descartes’ account, by stressing the origin of all motion in God and denying powers to cause motion or changes in motion to bodies. As Roger Ariew (Descartes and the Last Scholastics (Ithaca, NY, 1999), 95) notes, this very popular book, quickly translated into English, was the seventeenth-century equivalent of a coffeetable book, the English translation advertising itself as containing ‘more than a hundred sculptures’ and being of ‘use and delight to the Ingenious of Both Sexes’. 26 My choice of Malebranche and Spinoza should not be taken to imply that these were the only metaphysical systems indebted to Descartes current at the time. In France, as well as Le Grand, two particularly important such systems were that of Desgabets, few of whose extensive writings were published before the twentieth century, although one anti-Malebranchean work did appear in his lifetime, Critique de la Critique de la recherche de la ve´rite´, ou l’on de´couvre le chemin qui conduit aux connoissances (Paris, 1675); and Pierre-Sylvain Regis, Syste`me de philosophie, contenant la logique, la metaphysique, la physique et la morale (2 vols., Paris, 1690). In the Netherlands, Arnold Geulincx developed an inﬂuential occasionalist metaphysics in competition with that of Malebranche, one which had a number of parallels with the Spinozean system: see e.g. his Physics vera, quae versatur circa hunc mundum (Leiden, 1688), and Metaphysica vera et ad mentum peripateticam (Amsterdam, 1691). 27 Malebranche had effectively eclipsed Descartes in the eighteenth century. An indication of just how effectively is given in a letter from Hume advising a friend on what to read as background to his Treatise. Hume recommends Malebranche, whose work was widely available, and Descartes, remarking that the Meditationes is ‘not easy to get hold of ’: see R. H. Popkin, ‘So, Hume Did Read Berkeley’, in idem, The High Road to Pyrrhonism (Indianapolis, 1993), 291. 28 On Spinoza’s Principia, see Jonathan Israel, ‘Spinoza as an Expounder, Critic, and “Reformer” of Descartes’, Intellectual History Review 17 (2007), 59–78.

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Christianity was restricted to providing moral guidance. Cognitive judgements were subject not to religious authority but exclusively to clear and distinct ideas. In the Ethica, composed in the 1660s and 1670s,29 it turned out that clarity and distinctness were largely the preserve of Cartesian natural philosophy, which, in its idiosyncratic Spinozean version, then became the model for all cognitive disciplines, including (as had been evident in the Tractatus) areas such as biblical philology. Moreover, Spinoza had no hesitation in using the criteria by which Christianity was to be judged, namely its ability to encourage piety and morality, to compare it with his own wholly secular construal of the human condition and its associated naturalized morality, which he sets out to show resolves fundamental questions about freedom and morality much better than religious treatments of these questions.30 Spinoza himself presented his system as the logical development of Cartesianism, and indeed it takes its starting point from an oddity in Descartes’ account of substance. In Part I of the Principia, Descartes offered two incompatible deﬁnitions of substance, one after the other. First he deﬁnes it as ‘whatever exists in such a way that it needs no other thing in order to exist’ (art. 51) and then as ‘whatever needs only the participation of God in order to exist’ (art. 52). It is an indication of Descartes’ cavalier attitude to metaphysics that he allows such an equivocation in a fundamental category, but the fact is that his conception of substance does no real work in the discussion of the distinction between God, mind, and matter in what follows: what drives and controls that discussion is the doctrine of clarity and distinctness.31 Nevertheless, the equivocation in the notion of substance is something that would have been unthinkable in a scholastic metaphysical treatise, and it is scholastic metaphysics that set the ground rules for metaphysical discussion. Spinoza, who perfected what might be termed the ‘Trojan horse’ strategy of adopting the language of his opponents and apparently playing by their rules, while at the same time substituting new meanings for central terms, took metaphysics as seriously as he took the Cartesian criterion of clarity and distinctness. Starting from Descartes’ ﬁrst deﬁnition of substance he is quickly able to show that there can only exist a single substance, and that traditional distinctions between God, mind, and matter do not make sense in metaphysical terms. The result was a metaphysical system of extreme religious and moral heterodoxy. By contrast, Malebranche was concerned to use metaphysical foundations to establish orthodoxy in his De la recherche de la ve´rite´, the ﬁrst edition of which appeared in 1674. However, although the metaphysical language employed is of necessity that of scholasticism (as it was for Spinoza), for Malebranche orthodoxy does not consist in an Aristotelian Thomism but in an Augustinian 29 30 31

The Ethica ﬁrst appeared in Opera Posthuma (Amsterdam, 1677). See Gaukroger, Emergence, 471–92. See idem, Descartes’ System, 85–92.

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reading of Cartesianism, reﬂecting the widespread revival of Augustinianism in France in the second half of the seventeenth century.32 Malebranche saw himself as a Cartesian, as developing a core strand of thought in Descartes in a more logical and more fully worked-out way. Descartes had distinguished three different kinds of substance—inﬁnite substance (God), ﬁnite spiritual substance (mind), and ﬁnite extended substance (matter)—but he provided no discussion of the systematic relations between the three. By contrast, Malebranche treated a systematic account of these questions as the key to a coherent metaphysics. The bulk of De la recherche—ﬁve of the six books—is devoted to an account of how the errors due to the mind’s union with the body arise. A distinctive feature of this account is the use to which he puts Augustinianism in rejecting a number of doctrines to which Descartes was ﬁrmly committed. He rejects Descartes’ view that some of our ideas are innate, for example, and even that ideas are mental entities. Following Augustine, he argues that what we know most clearly are eternal, unchanging essences, and these can only exist in something which is itself eternal and unchanging, namely God. God makes up a realm of unchanging archetypes, very similar to Plato’s realm of unchanging Forms. When we contemplate non-sensible, purely intelligible things, we contemplate them not in ourselves but in God. Pure geometrical ﬁgures, for example, do not exist in our mind: rather, they have a completely objective independent existence in an intelligible world which Malebranche identiﬁes with God. This leads him to distinguish two kinds of ideas: sensory ideas, which do exist in our mind, and which we experience in virtue of the union of our mind with our body, and clear and distinct ideas—what he calls ideas properly speaking—which exist in God, and which we experience in virtue of the union of our mind with God. The difference between the two kinds of ideas is captured, Malebranche argues, in the different ways in which they represent their objects. Clear and distinct ideas resemble what they represent: our idea of a circle resembles a circle. By contrast, sensory ideas, such as our ideas of heat and colour, do not resemble their objects, which are merely corpuscular agitations; rather, they signal or signify to the mind some bodily state.33 On Malebranche’s account, physical enquiry must conﬁne itself to the former, namely those phenomena that can be characterized in terms of clear and distinct ideas. This approach is complemented by his commitment to occasionalism, which held that bodies could not engage in genuine physical interactions—for 32 See Henri Gouhier, Carte´sianisme et augustinisme au XVII e sie`cle (Paris, 1978); and Jean Dagens, Be´rulle et les origines de la restauration catholique (Paris, 1952). 33 See also his formulation of this doctrine, and his assessment of its importance, in chapter 5 of his Re´ponse de l’Auteur de la Recherche de la Ve´rite´ au livre de M. Arnauld, Des vraies et de fausses ide´es (Rotterdam, 1684).

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example those typically causing changes of speed and direction of motion in collision—because they were completely inert and purely passive.34 Any activity in the physical world has its origins in God’s will, and is due to God recreating bodies in different positions at each instant of time. God’s activity, however, is regular, and its regularity discoverable by experimental and theoretical means. Above all, at the phenomenal level, it is evident that this activity occurs only when bodies are in contact, and it takes a precise form governed by laws of motion and rules of impact. Since we can only register God’s mode of acting in the world, not comprehend it, everything we can say about physical processes can be said as a description at this phenomenal level. Indeed, this phenomenal realm is constitutive of the physical realm. It is somewhat less substantial than what we would normally think of as the physical realm, of course, but on Malebranche’s account this is because we have been misled by secondary qualities, which we take to be real properties of things, but which are in fact merely additions of the perceiving mind.35 This account of the nature of the world had an important impact on the early eighteenth-century understanding of natural philosophy, because it was around Malebranche that an elite group of mathematicians, concerned with problems in analysis36 and its application in mechanics, formed in Paris in the 1690s. It is easy to see how natural philosophy can be assimilated to mechanics, and in turn to mathematics, on the Malebranchean picture. The properties of geometrical ﬁgures are objective: they are not merely imaginings of particular minds, and they are not subject to any exercise of the will. Yet their objectivity does not derive from their corresponding to something in an external physical world, because they do not correspond to anything in the world: they are abstract. Their objectivity must derive from their correspondence to something in a nonphysical, non-mental realm, and the divine realm is the only other option. On Malebranche’s model, it is the same with other general ideas: they exist in a purely intelligible realm, which he identiﬁes with God. When it comes to perception, both ideas and sensations are needed, but when physical objects and processes are stripped down to their primary qualities, we have something describable in purely mechanical terms.

34 See in particular Malebranche, De la recherche de la ve´rite´, E´claircissement XVI: ‘Touchant l’efﬁcace attribue´e aux causes secondes’. I have used edition of G. Rodis-Lewis (Paris, 1979). 35 D’Alembert will put this Malebranchean principle to very productive use in his article on ‘force’ in the Encyclope´die, writing that the ‘contestant’ notion of force (which Newton had denied in his third law of motion) with its idea of a ‘struggle’ between forces, is difﬁcult to rid ourselves of because we have a tendency to transfer things which we observe in our own bodies to inanimate objects. 36 In the technical mathematical sense of the term, ‘analysis’ in this period comprised mathematical techniques for ﬁnding tangents to curves, ﬁnding the area enclosed by a curve (‘quadrature’), and ﬁnding the arc length of a curve (‘rectiﬁcation’). The Malebranche group employed calculus, which provided an algorithmic method of dealing with the ﬁrst two.

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It was in Malebranche’s circle of mathematicians in the Acade´mie des Sciences that the project of identifying natural philosophy with ‘rational mechanics’, as a description of a rariﬁed abstract domain, pursued purely by means of mechanics and increasingly sophisticated analytical tools, received its strongest impulse. Although Malebranche did himself deal with physical questions, and was concerned to develop vortex theory into a viable physical account of planetary stability,37 the members of the Malebranche circle were concerned exclusively with the mathematical description of the phenomena. Mathematicians such as Varignon had no interest in Malebranchean metaphysics as such. To the extent that their work was the continuation of any tradition, it was the programme in kinematics as developed by Huygens, who had no time for metaphysics. What Malebranchean metaphysics did was to sanction a conception of mechanics that eschewed notions of force and power, where there was no more to causation than transfer of motion/momentum, while at the same time reinforcing the notion that mechanics was nothing if it was not clear and distinct, and that clarity and distinctness were manifested paradigmatically in a discourse that conﬁned itself to describing the motions of bodies (or points) in analytic terms. Malebranche’s own project was more ambitious. The ﬁrst lines of De la recherche bring out his conception of the moral imperative lying behind the formulation of the correct metaphysics: The Mind of Man is, as it were, by its Nature situated between its Creator and Corporeal Creatures; nothing, according to St. Austin, being above it but GOD, nor beneath it but Body. But as the great Elevation it obtains above all Material Beings, is no hindrance to its uniting with them, and even to its Depending, after a sort, upon a Piece of Matter; so, notwithstanding the inﬁnite distance between the Sovereign Being and the Humane Mind, the latter is immediately and most intimately united with the former. This last Union exalts the Mind above all things; ’tis this which gives it Life and Light, and all its Happiness; And of this Union it is St. Austin speaks in very many Places of his Works, as of that which is most Natural and Essential to it: On the contrary, the Union it has with

37 See his account of terrestrial gravitation in the 1712 addition (}18) to E´claircissement XVI of De la recherche. Descartes had accounted for weight of a body in terms of a pressure exercised on it, but he had given two different accounts of it: in ch. 11 of Le Monde he had explained it in terms of the rapid motion of celestial matter around the earth, which creates a pressure directed towards the centre of the earth, whereas in the Principia, he explained it in terms of the same forces that cause water to form droplets, where the forces acting on the water are equal from all sides and so press all the constituent parts in towards the centre (IV art. 20). Rohault in particular had developed the ﬁrst approach, but Malebranche objects that calculation shows that the celestial matter would have to move seventeen times faster than the earth: yet while we would expect such a motion to be detectable it would seem it has no effect at all on terrestrial events, even in the case of something as sensitive as a falling feather. Malebranche therefore favours the second account, insisting that the planets move at the same speed as the surrounding celestial matter. To deal with standard objections to this approach, he suggests that the tiny vortices constituting celestial matter generate a tremendous centrifugal force which makes them elastic, and terrestrial gravity is due to the interaction between the solid earth and these elastic, highly energetic vortices, which in effect act as powerful little springs.

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the Body extremely debases it, and is at this Day the Principal Cause of all its Errours and its Miseries.38

By metaphysics, he tells us, ‘I mean the general truths that can serve as principles for the particular sciences’.39 Elsewhere, he writes: ‘A good metaphysics is one which must regulate everything, and I will try to establish the principal truths grounding religion and morality.’40 We may distinguish two different kinds of claim being made here. One thing that could be meant is that metaphysics provides and sanctions particular principles which might best be thought of as methodological/epistemological. In particular, they specify precisely and in their most general terms just what clarity and distinctness consist in; they set out the constraints that the criteria impose on the appropriate subject matter, not merely in physical theory but in the most general case, including morality and religion; and they explain why these qualities cannot be manifested, for example, in many traditional and contemporary forms of physical enquiry, which must therefore be abandoned. This is something not too far removed from the Cartesian aspirations for metaphysics. However, on a stronger reading the statements are closer to the Neoplatonist project, which would have perhaps been encouraged by the commitment to a form of Augustinianism (itself heavily dependent on Neoplatonism) in Malebranche. Here it is a question of metaphysics actually generating fundamental a priori truths which have a universal standing, all other areas of enquiry in effect being sub-disciplines of metaphysics. It is never quite clear in Malebranche which of these projects he is advocating. When we turn to Leibniz, however, we shall see that there is no ambiguity at all: the task of metaphysics is to generate fundamental universal truths. Not only is this a requirement Leibniz places on his own metaphysics, but he reads this as a sine qua non of any metaphysical project. In short, there is a distinction to be made between a weak construal of the aspirations of metaphysics, which I have associated with Descartes, and which understands it to be a formulation of an effectively a priori set of constraints on any discipline that purports to make cognitive claims, and a strong construal, which we shall see at work in Leibniz, whereby metaphysics consists of a priori fundamental truths and principles on which all other truths and principles rely. We shall be exploring the Leibnizian programme in Chapter 3. For the moment, I simply want to draw attention to two things. First, the kind of metaphysical 38 De la recherche de la ve´rite´, Pre´face. Translation from Father Malebranche his treatise concerning the search after truth The whole work complete. To which is added the author’s Treatise of nature and grace: being a consequence of the principles contained in the search. Together with his answer to the animadversions upon the ﬁrst volume: his defence against the accusations of Monsieur De la Ville, &c. relating to the same subject. All translated by T. Taylor . . . (2 vols., London, 1700), i. [i]. ‘Austin’ is a standard early-modern English contraction of ‘Augustine’. 39 Malebranche, Entretiens sur la me´taphysique, Dialogue 6.2: Œuvres comple`tes, ed. Andre´ Robinet (20 vols., Paris 1958–78), xii. 133. 40 Malebranche to Pierre Berrand, 23 December 1686: Œuvres, xviii. 42.

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enterprises that we ﬁnd at the end of the seventeenth century are quite different from those we ﬁnd at the beginning of the century. Not only are they uniformly focused on natural philosophy (a characteristic they share with Thomism, but not with Scotism and Neoplatonism), but they place metaphysics at the starting point of cognitive endeavours rather than at the end. What comes at the end is natural philosophy, for this is now what knowledge of the world consists in: the only issue is how metaphysics guides or constrains natural philosophy. Second, the move against metaphysics that we detect mid-seventeenth century in Gassendi and in Royal Society apologists, and which has become well entrenched by the early decades of the eighteenth century, is a rejection of both the strong and the weak conceptions of the task of metaphysics. To the extent that guidance or constraint is required—and there is dispute as to how much it is required—it is to be supplied either by Christian teaching or, particularly with the emergence of deism, by ‘reason’. P H Y S I C O - T H E O L O GY If a move in the direction of increasing abstraction was a feature of the attempt to provide a metaphysical grounding for an understanding of the world, physicotheology moved in the opposite direction, for right from the beginning it had been associated with natural history, a strongly observational and classiﬁcatory set of disciplines. Boyle in particular had seen natural history very much as a model for natural philosophy more generally, and he had construed the ultimate aim of natural philosophy as being that of revealing evidence of God’s purposes in nature, and the inactivity of matter demanded by mechanism as highlighting the need for a divine active role in the guidance of natural processes. By the 1650s and 1660s, Boyle and Sprat, the Royal Society apologist par excellence, were talking of natural philosophy in terms of a religious ofﬁce, and natural philosophy was taken as a non-partisan way—that is, one free of sectarian confessional issues—of engaging religious questions of divine nature and purpose. The upshot of this was the transformation of natural philosophy from a merely technical grasp of the world into something approaching the kind of natural understanding that was appropriate to a view of the natural world as God’s creation. One of the preconditions for physico-theology was the establishment of some degree of commensurability between its two components, natural philosophy and theology. In terms of speciﬁc enquiries, the attempt to establish a connection was invariably made at the level of natural history and natural theology. Natural history was a discipline that dated back to classical antiquity, but it was not treated as part of natural philosophy on the Aristotelian conception that prevailed in the Middle Ages and Renaissance. Moreover, its incorporation into natural philosophy in the course of the second half of the seventeenth century was problematic. In particular, it was not, and could not

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have been, systematically integrated with the quantitative discipline of mechanics, which not only had been incorporated into natural philosophy, but, with the publication of Newton’s Principia, was increasingly seen by many as the core of natural philosophy. Natural history remained an anomalous part of the natural-philosophical enterprise as far as a mechanical model was concerned. But because natural philosophy, in its broadest terms, had by this time become, for many natural philosophers, something that offered an understanding of God’s purposes in nature, and because natural history was particularly well suited to this kind of understanding, it could not be dismissed. Instead, its credentials as a core part of the natural-philosophical exercise—perhaps in some respects the core part, in competition with a mechanist model—were reinforced through its alliance with natural theology. While the idea of a natural theology can be traced back at least to Cicero, and although it had formed part of Origen’s theology, it was of little interest as long as theological issues were focused on shared sacred texts, and it came back into circulation only with the attempt to engage those, such as Moslems, who had different sacred texts, or to deal retrospectively, in the new climate of philosophical sophistication of the thirteenth century, with an ancient Greek philosophical tradition which had no sacred texts. In the wake of the Reformation, natural theology took on a newly signiﬁcant role, as fundamental and irreconcilable differences emerged between those who took the same texts as sacred, ruling out any generally accepted textual basis for theological clariﬁcation. Here, the connection between natural theology and revelation becomes highly problematic, interpretation of revelation having become sufﬁciently contentious that natural theology started to take on a degree of independence. At the same time that natural theology was becoming independent of revelation, it joined forces with an enterprise which offered an account of the world free from sectarian dispute. A direct union was envisaged, not one that proceeded via metaphysics for example. There were a number of attacks in Britain on the idea of metaphysics grounding or mediating the relation between natural philosophy and divinity in the seventeenth century.41 As physico-theology began to take shape as a serious enterprise, in Boyle and the Royal Society apologists of the 1660s, the attempt to impose a pre-given system on natural philosophy was criticized extensively, but metaphysics itself was not singled out for attack: it is rather that the project envisaged was not one that could have been realized through metaphysics. The most prominent and enthusiastic advocate of physico-theology was Boyle, who 41 In some respects, such a view can be traced back to Bacon. In a 1622 letter, Bacon had written, ‘Don’t trouble yourself about metaphysics. When the true physics has been discovered, there will no longer be any metaphysics. Beyond the true physics there is only divinity.’ Francis Bacon to Father Barazano, 30 June 1622: The Works of Francis Bacon, ed. James Spedding, Robert Leslie Ellis, and Douglas Denon Heath (14 vols., London, 1857–74), xiv. 375.

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considered natural philosophy to be a way of engaging religious questions of divine nature and purpose that was free of the sectarian confessional issues that had attended discussion of such questions, particularly in the wake of the English civil war. Traditional scholastic metaphysics would certainly have been considered too partisan for such a role. By contrast, Descartes’ procedure of clearing the mind of all prior beliefs and starting from one’s own metaphysical resources was rejected in England because associated with enthusiasm, that is, the idea that one could have direct unmediated access to religious truths.42 For Boyle, and for physico-theologians generally, Christianity and natural philosophy were equal partners in a search for a single shared truth, and a foundational metaphysics simply had no role in such a conception. Formative as Boyle’s views were, however, it was only from the 1680s, beginning with the work of Burnet on reconciling Genesis with natural-philosophical theories of the formation of the earth, that physico-theology came to assume the dominant position, particularly in natural history, which it was to retain up to the middle of the nineteenth century.43 The idea was that natural philosophy and theology could be made to converge on a shared set of fundamental truths, which would then act as a basis for a comprehensive understanding—functional and teleological as well as material and mechanical—of the natural realm. For this to be a success, however, natural theology and natural philosophy had to be made commensurate with one another in a way quite different from anything that had been demanded from earlier, scholastic attempts at reconciliation. While natural history had traditionally been seen in 42

See Gaukroger, Emergence, 221–2. The idea that nature manifested the wisdom, benevolence, and glory of God was a commonplace in sixteenth- and seventeenth-century thought, but this was not connected with an interest in studying natural history, and it is noteworthy that writers who attacked atheism did not invoke physico-theology before the 1690s, although they regularly invoked it from then on. See Neal C. Gillespie, ‘Natural History, Natural Theology, and Social Order: John Ray and the “Newtonian Ideology”’, Journal of the History of Biology 20 (1987), 1–50. More generally, physico-theology seems to have ﬂourished wherever Protestantism ﬂourished. Its high point in Germany was from 1730 to the 1760s, when there appeared a plethora of natural history books and essays drawing the physico-theological consequences of roses, tulips, grass, water, stones, insects, snails, locusts, ﬁsh, bees, and birds: see William Clark, ‘The Death of Metaphysics in Enlightened Prussia’, in William Clark, Jan Golinski, and Simon Schaffer, eds., The Sciences in Enlightened Europe (Chicago, 1999), 423–73: 434; and, more generally, Wolfgang Philipp, Das Werden der Aufkla¨rung in theologiesgeschichtlicher Sicht (Go¨ttingen, 1957). In 1774, Herder claimed he could distinguish ﬁfty different systems of Physiktheologie in Germany. In the Netherlands, physicotheology effectively began with Bernardus Nieuwentijdt, Het regt gebruik der werelt beschouwingen, ter overtuiginge van ongodisten en ongelovigen (Amsterdam, 1715), which was translated into English as The Religious Philosopher: Or, The Right Use of Contemplating the Works of the Creator (3 vols., London, 1719) with a laudatory introduction by Desaguliers, who refers to the author as ‘the Dutch Ray’. Recent research has traced a tradition of physico-theology in the Netherlands well into the nineteenth century: Ernestine Van der Wall, ‘Newtonianism and Religion in the Netherlands’, Studies in History and Philosophy of Science 35 (2004), 493–514. Although physico-theology went into rapid decline after the middle of the nineteenth century, it did not disappear completely: see Bernard Lightman, Victorian Popularizers of Science: Designing Nature for a New Audience (Chicago, 2007), ch. 8. 43

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terms of a reading of nature that aimed to seek out divinely instituted signs which might reveal the purpose of creation, it was not considered part of natural philosophy proper. Note also that natural philosophy proper, on the traditional Thomist understanding, was quite separate from theology in that it relied not on revelation, but on sensation. The task of physico-theology, by contrast, was to bring Christian theology and natural philosophy close enough together so that their projects were not only not at cross-purposes, but had a shared focus. One way to do this was to identify what they had in common, but this approach faced signiﬁcant difﬁculties. Christianity has a mythological structure: it offers a way of coming to terms with the world in terms of our fears, wishes, desires, and beliefs, with a view to bringing coherence and integrity to these in a way that a purely cognitive representation of the world could not. However, such a mythological structure is necessarily deﬁned in functional terms, and could hardly make claims to unique credence in its own right since there might be— and are—various different kinds of things that meet these needs more or less successfully but in rather different ways. They may not even be religious: such mythological structures had abounded in Hellenistic philosophy for example, and, with the rise of Romanticism, aesthetic mythologies will begin to replace religious ones. The absolutist ambitions of seventeenth- and eighteenth-century Christianity could never have allowed it to consider itself purely in such mythological terms:44 it was not proposing itself as one religion among many, but as the only true religion. It was therefore crucial that it assumed cognitive authority, for this provided the only terms on which it could mark itself out as making unique demands on our credence. Hence the unprecedented bitterness of the reaction to Spinoza’s arguments, in his Tractatus Theologico-Politicus, which set out to demonstrate that religions had no cognitive authority, and should be judged on what were in effect exclusively moral grounds.45 From the Church Fathers onwards, once the Pelagian construal of Christianity as primarily a moral system had been rejected,46 and particularly once the medieval 44 ¨ ber The shift came at the turn of the eighteenth century, with the work of Schleiermacher—U die Religion: reden an die Gebildeten unter ihren Vera¨chtern (Berlin, 1799), Der christliche Glaube: nach den Grundsa¨tzen der evangelischen Kirche im Zusammenhange dargestellt (2 vols., Berlin, 1821– 2)—which formed the basis for the liberal ecumenical form of Christianity that came to prominence for a while in the second half of the twentieth century. 45 See Theo Verbeek, Spinoza’s Theologico-Political Treatise (Aldershot, 2003). Spinozism was heavily censored and marginalized, but propagated through underground pamphlets. See Jonathan Israel, Radical Enlightenment: Philosophy and the Making of Modernity 1650–1750 (Oxford, 2001); and idem, Enlightenment Contested: Philosophy, Modernity, and the Emancipation of Man 1670– 1752 (Oxford, 2006). Israel argues that Spinozism had a very signiﬁcant impact on radical Enlightenment political thinking, but this seems to me questionable for the kinds of reasons set out in Theo Verbeek, ‘Spinoza on Natural Rights’, Intellectual History Review 17 (2007), 257–75. Cf. Ian Hunter, ‘Multiple Enlightenments: Rival Aufkla¨rer at the University of Halle, 1690–1730’, in Martin Fitzpatrick, Peter Jones, Christa Knellwolf, and Ian McCalman, eds., The Enlightenment World (London, 2007), 576–95: 590–2. 46 The rejection of Pelagianism was basically a choice between Pelagius and Augustine, and the decisiveness of the rejection by the Western church was not at all reﬂected in the Eastern church, which remained much more sympathetic to the Pelagian position: see Jaroslav Pelikan, The Emergence of the Catholic Tradition (100–600) (Chicago, 1971), 316.

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attempts to establish a systematic Christian theology on a philosophical basis had begun, Christianity had offered a cognitive representation of the world. Indeed, in the wake of the Investiture Controversy (1050–1122), with its separation of powers over the secular and spiritual realms, the Church jealously guarded its authority over intellectual enquiry as part of its newly acquired monopoly in the spiritual realm. The various disciplines that made up natural philosophy by the 1680s— mechanics, optics, matter theory, the newly emerging dynamics, natural history, anatomy, physiology—made no claim, individually or collectively, to provide a mythological structure of the kind offered by Christianity. To the extent that they offered an account of the world and our place in it, only the Renaissance naturalists and Spinoza had suggested a natural philosophy that might challenge or replace Christianity on this question. Otherwise it was a question of complementing, helping strengthen, the Christian world-view. This could be done only by reinforcing its conception of the world, not by critically engaging its mythological structure but sharing in it. Such reinforcement, in turn, could only come on condition of commensurability between the two components, natural philosophy and Christian theology, where commensurability could only be one of cognitive content. Physico-theology was a movement strongly associated with Protestantism, which had always seen itself as offering a more rational form of theology than Catholicism,47 and the movements we shall be discussing were very much associated with Protestantism,48 though the consequences of rationalization quickly went beyond the doctrines even of liberal Protestants. Physico-theology blossomed in the 1690s, with formative works by Ray (1691–3), Woodward (1695), Whiston (1696), and Keill (1698).49 The catalyst had appeared in the previous decade: Thomas Burnet’s Telluris theoria sacra, the ﬁrst volume of which appeared in Latin in 1680.50 Burnet focused on the incompleteness of 47

See e.g. John Tulloch, Rational Theology and Christian Philosophy in England in the Seventeenth Century (2 vols., Edinburgh, 1874). 48 See Peter Harrison, The Bible, Protestantism, and the Rise of Natural Science (Cambridge, 1998). 49 John Ray, The Wisdom of God Manifested in the Works of Creation (London, 1691); idem, Miscellaneous Discourses Concerning the Dissolution and Changes of the World (London, 1692); idem, Three Physico-Theological Discourses, concerning: I the Primitive Chaos, and the Creation of the World. II the General Deluge, its Causes and Effects. III the Dissolution of the World, and Future Conﬂagration (London, 1693). John Woodward, An Essay toward a Natural History of the Earth: and Terrestrial Bodies, especially Minerals (London, 1695). William Whiston, A New Theory of the Earth, from its Original to the Consummation of all Things (London, 1696). John Keill, An Examination of Dr. Burnet’s Theory of the Earth with some Remarks on Mr. Whiston’s New Theory of the Earth (Oxford, 1698). 50 Thomas Burnet, Telluris theoria sacra: orbis nostri originem et mutationes generales, quas aut jam subiit aut olim subiturus est, complectens (London, 1680); idem, The Theory of the Earth: Containing an Original of an Account of the Earth, and of all the Changes Which it Hath Undergone, or is to Undergo Till the Consumation of All Things. The First Two Books, Concerning the Deluge, and Concerning Paradise (London, 1684). The second Book appeared in Latin as Telluris theoria sacra. Libri duo posteriores de conﬂagratione mundi et de futuro atatu rerum (London, 1689).

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revelation as an account of the formation of the earth, and sought to render it complete by supplementing it with the Cartesian account of its geological formation. Since the latter was an explicitly hypothetical theory, a rational reconstruction of a geological process which did not make reference to datable events, Burnet set out to show how revelation could be used to supply concrete historical details. Each of the accounts was understood to be incomplete as a description of the whole process, but since Burnet considered them both true in substance, if not in every detail, and since he also considered that truths, whatever their provenance, cannot contradict one another, the combination of the two should, he reasoned, yield something far more comprehensive than either taken by itself.51 As far as revelation was concerned, Burnet’s view was that Genesis was written to accommodate the capacities of the ignorant, and that a literal reading of Genesis could not possibly yield an understanding of how the cosmos was formed. The idea was not that the account in Genesis should be abandoned, but rather that its interpretation had to be guided by whatever understanding could be gleaned from natural philosophy. As far as natural philosophy was concerned, any attempt to offer an account of the formation of the earth had to describe a historical process, but the account Burnet considers the best, that of Descartes, offered merely a hypothetical reconstruction of events, suggesting that this was a path that God could have followed, not the one he did follow.52 Burnet’s project was therefore to ﬂesh out Descartes’ rational reconstruction of the earth’s formation as a real historical process, and for this Genesis, which provided the only available account there was of the early history of the formation of the cosmos, was crucial. Burnet’s reconstruction was, as might be expected, contentious in a number of respects, with his geological reconstruction requiring that mountains were formed at the same time as the Flood, in direct contradiction with the Genesis account, where they pre-existed the Flood. Moreover, his combination of the Cartesian theory of the formation of the earth with Genesis led him to the view that the world in its original state was as God designed it, but the world in its present state was not: it had degenerated through the geological processes that the Cartesian theory describes, and it was therefore wholly inappropriate to use it as a basis for devotion and understanding of God’s intentions in creation.53 Indeed, Burnet’s use of Cartesian natural philosophy was itself contentious, for there were alternative natural philosophies, not least—by the 1690s—that of Newton, which offered more scope for divine intervention in natural events, and Woodward for one argued at length that the 51

See my discussion of Burnet and his predecessors in Gaukroger, Emergence, 492–505. Nevertheless, there had been attempts by Cartesians to show that Descartes’ cosmology was in fact compatible with the ﬁrst three books of Genesis: see e.g. Johannes Amerpoel, Cartesius Mosaizans seu . . . conciliatio philosophiæ Cartesii cum historia creationis per Mosem traditia (Leuwarden, 1669); and Ge´raud de Cordemoy, Copie d’une lettre ´ecrite a` sc¸avant religieux de la Compagnie de Je´sus (Paris, 1669). 53 Burnet, Telluris theoria sacra, 83. 52

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scale of the Flood was such that it could not be explained in natural terms alone but required a supernatural power.54 There were those who sought to refute Burnet simply by pitting scriptural passages against his claims,55 but it should be noted that this was not an especially common response. In the main, the idea that one could combine natural philosophy and Genesis was not ruled out: after all, those natural philosophers who were party to these disputes accepted the truth of Genesis at some level, and those who worried about recent natural-historical reconstructions of the formation of the earth were not opposed to natural history as such, but were concerned about its potential conﬂict with Genesis. That there should not be such conﬂict was a shared assumption: as Burnet put it, ‘We are not to suppose that any truth concerning the natural world can be an enemy to religion: for Truth cannot be an Enemy to Truth, God is not divided against himself.’56 The problem was that not everyone believed that Burnet had successfully effected such a reconciliation: he was accused of conceding too much to the natural-history side of the equation, and there was signiﬁcant criticism of him as a Spinozist and Socinian, and as a free thinker.57 Burnet had been particularly concerned by the fact that the amount of water required for the Flood, if it did indeed rise to the mountaintops, would have been several times that available in the oceans, and he was aware of writers such as La Peyre`re, who had used such considerations to conclude that the Flood could not have been a universal event but was more likely to be an episode in local Jewish history.58 Clearly, Burnet concluded, if the two accounts are to be reconciled, the world must have been very different in its earlier stages than it is now, and he speculates that in the early stages of its development—corresponding to the terrestrial paradise—it would have had a perfectly smooth spherical surface, 54 Woodward, Essay, 58, 165. On Woodward, see Paolo Rossi, The Dark Abyss of Time: The History of the Earth and the History of Nations from Hooke to Vico (Chicago, 1984), 217–22; and Rhoda Rappaport, When Geologists Were Historians, 1665–1750 (Ithaca, NY, 1997), 149–60. 55 See e.g. Erasmus Warren, Geologia or a Discourse concerning the Earth before the Deluge (London, 1690). There were also works that set out to show that Burnet had misinterpreted biblical passages, such as Herbert Croft, Some Animadversions Upon a Book Intituled The Theory of the Earth (London, 1685). 56 Burnet, The Theory of the Earth, a2. 57 For criticism of him as a Spinozist and Socinian, see Jean Graverol, Moses Vindicatus . . . adversus Thomas Burnetii Archeologias Philosophicus (Amsterdam, 1694); and for criticism of him as a freethinker, see Archibald Lovell, A Summary of Material Heads which may be enlarged and improved into a complete Answer to Dr. Burnet’s Theory of the Earth (London, 1696). Lovell notes that Burnet’s reconstruction treats the earth as a paradise up to the time of the Flood, ignoring the scheme of sin and redemption that began with Adam and Eve. On the reception of Burnet, see Rappaport, When Geologists Were Historians, ch. 5; Rossi, The Dark Abyss of Time, 66–75; and Peter Harrison, ‘The Inﬂuence of Cartesian Cosmology in England’, in Stephen Gaukroger, John Schuster, and John Sutton, eds., Descartes’ Natural Philosophy (London, 2000), 168–92. 58 Burnet, Telluris theoria sacra, 10–15; Isaac de La Peyre`re, Prae-Adamitae, sive exercitatio super versibus duodecimo, decimotertio, & decimoquarto, capitis quinti Epistolae D. Pauli ad Romanos ([Amsterdam], 1655).

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subsequently broken open by various forms of violent geological activity which resulted in mountains and ocean basins. One aspect of Burnet’s approach was the apparent discrediting of the Mosaic account, a question on which Newton took issue. In a letter to Burnet of 1681, for example, Newton pointed out that to claim that Moses wrote for the ignorant, a claim that Newton does not deny, does not mean that what he wrote is false: ‘As to Moses I do not think his description of ye creation either Philosophical or feigned, but that he described realities in a language artiﬁcially adapted to ye sense of ye vulgar.’59 Newton makes it clear that Moses depicted the process of creation exactly as it occurred: as he puts it, ‘the things signiﬁed by such ﬁgurative expressions are not ideall or moral, but true’.60 In 1696, a revised version of Burnet’s thesis was offered in Whiston’s New Theory of the Earth. Whiston was a self-confessed disciple of Newton61—the New Theory carried the dedication ‘Summo Viro Isaaco Newton’—and he was probably familiar with the letter to Burnet.62 His intention was to take a more Newtonian stand. Newton himself had made his commitment to physicotheology clear as early as 1692 in his correspondence with Bentley, telling Bentley that: ‘When I wrote my treatise about our Systeme [the Principia] I had my eye upon such Principles as might wrk considering men for the beleife of a Deity & nothing can rejoyce me more then to ﬁnd it usefull for that purpose.’63 Moreover, he clearly saw such a conception as involving a rejection of at least one of the mainstays of mechanism, construed here along the lines of Epicureanism: ‘ye diurnal rotations of ye Sun & Planets as they could hardly arise from any cause purely mechanical . . . they seem to make up that harmony in ye system wch . . . was the effect of choice rather than of chance.’64 Bentley himself incorporated this Newtonian philosophy into his physico-theology in his Boyle Lectures, published in 1693,65 setting a precedent for Whiston. Whiston begins the New Theory by recounting how his infatuation with Burnet’s Theoria sacra was overcome on reading Newton’s Principia, and his main thesis is that: ‘The Mosaick Creation is not a Nice and Philosophical 59

Newton to Burnet, [January 1681]. Isaac Newton, The Correspondence of Isaac Newton, ed. H. W. Turnbull, J. F. Scott, A. R. Hall, and Laura Tilling (7 vols., Cambridge, 1959–77), ii. 331. 60 Newton, Correspondence, ii. 333. 61 On the history of the relations between Whiston and Newton, see Stephen D. Snobelen, ‘William Whiston, Isaac Newton, and the Crisis of Publicity’, Studies in History and Philosophy of Science 35 (2004), 573–603. More generally on Whiston, see James E. Force, William Whiston: Honest Newtonian (Cambridge, 1985). 62 See Rossi, The Dark Abyss of Time, 67–8. 63 Newton, Correspondence, iii. 233. 64 Ibid., 236. On Newton’s natural-theological commitments in the Principia, see I. Bernard Cohen, ‘Isaac Newton’s Principia, the Scriptures and Divine Providence’, in Sidney Morgenbesser, Patrick Suppes, and Morton White, eds., Philosophy, Science and Method (New York, 1969), 523–48. 65 Richard Bentley, A Confutation of Atheism from the Origin and Frame of the World (London, 1693).

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account of the Origins of All Things, but an Historical and True Representation of the formation of our single Earth out of a confused Chaos, and of the successive and visible changes thereof each day, till it became the habitation of Mankind.’66 Rejecting the Cartesian natural philosophy underpinning Burnet’s account of the tilting of the Earth’s axis to explain the Flood, he turned to Newton’s account of the comet of 1680/1, arguing that the vapours of the comet’s tail would have been enough to bring on the torrential rain that caused Noah’s Flood. Yet the difﬁculties of reconciling the Mosaic account with a natural-historical one are evident. For one thing, Whiston cannot accept that the biblical account of creation is an account of the creation of the cosmos: it reads much more like an account of the creation of the earth, which is quite a different matter. Moses’ account, Whiston insists, was neither literal nor allegorical. It is ‘a historical and true representation of the formation of our single earth’, but the standard literal interpretation of the Mosaic account ‘represents all things from ﬁrst to last so disorderly, confusedly, and unphilosophically, that ’tis intirely disagreeable to the Wisdom and Perfection of God.’67 A more consistently Newtonian approach was that of Keill’s An Examination of Dr. Burnet’s Theory of the Earth of 1698, where a strong contrast is drawn between the Cartesian view (which Keill equates with Epicureanism) of a nature devoid of, and in no need of, ﬁnal causes, and the Newtonian stress on the need for God’s intervention in and regulation of his creation. The thrust of this physico-theological approach had been brought out explicitly in Ray’s The Wisdom of God of 1690, where the incompleteness of mechanism was stressed, in particular its inability to deal with the phenomena examined in natural history. Of course, mechanists would have pointed out that what they were advocating had no bearing on the questions of biological taxonomy that primarily interested Ray, but these same mechanists had urged the comprehensiveness of their system when arguing against advocates of experimental philosophy, for example,68 and comprehensiveness is not something that one can be selective about. Ray’s point, one that will be repeated in various forms over the next century and a half, is essentially that we should not seek a comprehensive view of nature in purely natural terms, for the unity of the natural realm lies in its instantiation of a divine plan, and in seeking to understand this divine plan, natural philosophy cannot proceed as if it required no resources outside its own. What I want to draw attention to here is the way in which natural philosophy comes to be locked into an enterprise that is in crucial respects quite unprecedented. In particular, in the ﬁnal analysis it does not matter whether it is natural philosophy or natural theology/revelation that is doing the work. Burnet focuses on the inadequacies of a literal understanding of Genesis and how these might be 66 67 68

Whiston, A New Theory of the Earth, 3. Ibid., 64. I shall return to the questions raised here in Chapters 5 and 6.

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made good by interpreting it using a natural-philosophical account of the formation of the earth. Ray, by contrast with Burnet’s view that nature in its present state is degenerate, insists that it is the ﬁnished product of divine wisdom, and he focuses on the incompleteness of natural philosophy as a description of natural phenomena, an incompleteness that can be made good only by incorporating it into a natural-theological understanding. But in both cases the aim of the exercise is to secure a union of natural theology/revelation and natural history/ natural philosophy. The different means by which this was achieved, and the different motivations that drove the two programmes, must not blind us to the fact that something very similar, and very radical, is being proposed in both cases: natural history/natural philosophy is being incorporated into a representation of the world provided by Christianity. The two are being uniﬁed into something that offers a general picture of the world and our place in it. Note, however, that it is Christianity’s world-view that natural philosophy becomes party to on this conception, not the other way around. What was required of and offered by the comprehensive conception of the world at stake was shaped by considerations internal to the mythological aspirations of Christianity. In this respect, Christianity is very much the dominant player, and the move is one that will have profound repercussions for the cultural standing of natural philosophy. In another respect, however, natural philosophy was able to occupy a commanding position. The critical point of contact between theology and natural philosophy for most practical purposes was between biblical criticism and natural history, but the book of nature and the book of revelation were, nevertheless, different kinds of ‘book’ and very different standards of credence were involved.69 Combining resources meant that some degree of assimilation of the one to the other was needed. The channels between natural history and biblical interpretation had been open at a methodological level since the sixteenth century, as standards of textual investigation, embodying a new understanding of notions of objectivity and impartiality, became incorporated into naturalhistorical enquiry, which in the course of the seventeenth century came to provide a model in important respects for natural philosophy more generally.70 69 A qualiﬁcation is necessary here, for at the extreme these standards may be collapsed into one another. I have in mind the infamous ‘Wertheim bible’ of 1735—[Johann Lorenz Schmidt], Die go¨ttlichen Schriften von der Zeiten des Messie Jesus (Wertheim, 1735)—in which the text of the bible is translated into straightforwardly natural-philosophical terms. The opening of Genesis is translated: ‘All worldly bodies, and our earth too, were created at the beginning by God. Concerning Earth in particular, it was at the start completely desolate: it was surrounded with a dark fog, and water ﬂowed around it, atop which a strong wind began to blow.’ A footnote explains this mysterious ‘wind’ (Hebrew rauch, commonly translated into Greek as pneuma, and into Latin as spiritus) in these terms: ‘Because the vapours would prefer to thin and rise into the sky at the equator, rather than at the poles, thus the equilibrium of the ﬂowing material would be destroyed. Hence the wind.’ Quoted in Jonathan Sheehan, The Enlightenment Bible: Translation, Scholarship, Culture (Princeton, 1995), 122. 70 See Gaukroger, Emergence, ch. 4.

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But these standards had been directed towards textual matters, and although they occasionally bore on content, this was not the focus of their concern. Physicotheology was a matter of content, however, for it worked with the content of Christian teaching about the natural realm, or matters that had a bearing on how the natural realm was to be understood, just as it worked with the content of natural philosophy, attempting to reconcile these contents or show how they were mutually reinforcing. There were disagreements within natural philosophy, but there were also disagreements about just what Christian doctrine committed one to, especially in the wake of the Reformation and the religious conﬂicts that had accompanied the Civil War in England, where a collapse of central government had allowed a degree of independent theological speculation and nonconformism that did not disappear with the Restoration, and indeed was encouraged with the Act of Toleration (1689), and the lapse of the Licensing Act (1695), which had enforced pre-publication censorship. In the 1690s, there developed a sense that disputes within Christianity could and should be settled in a way that at least paralleled that in which disputes in natural philosophy were settled. One of the upshots of physico-theology was that the question had to be raised whether Christian beliefs were not in fact subject to the same kinds of probing that natural-philosophical beliefs were subject to, for if the two were to act in tandem, this would provide a requisite degree of methodological commensurability. Moreover, since developments in biblical philology had already involved the application of cognate standards to sacred texts,71 the move to making Christianity, and more generally ‘religion’, a subject of study in its own right did not emerge wholly without precedent. What was wholly without precedent was the idea that there were cognitive standards that could have a universal application, to natural philosophy and Christian revelation equally. THE RATIONALIZATION OF RELIGION The emergence of a concern to provide rational foundations for Christianity— ‘rational’ in the sense of something that derives its cogency and legitimacy from the fact that it does not assume any particular doctrines but proceeds via reason alone—was, at least in a general sense, not a new project. Anselm in the eleventh century and Lull in the thirteenth had each attempted to base theology on a rational, doctrinally neutral basis with the aim of convincing Muslims and heretics of orthodox Christian doctrines such as the Trinity and the Incarnation. But the projects designed to provide rational foundations that emerged in the late 71 Developments in biblical philology, which began in the ﬁfteenth century in Valla, came to a head in the ‘Berleburger Bible’: [Johann Friedrich Haug et al.], Die Heilige Schrift Altes und Neues Testaments: nach dem Grund-text aufs neue u¨bersehen und u¨bersetzet (8 vols., Berlenberg, 1726–40). See the discussion in Sheehan, The Enlightenment Bible, ch. 4.

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seventeenth century went well beyond earlier attempts to induce Islam and the heterodox into the fold of true religion by rational means. There had been much dispute in the Middle Ages and Renaissance over what kind of deviation from religion—from the true religion, Christianity—Islam was. Theologians asked what form of heresy Islam embodied, whether it was a mixture of Judaism and idolatry or a mixture of Judaism and Nestorianism, for example. But the late seventeenth-century move to construe religions in terms of their cognitive content enabled one to distinguish them in terms of sets of beliefs. A religion was simply a set of beliefs, and different religions comprised different fundamental sets of beliefs. On this conception, Islam was not a heresy, because it shared too little with Christianity to be construed as a variant form of Christianity; nor was it a form of paganism because, like Christianity, it was monotheistic, had sacred texts, forms of religious ritual, and so on. It was another religion: and from the late seventeenth century onwards we witness a growing sense that Christianity was one of a number of religions. As we might expect, criteria for what counted as a religion on this conception tended to be highly Christocentric, and Mohammed was substituted for Jesus in a completely inappropriate way, as if someone regarded in Islam as a prophet was the equivalent of someone regarded as God in Christianity, with the result that Islam was routinely referred to as ‘Mohammedism’ (or some cognate term) throughout the modern era. But the crucial point for present purposes is the development of the idea of ‘religions’ in the plural: other systems of belief were not merely heresy or paganism but things that had a standing in their own right.72 If they were mistaken, the mistake was not appropriately analysed as a form of heresy. It is crucial to note here that these religions were marked out from one another by cognitive content, i.e. sets of beliefs, because as well as the importance for such an approach of distinguishing religions in cognitive terms, there was the correlative question of what to include within Christianity, and how to include it. There was a perceived need, in the face of a very wide diversity in sectarian beliefs, to discern a core set of Christian beliefs so that divergent sects could at least be recognized as Christian, even if deemed heretical by their opponents. We can identify two broadly contrasting positions in response to this. Both reject the idea that revelation alone supplies a sufﬁcient vindication for, or even a sufﬁcient identiﬁcation of, Christian beliefs. The ﬁrst seeks to establish a universal basis for some basic Christian beliefs, and morality in particular. We need to 72 See Peter Harrison, ‘Religion’ and Religions in the English Enlightenment (Cambridge, 1990); Wilfred Cantwell Smith, The Meaning and End of Religion (London, 1978). In fact, the division of religions up to the nineteenth century was fourfold: Christians, Jews, ‘Mohammedans’, and the rest, where the last category comprised heathens, pagans, idolaters, and polytheists. In the course of the nineteenth century, this classiﬁcation of world religions was replaced by one that recognized ten to a dozen religions on the basis of an explicit linking of religious confessions and racial groups (e.g. Muslims/Arabs, and Christians/Western Europeans): see Tomoko Masuzawa, The Invention of World Religions (Chicago, 2005).

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distinguish two rather different means of securing this, however: a metaphysical version and a physico-theological one. On the one hand there is Leibniz, who believes that only metaphysical grounding will be effective. On the other, there are those such as Clarke who seek to ground morality, and by extension Christian belief, in natural events. By contrast with both of these, an alternative seeks to establish a form of pluralism in religious and moral beliefs. Here again we can identify different streams. Locke attempts to keep this pluralism within the framework of a minimal Christianity, for example, whereas deists such as Toland are prepared to contemplate a wholly ‘rational’ natural theology as a means of reforming Christianity from outside. Despite the very signiﬁcant differences between these programmes, they were all committed to the reduction of Christian natural theology to its cognitive content, to a set of explicit beliefs whose content could be compared with beliefs of different provenance. This allows for the ‘rationalization’ of religion whereby a general ordering is possible in which beliefs fundamental to any form of Christianity can be identiﬁed and distinguished from those peculiar to particular confessional understandings. Note, however, that it also allows there may still be a non-propositional element in Christianity, manifested in ritual, sacraments, etc. in the case of Catholicism and Anglicanism, and a narrower range of practices of piety in the case of the various forms of Puritanism: in both cases offering moral constraints on the conduct of daily life, particularly through the effective moralization of human aspirations, fears, and desires.73 It is the combination of these two, a set of beliefs and a non-propositional mythological structure, that enabled Christianity to engage with the world in a distinctively successful way, and what made it so resistant to dislodgement by radical programmes, such as those espoused by Spinoza and (arguably) Bayle, where any non-propositional content is reduced out of the picture, in the manner of the Epicureans, as if any fears and desires not able to be anchored in some cognitive system are merely irrational and thereby, on analysis, not genuine. We shall return to these questions later in the book. For the moment I want to examine more closely what the rationalization of religion amounts to. Whatever route and strategy was chosen, natural-theological and moral and political beliefs developed a degree of autonomy with respect to Christianity. In some cases, it was natural philosophy that took up the slack directly. In others, it was a metaphysics speciﬁcally geared around a particular natural philosophy that did the work. In yet others, it was a conception of enquiry derived in large part from developments in natural history and experimental natural philosophy that guided the programme. In each case, perceived deﬁciencies in Christian theology 73 See the brillant studies of ‘culpabilization’ in the West by Jean Delumeau on these questions: La Peur en occident (XIV e–XVIII e sie`cles): Une cite´ assie´ge´e (Paris, 1978); Le Pe´che´ et la peur: La culpabilisation en occident, XIII e–XVIII e sie`cles (Paris, 1983); Rassurer et prote´ger: Le sentiment de se´curite´e dans l’occident d’autrefois (Paris, 1989); L’Aveu et le pardon (Paris, 1992).

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are made good by natural philosophy coming to the rescue, as it were, by those concerned for the well-being of Christianity: even with the deists of the period, the aim is to reform Christianity, not to replace it with something different. One of our concerns will be to keep track of how natural philosophy comes to be transformed to meet the new demands placed on it by these developments, and to get some sense of how it emerges as an integral part of a picture of the world and our place in it. Let us begin with the metaphysical conceptions. In the comprehensive metaphysical systems of Spinoza and Leibniz, politico-theology is connected with natural philosophy through the intermediary of metaphysics, conceived as a genuinely foundational and autonomous discipline. In the Spinozean version of this project, for example, Christianity and natural philosophy were wholly subsumed under a general metaphysics, Christianity being effectively replaced in its cognitive and moral dimensions.74 In the Leibnizian version, the role of metaphysics was reconstrued so that it was in a position to provide an underpinning for both natural philosophy and theology equally: to the extent to which they can be grasped by human capacities, both have their source and rationale in metaphysics. In the case of natural philosophy, for example, Leibniz not only stresses the need for metaphysical grounding, but the moral and religious imperative that lies behind it: There is in motion something other than what is purely geometrical, that is, than extension and its bare modiﬁcation. And in order to consider it properly, we must recognize that it is necessary to add to it some higher or metaphysical notion, namely that of substance, action, and force. This consideration seems to me important, not only in order to become acquainted with the nature of extended substance, but also so as not to exclude higher and immaterial principles, to the detriment of piety.75

Leibniz’s metaphysical construction of Christianity is best considered in the context of the disputes over politico-theology. In continental Europe, politicotheological questions were shaped by the legacy of the brutal, fratricidal wars of religion that characterized much of Europe throughout the second half of the sixteenth century and ﬁrst half of the seventeenth.76 The Thirty Years War that had devastated and paralysed Europe, cutting the population of the German states alone from twenty-one million to thirteen million and obliterating its economy, came to an end in 1648 with the Treaty of Westphalia, in which the civil and confessional realms were effectively separated, as states came to be deﬁned in territorial rather than confessional terms.77 There were a number of 74 See Gaukroger, Emergence, 471–92; and more generally Jonathan Israel, Radical Enlightenment, and idem, Enlightenment Contested. 75 Leibniz, phil. Schriften, iv. 465. 76 See Martin Heckel, Deutschland im konfessionellen Zeitalter (Go¨ttingen, 1983); and Ian Hunter, Rival Enlightenments (Cambridge, 2001). 77 See Howard Hotson, ‘Irenicism in the Confessional Age: The Holy Roman Empire, 1563– 1648’, in H. Louthan and R. Zachman, eds., Conciliation and Confession: Struggling for Unity in the Age of Reform (Notre Dame, Ind., 2004), 228–85; and Robert Bireley, ‘The Thirty Years War as Germany’s Religious War’, in K. Repgen, ed., Krieg und Politik, 1619–1648 (Munich, 1988), 85–106.

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different kinds of response to this. By contrast with the Hobbesian approach, the idea that it was the duty of human beings to seek theological truth and moral perfection was taken as given in the disputes that followed. Rather, the question was whether the civil sphere should reﬂect this search. In the domain of moral and political philosophy, this led to a division between those who saw the bloody confessional conﬂict as being resolved by separating confessional issues completely from civil ones, and those who saw it as being resolved by reconciliation of confessions through some fundamental recasting of religious and moral precepts. At least a good deal of the motivation behind the ﬁrst approach, as developed in Pufendorf and subsequently elaborated by Thomasius, was practical.78 The price of allowing confessional conﬂicts to enter the civil realm was perpetual violence, and this was simply too high a price to pay. The unique claims to truth and salvation of confessional opponents were all-or-nothing claims on which salvation hinged, and because of this no compromise was possible. Once such disputes were transplanted into the civil domain, making redundant or even simply immoral the compromise, negotiation, and balance that political theorists deemed appropriate to civil matters, the result was a form of uncompromising fratricide for which there was no political solution. Since it was far from clear that there could be any religious solution either, confessional questions had to be resolutely shifted out of the public sphere into that of the private. On this view, since confessional disagreement appeared to be irresolvable, there could be no possible gain in trying to place such disputed values at the basis of a civil governance. The Pufendorﬁan project of quarantining religious disputes from the civil realm raises a question about the moral basis of the law. It was generally considered that religion provided the basis for morality, and, given this, the removal of religious questions from the legal domain thereby risked the removal of morality from the legal domain, so that the pursuit of justice was replaced by the preservation of order. This view, traditionally associated with Hobbes’ defence of the nation state, is indeed what Pufendorf was advocating, as the only practical solution to the wars of religion: law had to be dissociated from notions of justice traditionally grounded in natural law, and instead directed towards the orderly resolution of disputes. But in that case, the challenge was to

78 Samuel Pufendorf, De Jure Naturae et Gentium Libri Octo (London, 1672); idem, De Ofﬁcio Hominis et Civis juxta Legem Naturalem Libri Duo (Frankfurt, 1673); idem, De Habitu Religionis Christianae ad Vitam Civilem (Bremen, 1687); Christian Thomasius, Institutiones Jurisprudentiae Divinae (Leipzig, 1688). On Pufendorf and Thomasius, see Hunter, Rival Enlightenments, chs. 4 and 5 respectively. On Thomasius, see Thomas Ahnert, Religion and the Origins of the German Enlightenment: Faith and the Reform of Learning in the Thought of Christian Thomasius (Rochester, 2006); Ian Hunter, The Secularisation of the Confessional State: The Political Thought of Christian Thomasius (Cambridge, 2007); and Kasper Risbjerg Eskildsen, ‘Christian Thomasius, Invisible Philosophers, and Education for Enlightenment’, Intellectual History Review 18 (2008), 319–36.

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show how the law could avoid the charge of arbitrariness.79 The problem was that there were competing confessional claims, and if one of these were preferred this could only be by an effectively arbitrary ﬁat, in which case we were back with the original problem, or by adopting a confessional basis for the state, which is exactly what the Treaty of Westphalia had attempted to go beyond. For those opposed to the Hobbesian or Pufendorﬁan solutions, some kind of moral foundation for law was needed, one that transcended religious sectarianism but at the same time reﬂected Christian values, whatever its source. Conﬂating the two, Leibniz maintained that the Hobbesian/Pufendorﬁan state had never existed either among civilized or barbarian peoples, and that it was neither possible nor desirable: the only real sovereign of the Hobbesian/Pufendorﬁan type is God, ‘whom alone one can trust in all things’.80 For Leibniz, the Pufendorﬁan approach, like that of Hobbes, was an amoral submission to an arbitrary authority, an abandonment of the search for a wellfounded moral and juridical basis for political decision making in favour of raison d’e´tat. In his view, a separation of the confessional and civil spheres could provide no lasting basis for civil governance because, as long as such governance lacked moral/theological grounding, it was in effect just an arbitrary exercise of power, and as such illegitimate. Hence the importance of engaging the cognitive dimension of religious belief, so that the task became that of providing, to the greatest extent possible, a foundation of such a suitably deep and comprehensive nature that it transcended particular confessional differences. Leibniz consequently sought the kind of absolute grounding that natural law had traditionally provided, but, sensitive to the deep confessional differences on matters of ‘true’ religion, he attempted to deal with the grounding of the law in a way that would settle the question for once and for all, by providing an ultimate metaphysical grounding for law, morality, and religion. The risks in this undertaking were signiﬁcant in that Spinoza had also sought to provide such a metaphysical grounding, but in a way that made no effort to preserve traditional Christian understandings of these. The condemnation of Spinoza had been swift and resolute, and although Leibniz’s aims are the exact opposite of Spinoza’s, the idea of providing a metaphysical grounding must have been compromised by the Spinozean episode. There can be little doubt that Leibniz was well aware of the dangers here, and this may seem to explain his concentration of resources on 79 There was an extra element in the dispute for Leibniz, for the Hobbesian view that the essence of the law is command required that the head of a state have absolute powers, and consequently not be bound to a higher power such as an emperor or pope, but this would have precluded the German principalities, which were subordinate to the Holy Roman Emperor, being sovereign states. Leibniz’s ﬁrst work on sovereignty, the Caesarinus Fu¨rstenerius of 1677, sets out to show that these principalities are properly constituted states, and that the Hobbesian absolutist criterion of statehood is faulty. See Patrick Riley’s introduction to his edition of Leibniz, Political Writings (Cambridge, 1972), 26–7. 80 See Leibniz, Political Writings, 28 for references.

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eclecticism rather than rational foundations in this case, by contrast with how he proceeds in natural philosophy. At a practical level, Leibniz spent much less time in trying to provide a metaphysical form of natural theology grounded in reason, than he did in attempting to reconcile various different religious beliefs.81 This attempted reconciliation was not to be effected through stripping them down to their fundamental rational beliefs, but rather through an eclecticism in which dogmas remained intact: Leibniz makes it clear, for example, that many Christian mysteries cannot be explained rationally but must be accepted on the basis of analogy.82 Yet matters are not so clear cut. On the face of it, there is in effect a distinction between what Leibniz seeks to achieve at the practical level, namely a form of eclectic agreement on religious doctrine which would be generally accepted and which would provide a basis for peace and stability in the state, and what he would ideally like to achieve at the theoretical level, namely a metaphysical form of natural theology grounded in unassailable truths of reason. But Leibniz had a distinctive and idiosyncratic understanding of metaphysics, and of how we arrive at metaphysical enlightenment. It is not so much a question of replacing one set of beliefs with a wholly different set of foundational principles, but of recognizing the perspectival nature of knowledge and seeking to achieve enlightenment by two principal means: by expanding these perspectives, and by reconciling various perspectives with a view to synthesizing a more comprehensive vision. We shall explore these questions in Chapter 3: for the moment I only want to draw attention to the fact that what I have been calling eclecticism may also be seen as a form of syncretism, and may in fact be a stage on the route to, rather than an alternative to, providing a foundational understanding. Nevertheless, nothing hangs on this in the present context: the contrast between Leibniz and Pufendorf, for example, remains as sharp as ever. One respect in which the Spinozean project had been especially contentious was in its attempt to develop a system of ethics that was wholly independent of religious considerations. It was generally assumed in the seventeenth century that Christianity provided the unique basis for morality, and that without Christianity there could be no morality. Richard Bentley warns against those who can ‘embrace the whole system of Christian Morals’, but ‘not as a collection of divine Statutes and Ordinances sent us by an express from Heaven, but only as useful rules of life, discoverable by plain Reason, and agreeable to natural Religion. . . . What need of so great a master to read mankind lectures of Morals, which they might easily learn without any teacher?’83 Lack of a Christian basis for morality in effect means no religion and morality for Bentley, and in his 1692 Boyle 81 See Jean Baruzi, Leibniz et l’organisation religieuse de la terre (Paris, 1907). Leibniz himself was as sympathetic to Catholicism as he was to Protestantism, and considered converting to the former: see Maria Rosa Antognazza, Leibniz: An Intellectual Biography (Cambridge, 2009), 256–9. 82 Essais de theodice´e: phil. Schriften, vi. 80–100. 83 Richard Bentley, Of Revelation and the Messias. A Sermon Preached at the Publick Commencement at Cambridge. July 5, 1696 (London, 1696), 4.

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Lectures he draws the consequences of this, telling us that: ‘if Atheism should be supposed to become universal in this Nation . . . farewell all Ties of Friendship and Principles of Honour; all Love for our Country and Loyalty to our Prince; nay, farewell all Government and Society itself, all Professions and Arts, and Conveniencies of Life, all that is laudable or valuable in the World.’84 Such an argument rested on two premisses. The ﬁrst was that the choice was between atheism and Christianity, a view possible while such phenomena as Judaism and Islam were treated as forms of heresy, rather than religions in their own right, and while paganism was treated as a confused precursor of Christianity—the victim of the weakness of human reason and the dominance of the passions—that nevertheless contained some religious insights which Christianity had clariﬁed and put in a sacramental context. The second was that atheism was a perverted act of will rather than an intellectual judgement. Bentley, for example, writes that ‘speculative Atheism does only subsist in our Speculation; whereas really human Nature cannot be guilty of the Crime: That indeed a few sensual and voluptuous Persons may for a Season eclipse this native Light of the Soul; but can never so wholly smother and extinguish it, but that at some lucid Intervals it will recover itself again, and shine forth to the Conviction of their Consciences.’85 In general, it was taken as given that not only had all cultures embraced religion of one kind or another, but also that there had been no great thinker who had espoused atheism. Cicero had argued that such universality and unanimity indicated that belief in religion was a ‘law of nature’,86 and in combining this with the view that Christianity was the only religion, everything else being merely heresy or a confused pagan precursor, Christian theologians generally felt conﬁdent about the Christian foundations of morality and social order. Bentley refers to ‘the commonly received Notion of an innate Idea of God, imprinted upon every Soul of Man at their Creation, in Characters that can never be defaced’.87 In fact, Jean de Le´ry’s Voyage of 1578 had noted that the Brazilian Indians had no religion at all, not even polytheism,88 and from the beginning of the seventeenth century Jesuit travellers to China had disputed with other religious orders on the question of the universality of religion, provoked by encountering the seemingly impossible: a well-ordered and apparently moral atheist society.89 Nor was antiquity free from such questioning: from the middle of the seventeenth century there was signiﬁcant dispute over whether Aristotle had been an atheist, and from 84 Richard Bentley, Eight Sermons, Sermon I, in [Boyle Lectures], A Defence of Natural and Revealed Religion: Being a Collection of Sermons preached at the Lecture founded by the honourable Robert Boyle Esq. . . . (3 vols., London, 1739), i. 1–87: 11. 85 Ibid., 2. 86 Cicero, Tusculanae disputationes, 1. 13. 87 Bentley, Eight Sermons, op. cit., 2. 88 Jean de Le´ry, Histoire d’vn voyage fait en la terre dv Bresil, avtrement dite Amerique (La Rochelle, 1578). 89 See Alan Charles Kors, Atheism in France, 1650–1729, i: The Orthodox Sources of Disbelief (Princeton, 1990), 62–3.

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the end of the century over whether Plato had been an atheist.90 The problem was that a broad deﬁnition of religion saved the view that religion was a universal phenomenon only at the cost of the Judaeo-Christian conception of God losing its centrality, whereas a narrow deﬁnition made atheism appear widespread.91 Matters came to a head with the publication of Bayle’s defence of the possibility of a virtuous atheist, beginning with his 1682 letter on comets. On the basis of a comprehensive search of what was by this time a very substantial body of travel literature, Bayle went on to deny, in this and subsequent publications, that religion was in fact universal and was something that attracted unanimous agreement. More radically, he also pointed out that, even if it were, this would in itself not constitute irrefutable grounds for accepting its legitimacy. In fact, Bayle argued, religion is neither necessary nor sufﬁcient for morality, and a society of atheists would still be governed by the desire for honour and reputations, as well as rewards and punishments.92 For Leibniz also, the argument from universality and unanimity was not sufﬁcient. He was well informed about Chinese rites and the debates on their status as ‘religions’,93 and it is far from clear that he was committed to the necessary universality of religion. Instead, Leibniz saw his task as being to reveal the underlying rationality of Christian morality in such a way that it was not relevant what degree of acceptance it might have enjoyed, or what historical claims could be made about the kind of agreement there might have been on the necessity of religion. The underlying rationality of Christian morality was something to be revealed by metaphysics, not by historical enquiry. Such an approach was paralleled in the physico-theological tradition in Clarke, who too sought to provide a rational foundation for Christian morality, that is, a defence of that morality that made no reference to Christian doctrine. Clarke did not set out to establish metaphysical foundations for morality, however, but ‘natural’ ones.94 What marks out Christian morality is the fact that it is the ‘natural’ morality: it corresponds to what is naturally right. This enables Clarke to deal with an otherwise troubling dichotomy in ethics, in that he 90

On the disputes over Aristotle, see ibid., 229–32. On those over Plato, see Martin Mulsow, Moderne aus dem Untergrund: Radikale Fru¨haufkla¨rung in Deutschland, 1680–1720 (Hamburg, 2002), 288–91. 91 See Kors, Atheism, 178–9. Cf. Dagmar von Wille, ‘Apologie ha¨retischen Denkens: Johann Jakob Zimmermanns Rehabilitierung der “Atheisten” Pomponazzi und Vanini’, in Friedrich Niewo¨hner and P. Pluta, eds., Atheismus im Mittelalter und in der Renaissance (Wiesbaden, 1999), 215–37. 92 Pierre Bayle, Lettre a` M.L.A.D.C. Docteur de Sorbonne, ou` il est prouve´ que les come`tes ne sont point le pre´sage d’aucun malheur (Rotterdam, 1682), }}133–6 and 172 respectively. 93 See E. J. Aiton, Leibniz: A Biography (Bristol, 1985), 325–32; and more generally David E. Mungello, Leibniz and Confucianism, The Search for Accord (Honolulu, 1977). 94 See Clarke’s Boyle Lectures: ‘A Discourse concerning the Being and Attributes of God, the Obligations of Natural Religion, and the Truth and the Certainty of the Christian Revelation’ and ‘A Discourse concerning the Unchangeable Obligations of Natural Religion, and the Truth and Certainty of the Christian Revelation’. Clarke, Works, ii. 513–733.

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accepts that God is completely free, and orders the world in a way that is constrained by nothing, for nothing could constrain such a perfect being, while on the other hand rejecting the voluntarist view, which he associates particularly with Hobbes, that goodness and truth are arbitrary. Clarke urges that God’s action must reﬂect natural standards of truth and goodness, rather than instantiate such standards arbitrarily. He attempts to reconcile these principles by means of a doctrine of the ‘ﬁtness of things’, whereby nature has a moral aspect which mirrors its physical aspect, both moral and physical aspects being knowable by reason. The idea is that any rational being will guide its conduct in terms of these moral principles. Since God is completely rational, he follows them completely, but in our own case we are also inﬂuenced by passions which act against reason, and cause us to behave immorally on occasion, and it is from this that the need for established religions arises.95 The idea of the grounding of Christian morality on a natural basis was not unprecedented, but it usually rested on the postulation of some innate moral sense. In 1660, in his ﬁrst draft of the ﬁrst of the Essays on the Laws of Nature, Locke had originally quoted Grotius’ view that the basis of morality lay in nature with approval and wrote that moral and religious principles found at different places at different times must be due to a universal cause. However, he subsequently deleted this passage and instead, in the third Essay, proceeded to deny the existence of any innate principles.96 His response to what he sees as the radical and widespread variation in moral and religious principles is not to put this down to the Fall, as many of his contemporaries were wont to do, but rather to argue that sense experience and reason were what should be relied upon to guide morality. In the Essays these new criteria are conﬁned to morality, but by the 1690s, in the Essay Concerning Human Understanding and in the essays on the ‘reasonableness of Christianity’, religion also has come under their sway, as Locke comes to deny all innate ideas, including moral and religious principles.97 Others had argued for the importance of experience in developing a moral sensibility. Richard Cumberland, for example, in his inﬂuential De legibus naturae of 1672 had argued that our moral sense comes through experience, 95 Clarke had a distinctive view of the priesthood in established religions, however, and he conceived clerical ofﬁce exclusively in terms of the function of teaching the reasons for the duties and obligations that arose from the nature of things. See Jeremy Schmidt, ‘An Order of Philosophers? Samuel Clarke’s Moral Theory and the Problem of Sacerdos in Enlightenment England’, Intellectual History Review 18 (2008), 361–74. 96 See John Marshall, John Locke: Resistance, Religion and Responsibility (Cambridge, 1994), 30–1. 97 In the light of this, it is perhaps not surprising that in 1703 there was an attempt at Oxford to suppress informal study of Locke’s Essay Concerning Human Understanding. This informal study had been encouraged with the appearance of John Wynne, An Abridgement of Locke’s Essay concerning humane understanding (London, 1696). By mid-century, by contrast, such abridgements and paraphrases of the Essay were part of the required curriculum at Oxford: see B. W. Young, Religion and Enlightenment in Eighteenth-Century England (Oxford, 1998), 7.

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and that what we learn from this experience is that nature is designed in such a way as to preserve its constitution through mutual cooperation. But on Cumberland’s view, experience reveals something about the ﬁnal causes underlying nature, including human nature. Locke certainly believes we learn about basic moral and religious principles through experience, and he expects that these will conform to Christian teaching, but it is more a question of building up an understanding through experience and reason, an understanding that has no guarantees, rather than, as it is for Cumberland, a question of uncovering something that is there for all to see, even if some (such as Hobbes) choose not to acknowledge it. The certainties that inform Cumberland’s approach are largely absent from that of Locke. In 1689, in his Letter on Toleration, he notes that ‘what is established by law’ in theological matters was in fact hardly a reliable basis for religious observance: our modern English History affords us fresh Examples, in the Reigns of Henry the 8th, Edward the 6th, Mary, and Elizabeth, how easily and smoothly the Clergy changed their decrees, their Articles of Faith, their Form of Worship, every Thing according to the Inclination of those Kings and Queens. Yet were those Kings and Queens of such different Mind in Point of Religion, and enjoined thereupon such different Things, that no Man in his Wits (I had almost said none but an Atheist) will presume to say that any sincere and upright Worshipper of God could, with a safe Conscience, obey their several decrees.98

As is evident from this account, what was at issue here was above all a question of politico-theology. And indeed there was one ‘atheist’, Spinoza, who had in effect presumed to say, as Locke put it, that ‘any sincere and upright Worshipper of God could, with a safe Conscience, obey their several decrees’, for Spinoza had notoriously construed religion as having no cognitive standing, being simply a matter of securing peace and stability, which he construed in turn as a matter of following what was in effect the arbitrarily—or perhaps pragmatically—chosen confession of the sovereign.99 Nor was the problem of authority in religious matters conﬁned to secular rulers. Richard Simon’s Histoire critique de Vieux Testament of 1678 set out to establish the authority of the Catholic Church by showing the dangers of individuals trying to interpret scripture for themselves, by demonstrating that there were numerous uncertainties in the text of the Old Testament, and that the choice was between the authority of the Church and chaos.100 But the profound difﬁculties and ambiguities of interpretation he 98 Locke, A Letter Concerning Toleration in The Works of John Locke Esq (2nd edn., 3 vols, London, 1722), ii. 242. 99 For Spinoza it was a question of making sure that the confession adopted by the state was adhered to, and no other, although he realized that censorship and repression were counterproductive, and that there were practical limits to what the sovereign could achieve. See Verbeek, Spinoza’s Theologico-Political Treatise, ch. 2. 100 A good part of the problem raised by Simon centred on the authenticity of received texts. In antiquity, there had been many claims and counter-claims over authenticity, and Simon noted that there was no more reason to accept New Testament books than there was to reject apocrypha: see

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raised made the Church’s decisions look not authoritative but wholly arbitrary, and it was unclear that there was much to choose between the interpretations it sanctioned and chaos. The point was not lost on Locke, who, in a letter of 1685, noted the dilemma: either one considered ‘everything in holy writ’ to be equally inspired by God, in which case one could not dismiss the apocrypha, or, if one allowed that ‘certain parts are to be considered as purely human writings, then where in the Scriptures will there be found the certainty of divine authority?’101 The various attempts to trim Christianity down to its essence, attempts that grew exponentially in number and intensity from the end of the 1680s, were a response to these problems, and were in large part due particularly to concerns with politico-theology. While England had escaped involvement in the Thirty Years War, it faced analogous problems during its own Civil War and its aftermath. Locke’s assessment in his 1660 Essays on the Law of Nature is unequivocal, asking: ‘For is there anything so abominable, so wicked, so contrary to all right and law, which the general consent, or rather the conspiracy, of a senseless crowd would not at some time advocate? Hence we have heard of the plunder of divine temples, the obstinacy of insolence and immorality, the violation of temples, and the overthrow of kingdoms.’102 The remedy to this did not come with the re-establishment of the Church of England in 1662, however, for instead of achieving a uniform religion, it resulted in severe divisions, with 1,700 clergymen resigning or ejected from their parishes. Even so, this was mild compared to Louis XIV’s 1685 revocation of the Edict of Nantes, removing recognition from and instituting deadly persecution of Protestants, a development Locke viewed with alarm from the Netherlands. Locke’s view was that political society was needed if there was to be peace, prosperity, and liberty, but that the individual’s moral and religious judgements remained sacrosanct, and he was at pains to defend their autonomy. As he puts it later in the Essay: ‘it would methinks become all men to maintain Peace, and the common Ofﬁces of Humanity and Friendship, in the Diversity of Opinions; since we cannot reasonably expect, that any one should readily and obsequiously quit his own Opinion, and embrace our’s with a blind Resignation to an Authority, which the Understanding of Man acknowledges not.’103 e.g. Richard Simon, A Critical History of the Text of the New Testament (London, 1689); 21, 31. Such questions of authenticity were taken up independently in England in John Toland, Amyntor: Or, a Defence of Milton’s Life (London, 1699); and William Whiston, Primitive Christianity reviv’d (London, 1712). See the discussion in Sheehan, The Enlightenment Bible, ch. 2. 101 The Correspondence of John Locke, ed. E. S. de Beer (9 vols., Oxford, 1976–89), ii. 748–9. The size of the problem became clearer with the posthumous publication of John Mill’s variant readings—of the order of 30,000 of them—of the New Testament: Daniel Whitby, Examen variantium lectionum Joannis Millii in Novum Testamentum (London, 1710). 102 John Locke, Essays on the Law of Nature: The Latin Text with a Translation, Introduction and Notes, Together with Transcripts of Locke’s Shorthand in His Journal for 1676, ed. W. van Leyden (Oxford, 1958), 160 [text]/161 [trans]. 103 Locke, Essay concerning Human Understanding, IV. xvi. 4.

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What one has, then, is an autonomous realm of personal religion and morality, but one that cannot be extrapolated to the state level, in the sense of forming the basis for a state-sanctioned religion. As Locke makes clear on a number of occasions, political society has been set up to resist foreign invasion, to prevent injury, and to protect property, and its means are strictly limited to securing these ends. The conﬁnement of religious belief to the private realm, however, does not prevent Locke from raising the question of the ‘reasonableness of Christianity’. Indeed, on the question of what Christianity commits one to, Locke espouses quite a radical minimalism, telling us in The Reasonableness of Christianity, that ‘the belief of Jesus of Nazareth to be the Messiah, together with those comcomitant Articles of his Resurrection, Rule, and coming again to judge the World, be all the Faith required as necessary to Justiﬁcation’.104 Radical minimalism of this kind was in fact becoming well entrenched by the 1690s. In his Discourse on Free-Thinking (1713), Anthony Collins, quoting John Tillotson—who was appointed Archbishop of Canterbury in 1691, and whose sermons were published in the mid-1690s—notes: What a Christianity, and how different from that of the Imposers of Creeds, Ceremonies, and particular Forms of Ecclesiastical Government, does [Tillotson] set before us. All the Dutys, says he, of Christian Religion which respect God, are no other but what natural Light prompts Men to, excepting the two Sacraments, and praying to God in the Name and by the Mediation of Christ. And even these things (which lay no Obligation upon us, but as they are the pure positive Commands of God) he justly observes, are of less moment than any of those parts of Religion which in their own nature tend to the Happiness of human Society.105

Our present concern is less with the radicalness of some of the proposals, as with the legitimacy of assessing Christian doctrine in this way. In the Preface to his Christianity Not Mysterious (1696), John Toland laments that, in his age, ‘a Man dares not openly and directly own what he thinks of Divine matters, tho it be never so true and beneﬁcial, if but it slightly differs from what is receiv’d by any Party, or what is established by law.’ Yet, as he points out, The Pravity of most Mens Dispositions, and the Ambition of particular Persons makes this matter seem less strange in Politick and Secular Affairs; and yet a Man may not only make new Discoveries and Improvements in Law or Physick, and in the other Arts and Sciences inpunibly, but also for so doing be deservedly encourag’d and rewarded.106

104

Locke, Works, ii. 538. Anthony Collins, A Discourse of Free-Thinking, occasion’d by the Rise and Growth of a Sect call’d Free-Thinkers (London, 1713), 173–4. Cf. Charles Leslie on Tillotson: ‘He is owned by the atheistical wits of all England as their true primate and apostle’ ([Charles Leslie], The Charge of Socinianism against Dr Tillotson Considered, By a True Son of the Church (Edinburgh, 1696), 13). 106 John Toland, Christianity Not Mysterious (London, 1696), v. Toland’s idea of religion being open to the same kinds of investigation as natural philosophy is explored in detail in Manlio Iofrida, La Filosoﬁa di John Toland (Milan, 1983). 105

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The comparison of the skills of theologians with members of the legal and medical fraternities was also made by Collins, in 1713, but with a different point: No Men is excluded from studying Law or Physick, because there are several of those Professions, nor from following his own Judgment when he is sick or in Law; nor is there any reason why a Man, who is not a Doctor in Physick or a Serjeant at Law, may not understand as much Law and Physick as either of them. In like manner, the setting Men apart for the Study of Divinity, does not exclude others from the Study of Divinity, nor from following their Judgment about a Point in Divinity, nor from knowing as much Divinity as any Doctor in Divinity, And by consequence there is no necessity to rely on any Man’s Judgment, either in Law, Physick, or Divinity.107

Toland’s point is that in disciplines such as law and medicine, there is constant progress in understanding, effected through the critical engagement of the practitioners of these disciplines, and it is not clear why religion should be any different. By contrast, Collins’ argument is that one can understand the law and medicine without going through any special training: one can teach oneself these things and there is no restriction on following one’s own judgement on legal and medical matters in particular cases that affect one personally, even though one’s grasp of these subjects is not as broad as those trained in the disciplines: I could proceed to give an account of how they dispute about the Priests power to absolve men from their Sins, about the Independency of the Church on the State, about the Sacrament being a proper Sacriﬁce, about the real Presence in the Sacrament, about the Priests of the Christian Church being proper Priests; and indeed about every Point in the whole Christian Religion, as well as about the Meaning of almost every Text in the Bible: But what I have produc’d being sufﬁcient to prove their Divisions about the meaning of the Scripture in matters of the greatest importance, I may justly conclude that it is necessary for every Man, instead of relying upon them, to think freely for himself.108

In this case, the question arises what the ultimate authority of theological judgements derive from. The answer is that it can only lie in their rational basis, a doctrine eighteenth-century thinkers traced back to Locke. Hume, for example, tells us that ‘Locke seems to have been the ﬁrst Christian, who ventured openly to assert, that faith was nothing but a species of reason; that religion was only a branch of philosophy; and that a chain of arguments, similar to that which established any truth in morals, politics, or physics, was always employed in discovering all the principles of theology, natural and revealed.’109 The attempt to provide a rational basis for Christianity110 was matched by attempts to provide a rational basis for natural philosophy, and this will be one of 107

Collins, A Discourse of Free-Thinking, 107–8. Ibid., 76. ‘Thinking freely’ is deﬁned (ibid., 5) as using the understanding to establish the meaning of any proposition, and the evidence for it, and to judge ‘of it according to the seeming Force or Weakness of the Evidence’. 109 David Hume, Essays and Treatises on Several Subjects (2 vols., Edinburgh, 1793), ii. 486. 110 Note that we are not dealing with a sceptical-style rationalism here. Discovery of this rational basis is pursued by the English deists primarily through biblical hermeneutics. 108

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our concerns in subsequent chapters. It is instructive that the project of providing rational foundations was so general: instructive, but hardly surprising. If Christianity and natural philosophy were both treated simply as their cognitive contents and nothing more, then for the purposes of their alliance they were both committed to the goal of enhancement of these cognitive contents. In both cases, the aim was to build up and strengthen the ediﬁce, identifying fruitful paths and avoiding dead ends. Cognitive programmes do not, in themselves, necessarily carry such commitments. Often they have deﬁnite ﬁxed tasks which, when accomplished, bring the programme to an end. But this generally occurs when such programmes are considered as technical ones. What the alliance of natural philosophy—by this stage incorporating previously purely technical programmes such as mechanics—and a Christian natural theology does is to provide these programmes with a quite different, more generally conceived purpose, one that goes beyond the resolution of internally generated/formulated questions, and seeks resolution not only of general issues about the nature of the world, but of our knowledge of it and our place in it. What is distinctive is not that such questions are asked—they had been the staple of philosophical speculation since remote antiquity—but the combination of resources that was thought to put one in the right position to answer such questions. In itself, natural philosophy was a narrowly focused discourse. Even an ambitious explanatory programme such as mechanism, which was really the ﬁrst developed natural philosophy in the modern era to consider itself able to explain all physical phenomena, did so only by removing much of what had traditionally fallen under the rubric of natural philosophy from its domain of explanation, using the doctrine of primary and secondary qualities to exclude anything not mirrored in micro-corpuscular states as merely an effect of the perceiving mind, and denying any autonomy to vital phenomena.111 Christianity, by contrast, had traditionally laid claim to universal competence in all matters of understanding the world and our place in it, most notably in its Augustinian version, but this was a claim that was decisively weakened in the course of the seventeenth century. On the face of it, the prospects of a union of the two faring any better look dim. Indeed, they are dim, but what is of primary importance for the questions with which we are concerned is understanding the way in which natural philosophy is reshaped in order to meet the demands of a signiﬁcantly expanded and qualitatively transformed set of aims. 111

See Gaukroger, Emergence, ch. 9.

2 The Mathematical Principles of Natural Philosophy We have seen that many of the questions about the aims and standing of natural philosophy that arose from the late 1680s onwards turned, in one way or another, around Newtonianism. With its publication in 1687, Newton’s Philosophia naturalis principia mathematica gradually but decisively replaced Descartes’ Principia Philosophiae (1644) as the canonical text of the new natural philosophy. This was indeed Newton’s intention, and his opposition to Cartesianism had grown radically around late 1684 / early 1685 with the composition of ‘De gravitatione et aequipondio ﬂuidorum’,1 in which he rid himself of the last vestiges of Cartesian natural philosophy. As for the Principia itself, not only did Newton himself refer to his book as Principia philosophiae both in and out of print, but the similarity in the titles takes on a new signiﬁcance when one compares the typography of the title pages of the three editions of the Principia, for in each of them the words Principia and Philosophiae are in larger type than the other two and in bold face (see Fig. 2.1), and in the third edition they are printed in red ink. At the beginning of Book III of the Principia, which contains his ‘system of the world’, Newton tells us that he had composed an earlier version in a ‘popular’ form.2 This less technical draft, which was printed after his death as a separate work,3 shorn of the mathematics of Books I and II, is in a more traditional, largely non-mathematical, natural-philosophical genre, which is that of Descartes’ own Principia, and brings out the parallels in a striking way. It is also worth noting in this connection that when, as a result of a dispute with Hooke over whether Hooke should receive credit for the inverse square law, Newton brieﬂy considered withdrawing Book III, he renamed the remaining ﬁrst 1 The text and translation of ‘De gravitatione’ are given in Unpublished Scientiﬁc Papers of Isaac Newton, ed. A. Rupert Hall and Marie Boas Hall (Cambridge, 1962), 89–156. The dating— signiﬁcantly later than that originally given by the Halls in their edition—is established in Betty Jo Teeter Dobbs, The Janus Face of Genius: The Role of Alchemy in Newton’s Thought (Cambridge, 1991), 139–46. 2 Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, ed. and trans. I. Bernard Cohen and Anne Whitman (Berkeley, 1999), 793. 3 Isaac Newton, A Treatise of the System of the World . . .Translated into English (London, 1728). The original Latin version can be found in Newton, Opera, iii. 176–242. For details, see I. Bernard Cohen, Introduction to Newton’s ‘Principia’ (Cambridge, 1971), 327–35.

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Fig 2.1

two books of the treatise ‘De motu corporum libri duo’: it would then no longer have been a genuine principia philosophiae, for the philosophia came in Book III.4 Books I and II provided the new mechanics that grounded the cosmology of Book III, and Book I, in particular, could have been, and to some extent was, read independently of it. Those who devoted themselves to mechanics could accept Book I without accepting Book III, and this was important because it was widely assumed in the 1690s that the vortex theory was manifestly superior to the 4 On the conscious contrast on Newton’s part between his Principia and that of Descartes, see I. Bernard Cohen, ‘A Guide to Newton’s Principia’, in Newton, The Principia, Cohen and Whitman edn., 1–370: 43–9.

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Newtonian theory of gravitation set out in Book III, and that as a result the Newtonian system of natural philosophy was so fatally ﬂawed as not to require detailed refutation.5 Jakob Bernoulli took virtually no interest in the Principia, for example, and it was not until the priority dispute over the calculus began in 1699, with the claim by Newton’s disciple Fatio de Duillier that Leibniz had plagiarized Newton’s calculus,6 that his brother Johann Bernoulli was prompted to subject the mathematics and mechanics of the Principia to critical scrutiny, with the result that, while gravitation was still the core physical issue in dispute, parts of the mechanics of Books I and II now began to be called into question.7 To appreciate what is at issue here properly, we need to understand in what ways the Principia involved a rethinking of physical questions, a rethinking which goes to the heart of the transformation of natural philosophy in the late seventeenth and eighteenth centuries, in which there was a fundamental shift in the resources deployed in physical enquiry. The rethinking overturned the dominant natural philosophy of the time, that defended by Descartes in his Principia, which had set out the fundamentals of a mechanist micro-corpuscularian model of physical processes. Newton offers something completely different. Whereas mechanism was a natural philosophy that premissed its use of mechanics on a particular understanding of the nature of matter, Newton severs the connections between mechanics and matter theory, in the process cutting mechanics adrift from a number of natural-philosophical issues that, at least since Aristotle, had been considered to constitute the core of the discipline. FROM PRINCIPIA PHILOSOPHIAE TO PRINCIPIA M AT H E MA T I C A Newton’s Principia overshadowed all other natural-philosophical enterprises of the period, and critical scrutiny of what its achievement consisted in will help us understand in what ways it became a model of natural-philosophical enquiry, 5 Huygens, for one, found Newton’s idea of gravitational attraction ‘absurd’: Huygens to Leibniz, 18 Nov. 1690: Œuvres comple`tes de Christiaan Huygens (22 vols., The Hague, 1888–1950), ix. 538. He did however accept that Newton had established the inverse square law beyond doubt and that he had demolished vortex theory, which Huygens had defended up to his reading of the Principia. 6 Nicolas Fatio de Duillier, Linea Brevissimi Descensus Investigatio Geometrica Duplex. Cui addita est Investigatio Geometrica Solidi Rotundi, in quod Minima ﬁat Resistentia (London, 1699), 18. In fact, the question of who discovered calculus ﬁrst had been put on the agenda earlier that year with the publication of the third volume of Wallis’ Operum mathematicorum (3 vols., Oxford, 1693–9), in which Wallis published mathematical correspondence between Leibniz, Oldenburg, and Wallis himself. L’Hoˆpital wrote to Leibniz on 13 July warning him that ‘the English are using every means possible to attribute the glory of this invention to their nation.’ See Leibniz, Mathematischen Schriften, ed. C. I. Gerhardt (7 vols., Berlin and Halle, 1849–63; repr. Hildesheim, 1971), ii. 336. On the whole episode, see A. Rupert Hall, Philosophers at War: The Quarrel between Newton and Leibniz (Cambridge, 1980), ch. 6. 7 Newton added a new proof of Proposition 10 of Book II in the second edition in response to to a criticism made by Johann Bernoulli: see The Mathematical Papers of Isaac Newton, ed. D. T. Whiteside (8 vols., Cambridge, 1967–81), viii. 50–5 and 373–434.

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and in what ways it did not. The latter is particularly important for us, not so much because this is a question that the standard ‘triumphalist’ histories of science ignore, but because our paramount aim is to understand how a culture emerges in which cognitive values generally are subordinated to scientiﬁc ones, and this requires that we be particularly sensitive to what exactly is doing the work in the image of science that is held up as the model. From the 1630s onwards, mechanism had gradually replaced Aristotelianism as the dominant natural philosophy, offering an account that was at least as comprehensive as that of Aristotelian natural philosophy. Moreover, it avoided many of the problems of compatibility that had plagued the relation between Aristotelian natural philosophy and Christian teaching—notably on the question of the immortality of the soul—by instituting a sharp division between the natural and supernatural realms. This division was largely in response to Renaissance naturalism, which had tended to treat God as immanent in his creation, thereby blurring the distinction between the natural and the supernatural, and drawing some particularly heterodox consequences from this. Mechanism was the doctrine that there was a single fundamental level of description of the material universe, that of inert micro-corpuscles acting on one another through transfer of some mechanically speciﬁable quantity, such as motion or momentum, on surface contact. The core claim of mechanism was that the behaviour of macroscopic bodies could, by means of a programme of reduction, be accounted for fully in terms of such micro-corpuscularian interactions, and the very inﬂuential Cartesian programme of biomechanics extended the explanatory claims of mechanism to all physical phenomena, including the organic. In this way, mechanism offered an account of the physical realm that purported to be comprehensive. To the extent to which a world-view was sought that had a natural-philosophical component, mechanism dislodged both Aristotelianism and Neoplatonism, and after the early decades of the seventeenth century it became established as the model for further natural-philosophical enquiry. There were in effect three components in the mechanist project. First, there was the description of the behaviour of the micro-corpuscles of which material things were constituted. Second, there was the reduction of macroscopic behaviour to the behaviour of these underlying micro-corpuscles. Finally, there was the exclusion of macroscopic physical phenomena not susceptible to this kind of analysis, primarily through the doctrine of primary and secondary qualities and, in the case of living organisms, through biomechanics.8 The ﬁrst of these three components took the form of mechanics, which must be distinguished from mechanism. Mechanics had been pursued since antiquity, whereas mechanism was a seventeenth-century phenomenon. The greatest exponent of mechanics in the ﬁrst half of the seventeenth century, Galileo, was neutral on most questions concerning mechanism, and its greatest exponent in the second half of the century, Newton, was antithetical to mechanism in a number of respects. Yet it 8

See Gaukroger, Emergence, ch. 9.

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was as crucial for Galileo and Newton as it was for mechanists that mechanics be a natural-philosophical theory, albeit a highly mathematical one, and not simply a form of practical mathematics that dealt merely with mathematical idealizations, as it had been construed on the Aristotelian conception. Nevertheless, there was a radical difference in the ways in which Galileo and Newton, on the one hand, and a mechanist such as Descartes, on the other, secured this. Mechanics had been construed as a form of practical mathematics in antiquity, and was not treated as part of natural philosophy proper. Various attempts were made to incorporate it into natural philosophy in the sixteenth and seventeenth centuries, and the majority of these took the form of tying mechanics into matter theory in one way or another.9 Some tried to reform the Aristotelian Mechanica tradition, which had accounted for the mechanical behaviour of the lever in terms of Aristotelian natural philosophy, drawing in particular on its distinctive teleological understanding of motion as something that is resolved in the state of rest. The sixteenth-century mathematicians who took up this option attempted, in vain, to prise apart the connection between Aristotelian matter theory and mechanics while at the same time using the former to confer physical standing on the latter. Others, notably Descartes, tried to ﬂesh out statics in terms of a wholly new mechanist matter theory, thereby providing it with physical signiﬁcance. For Descartes, what made mechanics a foundational physical discipline was the fact that it could be used to describe the behaviour of the microcorpuscles which his matter theory dictated were the ultimate constituents of the physical realm. Matter theory was the starting point. This was very much the traditional view of natural philosophy. For Aristotle, the Platonists, the Stoics, and the Epicureans, for example, physical theory was just matter theory, which is why mechanics was deemed to be marginal to physical enquiry. Early-modern corpuscularians such as Bacon were locked in to this tradition, but the mechanists were prepared to combine matter-theoretical and mechanical considerations, so that while Baconian cosmology was driven exclusively by matter theory, for example, Cartesian cosmology was guided by a combination of matter theory and mechanics, with the latter doing the bulk of the explanatory work.10 Nevertheless, it was matter theory that shaped the role for mechanics in the mechanist scheme of things, because what was important about mechanics was its ability to describe micro-corpuscularian behaviour, once matter theory had identiﬁed the fundamental level of physical explanation as lying with an account of the behaviour of microcorpuscles. There was no distinction in mechanics itself between the microscopic and the macroscopic, and a fortiori no notion of explaining the macroscopic in terms of the microscopic. Putting mechanics to use in a context shaped by matter theory transformed it from a set of merely technical, if practically orientated, 9

See ibid., ch. 8. See Stephen Gaukroger, ‘The Role of Matter Theory in Baconian and Cartesian Cosmologies’, Perspectives on Science 8 (2000), 201–22. 10

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geometrical theorems into a description—in some respects the description—of the physical world. Mechanics enters the mechanist picture at the most fundamental level, and this is why the kinds of issues about the completeness and purview of mechanics that are raised by the Newtonian account of planetary orbits was such a serious one. The Galilean approach to establishing the physical relevance of mechanics was completely different from the mechanist one. Galilean kinematics was not motivated by, or shaped by, or pursued in the context of, matter theory. It was quite independent of matter-theoretical considerations, and the idea of the microscopic realm having a special explanatory role is absent from Galileo’s discussion of mechanics (though it does occupy him in a number of other natural-philosophical contexts). For Galileo, the issue of what makes mechanics a physical discipline is resolved by showing how a geometrically precise kinematic description of bodies falling freely in a void—a situation we never witness—can be systematically modiﬁed, in the light of factors that have been identiﬁed by his kinematics, so that it yields a kinematic description of the observable behaviour of bodies falling in resisting media. What the Galilean procedure demonstrates is that one does not have to account for a complex physical phenomenon directly if one can show how it can be connected systematically to something that one has analysed fully. Galileo’s laws of falling bodies and projectile motion describe physical events, as opposed to mere mathematical idealizations, not because they can be associated with matter theory, but because a series of observationally and experimentally based procedures enables one to understand what is happening in the complex case in terms of what mechanics has identiﬁed as the simplest and most general case. What Galileo was able to show was that the only factor that characterized free fall in every case of free fall—no matter what the mass or shape of the falling body, no matter what the density of the medium—was a uniformly accelerated rectilinear motion, and the behaviour of the body was modiﬁed as other components, whose kinematic effects could be speciﬁed, were added to this uniformly accelerated motion. What makes fall in a void the primary case for analysis is that this is the unique case in which the only universal component of free fall is the sole factor operative, so it is the case that one needs to analyse before one can turn to the others. Newton will structure the Principia along similar lines. As its title explains, it deals with ‘the mathematical principles of natural philosophy’, and it was as important for Newton that he was dealing with natural philosophy as it was that he was dealing with it mathematically. But the connection was not made through a linking of mechanics to matter theory, the standard route for a mechanist. Having described, in Book I, the behaviour of dimensionless points of unit mass in empty space, he does turn to matter theory in the second half of Book II, considering the motion of bodies in ﬂuids and the motions of ﬂuids, but the discussion proceeds at the level of macroscopic phenomena, and the aim is to

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understand how the mechanical behaviour of the bodies described in Book I is modiﬁed once a medium is introduced.11 The contrast between establishing the physical credentials of mechanics by the mechanist route of attempting to connect it with matter theory, and by the Galilean route of showing how to connect the situations described in his kinematics, namely the behaviour of isolated bodies in a void, to experimentally accessible cases of bodies moving through resisting media, was associated, indirectly but crucially, with the contrast between hydrostatic and kinematic models for mechanics, and for dynamics in particular. There were two models for a general mechanics from the 1630s onwards: one based on statics and one based on kinematics. Descartes attempted to build a general cosmology on a statically modelled mechanics, and the system he offered, in which bodies were moved by ﬂuids in which they were immersed, had some signiﬁcant advantages over one based on kinematics, not least in that all physical inﬂuence was restricted to contact action. Nevertheless, in constructing a dynamics, Newton opted instead for the Galilean kinematic model, in which the behaviour of bodies in an otherwise empty space was analysed geometrically. Mechanists had certainly not neglected kinematics—Huygens was one of its greatest exponents—and indeed if the criteria of clarity and distinctness to which Cartesian mechanism adhered were strictly observed, then exchange of motion, a mainstay of kinematics, was constitutive of physical activity at the micro-corpuscularian level. But such exchanges required contact between the surfaces of the corpuscles: bodies separated by empty space could not interact. Here the hydrostatic model showed its mettle, for if the cosmos were a plenum then there would be no empty spaces between bodies. If, somehow, hydrostatics and kinematics could be combined, then contact action could serve as a mechanical basis for any physical behaviour. The problem was that hydrostatics and kinematics pulled in different directions.12 The key notion in hydrostatics was that of equilibrium, and in the context of the problem of what secured the stability of planetary orbits, for example, this meant that an outward force from the central sun, to which the planet was effectively joined by means of the intervening ﬂuid matter, was exactly balanced by rapidly moving matter pressing it inwards towards the centre. The notion of equilibrium suggested that bodies in disequilibrium were in a state where the forces acting on them were unbalanced, causing the bodies to move to, or restore, the state of equilibrium, in which the forces were exactly balanced. When one puts unequal weights on a balanced lever for example, a disequilibrium is created and the original equilibrium is restored by the appropriate motion 11 Actually, the situation is complicated, as we shall see, by the fact that, in the ﬁrst part of Book II, it looks like he is about to model ﬂuids on aggregates of microscopic mass points. But this approach is effectively abandoned once he turns to material ﬂuids, whose behaviour is described phenomenologically, not in micro-reductionist terms. 12 See Gaukroger, Emergence, 403–13.

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of the arms of the lever. On this conception, equilibrium is a natural state, to which all bodies or systems of bodies tend. But once Newton, following up an insight of Hooke’s, started to analyse planetary motion in terms of a rectilinear trajectory combined with an accelerated attractive force towards the sun, there was no longer any sense in which orbital motion was a ‘natural’ motion, and talk of dynamically balanced and unbalanced motions became highly problematic. As Newton soon realized, both in attempting to construct a parallelogram of forces and in elaborating his third Law of Motion, all motions are dynamically ‘balanced’. A body accelerating towards the earth does not behave in this way because of a surfeit of force pushing in the direction of the earth and overwhelming the force acting in the other direction; it behaves in this way simply because this is the resultant of the forces acting on it. So, for example, just as when we resolve the parabolic trajectory of a cannonball into a horizontal uniform rectilinear component and a vertical uniformly accelerated component, it would be nonsense to talk of a balance or lack of balance between these components, so similarly it would be nonsense to talk of a balance or lack of balance between the dynamical correlates of these components. The ‘contestant’ notion of forces, so central to Descartes’ conception for example, in which dynamic interactions are seen in terms of one force overwhelming another, is decisively abandoned by Newton.13 On the Newtonian conception, forces are associated with components of motion. Newton uses Galilean kinematics as the skeleton on which to ﬂesh out a dynamics: kinematics separates out and identiﬁes the components, and the task of dynamics is to associate each of these components with a distinctive force. The Newtonian analysis of planetary motion is an exemplary case, where he is able to show that the curve a planet would follow if its attraction towards the sun were inversely proportional to the square of its distance was an ellipse. Note that this is quite different from Kepler’s demonstration of elliptical orbits. Kepler calculated, on the basis of a mass of records of observations he had inherited from Tycho Brahe, that planetary orbits follow elliptical paths, but as far as the geometry was concerned, Kepler had calculated that these must be deviations from the ‘true’ orbits, which are circular. To enable him to move from geometrical circular orbits to observed elliptical ones, he invoked a complex theory of planetary librations caused by alignment and deﬂection of magnetic threads. In other words, planetary orbits are essentially circular—as he believed was clear from consideration of the geometrical archetypes on which 13 See Alan Gabbey, ‘Force and Inertia in the Seventeenth Century: Descartes and Newton’, in Stephen Gaukroger, ed., Descartes: Philosophy, Mathematics and Physics (New York, 1980), 230– 320. The contestant notion was slow to die out and we can even ﬁnd it in one of the pioneering classics of analytical mechanics: in discussing the force of inertia, Hermann talks of ‘a struggle between the acting and the passive body, and without this kind of struggle no action of the agent can be conceived as acting in the patient body’: Jacob Hermann, Phoronomia, sive de viribus et motibus corporum solidorum et ﬂuidorum libri duo (Amsterdam, 1716), 3.

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the cosmos was constructed—and contingently elliptical, and it is matter theory that explains the contingencies of planetary orbits. Newton, by contrast, does not evoke matter theory at all in his demonstration of elliptical orbits. It is purely a matter of geometry and kinematics: the ellipse is not a deviation from a circle, and an elliptical orbit is not a deviation from a natural circular orbit. Newton’s procedure of developing his dynamics by ﬂeshing out kinematics had two fundamental drawbacks, however, and gravitation lay at the heart of them both. First, it relinquished the hard-earned prize of mechanism, namely the conﬁnement of all causation to contact action. If the sun and the earth weren’t in material contact with one another, how could any causal inﬂuence be transmitted? It would seem that such transmission could not be a question of mechanics, but in that case the mechanical system of the Principia is fundamentally incomplete, and Newton offered no clue as to how this incompleteness might be made good. He was especially reluctant to draw any connections between matter theory and his mechanics, conﬁning himself to a few enigmatic remarks in the General Scholium at the end of the second and third editions of the Principia:14 and it is an indication of the depth of the problem that these short enigmatic remarks attracted far more discussion than the rest of the Principia in the eighteenth century. But without a connection between matter theory and mechanics, mechanists could, and for a long time did, for practical purposes simply consider Newton’s system as a novel and interesting system of mechanics, but not a system of natural philosophy. The second drawback was that ﬂeshing out the Galilean kinematic model was an all-or-nothing affair as far as dynamics was concerned. The idea was to start with the behaviour of an isolated body, and determine how this behaviour was modiﬁed as it was subjected to forces. The kinematics separated out inertial states—rest and uniform rectilinear motion—from other physical behaviour, and the task was then to allocate forces to account for this other physical behaviour. This worked spectacularly well in the case of isolated bodies and contact interactions between bodies. But starting from an isolated body was of no help in understanding gravitation, which appears only once we have more than one body.15 To make matters worse, once the second body is introduced, the behaviour of the ﬁrst body, the reference body as it were, is altered. Because gravitational attraction is mutual attraction, we can no longer talk of the bodies under analysis being at rest, or in an inertial state, because strictly speaking 14 In fact Newton did draft (in two extant versions) a general conclusion to the ﬁrst edition of the Principia which opened up the contentious question of the forces between particles of matter, but thought better of publishing it: Unpublished Scientiﬁc Papers, 320–47. 15 Newton makes it clear at two places in the Principia—in the Scholium to corollary 6 of Law 2 in the ‘Axioms, or Laws of Motion’ (Cohen and Whitman edn., 427–8) and in Book III, prop. 7 (ibid., 811)—that gravitational attraction must be mutual because it is governed by the third law of motion. But the third law states the equality of action and reaction of forces, and since in the case of a one-body universe there can be no reaction, there can be no force.

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‘neither the attracting nor the attracted body can be at rest, but both . . . revolve about a common center of gravity as if by mutual attraction’.16 It begins to look as if the dynamics of non-gravitating bodies is quite different from the dynamics of gravitating bodies, and that the Galilean model, while crucial to the former, is perhaps an obstacle to the latter. THE S TRUCTURE OF NEWTON’S PRINCIPIA Book I of the Principia sets out, in a systematic fashion, a mathematical account of the basic principles of mechanics. The models are Galileo and Huygens, and the starting point is a mechanically simple system, the motion of a minimally characterized body around a mathematical centre of force. The body is minimally characterized in the sense that its material characteristics are effectively reduced out of existence: it is dimensionless, being a mass point, and its mass is simply a unit mass. It is not material, in the sense that it is not something that could be analysed in terms of matter theory, but it is physical. In this respect, it is very much the standard kind of body investigated in mechanics. The body moves in a void, so its motion is unhindered by resistance or any other external medium-dependent factor, and it moves not around a physical object but around a mathematical point. The basic mechanical task is to describe the motion of this body, and, once this is done, to start varying the circumstances— most notably, replacing the mathematical centre of force by a mass point so that the system described is now a two-body system, then introducing a third body which interacts with these, and ﬁnally introducing a medium that offers resistance to the motion of the bodies—in order to build up a model powerful enough to capture the motions of planets around the sun, which will be the aim of Book III.17 The origins of the Principia lie in the progressively revised tract De motu,18 which Newton began in response to a visit from Halley in August 1684, when Halley asked him what shape the orbit of an orbiting body would be if it was attracted to a central body with a force that varied inversely as the square of the 16

Principia, Book 1, sect. 11: Cohen and Whitman edn., 108. Of the many general accounts of Newton’s Principia, I have found three to be especially useful: Cohen, ‘A Guide to Newton’s Principia’; Dana Densmore, Newton’s Principia: The Central Argument (Santa Fe, 1996); and John W. Herivel, The Background to Newton’s Principia: A Study of Newton’s Dynamical Researches in the Years 1664–84 (Oxford, 1965). On the more speciﬁc question of Newtonian dynamics, the following are invaluable: Richard S. Westfall, Force in Newton’s Physics: The Science of Dynamics in the Seventeenth Century (London, 1971); J. Bruce Brackenridge, The Key to Newton’s Dynamics: The Kepler Problem and the Principia (Berkeley, 1995); Franc¸ois De Gandt, Force and Geometry in Newton’s Principia (Princeton, 1995). Indispensable material for understanding the background to the Principia is provided in Richard S. Westfall, Never At Rest: A Biography of Isaac Newton (Cambridge, 1980). 18 The Mathematical Papers of Isaac Newton, vi. 1–455. 17

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distance. Newton knew the answer to the question—an ellipse—and he had two crucial pieces of understanding that lay at the basis of the treatment of the question in De motu. The ﬁrst was mathematical: at the beginning of the 1670s, he had developed a method of ‘ﬂuxions’ which enabled him to deal with continuously changing quantities. This was crucial, for to work out the nature of the orbit meant balancing changing velocities and changing distances, something that went beyond traditional mathematical techniques. The second had to do with the nature of force. Before his correspondence with Hooke of 1679, Newton, like Huygens, had analysed circular motion (and by extension curvilinear motion generally) in terms of the force that a body moving in a circle exerts as it endeavours to recede from the centre. Hooke convinced him that that motion should be analysed instead in terms of a force towards the centre, which holds the orbiting body in a closed orbit.19 Putting Hooke’s insight, that centripetal force had to replace centrifugal force, together with the mathematical techniques that Hooke lacked, Newton was able to take a crucial step, showing how orbits were generated and why they had the features—shape, changes in velocity, stability, etc.—that they did. Reversing Halley’s original question in order to make the problem easier to deal with, he demonstrated that an elliptical orbit around an attracting centre located at one focus of the ellipse entails an inverse square attraction. Note that the elliptical orbit described here matches that described in Kepler’s ﬁrst law, but the way in which it is generated does not. As I have indicated, Kepler had assumed that, in the absence of various forces due to the quasi-magnetic material constitution of bodies, the orbits would be perfectly circular, and he was obliged to provide a long, complicated, and unsatisfactory account of the interaction between solar and planetary magnetic alignments needed to bend these circular orbits into ellipses. The mathematics generates the circular orbits in which the sun pushes the planets, while the subsequent application of matter theory transforms these into elliptical orbits. Newton’s mathematics, by contrast, directly generates elliptical orbits. Having shown the connection between inverse square attraction and Kepler’s ﬁrst law, he is then able to show that Kepler’s second law—that the radius vector drawn from the sun to the planet sweeps out equal areas in equal times—is a consequence of such inverse square attraction. The third law—that the squares of the times taken to describe their orbits by two planets are proportional to the cubes of the major semiaxes of the orbits—follows straightforwardly from the fact that the attraction is central attraction. The various drafts of De motu show a concerted reworking of the foundations of dynamics in an attempt to provide a compelling basis for these results, and it is from these reworkings that the systematic dynamics of the Principia emerges. Newton begins the Principia by introducing a number of deﬁnitions, and the 19

See especially Hooke to Newton, 24 November 1679: Newton, Correspondence, i. 297. See the discussion in Gaukroger, Emergence, 430–40.

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basic laws of motion. The deﬁnitions are of ‘quantity of matter’, ‘quantity of motion’, ‘vis insita’, and ‘centripetal force’ and its measures.20 Quantity of matter is deﬁned as arising from density and volume, and is in effect the product of these two. The technical term ‘mass’ can be substituted, and it is invariant, by contrast with weight which, as Newton was aware from the reports of astronomers who had carried pendulum clocks to distant parts, varies from place to place. Mass has a complex relation to change of motion in bodies in that the force required to change a body’s motion is proportional to its mass, and to its gravitational attraction, which also depends on the body’s mass. While we are dealing with a mass point orbiting a mathematical centre, as in the early sections of Book I, the notion plays no role, but once a second body is introduced it becomes crucial, and the development of the concept of mass was a late innovation which appears only in the very last draft of De motu.21 ‘Quantity of motion’ is the product of mass and velocity, what was subsequently called momentum, and is comparatively straightforward. ‘Vis insita ’, by contrast, is a notion that carried the baggage of a complex history: indeed, the various reformulations of what exactly vis insita was form the backbone of the radical conceptual developments in De motu.22 It started out as the force inherent in a body by which that body maintained itself in rectilinear motion, identical with the force by which the body resisted changes to its state, and indeed offered a source of this latter force, explaining how it arose, for the force by which bodies resist changes of state depends on what state they are in: speciﬁcally, what their mass and velocity are. But such a conception violated the indistinguishability of uniform rectilinear motion and rest, so Newton made vis insita responsible for both states, deﬁning it explicitly as the power by which bodies persevere in these states. Finally, he realizes that this is fundamentally misconceived, and in its place develops a notion of inertia whereby rest and uniform rectilinear motion no longer required the action of a force or power to maintain them, so that resistance to changes of state is now conceived as unconnected with bodies continuing in inertial states. The notion that forces are not required to maintain bodies in inertial states is an absolutely fundamental development, but Newton’s terminology—he uses vis insita and vis inertiae as equivalent terms in the Principia for example—is sometimes a little confusing in the light of the fact that in earlier natural-philosophical practice a vis inertiae is a force that keeps a body in an inertial state, whereas for Newton it is something quite different: it is a force that is exerted to resist changes to an inertial state. Finally, ‘centripetal force’, along with inertia the key conception in the new dynamics, is introduced in a physically neutral way. It is any force by which bodies are drawn towards, or impelled towards, or in any way tend 20

Newton, The Principia, Cohen and Whitman edn., 403–15. The expression ‘corporis vel massae’ ﬁrst appears in the last De motu corporum draft, of 1684 or 1685: Mathematical Papers, vi. 92. 22 See my discussion in Emergence, 447–9, for more detail and references. 21

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towards, a centre, and the examples that he gives are terrestrial gravity, magnetic attraction, and ‘that force, whatever it may be, by which the planets are continually drawn back from rectilinear motions and compelled to revolve in curved lines’. The last description is, as it stands, compatible with an account in which vortical matter presses inwards on the planet, and Newton stresses that his interest, in Book I, is conﬁned to the mathematical description of the force that keeps a body in a precise orbit, and with how a body with a given velocity is deﬂected from a rectilinear path by a given force. Newton’s laws of motion parallel Descartes’ laws of nature, and were clearly meant to replace them. One of Descartes’ main targets in his natural philosophy had been Aristotelianism, and his account of motion as translation is formulated in response to the Aristotelian conception whereby motion (or at least natural motion, that is, internally generated motion) is a particular form of change whereby a body realizes some natural goal: in the case of local motion, the motion comes to an end when this goal is realized. Because of the polemical context within which Descartes’ treatment of motion is formulated, the structure of his account mirrors, so as to refute, competing notions, and the key instrument here is his appropriation of the Aristotelian/scholastic vocabulary of substance, attributes, and modes. Since this metaphysical vocabulary lies at the centre of the Aristotelian account, the most effective way to the core of the Aristotelian account was by engaging this vocabulary. But Descartes’ engagement with it involved a reworking of the terms in fundamental ways, and instead of a teleological account of motion, what he offers is a modal account in which rest is not the outcome of motion, as it is in the Aristotelian treatment, but something on a par with it, in fact its modal contrary.23 It is central to Descartes’ project that we understand motion/rest as a mode of a substance before we can understand the causes of motion, the reverse of the Aristotelian way of proceeding. A mode can be thought of as a way of being of a substance: the essential attribute of matter, what makes it matter in the ﬁrst place, is material extension, and material extension can either be at rest or moving: these are two contrary modal states. However, motion itself also has modal states, for it is always motion in a particular direction (relatively deﬁned in Descartes), and this directedness of motion, which Descartes terms ‘determination’, is a mode of a mode, that is, a second-order mode. His ﬁrst law of nature speciﬁes that ﬁrst-order modes do not change without an external cause: a body remains in the same state of motion or rest in the absence of external causes. His second law speciﬁes that second-order modes do not change without an external cause: the direction of a body’s motion does not change in the absence of an external cause. The need for two separate laws is not dictated by the exigencies of his metaphysical categories, however: they just enable him to formulate a distinction that he needs to capture for 23

See ibid., 289–303.

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reasons internal to his mechanics. Speciﬁcally, Descartes needed to separate considerations of speed of motion and direction of motion because of the way in which he thought of collision. The corpuscles involved in collision were hard in the sense of non-deformable, that is, inelastic, yet conservation of amount of motion in collision was a basic principle of Cartesian mechanics. Motion could not be lost in collision. This, Descartes believed, was evident in the equality of the angle of incidence and the angle of reﬂection in the interaction of a light ray (which we can think of for these purposes as being made up of a stream of light corpuscles) with a reﬂecting surface. If the motion and direction of motion of the ray were part of the same thing, then in order for the discrete change of direction at the point of reﬂection to occur the light corpuscles would have to cease one motion and start another, but the question then arises where the new motion comes from (remembering that we are dealing with inelastic bodies). Descartes concludes that the motion itself cannot be interrupted, only its direction; or, more accurately, one component of its direction. Newton’s ﬁrst law collapses Descartes’ ﬁrst two laws, stating that bodies remain in a state of rest or uniform rectilinear motion unless acted upon by external forces. Huygens, Wren, Wallis, and Newton himself had rejected the Cartesian rules of collision and, concentrating on elastic collisions, had replaced these with new rules in which, although many questions still remained open, as the subsequent history of the vis viva disputes bear out,24 one thing that did emerge clearly was that Descartes’ separation of speed and determination no longer had any rationale. Newton’s ﬁrst law bears a distinct resemblance to the ﬁrst ‘hypothesis’ that Huygens, who was one of the earliest to reject Descartes’ rules of collision, set out in his 1673 Horologium, which stated that in the absence of gravity and air resistance, a body would continue in uniform rectilinear motion,25 indicating the naturalness of the move to a single inclusive law once problems with describing collision had been resolved. Newton’s second law states that ‘a change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.’ In the deﬁnition of impressed force, Deﬁnition 4, he tells us that ‘there are various sources of impressed forces, such as percussion, pressure, or centripetal force.’ The ﬁrst of these causes a discrete instantaneous change in momentum, whereas the second and third produce accelerations. There are two distinct kinds of effects, and these are produced by two distinct kinds of cause.26 24 See Wilson L. Scott, The Conﬂict between Atomism and Conservation Theory, 1644–1860 (London, 1970); and Thomas L. Hankins, ‘Eighteenth-Century Attempts to Resolve the Vis Viva Controversy’, Journal for the History of Ideas 56 (1965), 281–97. 25 As noted by Cohen, ‘A Guide’, 110–11. 26 The importance of this difference is not always grasped at ﬁrst, and an intuitively useful way of picturing the difference is one that impetus theorists had used, namely by contrasting continuous change with the change in daylight hours in autumn, where there is a shortening of days (actually an accelerated shortening of days). In other words, in the discontinuous case one has a series of seemingly independent events which are quite discrete (because they are separated by periods of darkness).

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Newton is inclined here to conﬂate the two, but he has to use one of them as his model, and his explanation of the law makes it clear that his model is discontinuous, and not continuous force. Certainly the former would have been readily accepted by his audience, whereas the latter would have been contentious, so what he discusses is the former. Cohen has argued that, given the controversy surrounding the existence of gravitation as an attractive force acting at a distance, the otherwise surprising choice of impulsion, which does not imply action at a distance, makes sense if Newton wanted to set out a mathematical account that was as physically neutral as possible27 before coming to the question of how this account is best realized in physical terms in Book III.28 But Newton’s treatment is not physically neutral: it is a misleading conﬂation of different cases. It tells us that, in general terms, a discontinuous analysis on the model of hard-body collision covers all impressed forces, whereas not only is this not the case, but proceeding as if it were generates at best lack of clarity and at worst great confusion. Newton has to shift between punctiform and continuous forces at a number of crucial points in the Principia, and the transition is far from perspicacious.29 The third law, which states the equality of action and reaction, is, as I have already indicated, crucial to the break with the statical notions of equilibrium that dominated dynamics throughout much of the seventeenth century.30 Rather than thinking of forces exactly balancing one another in interactions between bodies, the outcome of such a collision should be seen on the model of the resultants of components of motion. This is indeed how Newton proceeds, ﬂeshing out the kinematically identiﬁed components of motion in terms of forces, although the transition from parallelograms of motion to parallelograms of force was problematic because of the shift between punctiform and continuous representations of force. Centripetal force, for example, produces a uniform acceleration, and so is naturally thought of as the product of mass and acceleration, on the model of free fall, but Newton was not always able to treat it as a continuous force, instead thinking in terms of it producing discontinuous increments of motion, on the model of repeated impact. But these are problems with the representation of forces, not with the rejection of the statical modelling of force and its replacement with a kinematic modelling.

27 See e.g. the Scholium to Deﬁnition 8 of the Principia: ‘I use interchangeably and indiscriminately words signifying attraction, impulse, or any sort of propensity toward a center, considering these forces not from a physical but only from a mathematical point of view’ (Cohen and Whitman edn., 408). 28 Cohen, ‘A Guide’, 112–13. 29 See D. T. Whiteside, ‘The Prehistory of the Principia from 1664 to 1686’, Notes and Records of the Royal Society of London 45 (1991), 11–61. This question is one that d’Alembert and Euler will devote a good deal of attention to clarifying. 30 See Gaukroger, Emergence, ch. 11.

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Book I of the Principia opens with an introductory section on the mathematical techniques to be employed, and a fundamental question underlying the success of the Newtonian dynamical system set out in the Principia was that of the mathematical resources that it deployed. I shall postpone consideration of this question until the next chapter, however, because although the mathematical techniques used by Newton were clumsy compared to the streamlined calculus algorithms being developed by Leibniz, and subsequently reﬁned by continental mathematicians led by the Bernoullis, the procedures employed in the Principia were nevertheless sufﬁcient to produce the key results of Book I, which is where the mathematics does the real work, and these results were beyond question. Book I sets out to explore centrally directed forces, beginning with the fruit of these mathematical techniques, Newton’s demonstration of Kepler’s second law: a moving body in one plane that is continually attracted to a centre will sweep out equal areas in equal times. This demonstration, as De Gandt puts it, ‘is, as it were, the emblem of a new conception of force, disembarassed of phantasms and indifferent to physical causes’.31 Newton represents the continuous force of attraction in terms of discrete impulses of force acting at successive instants. In Fig. 2.2, the central point is S, and we imagine a body to move initially from A to B during time t. If the body had received no impulse of force at B it would have moved, in another interval of time t, along the continuation of AB to c. It does receive an impulse of force at B however, giving it a component of motion towards S. If we draw cC parallel to BS, the point C at which it cuts BC is the position of the body at the end of the second moment. Triangles SAB and SBc have equal bases—AB and Bc—and an equal side—SB—and so are equal in area. Triangles SBc and SBC share the same base—SB—and stand between two parallels, so are also equal in area. Therefore the triangle SBC described in the second moment is equal in area to the triangle SAB described in the ﬁrst moment. If we now let the moments of time be progressively diminished so that the force tends to a continuous action, the line ABCDEF becomes a curve, and a body following this curve will sweep out equal areas in equal times. Sections 2 and 3 deal generally with the cases of motion in a circle, and motion following conic sections. In particular, Newton demonstrates that motion in an elliptical orbit satisﬁes the inverse square attraction law, exploring various other cases, including that of several non-interacting bodies moving around a common centre (prop. 14), and offering a demonstration that a body with an initial rectilinear motion subjected to an inverse square force will produce an orbit along a conic section (prop. 13 coroll. 1). Sections 4 and 5—a mathematical interpolation which Newton considered at one point removing as it breaks the ﬂow of the argument—describe various questions in the geometry of conic sections, while Section 6 moves to naturally occurring orbits, namely parabolas 31

De Gandt, Force and Geometry, 272.

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e

f E

d

F D Z

c

C

B

V

S

A

Fig 2.2

and ellipses. The treatment in Section 7 of bodies in rectilinear motion upward and downward, under various forces, ends with procedures for ﬁnding areas under curves—integration—and it is these techniques that are used in the most mathematically advanced part of the Principia, prop. 41 of Section 8, where the action of a centripetal force which is some unspeciﬁed function of distance is investigated. The degree of complexity is increased in Section 9 as Newton considers movable orbits (important for his account of lunar motion), and then again, in Section 10, as he proceeds beyond the kinds of orbits discussed to this point, in which the orbit is described in a plane which passes through the centre of the forces, to those cases where it does not pass through the centre, which he examines in terms of motion along non-resistant surfaces. This effectively completes his treatment of motion of a body around a mathematical centre, and in Section 11, the mathematical centre of motion is replaced by a body, so that a transition is now made to the signiﬁcantly more difﬁcult case of a two-body system, then three- and four-body systems, in which various perturbations distort the elliptical shape of orbits. In Sections 12 and 13, the dimensions of these bodies are ﬂeshed out in terms of the behaviour of spherical and nonspherical bodies under the action of a centripetal force. Finally, in Section 14,

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Newton turns his attention to the behaviour of micro-corpuscles, offering some demonstrations in support of a corpuscular theory of light.32 Book I deals with motion in empty space, and in Book II, which offers a less conﬁdent and less secure treatment compared to the other two Books, and underwent continuous revision, especially for the second edition, Newton turns to the properties of the medium generally—hydrostatics, resistance of the medium to moving bodies, propagation of perturbations, motions of vortices— but the kind of medium at issue in the ﬁrst four sections of Book II is rather different from that in subsequent sections. The ﬁrst four sections are effectively a continuation of Book I: they are in fact based on propositions that came at the end of Book I in the original draft.33 In one respect they follow on naturally from the ﬁnal section of Book I, on micro-corpuscles, for Newton conceives of the ‘rare medium’ which is the subject of the early sections of Book II as made up of aggregates of interacting mass points/micro-corpuscles, depending on whether he conceives them in the mechanical or the material mode. In principle, a ‘rare medium’ can be subjected to the same kind of analysis that has been applied to mass points in Book I, although in fact such a medium is far more difﬁcult to handle, and the mathematical techniques needed for analysis of the behaviour of the various kinds of media, especially the elastic media central to Newton’s treatment, were really only built up in the middle of the eighteenth century.34 Despite their continuity with Book I, however, the topics chosen in the early sections of Book II have a decidedly practical basis, dictated by the kinds of resistance that bodies orbiting in or falling through a ‘rare medium’ are likely to encounter. The ﬁrst three sections deal respectively with the case in which resistance is proportional to velocity, that in which it is proportional to the square of velocity, and that in which it is a combination of both, and the fourth examines spiral motion in a ‘rare medium’. When Newton turns to ﬂuids in Section 5, the tenor of the discussion changes. Whereas the discussion of the ‘rare medium’—characterized as ‘consisting of particles that are equal and arranged freely at equal distances from one another’35 and something which is neither elastic nor ﬂuid—had avoided talk of forces, and 32 Earlier, in reporting his prism experiments, Newton had refused to speculate on whether light was corpuscular or not, and implicity criticized the Cartesian theory whereby what was effectively an a priori micro-corpuscular model drove the explanation of the behaviour of light. In coming here to defend its corpuscularity, his approach is quite different from that of Descartes. Instead of mechanizing matter theory, as Descartes had done, he is attempting to ﬂesh out mechanics in material terms, to move from mass points to micro-corpuscles, a move that seems peculiar to his optics, for, as we shall see, his usual procedure is to treat questions in matter theory quite separately from those in mechanics. 33 Cohen, ‘A Guide’, 164. 34 See Clifford Truesdell, ‘Rational Fluid Mechanics, 1687–1765’, Leonhardi Euleri opera omnia series 2, vol. xii (Zurich, 1954); idem, ‘Rational Fluid Mechanics, 1765–1788’, Leonhardi Euleri opera omnia series 2, vol. xiii (Lausanne, 1955). 35 Principia, Book II, Section 7, prop. 33: Cohen and Whitman edn., 728.

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an attempt was made to engage its constitution in wholly mathematical terms, the deﬁnition given of a ﬂuid does not mention anything about its supposed constitution from mass points or corpuscles.36 On the contrary, it is decidedly phenomenological: ‘A ﬂuid is any body whose parts yield to any force applied to it and yielding are moved easily with respect to one another.’37 This character is matched by the discussion, which relies more on experimental results and less on mathematics because of the inherent complexity of the phenomena, a complexity that precludes any remotely comprehensive mathematical modelling of ﬂuids.38 Water is the paradigmatic ﬂuid, but the ‘rare medium’ in the early sections could only be air, yet it is also treated as a ﬂuid in the later ones: in Sections 6 and 7, for example, which examine the effects of ﬂuids on motion of a pendulum, air and water are treated equally as ﬂuids. Newton does raise the question of the constitution of ﬂuids, as in Proposition 23 for example: If the density of a ﬂuid composed of particles that are repelled from one another is as the compression, the [forces of repulsion] of the particles are inversely proportional to the distances between their centres. And conversely, particles that are repelled from one another by forces that are inversely proportional to the distances between their centres constitute an elastic ﬂuid whose density is proportional to the compression.39

But he then adds a crucial qualiﬁcation, telling us that ‘whether elastic ﬂuids consist of particles that repel one another is, however, a question for physics. We have mathematically demonstrated a property of ﬂuids consisting of particles of this sort so as to provide natural philosophers with the means with which to treat that question.’40 Newton himself shifts between a modelling that answers to his mathematical treatment and one that answers to his physical intuitions. Consider the case of air: he believes that air comprises particles repelled by forces inversely proportional to their distances, but in Proposition 23 for example he attempts to show that the effects of these forces are negligible in the case of a body of high

36 Compare Hooke, for example, in the Micrographia, who offers the routine mechanist explanation for the behaviour of ﬂuids in accounting for their properties: ‘First, what is the cause of ﬂuidness: And this, I conceive, to be nothing else but a certain pulse or shake of heat; for Heat being nothing else but a very brisk and vehement agitation of the parts of a body . . . the parts of the body are thereby made so loose from one another, that they easily move any way, and become ﬂuid.’ Robert Hooke, Micrographia: or some Physiological Descriptions of Minute Bodies made by Magnifying Glasses (London, 1665), 12. 37 Principia, Book II, Section 5, Deﬁnition: Cohen and Whitman edn., 687. 38 Fluid mechanics has remained, and is likely to remain, an intrinsically experimental discipline. This is obscured in Truesdell’s pathbreaking treatment of ﬂuid mechanics, which misleadingly treats it as a form of applied mathematics. The signiﬁcance of experiment right from the very start is brought out in Julia´n Simo´n Calero, The Genesis of Fluid Mechanics, 1640–1780 (Dordrecht, 2008). See also George E. Smith, ‘The Newtonian Style in Book II of the Principia’, in Jed Z. Buchwald and I. Bernard Cohen, eds., Isaac Newton’s Natural Philosophy (Cambridge, Mass., 2001), 249–313. 39 Principia, Book II, Section 5, prop. 23: Cohen and Whitman edn., 697. 40 Scholium to prop. 23; Cohen and Whitman edn., 699.

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velocity moving through the air, allowing him to ignore the dynamical relations between the particles making up the medium: And since similar, equal, and equally swift bodies, in mediums which have the same density and whose particles do not recede from one another, impinge upon an equal quantity of matter in equal times (whether the particles are more and smaller or fewer and larger) and impress upon it an equal quantity of motion and in turn (by the third law of motion) undergo an equal reaction from it (that is, are equally resisted), it is manifest also that in elastic ﬂuids of the same density, when the bodies move very swiftly, the resistances they encounter are very nearly equal, whether those ﬂuids consist of coarser particles or are made of the most subtle particles of all. The resistance to projectiles moving very quickly is not much diminished as a result of the subtlety of the medium.41

Notice how reference to ‘air’ here has been replaced by talk of the body moving through the ‘medium’.42 In Proposition 24 in the ﬁrst edition of the Principia, Newton supplemented the assimilation of air to a rare medium with an assimilation of a liquid to air, by imagining the air becoming so highly compressed that the constituent particles are forced closely together, sliding against one another, and where, ultimately, the elastic rebounds in collision are replaced by pressures which neighbouring particles in contact exert on one another. In this way, the behaviour of liquids could ultimately be assimilated to that of rare media. But, presumably realizing that this was little more than wishful thinking, he removed the argument from the second edition. Moreover, when the discussion turns to the propagation of motion in ﬂuids in Section 8, talk of particles drops out in favour of an ‘elastic medium’, and he argues that we should ‘think of the pulses as propagated by successive condensations and rarefactions of the medium’.43 Section 9 of Book II, on ‘the circular motion of ﬂuids’, has been treated by commentators from Clairaut onwards as providing the rationale for Book II, for it is explicitly directed against Cartesian vortex theory. Descartes had occasionally treated rotational motion as a form of perpetual motion, for example in his analysis of a stone in a sling in chapter 13 of Le Monde, and in his statement that the rotation of light corpuscles requires no input of force, suggesting that, dynamically speaking, this rotation is the same as the uniform rectilinear motion of the light corpuscle: a view that is the direct result of attempting to mix a hydrostatic understanding of equilibrium with kinematic understandings of inertial motion.44 Newton is not the victim of any such confusion. Vortices are not forms of inertial motion, so, if they do indeed play the role that Descartes and his followers imagined, then there must be some dynamic rationale for vortical motion. Newton reduces the dynamics of the vortex to basic mechanics 41

Prop. 33, coroll. 5; Cohen and Whitman edn., 728. See the discussion in Simo´n Calero, Genesis of Fluid Mechanics, 76–81, to which I am indebted here. 43 Section 5, prop. 42, case 2; Cohen and Whitman edn., 764. 44 See Gaukroger, Emergence, 412–13. 42

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a

b c K

d I

e H

G F S

A B C D E

Q

L M N O P

Fig 2.3

by imagining an inﬁnitely long cylinder rotating in a ﬂuid, with a cross-section as in Fig. 2.3. The rotation of the cylinder drags the segment, AFL, of homogeneous ﬂuid contiguous with it around its circumference, and this segment drags the next contiguous segment, BGM, around, and so on. He sets out to prove the hypothesis that ‘the resistance that arises from the lack of lubricity or slipperiness of the parts of the ﬂuid is, other things being equal, proportional to the velocity with which the parts of the ﬂuid are separated from one another’.45 What Newton is concerned with here is the idea of resistance to ﬂow, what we would think of as viscosity, and the argument is that, as motion is transmitted outwards from the centre from one concentric layer to the next, there must be a resistance, caused by viscosity, which is proportional to the relative velocity of the two contiguous layers. But if this were the case, then, he shows, Kepler’s third law would be violated. Proponents of vortex theory did not accept the proportionality between relative velocity and resistance,46 and the resistance in question is of necessity poorly deﬁned, for viscosity is an extremely complex phenomenon, lying well beyond the resources of the mathematics of the time. Nevertheless, what was needed from a satisfactory response to this kind of argument was the establishment of some other quantitative relation, and the defenders of vortex theory were unable to offer anything in this respect. Newton also identiﬁes a

45

Section 9, hypothesis, Cohen and Whitman edn., 779. In his prize-winning 1730 Acade´mie essay, ‘Essai d’une nouvelle physique ce´leste’, Johann Bernoulli set out to show that the layers of vortices do in fact follow Kepler’s area law exactly. See the discussion in Aiton, The Vortex Theory of the Planetary Motions, 228–38. 46

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second problem. Vortices cannot be self-sustaining: the motion issuing from the centre is dissipated as it transferred outwards through the contiguous layers, and if the vortex is to be sustained, it requires a constant input of energy at the centre. The aim of Section 9 was to highlight just what kind of investigation would be needed to show that vortices are in fact the basis of planetary orbits, and then to demonstrate that vortex theory in fact has no dynamic rationale. Although Newton was more successful in his treatment of the ﬁrst question than in that of the second,47 his project not only set new standards for rigour, but very effectively challenged vortex theory. Indeed, the attempt to deprive the vortex theory of any dynamical rationale at the end of Book II prepares the way for his advocacy of his alternative gravitation-based account of planetary orbits in Book III. Although Book III—if supplemented by the Deﬁnitions, the Laws of Motion, and ﬁrst three sections of Book I—can be read as a stand-alone text, as I have indicated, the momentum provided by the demolition of the vortex theory equips the reader to do something that Newton considers crucial for a proper understanding of the argument of Book III, namely to ‘lay aside the preconceptions to which they have become accustomed over many years’.48 In the ﬁrst edition of the Principia, Book III opened with a set of nine hypotheses. This proved to be problematic, for in the anonymous review of the ﬁrst edition of the Principia that appeared in the Journal des Sc¸avants on 2 August 1668, undoubtedly written by a Cartesian, possibly Re´gis, the author complains that the ‘system of the world’ that Newton offers consists merely of hypotheses which are largely arbitrary and which consequently can act as a foundation only for a treatise on pure mechanics. He bases his explanation of the inequality of the tides on the principle that all the planets gravitate reciprocally towards each other . . . But this is an arbitrary assumption, since it has not been proved, and the demonstration that is based on it can therefore only be one in mechanics. In order to make his work as perfect as possible, M. Newton has only to provide us with a Physics as exact as his Mechanics, which he can do by substituting true motions for the assumed ones.49

Such a criticism, were it legitimate, would completely undermine the claim of the Newtonian system to replace the Cartesian one, for the objection was that the former did not deal with real physical processes. To avoid prior judgement as to the nature of his project on semantic grounds, Newton’s response is to abandon the term ‘hypothesis’ in the second edition. The ﬁrst two of the ‘hypotheses’ of

47 See e.g. Smith, ‘The Newtonian Style in Book II of the Principia’; and P. F. Neme´nyi, ‘The Main Concepts and Ideas of Fluid Dynamics in Their Historical Development’, Archive for History of Exact Sciences 2 (1962), 52–86. 48 Principia, introduction to Book III: Cohen and Whitman edn., 793. 49 Passage quoted in Paul Mouy, Le de´veloppement de la physique carte´sienne 1646–1712, 256. Re´gis is Mouy’s suggestion for authorship of the review. See also Alexandre Koyre´, Newtonian Studies (London, 1965), 115.

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the ﬁrst edition became ‘Rules of Philosophy’, and a third was added, the remaining becoming ‘phenomena’, to which, again, a new item was added. In the third edition, a fourth ‘Rule’ was introduced, as was a new ‘phenomenon’ (number 2 in the revised numbering). This raises the question of the legitimacy of the revised nomenclature. The ‘phenomena’ which he separated out are not hypothetical, but comprise various astronomical observations, generalizations from these observations, and various observationally based laws, such as Kepler’s laws.50 The ﬁrst two ‘rules’, those carried over from the ﬁrst edition, are by contrast general pieces of guidance not restricted to natural philosophy: indeed, they would seem to owe a good deal to Robert Sanderson’s 1618 textbook on logic and rhetoric, Logicae artis compendium, and Newton developed them originally in a treatise on interpretation of the Apocalypse dating from around 1672.51 They tell us that we should only admit causes of phenomena that are ‘true and sufﬁcient’, and that we should only assign the same causes to natural effects of the same kind. The third Rule, introduced in the second edition, by contrast makes a strong, if by this stage uncontentious, empirical claim, asserting the legitimacy of extrapolating from certain observable and invariant qualities of bodies on earth to the sun, the other planets, planetary satellites, comets, and stars. Perhaps by way of a philosophical justiﬁcation of such an extrapolation, in the third edition Newton adds a fourth Rule, which states that inductive inferences cannot be tested against imagined or unveriﬁed hypotheses, and should be accepted until new evidence renders them more exact or provides counter-evidence. Whatever its connection to Rule 3, however, Rule 4 more generally recharacterizes natural-philosophical theories and claims in a way that directly challenges the idea that something lacking deductive certainty is merely hypothetical. The claim is that well-supported inductive inferences are not merely hypothetical: rather, they should be ‘considered either exactly or very nearly true’.52 Such a constraint is crucial for Book III in a way that it wasn’t for Book I, for once we leave the realm of pure (‘rational’) mechanics we also leave the realm of purely deductive demonstrations. The Preface to the Principia spells out the tasks of Book III and its relation to the other two Books in these terms: For the basic problem of philosophy seems to be to discover the forces of nature from the phenomena of motions and then to demonstrate the other phenomena from these forces. It is to these ends that the general propositions in Books I and II are directed, while in Book III our explanation of the system of the world illustrates these propositions. For in Book III, by means of propositions demonstrated mathematically in 50

See the very helpful account of the ‘Phenomena’ in Densmore, Newton’s Principia, 243–83. See Maurizio Mamiani, ‘To Twist the Meaning: Newton’s Regulae Philosophandi Revisited’, in Jed Z. Buchwald and I. Bernard Cohen, eds., Isaac Newton’s Natural Philosophy (Cambridge, Mass., 2001), 3–14. 52 Book III, ‘Rules’: Cohen and Whitman edn., 796. 51

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Books I and II, we derive from celestial phenomena the gravitational forces by which bodies tend toward the sun and toward individual planets. Then the motions of the planets, the comets, the moon, and the sea are deduced from these forces by propositions that are also mathematical.53

The ﬁrst eight propositions of Book III play the key role in this strategy, in that it is here that Newton establishes the fundamental principle that all bodies attract all other bodies in proportion to their quantities of matter and inversely as the square of the distance to their centres. Proposition 1 starts with the satellites of Jupiter. Granting (as Phenomenon 1 indicates) that equal areas are swept out in equal times during the orbits of the satellites, then were Jupiter stationary we could deduce from this that the satellites were impelled towards the centre of the planet. But Jupiter is orbiting the sun, which means that we have to subtract out the accelerative force that is moving the Jupiter-satellite system, to yield the force that impels the satellite towards the centre of Jupiter. This force results in equable circular concentric orbits,54 which have already been described in Proposition 4 of Book I, Corollary 6, which tells us that if their periodic times are as the 3/2 powers of their radii (which Phenomenon 1 establishes they are), then the centripetal forces will be inversely proportional to the squares of the radii. In the second edition, Newton extrapolates from this to the satellites of Saturn discovered by Huygens and Cassini. Proposition 2 uses analogous reasoning to establish that the planets are likewise impelled towards the sun, the centripetal force being inversely proportional to the squares of the radii. He notes in this context that, by Proposition 45 corollary 1 of Book I, if there were the slightest deviation from the inverse square law—if, for example, there were other forces acting on the planet—then this would result in an observable shift in orientation of the apsides. Proposition 3 states the inverse square law for the moon’s orbit around the earth. But although in this sense it is an analogue of the ﬁrst two Propositions, the same form of demonstration cannot be followed. In the cases of Jupiter’s (and Saturn’s) satellites, and that of the motion of the planets around the sun, we can compare the periodic times of the different bodies revolving around a central body, showing that the periodic times of the satellites in their orbit around Jupiter, and the planets in their orbit around the sun, are as the 3/2 powers of their radii. But in the case of the moon, no such comparison is possible, for we have only one orbiting body. Because the orbit is so close to a circle, there are other resources available from Book I for dealing with such a case (notably prop. 53

Author’s preface: ibid., 382. As Cohen (‘Guide’, 197) notes, Newton’s assumption of circular orbits is justiﬁed as an approximation because the orbits of the known planets, with the exception of Mercury, and known satellites of Jupiter and Saturn, were very close to circular. The crucial thing is not the shape but the fact that Jupiter is not at the centre of the orbit, which means that the area law determines the changes in velocity from aphelion to parhelion. 54

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45 coroll. 1), but these work on the assumption that the aphelia are at rest, whereas Newton notes a movement in the apsides of the moon of 3 30 in each revolution. Hinting that it is the inﬂuence of the sun that causes this shift in orientation of the apsides, he nevertheless leaves open the question of the cause for the moment, showing how we can subtract this force to isolate the centripetal force of the earth–moon relationship. Proposition 4 builds on these results, introducing gravitation as a physical force (by contrast with a mathematically describable phenomenon with no commitment as to its physical standing) for the ﬁrst time, and stating that it is gravitation that holds the moon in orbit around the earth. We have here an alternative dynamics to the Cartesian vortex theory whereby rapidly moving ﬂuids exert inward pressure on a centrifugally projected body. Even more important is the association of centripetal force with gravity, for up to this point in the Principia ‘gravity’ has simply meant terrestrial heaviness: the weight that we experience in ordinary bodies. What Newton is doing is identifying the weight of bodies on earth with the centripetal force that holds the moon in orbit around the earth, with a view to correlating the moon’s orbit with the measured acceleration of gravity at the surface of the earth. There are a number of steps in the demonstration.55 First, the moon’s orbit is the resultant of a tangential uniform rectilinear motion and an accelerated motion toward the earth, so we imagine the former removed and determine how far the moon would travel from its orbit to the earth in one minute. The precise ﬁgure he arrives at varies a little from the ﬁrst edition to later editions, where it is given as 151/12 Paris feet: it is initially based on Huygens’ calculation of gravitational attraction (hence the units chosen), but adjusted in the light of the disturbing force of the sun, the location of the common centre of gravity of the earth and the moon, and the centrifugal effect of the rotation of the earth.56 Second, we determine the accelerative force acting on the moon at the earth’s surface, assuming an inverse square force law, and calculate how far the moon would fall in one second at the surface. In other words, rounding out distances, we have looked at how the moon would accelerate if dropped from a distance of 60 earth radii: bearing in mind the distance it would traverse in one minute, we now look at what its acceleration would be closer to the surface, for example at a distance of one radius. The calculations show that, for the same length of fall, we can divide through by time and distance, so that instead of one minute and 60 radii we get one second and one radius: the moon would fall 151/12 Paris feet, on the assumption that the same centripetal force acts in both cases. Third, Newton now calculates how far a rock at a distance of one moon radius from the earth would travel in one second. 55 Like many others who have struggled to follow and teach Books I and III of the Principia, the appearance of Densmore, Newton’s Principia, came as a ray of light. I am especially indebted here to the careful and systematic account of Proposition 4, with suitably expanded proofs, 294–312. 56 See Westfall, Never at Rest, 732–4.

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It is the same. By Rule 2, which tells us we should attribute the same causes to natural effects of the same kind, we must conclude that both the fall of the rock and the centripetal component of the moon’s orbit have the same cause: gravitation. Proposition 5 then moves from the lunar case to those of the earlier Propositions, the other planetary satellites and the planets’ orbits around the sun: in these cases too, it is gravity that conﬁnes their motions to curvilinear orbits. Consequently, in the Scholium that follows Proposition 5, Newton says he will thereafter use the term ‘gravity’ where he had previously talked of ‘centripetal force’. Propositions 6 and 7 elaborate on gravity. Proposition 6 states that all bodies gravitate towards each of the planets, and establishes a relation between this gravitational attraction and the weight of the body. This is that the weights of bodies that are at an equal distance from the centre of any planet are proportional to the quantity of matter in the body. In other words, the weight of a body is proportional to its mass. This is a crucial result, for it enables Newton to connect the gravitational attraction exercised by a body (its ‘gravitational mass’) with the body’s resistance to acceleration (its ‘inertial mass’). The demonstration is empirical, and Newton, able to improve on the accuracy of experiments on falling bodies, reports on a number of experiments with pendulums having hollow bobs of the same size but ﬁlled with material of different speciﬁc gravities: any difference in the ratio of inertial to gravitational mass would be manifested as a difference in the period of vibration. To understand the signiﬁcance of this, we need only consider that Galileo had shown that all bodies fall to the earth with a uniformly accelerated motion in a void. In particular, he showed that two bodies of the same material but having different absolute weights, two lead balls for example, suspended from the same height and released simultaneously, reach the ground simultaneously. But if one of the balls has a greater mass than the other, and if gravitational attraction is directly proportional to mass then, other things being equal, the heavier body is subject to a greater gravitational attraction, which means its rate of acceleration must be greater. The reason this doesn’t happen, on Newton’s account, is that the increased gravitational attraction to which more massive bodies are subject is exactly counterbalanced by their greater inertia, manifested as resistance to acceleration. The Corollaries to Proposition 6 use its results to challenge competing accounts of weight and gravity. The ﬁrst two deal with the Cartesian understanding of weight, in which weight is accounted for functionally in terms of the vortical motions of surrounding bodies or ﬂuid in which it partakes, which depend on a number of factors, such as its shape and texture. Newton argues that his results show that weight is independent of such factors. The next two argue that the Cartesian account of the void precludes differences in speciﬁc weight, which in turn precludes them having different forces of inertia. Finally, Corollary 5 distinguishes gravitation from magnetism. The latter can increase and decrease within a body, and it is not a function of its quantity of matter;

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moreover, Newton does not believe magnetic attraction follows an inverse square law. One of the most signiﬁcant differences, however, is that magnetism does not act universally, and this leads to Proposition 7, which states that gravitation is universal, and that it is proportional to the amount of matter in the body. Moreover, in the Scholium following the statement of the laws of motion at the beginning of the Principia Newton attempts to show that the third law, which states the equality of action and reaction, applies not just to mechanical interactions (collisions) but to cases of attraction as well, dealing with magnetism and the mutual attraction between the parts of the earth, which will fall under gravity,57 and here in Book III he reasserts that gravitation must be a mutual attraction, by the third law.58 Proposition 8 offers one of the toughest challenges to Newton. It states that: ‘If two globes gravitate toward each other, and their matter is homogeneous on all sides in regions that are equally distant from their centres, then the weight of either globe toward the other will be inversely as the square of the distance between the centres.’59 On 20 June 1686, Newton wrote to Halley: ‘I never extended ye duplicate [inverse square] proportion lower then to ye superﬁcies of ye earth & before a certain demonstration I found ye last year have suspected it did not reach accurately enough so low down.’60 The problem Newton had faced was in its bare essentials this. Imagine a small body dropped from some point close above the surface of the earth. There is an inverse square gravitational attraction between the body (for these purposes we can consider it to comprise a single particle) and every particle making up the earth, some of which are very close to the body and therefore exercising a greater attractive force, some very far away and therefore acting with less force. Even given Newton’s speciﬁcation that we are dealing with homogeneous spheres, on the face of it, it is not evident that the sum of all the different forces exercised by the particles would act in such a way that the body would be attracted to the centre of the earth. The ‘certain demonstration’ to which Newton refers is one which shows that, no matter how close we get to the surface, the inverse square law will hold between centres of homogeneous bodies. It is a purely geometrical demonstration and is provided in Book I, Section 12, on ‘the attractive forces of spherical bodies’, Propositions 71–5. Having shown this, Newton proceeds in the Scholia to calculate the weights of equal bodies at the same distance from the centre of the planets, and at the surfaces of those planets, and then, from the fact that there are different accelerative forces on equal bodies at the same distance from their centres, and since this difference must be due to the planet, he is able to show that the ratio of accelerative forces is as the ratio of quantities of matter; this in turn enables 57 58 59 60

Principia, Cohen and Whitman edn., 427–8. Ibid., 811. Ibid. See the discussion in Densmore, Newton’s Principia, 356–95; and Cohen, ‘Guide’, 218–31. Newton, Correspondence, ii. 435.

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him to calculate the weights of Jupiter, Saturn, and the earth relative to that of the sun. Following a couple of Propositions noting that gravity decreases as one moves inwards from the surface of a planet, and that the motions of planets can continue ‘for a very long time’, Newton turns to the question of the mechanics of motion in the solar system, noting that the common centre of gravity of the system is at rest (prop. 11), and that the sun does not recede far from this centre (prop. 12). This brings him to what is in effect the culmination of the Principia, Proposition 13, which derives Kepler’s ﬁrst two laws from the principle of universal gravitation, dependent upon the demonstrations in Book I of course, but now offering a physical cause for the phenomena described in Kepler’s laws. The remainder of Book III is then able to explore the physical consequences of this for various aspects of planetary motions, the tides, comets, and, in some detail, the motion of the moon. The ﬁrst edition of the Principia ended somewhat in mid-air, with a discussion of comets. Newton had planned an account of the attractive forces between particles for the conclusion of the second edition,61 but abandoned this, concluding instead with a short ‘General Scholium’ whose importance is out of all proportion to its brevity. It raises three separate questions, all of them brieﬂy. First, it reiterates the consequences of the Newtonian account for vortex theory, noting that this theory is incompatible with the results that have been demonstrated, and deducing the existence of tracts of interplanetary empty space from the long-term constancy of planetary motions, and those of comets. Second, he deduces the existence of divine design from the functional complexity and elegance of the universe, concluding that ‘to treat of God from phenomena is certainly a part of experimental philosophy’ (‘experimental philosophy’ changed to ‘natural philosophy’ in the third edition). These points form a suitable general conclusion to the Principia, but then Newton adds two ﬁnal paragraphs. He begins: Thus far I have explained the phenomenon of the heavens and of our sea by the force of gravity, but I have not yet assigned a cause to gravity. Indeed, this force arises from some cause that penetrates as far as the centres of the sun and planets without any diminution of its power to act, and that acts not in proportion to the quantity of the surfaces of the particles on which it acts (as mechanical causes are wont to do) but in proportion to the quantity of solid matter, and whose action is extended everywhere to immense distances, always decreasing as the squares of the distances. . . . I have not yet been able to deduce from phenomena the reason for these properties of gravity, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this experimental philosophy, propositions 61

See the discussion in Cohen, ‘Guide’, 274–92; Cohen provides an English translation of the original draft conclusion, 287–92.

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are deduced from the phenomena and are made general by induction. The impenetrability, mobility, and impetus of bodies, and the laws of motion and the law of gravity have been found by this method. And it is enough that gravity really exists and acts according to the laws that we have set forth and is sufﬁcient to explain all the motions of the heavenly bodies and of our sea.62

Instead of concluding at this point, however, Newton adds a ﬁnal short paragraph which, it would be fair to say, does suggest a hypothesis about the nature of gravity, announcing ‘a very subtle spirit pervading bodies and lying hidden in them’, but declining to go into any detail. Yet here we have the makings of a substantial addition to Book III, or even a potential Book IV of the Principia, and this last short paragraph provoked intense speculation throughout the eighteenth century. The question was a fundamental one, and it is to this that we now turn. GRAVITATION: MATTER THEORY VERSUS MECHANICS The problem of gravitation forced open the question of the competing demands of matter theory and mechanics. Cartesian mechanist cosmology had worked with an account that integrated matter theory—the account of the behaviour of physical phenomena in terms of their material constituents—and mechanics— the account of the behaviour of physical phenomena in terms of their motions and the causes of these motions. The internal balance varied, and mechanics increasingly took on greater signiﬁcance, notably in Huygens, but the importance of integration remained paramount, for, in the mechanist tradition, mechanics without matter theory was simply not natural philosophy: it remained in the realm of practical mathematics. As I have indicated, on the Galilean kinematic model, the way in which one establishes that particular phenomena are genuinely physical bypasses matter theory, so that the physical and the material are no longer equated. Nevertheless, once one is in the realm of the dynamics of planetary motions, the materiality of the bodies involved would seem critically caught up in their dynamic characteristics. One might assume that mechanism, with its integration of matter theory and mechanics, should have been well placed to deal with this question. But Descartes had written forces out of his physical theory when he reformulated it in terms of ‘clear and distinct ideas’ in his Principia, and Huygens went to great lengths to redraft dynamic propositions in kinematic terms for the same reason.63 Consequently, the mechanist integration of matter theory and mechanics was of little use in dealing 62

Principia, Cohen and Whitman edn., 943. On the redrafting, see Westfall, Force in Newton’s Physics, 159–67; on the reasons, see Gaukroger, Emergence, 423–30. Cf. Fabien Chareix, La philosophie naturelle de Christiaan Huygens (Paris, 2006). 63

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with forces because mechanism was committed to avoiding talk of forces wherever possible, and the situation was exacerbated once non-contact forces entered the picture. These violated the basic assumptions and indeed much of the original motivation for mechanism, with the result that such forces simply could not be countenanced. It was Leibniz who made a concerted effort to reshape the mechanist project of integrating matter theory and mechanics in such a way as to ground dynamics, but, as we shall see in the next chapter, his reshaping was very radical, not only abandoning many of the basic tenets of mechanism, but reviving an Aristotelian metaphysics of substance that was anathema to mechanists, in order to provide a dynamics which could viably do without action at a distance. It was, then, not at all clear that an account that integrated matter theory and mechanics was automatically going to provide the answer. Even the most basic and generally accepted tenets of matter theory could prove problematic. In the ﬁrst edition of the Principia, for example, Newton had included, as Hypothesis III, the statement that: ‘Every body can be transformed into a body of any other kind and successively take on all the intermediate degrees of qualities.’ This is the doctrine of the unity and transmutability of matter, which was widely accepted and seemingly uncontentious. However, Newton subsequently realized that it was incompatible with his mechanics, for if all qualities were transmutable this included such qualities as solidity, on which mechanical interactions depended, and so the hypothesis was replaced in the second edition with the more qualiﬁed claim that ‘the qualities of bodies, which admit neither intension nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal properties of all bodies whatsoever.’64 While Newton, like every other natural philosopher, was concerned to reconcile mechanics and matter theory, he never seems to have been committed to mechanism, at least in his mature work, so the kind of integration required by mechanism, in its seventeenth-century versions, was not something to which he felt committed either. From the mid-1660s onwards, Newton was working on questions in mechanics and questions in matter theory independently of one another. In his earliest natural-philosophical writings, the Questiones quaedem philosophicae of 1664–5, he offers a mechanical account of weight/gravity.65 The account presented is an efﬂux theory, whereby gravity or weight is caused by a 64 See the discussion in James E. McGuire, ‘Transmutation and Immutability: Newton’s Doctrine of Physical Qualities’, Ambix 14 (1967), 69–95; Betty Jo Teeter Dobbs, The Foundations of Newton’s Alchemy: or ‘The Hunting of the Greene Lyon’ (Cambridge, 1975), 199–204, 231–2. The doctrine, suitably qualiﬁed, remained a staple of Newtonian chemistry, reappearing in paper on the nature of acids from around 1692, for example, as well as in the Opticks. 65 Certain Philosophical Questions: Newton’s Trinity Notebook, introductory essay, ed. and trans. James E. McGuire and Martin Tamny (Cambridge, 1983). See the editors’ discussion of gravitation and attraction, 275–92.

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stream of particles moving rapidly towards the surface of the earth from above, and pressing bodies in its path downwards.66 If these particles remained on the earth, however, they would cause it to swell, so they have to reascend, albeit in another form, for if it were in the same form the stream of particles would have the power to raise bodies upwards, just as it has the power to push them downwards in descending. Newton puts the difference down to speed: the ascending stream must move at a much slower rate than the descending one. He maintains that ‘the gravity of bodies is as their solidity’,67 that is, their weight is as the amount of material they contain, showing that what he wants is not just a qualitative rationalization of weight, along the lines of the Gassendi/Charleton mechanist approach, but something that establishes a quantitative connection, although he is unable to offer any guidance on this question.68 From the mid-1660s, Newton was also engaged in an alchemical/chemical study of the nature of matter. Around 1667 he had completed an Index Chemicus in which different substances are treated as distinct—that is, the idea of universal transmutability was absent—but in a series of alchemical ‘Propositions’ from around 1669 he introduces a vitalistically conceived ‘fermental virtue’ to account for the processes by which species of matter are reduced to fundamental parts and then reorganized into new species of matter.69 It was with this development that his mechanical assumptions and his matter-theoretical ones began to come together, and by the time of his paper ‘An Hypothesis explaining the Properties of Light discoursed of in my several papers’, read to the Royal Society in 1675,70 the properties of light were being explained in terms of an elastic particulate aether which, being denser outside bodies than within their pores, deﬂects light corpuscles by striking them in various ways. Newton speculates whether everything in nature might not be just ‘aether condensed by a fermental principle’, but the materiality of the aether presented immense problems, for the natural changes occurring in it sometimes seemed to be the effects of purely material causation, whereas at other times they were clearly the outcome of vital processes.71 The oscillation between vital and corpuscularian notions permeated the alchemical tradition in which Newton was working, a tradition that owed a good deal to the 66

Ibid., 362–4 [text]/363–5 [transcription], 426/7. Ibid., 430/431. This later became the assumption that pieces of solid matter of the same volume have the same inertial mass, an assumption Cotes criticized as arbitrary: see Arnold Thackray, Atoms and Powers: An Essay on Newtonian Matter-Theory and the Development of Chemistry (Cambridge, Mass., 1970), 16. 69 See Dobbs, The Janus Face of Genius, 24–33, 94–5; Thackray, Atoms and Powers, 24–6; McGuire, ‘Transmutation and Immutability’. 70 The paper was published in Thomas Birch, The History of the Royal Society of London, For Improving of Natural Knowledge, From Its First Rise (4 vols., London, 1756–7), iii. 247–69, 296–305. See also Newton, Correspondence, i. 362–86. 71 As pointed out in Alan Gabbey, ‘Newton, Active Powers, and the Mechanical Philosophy’, in I. Bernard Cohen and George E. Smith, eds., The Cambridge Companion to Newton (Cambridge, 2002), 329–57: 340–1. 67 68

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vitalist corpuscularian notions of Helmont, and it is not surprising that Newton’s attempts to construct a fundamental account of matter relied crucially on vitalistic conceptions, since it was often the vital notions that carried the explanatory load.72 In the treatise ‘Of Natures obvious laws & processes in vegetation’, dating from around the same time, he writes that natural processes are ‘either vegetable or purely mechanical’. As well as gravity, ‘vulgar chemistry’ is included in the category of the ‘purely mechanical’, and elsewhere this is taken to be the study of the ‘grosser’ parts of matter, which operates at a level of causation distinct from that of the vegetable, the explanation of which requires recourse to further causes, presumably of a different kind.73 In ‘An Hypothesis’, Newton makes an explicit link between gravitational and ‘vegetable’ functions, so that the gravitational aether, as Dobbs remarks, now comes to share in the activity of the vegetable spirit. ‘The gravitational particles’, she points out, ‘were not only thin and subtle; when condensed they became a “tender matter”, the “succus nutritious”, the “primary substance out of wch things generable grow”, or a “humid active matter”. By conﬂation with the active vegetable spirit, gravity had become in many ways an active principle.’74 In 1679, in a letter to Boyle, Newton turned his attention again to the aether as the cause of gravity, but here he offered two explicitly mechanical models that make no reference at all to active powers.75 The ﬁrst postulated differences in the density of the aether between that in the pores of bodies and that outside them, whereas the second translated this difference into aether particle size, postulating a decrease in size as one moved inwards from the upper atmosphere to the centre of the planet. On these models, the cause of gravity is the variation in tension in different parts of the aetherial system, which creates pressures, causing bodies to move. Newton was coming close here to something like the Cartesian view in which the position and motion of bodies—celestial bodies in particular—was due to the different pressures exerted on them by contiguous matter. Indeed, in discussing Burnet’s account of the formation of the earth in a letter of 24 72 As well as Dobbs’ works, cited above, see William R. Newman, ‘The Background to Newton’s Chymistry’, in I. Bernard Cohen and George E. Smith, eds., The Cambridge Companion to Newton (Cambridge, 2002), 358–68; Karen Figala, ‘Die exakte Alchemie von Isaac Newton’, Verhandlungen der Naturforschenden Gesellschaft Basel 94 (1984), 155–288; and more generally Antonio Clericuzio, ‘A Redeﬁnition of Boyle’s Chemistry and Corpuscular Philosophy’, Annals of Science 47 (1990), 562–89; idem, ‘From Van Helmont to Boyle: A Study of the Transmission of Helmontian Chemical and Medical Theories in Seventeenth-Century England’, British Journal for the History of Science 26 (1993), 303–34; William R. Newman, ‘The Corpuscular Theory of J. B. van Helmont and Its Medieval Sources’, Vivarium 31 (1993), 161–91; idem, ‘Boyle’s Debt to Corpuscular Alchemy’, in Michael Hunter, ed., Robert Boyle Reconsidered (Cambridge, 1994), 107–18; idem, ‘The Alchemical Sources of Robert Boyle’s Corpuscular Philosophy’, Annals of Science 53 (1996), 567–85. 73 See the discussion in Dobbs, The Janus Face of Genius, ch. 4. 74 Ibid., 103. 75 Newton to Boyle, 28 Feb. 1679: Correspondence, ii. 288–96. See the discussion in Dobbs, The Janus Face of Genius, 117–19.

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December 1680, Newton explicitly invokes vortices, telling us that ‘Ye heat of ye Sun rarefying yt side of ye Chaos yt ley next it, or by ye pressure of ye vortex or of ye Moon upon ye Waters, some inequalities might bee made in ye Earth, and then ye waters ﬂowing to those lower parts or cavities would make ye seas there.’76 Moreover, in his discussion of the comet of 1680 with Flamsteed,77 Newton has no qualms about using the vocabulary of vortices, and in his second edition of Varenius’ Geographia generalis (1681),78 he not only does not comment on Varenius’ use of vortices but continues to use illustrations of the earth’s vortex (a variant of that of Descartes in his Principia Philosophia) that he had prepared for the ﬁrst edition.79 Everything changes with the visit from Halley in August 1684, where Halley put to Newton the question about the curve described by a body under the effect of an inverse square attraction. Once Newton realizes that the substitution of centripetal for centrifugal force holds the key to dynamics, his thinking followed a new trajectory, but he immediately struck a profound problem. The construal of planetary orbits in terms of a combination of a uniform rectilinear motion and a uniformly accelerated motion directed towards the centre of the earth yielded Kepler’s laws, as Newton showed. The ﬁt between the mathematics and observed orbits, for example in the case of the equal areas law, was perfect. But this was the problem. If the planet were moving through an aether, one would not expect such a perfect ﬁt (in the way that projectiles travelling through the air deviate from the mathematical prediction for bodies travelling in a void, for example). That would only happen if it were completely unhindered and although, in Cartesian vortex theory, vortices move the body rather than offer resistance to it, Newton realized that the understanding of the behaviour of ﬂuids on which this relied was not viable. If the motion of the planet were analysed in terms of centripetal rather than centrifugal force, so that it was the planet and not any medium in which it might be embedded that was the primary mover, then it would be moving through that medium, and a particulate medium such as an 76

Correspondence, ii. 319. Ibid., ii. 340–67. 78 The Geographica, the ﬁrst edition of which appeared in 1650, was a standard reference work, drawn upon by natural historians in particular. Its long list of geological strata in the neighbourhood of Amsterdam, for example, was cited by a number of writers, beginning with Birch, The History of the Royal Society of London, i. 265, and in 1695 it was used by John Arbuthnot to question Woodward’s account of the deposition of fossils: see Rappaport, When Geologists were Historians, 164–5, 173–4, on the uses of Varenius in geological debates; and more generally W. Warntz, ‘Newton, the Newtonians, and the Geographia Generalis Varenii ’, Annals of the Association of American Geographers 79 (1989), 165–91. 79 See Dobbs, The Janus Face of Genius, 126–9. See also, D. T. Whiteside, ‘Before the Principia: The Maturing of Newton’s Thoughts on Dynamical Astronomy, 1664–1684’, Journal of the History of Astronomy 1 (1970), 5–19. The illustrations are reproduced in Dobbs from Bernhardus Varenius, Geographica generalis . . . , Ab Isaaco Newton Math. Prof. Lucasiano Cantabrigienses. Editio Secunda Auctior & Emendatior (Cambridge, 1681), fold-out plates placed between pages 298 and 299. They are at the end of the document in the EEBO version. 77

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aether, no matter how ﬁne, would offer resistance to a body moving through it. Newton’s reaction to this problem seems to have been immediate, assuming Dobbs’ convincing argument for a 1684 dating of two works, De aere et aethere and De gravitatione.80 De aere et aethere touches on the question of retardation by a medium in the context of the motion of a pendulum in an evacuated glass jar. Before evacuation we would expect gradual retardation of the pendulum by the air, but Newton notes that the pendulum is retarded almost to the same degree in an evacuated jar, ‘although that motion ought not to cease unless, when the air is exhausted, there remains in the glass something much more subtle which damps the motion of the bob’.81 Not long after he broke off composition of De aere, Newton performed the experiments with hollow pendulum bobs reported in Proposition 6 of Book III of the Principia. As he increased the amount of matter in the bob, he expected to observe a retardation because of the larger number of moving particles interacting with the stationary medium. But in fact he found no retardation, concluding in the ﬁrst edition of the Principia that the aether probably did not exist, although he removed this from later editions as he began to countenance an aether again after 1706.82 In De gravitatione, probably composed just after the pendulum experiments, Newton abandons a material aether completely. This is the work in which Newton comes to terms most explicitly with Cartesianism. First, he deﬁnes motion, which Descartes had taken as a completely clear well-deﬁned notion, in terms of force, which mechanists generally took to be obscure and problematic. Change of place is, he argues, merely an external result of motion, it is not what motion actually is: motion itself needs to be characterized and explained in terms of something internal to the body, force. In Deﬁnition 5 we are told force is the causal principle of motion and rest, and that ‘it is either an external one that generates or destroys or otherwise changes impressed motion in some body; or it is an internal principle by which existing motion or rest is conserved in a body, and by which any being endeavours to continue in its state and opposes resistance.’ And in Deﬁnition 8 inertia is deﬁned as ‘force within a body, lest its state should be easily changed by an external exciting force’.83 Second, Newton departs from mechanism even more radically in his treatment of the nature of matter. Maintaining that Descartes’ identiﬁcation of matter and extension distances God from matter to too great an extent, he argues that what characterizes matter is something like a force. The argument works in terms of a hypothetical reconstruction of God’s creation of matter. First, God makes some region of space impervious to already existing bodies by creating an impenetrable region of space. Impenetrability, 80 81 82 83

See Dobbs, The Janus Face of Genius, 132–46. Newton, Unpublished Scientiﬁc Papers, 227–8. See Dobbs, The Janus Face of Genius, 137 n. 43. Newton, Unpublished Scientiﬁc Papers, 114 [text] / 148 [trans].

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which had been merely a derived essence of matter for Descartes,84 now becomes its only essence. Second, having established this region of impenetrability, he allows it to move, according to certain laws. Third, this mobile impenetrable region is opaque (we can think of this, for example, in terms of the ability to reﬂect or refract light corpuscles, although Newton himself doesn’t specify what this opacity consists in) and hence such regions are visible; and because it is impenetrable, it is tangible. In short, it is a body: It would have shape, be tangible and mobile, and capable of reﬂecting [in collision] and being reﬂected, and no less constitute a part of the structure of things than any other corpuscle, and I do not see that it would not equally operate upon our minds and in turn be operated upon, because it is nothing more than the product of the divine mind realized in a deﬁnite quantity of space. For it is certain that God can stimulate our perception by his own will, and thence apply such power to the effects of his will.85

If the rejection of the Cartesian equation of matter and extension seemed at ﬁrst to present us with a conception of matter on which it is essentially active, its identiﬁcation with a force that turns out to be in an important respect divine suggests rather that it is a passive mass activated by an active principle, a notion that has resonances in Newton’s alchemical studies, and which he will develop later in the Queries to the Opticks. Notice, however, how close to occasionalism this conception is pushing Newton, very much along the lines of his continental contemporaries. The idea that God stimulates our perceptions by his will suggests that our perceptions have God, not a physical world, as their direct source. The need to accommodate forces while at the same time failing to ﬁnd a place for them in the physical realm is the pressing problem for all those natural philosophers of the 1680s and 1690s who aspired to a complete natural philosophy, and it is striking how close Newton comes to the solutions of Malebranche and Leibniz, which, in their different ways, remove forces from the physical realm and locate them respectively in the supernatural and in the metaphysical realms. Unlike Malebranche and Leibniz, however, Newton does not ultimately come down on the side of such a solution, being prepared to sacriﬁce claims to a complete natural philosophy and simply reserve judgement on the nature of matter, and in particular the nature of gravitational attraction. Sacriﬁcing claims to completeness was of course a problematic strategy, because Newton was presenting his system, as set out in the Principia, without offering answers to fundamental questions which advocates of the main competing system, the mechanist vortex theory, had claimed to answer. Moreover, the answer they

84 See Descartes to More, 15 April 1649: Œuvres, v. 341–2; also Reply to Sixth Set of Objections to the Meditationes: ibid., vii. 442. See also Descartes to More, 5 February 1649: ibid., v. 269, on the problem of why extension should be given preference over impenetrability if they are coextensive. 85 Newton, Unpublished Scientiﬁc Papers, 106 [text]/139 [trans].

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provided was couched in terms of purely mechanical interactions:86 exactly how Newton would have liked, ideally, to deal with such questions, had this been possible. Not surprisingly, by the 1690s, in the wake of the publication of the Principia, Newton had become a good deal more circumspect about the nature of gravity. In the paper on acids, which dates from around 1692,87 he offers an account of matter in terms of hierarchies of increasingly complex aggregations of particles, held together by short-range attractive forces, perhaps suggesting that the vegetable and the mechanical can shade into one another. Ever since the early Questiones, he had grouped the questions of cohesion and gravity together, but it is not clear that he believed that such short-range forces threw any light on gravity. On 17 January 1693, he wrote to Bentley: ‘You sometimes speak of gravity as essential & inherent in matter: pray do not ascribe that notion to me, for ye cause of gravity is what I do not pretend to know, & therefore would take more time to consider of it.’88 In other words, he was not even prepared to commit himself to the idea that the answer lies in matter theory.89 In a follow-up letter of 25 February, he indicated to Bentley why he believed that matter theory would not be sufﬁcient if we assumed that the gravitating particles were not in contact with one another: Tis unconceivable that inanimate brute matter should (without ye mediation of something else wch is not material) operate upon & affect other matter wthout mutual contact; as it must if gravitation in the sense of Epicurus be essential & inherent in it. And this is one reason why I desired you would not ascribe innate gravity to me. That gravity should be innate inherent & essential to matter so yt one body may act upon another at a distance through a vacuum wthout the mediation of any thing else by & through wch their action or force may be conveyed from one to another is to me so great an absurdity that I beleive no man who has in philosophical matters any competent faculty of thinking can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws, but whether this agent be material or immaterial is a question I have left to ye consideration of my readers.90

That Newton was in fact still considering an immaterial agent is evident from a memorandum for 20 February 1697 by David Gregory, in which he mentions

86

See Aiton, Vortex Theory, chs. 4 and 7 for details. De natura acidorum, in Newton, Correspondence, iii. 205–14. It was ﬁrst published in John Harris, Lexicon Technicum or an Universal English Dictionary of Arts and Sciences (2 vols., London, 1704–10), ii. sig. b3v–b4v, but had circulated in manuscript form for up to two decades before publication. 88 Newton, Correspondence, iii. 240. 89 Cf. the letter of 30 March 1694 from Fatio de Duillier to Leibniz, in which he tells Leibniz that Newton is undecided on the nature of gravity, between the view that it is ‘inherent in matter according to an immediate law of the creator of the universe’ and the idea that it is produced by a mechanical cause: ibid., iii. 309. 90 Ibid., iii. 253–4. 87

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Wren smiling at Newton’s belief that gravity ‘does not occur by mechanical means, but was introduced originally by the Creator’.91 In the Optice, the Latin translation of the Opticks that appeared in 1706, incorporeal ‘active principles’ are introduced in Query 23: ‘It seems to me farther, that these Particles have not only a Vis inertiae, accompanied with such passive Laws of motion as naturally result from that Force, but also that they are moved by certain active Principles, such as is that of Gravity, and that which causes Fermentation, and the Cohesion of Bodies.’ In fact, Newton had elaborated in a little more detail to David Gregory, who reports that at a meeting with him on 21 December 1705, Newton had discussed proposed addenda to the Optice, and had questioned whether he should put the last Query in the following form: What is the space that is empty of bodies ﬁlled with? The plain truth is, that he believes God to be omnipresent in the literal sense; and that as we are sensible of objects when their images are brought home within the brain, so God must be sensible of every thing, being intimately present with every thing: for he supposes that as God is present in space where there is no body, he is present in space where a body is also present. But if this way of proposing this his notion be too bold, he thinks of doing it thus. What cause did the Ancients assign of gravity? He believes that they reckoned God the cause of it, nothing else, that is no body being the cause; since every body is heavy.92

Yet some time between 1706 and 1713, Newton moved back in the direction of an aether theory. In 1713, in the General Scholium to the second edition of the Principia, as we saw above, he announced the existence of ‘a very subtle spirit pervading bodies and lying hidden in them’. The catalyst seems to have been the experiments of Hauksbee on electrical attraction and electro-luminescence.93 Hauksbee was Hooke’s successor as Curator of Experiments at the Royal Society from 1703 until his death in 1713.94 We shall have occasion to look at his experiments in Chapter 5. For the moment, it is sufﬁcient to note that they were concerned with triboelectrical phenomena (those produced by rubbing), which were subjected to several different kinds of variation of parameter, most notably by being observed in glass tubes at various degrees of evacuation, and they produced a number of very striking forms of static electrical attraction, and some spectacular electroluminescence. Hauksbee conceived the experiments so as to demonstrate how and why ‘electrics’—bodies which when rubbed exercise an attractive power—behaved in the way they did. In a set of ‘Observations’ that 91

Ibid., iv. 266 [text]/267 [trans]. Quoted in W. G. Hiscock, David Gregory, Isaac Newton and their Circle (Oxford, 1937), 29. 93 See Henry Guerlac, ‘Francis Hauksbee—expe´rimenteur au proﬁt de Newton’, Archives Internationales d’Histoire des Sciences 16 (1963), 113–28; idem, ‘Sir Isaac and the Ingenious Mr. Hauksbee’, in I. Bernard Cohen and Rene´ Taton, eds., Me´langes Alexandre Koyre´ (2 vols., Paris, 1964), i. 228–53. 94 On his activities in this capacity, see Marie Boas Hall, Promoting Experimental Learning: Experiments and the Royal Society, 1660–1727 (Cambridge, 1991), 116–32. 92

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Newton had planned for the second English edition of the Opticks, composed some time between 1715 and 1717, he describes Hauksbee’s experiments and accounts for them in terms of an aether: that gross bodies contain within them a subtile Aether or Aetherial elastic spirit wch by friction they can emit to a considerable distance, & which being emitted is found sufﬁciently Subtile to penetrate & pass through the body of glass, & sufﬁciently active to emit light at a distance from the gross body if it be there put into a trembling agitation, as is manifest by the following Phaenomena shewd to the R. Society by Mr. Hawksby.95

As Guerlac has pointed out, Newton identiﬁed the electrical efﬂuvium whose existence Hauksbee believed he had demonstrated with a subtle, penetrating, elastic, and highly active matter pervading all bodies, which he refers to as an ‘aether’.96 The aether is introduced gradually in the Queries in the published version of the second edition of the Opticks (1717). In Query 17, it is an explicitly optical medium, whereas in Query 18 it is expanded to account for the transmission of heat, at which point it is transformed into a celestial medium: And do not hot bodies communicate their heat to contiguous cold ones, by the vibrations of this medium propagated from them into the cold ones? And is not this medium exceedingly more rare and subtile than the air, and exceedingly more elastick and active? And doth it not readily pervade all bodies? And is it not (by its elastick force) expanded through all the heavens? 97

This universal medium is different from something that merely transmits heat and light.98 Queries 19 and 20 are devoted to showing that the medium inside bodies is rarer than that outside them, that the increase in rarity is gradual, and that this, plus the extreme elasticity of this medium, is the cause of mutual gravitational attraction. In Queries 21 and 22, he sets out to establish that the particles of the aether must be much smaller than those of air, and that the aether he is postulating here is very different from that postulated elsewhere—presumably he has the Cartesians particularly in mind here—in that the resistance is so small that planets would suffer no appreciable diminution in their motion over a 10,000-year period. Of course, Newton’s aether and that of the Cartesians serve very different functions, functions that depend on the degree of density of the medium in which the planets move. The Cartesian aether has to physically drag planets around, and clearly has to be very dense if it is to be able to do this, 95 Quoted in Henry Guerlac, ‘Newton’s Optical Aether: His Draft of a Proposed Addition to His Opticks’, Notes and Records of the Royal Society of London 22 (1967), 45–57: 48. 96 Ibid., 48. 97 Opera, iv. 222. 98 See Roderick W. Home, ‘Newton on Electricity and the Aether’, in Zev Bechler, ed., Contemporary Newtonian Research (Dordrecht, 1982), 191–213; cf. idem, ‘Newton’s Subtle Matter: The Opticks Queries and the Mechanical Philosophy’, in J. V. Field and Frank A. J. L. James, eds., Renaissance and Revolution: Humanists, Scholars, Craftsmen and Natural Philosophers in Early Modern Europe (Cambridge, 1993), 193–202.

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whereas the major constraint on an aether in the Newtonian system is that it cannot offer resistance to the motion of the planets, for we know that the proof of Kepler’s area law operates with a body moving without resistance, and that the result exactly matches the observed behaviour of the planets. As a further indication of the generality of the terms in which Newton is treating the aether by this stage, in Queries 23 and 24 he treats sensory and motor excitations in terms of the action of this aether in the capillaries of the nerves. As Dobbs points out, this last of Newton’s aethers is a peculiar hybrid: it is not a dense aether in which the particles act mechanically through impact, so despite his regular denials in these Queries that he has postulated an ‘occult quality’, mechanist natural philosophers would have found nothing to answer their criticisms in the account that Newton gives.99 Moreover, in the lengthy ﬁnal Query 31, which sets out his matter theory, he returns to the doctrine of active principles: And thus Nature will be very conformable to herself, and very simple; performing all the great motions of the heavenly bodies by the attraction of gravity, which intercedes those bodies; and almost all the small ones of their particles, by some other Attractive and Repelling powers, which intercede the particles. The vis inertiae is a passive principle, by which bodies persist in their motion or rest; receive as much motion in proportion to the force impressing it, and resist as much as they are resisted. By this principle alone there never could have been any motion in the world. Some other principle was necessary for putting bodies into motion; and now they are in motion, some other principle is necessary for conserving the motion. For from the various compositions of two motions, it is very certain that there is not always the same Quantity of motion in the world.100

Then, after offering a number of demonstrations of this loss of motion, he concludes: Seeing therefore that the variety of motion, which we ﬁnd in the world, is always decreasing; there is a necessity of conserving and recruiting it by active principles: such as are the cause of gravity, by which planets and comets keep their motions in their orbits, and bodies acquire great motion in falling; and the cause of fermentation, by which the heart and blood of animals are kept in perpetual motion and heat; the inward parts of the earth are constantly warmed, and in some places grow very hot; bodies burn and shine; mountains take ﬁre; the caverns of the earth are blown up; and the sun continues violently hot and lucid, and warms all things by his light. For we meet with very little motion in the world, besides what is owing to these active principles. And if it were not for these principles, the bodies of the earth, planets, comets, sun, and all things in them, would grow cold and freeze, and become inactive masses; and all putrefaction, generation, vegetation and life would cease, and the planets and comets would not remain in their orbs.101 99 100 101

Dobbs, The Janus Face of Genius, 228. Opera, iv. 258. Ibid., 259–60.

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We have come a very long way from mechanism here, but we have also come a long way from mechanics, for although active spirits are invoked to account for the action of gravity, and although they are supposed to provide a principle that underlies and uniﬁes the whole natural-philosophical realm,102 mechanics included—indeed mechanics as the centrepiece—they do so at a price, one that threatens the achievement of the Principia. For if the ultimate foundations of the very precise and comprehensive system of mechanics set out in the Principia ultimately rests on this slender and obscure doctrine of active powers, then the credibility of the former depends ultimately on the credibility of the latter. Hence it is not surprising that the General Scholium of the Principia and the Queries of the Opticks played the central role in the natural-philosophical culture that developed in the wake of Newton’s work. In fact, the uneasy tension between a strict mechanics and a general natural philosophy based on active principles is replaced by a bifurcation: a serious attempt to ground dynamics, in particular, at the metaphysical level, and, in sharp contrast, an approach that builds on the ‘experimental philosophy’ of Boyle and on Newton’s early work on the production of a spectrum via a series of prisms, shunning systematic aspirations as misconceived. 102

It should be said, however, that there is a case to be made that Newton continued to think of electricity and magnetism in strictly corpuscular, non-aetherial terms: see Home, ‘Newton on Electricity and the Aether’ and idem, ‘Force, Electricity, and the Powers of Living Matter in Newton’s Mature Philosophy of Nature’, in Margaret Osler and Paul Lawrence Farber, eds., Religion, Science and Worldview (Cambridge, 1985), 95–117.

PART II

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3 The Metaphysical Unity of Natural Philosophy Between the publication of the Principia in 1687 and the general assimilation of Newtonianism in continental Europe in the 1730s, there was a prolonged debate over the value of pursuing systematic forms of understanding, a debate which had begun in the 1660s, but which took on a new urgency after the 1680s. Metaphysical accounts had proceeded on the assumption that natural philosophy was, or should be, part of a more general systematic enterprise which provided a comprehensive understanding of the world and our place in it; and on the assumption that natural philosophy was an inherently systematic enterprise in its own right. These were questions that had profound implications for the ability of natural philosophy to act as a model for other areas of enquiry, for this ability was crucially tied in with its standing as something that was uniﬁed and comprehensive. For many late seventeenth- and early eighteenth-century natural philosophers, if anything could act as a model for other forms of knowledge and displace the ancient and medieval models, it was Newton’s Principia. Yet the Principia appeared at just the time when the very idea of a general model for knowledge, of the kind that ancient and medieval systems had offered, was being questioned. At stake here were questions about whether it was a sine qua non of successful explanation in natural philosophy that it be an intrinsically uniﬁed ﬁeld of enquiry; and whether successful natural-philosophical explanation was conﬁned to systematic accounts. Mechanism had satisﬁed these criteria in a straightforward way. Its project of explanation through micro-corpuscularian reduction meant that there was a common level of causation: all non-microscopic physical events were to be accounted for in terms of the behaviour of their microscopic constituents, which could be described in terms of basic mechanics. The reduction secures uniﬁcation, for every physical event is now essentially a micro-corpuscularian interaction; and since this interaction is just a question of mechanics, which is a highly systematic form of enquiry, proceeding in an axiomatic geometrical fashion, the systematic nature of explanation is secured. Once mechanism had been abandoned, however, these questions were no longer so easily settled. While they were left unresolved, the ability of natural philosophy to act as general model for enquiry was in question.

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Just what was at issue here is best pursued by examining, in detail, two contrasting responses. In this chapter we shall be looking at Leibniz’s attempt to establish a metaphysical foundation for all forms of enquiry, something that both grounds and uniﬁes natural philosophy as part of a larger cognitive project, for which natural philosophy turns out to be the model. We shall also be exploring how the most inﬂuential of Leibniz’s contributions to natural philosophy—his conception of mathematics as an abstract algorithm—contributes to a particular understanding of natural philosophy. The connections between Leibniz’s metaphysics and his dynamics have been recognized, if not always explored, in the philosophical literature on Leibniz, so that, while reading him in the context of natural philosophy is not the standard way of approaching him, it is not unprecedented.1 Locke, to whom I shall turn in Chapter 4, is a different matter. He has been read almost exclusively in the context of a wholly inappropriate epistemological ‘rationalism versus empiricism’ distinction deriving from considerations that only came into play in Kant, and which act to disort key features of Locke’s thought. Many of these features happen to be those of most interest to us: from the question of what to do when systematic enquiry fails, and the attempt to legitimate non-systematic forms of enquiry, to the extent to which his views on knowledge develop out of medical debates, and the extent to which he uses travel writings to help formulate and defend his views not just on on moral, political, and religious questions, but on epistemological ones also. Reading Locke as a natural philosopher yields an image of him very much at odds with prevailing ones, but it is a reading that enables us to understand the decisive role that his thought played in the ﬁrst half of the eighteenth century. Moreover, it allows a form of ‘empiricism’ to come to light—namely empiricism as a successor to, and philosophical reﬁnement of, seventeenth-century ‘experimental’ natural philosophy—which is intimately tied up with natural-philosophical practice, and is quite distinct from the speculative epistemology to which it is reduced in the ‘rationalism/empiricism’ debates. In Chapter 5, we shall explore this naturalphilosophical version of empiricism and its indebtedness to Locke. L E I BN I Z A N D TH E U N IT Y O F K N O W L E D GE It was above all Leibniz who gave metaphysics a foundational role in natural philosophy, a foundational role that had been occupied in the mechanist tradition by micro-corpuscularianism. For the mechanist, macroscopic physical processes are the effect of interactions between microscopic corpuscles, interactions that can (ultimately) be described exhaustively in terms of the speed, direction, and mass/weight of the corpuscles. Leibniz accepts something akin to micro1

See e.g. the accounts in Martial Gueroult, Dynamique et Me´taphysique Leibniziennes (Paris, 1934); and Daniel Garber, Leibniz: Body, Substance, Monad (Oxford, 2009).

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corpuscularian foundations in the case of natural philosophy, but argues that such foundations cannot have an absolute foundational standing: for this, one must descend to a more fundamental level, which, for reasons he sets out, can only be metaphysics. In a natural-philosophical context, Leibniz seeks to establish these ultimate foundations through reﬂection on anomalies in Cartesian physical theory, arguing that mechanism cannot supply the requisite criteria of identity for bodies needed for a full theory of the physical behaviour of bodies: this must be a task for metaphysics. General theories of individuation and unity would indeed traditionally have fallen under the rubric of metaphysics, and this was one of the basic problems dealt with in Sua´rez’s Metaphysicarum disputationem, for example, a work that played a signiﬁcant role in Leibniz’s understanding of scholasticism, in that it supplied the assumed understanding of metaphysics in his scholastic education.2 But to argue that there were particular issues that arose in physical theory that were only resolvable in metaphysical terms is not the same thing as maintaining that metaphysics provides the foundations for natural philosophy, and the latter claim is not something for which there is any precedent or support in the scholastic tradition. The issues here are general ones for Leibniz, as we have seen, and natural philosophy is in no way unique in requiring metaphysical foundations: ultimately, it would seem that any discourse making cognitive claims requires metaphysical grounding. What is so striking about Leibniz’s proposal is the fact that he took the general metaphysical project out of the strictly scholastic context in which it originated and which conferred its signiﬁcance on it, reworking it in terms of his notions of perspective and harmony, and presenting it in such general terms that it could also be assimilated to Lullian and Neoplatonist projects, which had quite different provenances. This had the effect of making it into a perennial philosophy, something virtually constitutive of any philosophical enterprise past, present, and future, in the sense that it is a gauge of the worth and success of philosophical systems.3 Philosophy becomes the project of providing the underlying philosophical foundations for theology, law, natural philosophy, and indeed any discipline, demonstrating their legitimacy in terms of their derivability from an underlying metaphysics. Having generalized the project in this way, one need no longer conﬁne oneself to the resources provided by scholasticism. Leibniz notes, in a 1679 letter to the Duke of Brunswick-Hanover, that, ‘in 2 On the importance of Sua´rez for Leibniz’s metaphysics, see Donald Rutherford, Leibniz and the Rational Order of Nature (Cambridge, 1995), ch. 4. On Sua´rez’s metaphysics itself, see JeanFranc¸ois Courtine, Suarez et le syste`me de la me´taphysique (Paris, 1990). On the importance of Sua´rez and late scholastic metaphysics for the German Lutheran educational system, see Ernst Lewalter, Spanische-jesuitische und deutsch-lutherische Metaphysik des 17. Jahrhunderts (Hamburg, 1935). 3 See Charles B. Schmitt, ‘Perennial Philosophy: From Agostino Steuco to Leibniz’, Journal of the History of Ideas 27 (1966), 505–32. On the eighteenth-century notion of a philosophical system, see Leo Catana, The Historiographical Concept ‘System of Philosophy’: Its Origin, Nature, Inﬂuence, and Legitimacy (Leiden, 2008); and Julia Candler Hayes, Reading the French Enlightenment: System and Subversion (Cambridge, 1999).

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order to lay the basis for these great demonstrations, I plan to preface them with the demonstrated elements of the true philosophy to help in understanding the main work.’ Note that the ‘true philosophy’ here is no longer scholasticism (nor anything derived from Lull or Neoplatonism), but something of Leibniz’s own devising: We need a new logic in order to know degrees of probability, since this is necessary in judging the proofs of matters of fact and of morals, where there are unusually good reasons on both sides and we are concerned only to know on which side to tip the scales. . . . We must also push metaphysics further than has been done, in order to have true notions of God and the soul, of person, substance, and accidents. And unless we have a profounder insight into physics, we cannot meet the objections raised against the history of creation, the deluge, and the resurrection of the body. . . . And to conclude, nothing conforms more truly with a true politics and the true happiness of mankind, even here below and in this life, than does my proposal about the inviolable and irresistible power of the sovereign over external goods and of the internal role which God exercises over souls through the church.4

The system even has its own means of demonstration, namely Leibniz’s ‘universal characteristic’, whereby ‘every line of this writing will be equivalent to a demonstration’.5 The project of providing metaphysical foundations is unlike that of microcorpuscular reduction in an important respect, and it is crucial to appreciate that it is not an alternative form of reduction. Metaphysical foundations do not provide an extra level of reduction, from the physical to the metaphysical for example, but a ‘perspective’. The idea that knowledge might offer a perspective on the world, and that the more fundamental the knowledge the more comprehensive the perspective, is the core of a distinctively Leibnizian project of uniﬁcation of knowledge which is quite different from anything in the scholastic or Neoplatonist traditions to which he was indebted in other respects in his thinking about fundamental questions. The search by some in the scholastic tradition for a uniﬁed conception of being that underlies all forms of existence, for example, could never have been thought of in terms of offering a perspective on something. Leibniz’s interest in the idea of perspective began early in his career, and he was particularly taken by the projective geometry of conic sections developed by Desargues and Pascal, which he considered superior to that of the Alexandrian geometers because, rather than offering separate proofs for individual theorems, they had offered demonstrations that displayed the harmony 4 Leibniz, Philosophical Papers and Letters, ed. and trans. L. E. Loemker (2nd edn., Dordrecht, 1976), 260–1. 5 Ibid., 261. While there can be no doubt that Leibniz’s project was a development of the general seventeenth-century concern with methodological rules, it went well beyond these. As Daston points out, a calculus of rationality of the kind that Leibniz is advocating, ‘was deemed superior to a mere method in that its rule yielded unique, unambiguous solutions that brooked no further argument’: Lorraine Daston, Classical Probability in the Elightenment (Princeton, 1988), xv.

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between all forms of conic section by establishing the conditions under which projective invariance held. In the early to mid-1670s, he became particularly interested in anamorphic perspectives, in which images are manipulated by being projected at different angles and on to different shaped surfaces—see Fig. 3.1, from Nice´ron’s La Perspective curieuse (1638)—and these various perspectival interests developed into a general interest in modes of representation that enable one to see everything at the same time.6 Unlike God, we are constrained to see things from particular perspectives, and Leibniz sees his task as discovering how our perspectives might be expanded in a radical way. In particular, as we shall see, he believed that the use of inﬁnitesimal analysis offered a way of going beyond our natural limitations in mathematics: or, as we might put it, it offered a way of expanding our perspective by artiﬁcial means. Leibniz’s metaphysical project is a generalization of this intuition that systematic understanding is a product of controlled expansion of perspective. Note that what is at issue here is not just increased generality and comprehensiveness, but generality and comprehensiveness that are generated through systematic connections. Note also that our grasp of the world is intrinsically and essentially perspectival in Leibniz’s view, so there is no question of transcending perspectival constraints: the issue is rather that of expanding our perspectival resources, and above all of harmonizing perspectives into a more comprehensive vision. If understanding takes the form of an essentially perspectival grasp, and ways can be devised of systematically expanding the perspective available to us, then, for Leibniz, the point of the philosophical exercise—and the goal of the intellectual formation of the philosopher—will be to aspire to a form of intellectual grasp that reveals to us systematic connections, typically in the form of an underlying harmony, between everything at the most fundamental level. Although we shall be focusing on natural philosophy, we must not lose sight of the fact that the systematic metaphysical grounding of natural philosophy is not a self-contained exercise, but part of a more general project of grounding any possible form of cognitive enterprise. Leibniz’s attempts to provide a systematic grounding for natural philosophy were seeded by a theological project. In his ‘Demonstrationes Catholicae’, composed in the late 1660s, he set out to reconcile Catholic and Protestant theology by treating theological questions in terms of an underlying metaphysical grounding. In 1679 he elaborated on what he had taken the scope of the ‘Demonstrationes’ to be:

6 See Matthew L. Jones, The Good Life in the Scientiﬁc Revolution: Descartes, Pascal, Leibniz, and the Cultivation of Virtue (Chicago, 2006), ch. 5. On anamorphic perspectives in the seventeenth century, see Betsy Newell Decyk, ‘Cartesian Imagination and Perspectival Art’, in Stephen Gaukroger, John Schuster, and John Sutton, eds., Descartes’ Natural Philosophy (London, 2000), 447–86.

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Fig 3.1

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It was to contain three parts. The ﬁrst was to deal with the demonstrations of the existence of God, of the immortality of the soul, and of all natural theology; for I did in fact have some surprising ones. The second part was to be about the Christian religion, or revealed theology, where I sought to demonstrate the possibility of our mysteries and to meet all the objections of those who claim to show the absurdity and the contradictions in the Trinity, the Incarnation, the Eucharist, and the resurrection of the body. . . . The third part was to treat of the church: here I have convincing proofs that the church hierarchy is of divine right, and I distinguish the limits of secular and ecclesiastical power.7

These are traditional questions that would have exercised sixteenth- and early seventeenth-century theologians. Indeed, signiﬁcantly earlier precedents can be found, and the project is reminiscent of that of Lull, in the thirteenth century, in which a general programme was devised to convince Muslims and Jews of the truth of fundamental Christian doctrines such as the Trinity and the Incarnation. The idea was that, by reﬂecting philosophically on divine attributes such as power, wisdom, and virtue, we would be led to conclude that such attributes belonged exclusively to God as conceived by Christianity. This kind of project depended on a collapsing of theology into metaphysics.8 One way to think of what was at issue is in terms of knowledge having a structure, a pre-given structure, and the task of the philosopher being to discover this structure and provide a means of negotiating it. We can ﬁnd such a conception very explicitly in Leibniz, and it begins very much as the idea of an encyclopedia in which all knowledge is subjected to a single systematic form of harmonious organization.9 This captures Leibniz’s conception of the role of metaphysics as a kind of master discipline, to which every other form of cognitive enquiry is ultimately subordinate. An image that he occasionally uses is that of an intellectual labyrinth, with his own philosophy as the thread of Ariadne.10 The theme of the unity of knowledge is absolutely fundamental to Leibniz’s understanding of everything from morality and law to natural philosophy. In a ‘memoire for an enlightened person’ dating from the mid-1690s, he writes:

7

Leibniz to John Frederick, Duke of Brunswick-Hanover, Autumn 1679: Philosophical Papers and Letters, 260. 8 Leibniz took both Lull and the Neoplatonists more seriously than most of his contemporaries, and the ‘universal characteristic’ of his early Dissertatio de arte combinatoria (1666) shows distinctively Lullian precedents, as Leibniz himself acknowledged: see ‘A New Method for the Learning and Teaching of Jurisprudence’ (1667), }24: Philosophical Papers, 88. 9 See Antognazza, Leibniz: An Intellectual Biography, chs. 1 and 2; Leroy E. Loemker, ‘Leibniz and the Herborn Encyclopedists’, Journal of the History of Ideas 22 (1961), 323–38; Massimo Mugnai, ‘Der Begriff der Harmonie als metaphysische Grundlage der Logik und Kombinatorik bei Johann Heinrich Bisterfeld und Leibniz’, Studia Leibnitiana 5 (1973), 43–73; and, more generally, Franc¸ois Duchesneau, Leibniz et la me´thode de la science (Paris, 1993), 55–85. The idea of knowledge as necessarily encyclopedic is present throughout Leibniz’s thinking, and is restated in a work from his last years, E´le´ments de la philosophie ge´ne´rale et de la the´ologie naturelle. 10 On his use of this image and its provenance, see Catherine Wilson, Leibniz’s Metaphysics: A Historical and Comparative Study (Manchester, 1989), ch. 1.

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As for me, I put forward the great principle of metaphysics as well as of morality, that the world is governed by the most perfect intelligence which is possible, which means that one must consider it as a universal monarchy whose head is all-powerful and sovereignly wise, and whose subjects are all minds, that is, substances capable of relations or society with God; and that all the rest is only the instrument of the glory of God and of the felicity of minds, and that as a result the entire universe is made for minds, such as it can contribute to their happiness as much as possible.11

If we are to come to terms with Leibniz’s idea of providing natural philosophy with a metaphysical foundation, there are two questions that we need to consider. First, we need to ask how Leibniz conceives of metaphysics and why he sees a need to ground natural philosophy in metaphysics. Second, we need to identify exactly what the natural philosophy is that Leibniz wants to defend, why he chooses one that appears to have such a poor ﬁt with the metaphysics that grounds it, and to what extent its metaphysical grounding shapes speciﬁc natural-philosophical doctrines or results. THE R OLE OF METAPHYSICS In its early development, Leibniz’s project had afﬁnities with both those of Malebranche and Spinoza,12 and although many of his ideas on metaphysics pre-date his familiarity with their systems, Leibniz’s style of working is one of engaging with contemporary views, and there can be little doubt that, in the evolution of his metaphysics, a sense of what was wrong with the Spinozean system and a sense of what was wrong with the Malebranchean one were crucial driving forces. As regards Malebranche, Leibniz tells l’Hoˆpital in 1695 that his account of pre-established harmony, one of the most distinctive Leibnizian doctrines, is not rejection of Malebranche’s views but a development of them,13 and nineteen years later he tells Re´mond that ‘the transition from occasional causes to pre-established harmony does not seem a difﬁcult one’.14 At ﬁrst sight, this afﬁnity is surprising. Malebranche had argued that phenomenal 11 Leibniz, Political Writings, 105: though Leibniz is not consistent on this question. In the The´odice´e for example, he writes: ‘the happiness of rational creatures is one of aims that God has in view, but it is neither his whole nor his ultimate aim.’ Phil. Schriften, vi. 169–70. 12 On Leibniz and Malebranche, see Andre´ Robinet, Malebranche et Leibniz: relations personnelles, pre´sente´es avec les textes complets des auteurs et de leurs correspondants revus, corrige´s et ine´dits (Paris, 1955). On Leibniz and Spinoza, see Georges Friedmann, Leibniz et Spinoza (Paris, 1962); and Mogens Laerke, Leibniz lecteur de Spinoza: La gene`se d’une opposition complexe (Paris, 2008). 13 Leibniz to l’Hoˆpital, 30 Sept. 1695: Math. Schriften, ii. 298–9. 14 Leibniz to Nicholas Re´mond, August 1714: phil. Schriften, iii. 625. On the complex relations between notions of causation in this period, see Kenneth Clatterbaugh, The Causation Debate in Modern Philosophy, 1637–1739 (London, 1999); and Vincent Carraud, Causa sive ratio: La raison de la cause, de Suarez a` Leibniz (Paris, 2002).

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description in terms of contact interactions that result in (but do not cause) changes in the kinematic states of the interacting bodies tells us all we need to, and can, know about physical processes. If we seek something more ‘real’ than these phenomenal processes, something which they reﬂect and which explains why they occur as they do, then what we come up against is not physical reality as such but divine reality. What is striking is that Leibniz’s very different attempt to make sense of natural philosophy by subjecting it to metaphysical foundations, an attempt that shows how we might reintroduce forces into the picture, thereby removing the phenomenal gloss that Malebranche puts on the world, also reveals, in the end, a very physically insubstantial world. As Leibniz wrote to Re´mond: ‘when Plato talked of ideas and Augustine of truth, their thoughts, which I ﬁnd very reasonable, were much the same, and this is the part of Father Malebranche’s system that I would like to see preserved.’15 As regards Spinoza, Leibniz shares with him a distinctive and unprecedented conception of a genuinely foundational role for metaphysics, stronger than anything to be found in Malebranche. Although Leibniz’s view of the tasks and nature of metaphysics were formed before his meeting with Spinoza in 1676, in which he discussed the latter’s unpublished metaphysical writings, there are striking similarities, as well as striking differences, between the two systems, as is clear from a 1678 letter, where, commenting on Spinoza’s recently published Ethica, he writes: I have found there a number of excellent thoughts which agree with my own, as some of my friends know who have also learned from Spinoza. But there are also paradoxes which I do not ﬁnd true or even plausible. As, for example, that there is only one substance, namely God; that creatures are modes or accidents of God; that our mind perceives nothing further after this life; that God himself does indeed think but neither understands nor wills; that all things happen by a kind of fatal necessity; that God does not act for the sake of ends but only from a certain necessity of nature.16

Nevertheless, whatever his disagreements, Leibniz, like Spinoza, is offering not just a uniﬁed foundational system of natural philosophy, but a uniﬁed system of the whole of knowledge, from natural philosophy to politico-theology, one in which the ultimate grounding is provided by metaphysics. By contrast with both Spinoza and Malebranche, however, Leibniz’s uniﬁed system of knowledge is rarely presented whole, and we are never provided with anything remotely comprehensive. He was well aware of, indeed apologetic about, the incomplete and fragmentary nature of his system, and in a letter of 1696 he admits he has not explained everything but rather advanced slowly, beginning with principles.17 Moreover, if we compare the four main pieces that 15

Leibniz to Nicolas Re´mond, 4 November 1715: phil. Schriften, iii. 659. Leibniz to Henry Justel, 14 February 1678: Philosophical Papers, 195. 17 Leibniz to Des Billettes, 14 December 1696: phil. Schriften, vii. 451. As Rutherford points out, Leibniz’s ‘corpus is for the most part no more than a vast collection of philosophical beginnings’: Leibniz and the Rational Order of Nature, 3. 16

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deal with his systematic views—the Discours de la me´taphysique, completed in the winter of 1685–6, the ‘Syste`me nouveau’ of 1695 (the ﬁrst published exposition of his philosophy), ‘De ipsa natura’ of 1698, and an untitled work on monads of 1714, known as the Monadology—there appears to be an unacknowledged shift in his view of the relation between his physical theory and his foundational metaphysics.18 Finally, there is the problem of eclecticism, particularly when it takes the form of an attempt to reconcile two radically antithetical systems, scholastic metaphysics and mechanist natural philosophy. Here we have the most signiﬁcant substantial difference between Leibniz and Spinoza. Spinoza’s metaphysics was designed to demonstrate a wholly uncompromising religious, moral, and political heterodoxy, whereas Leibniz’s view of the role of metaphysics, right from the very beginning, was of a supremely reconcilatory system that could bring together the most diverse conﬂicting viewpoints by discovering the metaphysical foundations of all thought. Leibniz’s conception of metaphysics was intimately connected with its reconciliatory role, yet to the extent to which one can ﬁnd precedents in the scholastic tradition, it was ﬁrmly within the Scotist/Sua´rezean camp, not the Thomist one. This is because its approach to reconciliation was not one of bridging, of ironing out incompatibilities, but rather one of syncretism and ultimately assimilation. The earliest version of Leibniz’s metaphysics was an eclectic system in which a Christianized Aristotelianism was superposed upon mechanism.19 In a paper from around 1668 on transubstantiation, he proposes a solution to the question of what the source of motion is in bodies. Accepting the mechanist claim that 18 See Rutherford, Leibniz and the Rational Order of Nature, ch. 6; and Daniel Garber, ‘Leibniz and the Foundations of Physics: The Middle Years’, in Kathleen Okruhlik and James Robert Brown, eds., The Natural Philosophy of Leibniz (Dordrecht, 1985), 27–130, who argues for a shift from a realist Aristotelian notion of substance in the 1680s and 1690s to the idealist philosophy of monads after that. He later modiﬁed this thesis in the light of the idealist reading of Leibniz’s whole career offered in Robert M. Adams, Leibniz: Determinist, Theist, Idealist (Oxford, 1994). See Daniel Garber, ‘Leibniz: Physics and Philosophy’ in Nicholas Jolley, ed., The Cambridge Companion to Leibniz (Cambridge, 1995), 270–352; and idem, ‘Leibniz and Fardella: Body, Substance, and Idealism’, in Paul Lodge, ed., Leibniz and his Correspondents (Cambridge, 2004), 123–40. Much of this material has now been collected together in book form: Garber, Leibniz: Body, Substance, Monad. 19 In the middle decades of the seventeenth century there were a number of Aristotelians who sought to reconcile Aristotle with mechanism. The books published by this group include Jacques Du Roure, La physique explique´e suivant le sentiment des ancients et nouveaux philosophes (Paris, 1653); Johannes de Raey, Clavis philosophiae naturalis sive Introductio ad contemplationem naturae aristotelico-Cartesiana (Leiden, 1654); Jean-Baptiste Du Hamel, De consensu veteris et novae philosophiae (Paris, 1663); Rene´ Le Bossu, Paralle`le des principes de la physique d’Aristote & celle de Rene´ Des Cartes (Paris, 1674). Leibniz had studied in Jena in the summer of 1663 with Erhard Weigel: see Konrad Moll, Der junge Leibniz (2 vols., Stuttgart/Bad Canstatt, 1978–82), i. 42–59; and more generally on Weigel, Hestermayer, Paedagogia Mathematica. Weigel contributed to Leibniz’s view of the late 1660s that the true reformers of philosophy were those who sought to reconcile modern philosophy with that of Aristotle. See Stuart Brown, ‘The Seventeenth-Century Intellectual Background’, in Nicholas Jolley, ed., The Cambridge Companion to Leibniz (Cambridge, 1995), 43–66: 47–8; and Antognazza, Leibniz, 50–67.

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matter is inert, Leibniz notes that as such it cannot act as a source of motion, and the question therefore arises what the source of motion is. This is a problem that goes to the heart of mechanism. When Descartes ﬁrst formulated his physical and cosmological system, in Le Monde, he thought it through in terms of quasidynamical notions derived from hydrostatics, and indeed it was these hydrostatical origins of his cosmological thinking that motivated him to think in terms of bodies being moved by ﬂuids, rather than as moving through empty space. Abandoning Le Monde in the wake of the condemnation of Galileo, however, he returned to physical and cosmological questions only a decade later, in his Principia, in which he translated the whole project into ‘clear and distinct’ terms, and the principal casuality was dynamics because forces were not something he was able to formulate in these terms.20 The exercise became one in kinematics, and this was how Huygens and Malebranche, for example, saw matters. Now it was a commonplace among seventeenth-century natural philosophers that God was the ultimate cause of motion in the cosmos, but Descartes’ Principia, in abandoning talk of forces, in effect made God the proximate source of all motion. Indeed, when Descartes’ doctrine of the continual recreation of the universe is taken into account (a doctrine motivated by the view that bodies do not have powers, even the power to maintain themselves in existence21), the picture that emerges is that of God recreating the universe at every instant with bodies in slightly different arrangements, so that all (apparent) motion is directly due to him. But the idea of God as the direct and immediate source of all motion in the universe, subsequently reinforced in the occasionalist development of Cartesianism, was highly counter-intuitive. There were some, such as Newton, who saw a need for God’s direct intervention (in maintaining the long-term stability of planetary orbits for example) on occasion, but the routine behaviour of bodies was considered to be due to causes—typically in the form of forces— inherent in bodies themselves. The problem was that the inertness of matter seemed to preclude the existence of such intrinsic forces. Leibniz believed that a fundamental rethinking of the notion of a body was required if an answer to this question was to be found. His strategy was to retain what he took to be true in the mechanist conception, but to go beyond it in order to make sense of how something passive like matter can move in the ﬁrst place. What makes something a body and hence a corporeal substance, rather than just a piece of matter, on Leibniz’s account, is mind, because mind provides a principle of activity,22 something that is a source of change and motion in the body: ‘Something is substance when taken together with a concurrent mind; 20

I dealt in detail with the questions canvassed here in Emergence, chs. 8 and 11. Descartes, Œuvres, vii. 48–9 (Meditation III). 22 Rutherford has pointed out—Leibniz and the Rational Order of Nature, 36–40—that it was a fundamental assumption of Leibniz’s idea of universal harmony that everything was active, and that this was a doctrine he took from the work that largely shaped his idea of universal harmony: Johann Heinrich Bisterfeld’s posthumously published Philosophiae Primae Seminarium (Leiden, 1657). 21

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something taken apart from concurrent mind is accident. Substance is union with mind. Thus the substance of the human body is union with the human mind, and the substance of bodies which lack reason is union with the universal mind, or God. The idea is the union of God with creature.’23 Mind here provides the form of the body, so that bodies in nature have identities in their own right, provided by their forms, and human beings have a special kind of identity because their forms are human minds. Matter, reduced to its basic mechanical and geometrical features, is a bearer of, or the vehicle for, properties such as hardness and impenetrability, not the source of these. To understand the source, we need to think of matter more in Aristotelian terms as a substratum on which or through which something non-material can act. But the problem with this account, as Leibniz quickly came to realize, was that what it was that made non-human substances substances in the ﬁrst place was not something intrinsic to them, but something extrinsic, God. As a consequence, the motion, impenetrability, and other physical qualities that they manifested were not their motion or their qualities because they did not follow from their natures. The beneﬁts that the adoption of an Aristotelian account of substance were supposed to deliver, in the form of a principle of internal activity and differentiation, had been negated by the substitution of God for internal principles. In response to these difﬁculties, in 1669 Leibniz began to reformulate his notion of substance.24 The driving issue was still the need for a reconciliation between mechanism and Aristotelian natural philosophy, and he identiﬁed the need for such reconcilation by means of what he saw as a number of ﬂaws in the mechanist account, three of which are worthy of note here. The ﬁrst concerns the nature of solidity. The Cartesian plenum was especially problematic in this respect: the movement of celestial bodies was movement in a rotating ﬂuid, but it was difﬁcult to understand just what allowed such bodies, which are made up of constituent corpuscles, to remain intact. The classical atomists had postulated atoms with hooks, but the Cartesian tradition, amongst others, had dismissed this, considering that bulk (variously conceived as weight or volume), speed, and direction of motion were all that could be invoked in explaining the physical behaviour of bodies, at least at the mechanical level.25 Descartes had considered adhesion to be simply a matter of bodies continuing to be in a stationary state with respect to one another, yet solid bodies reduced to a powder 23 ‘On Transubstantiation’: Philosophical Papers, 116. Cf. Leibniz to Jacob Thomasius, 30 April 1669: phil. Schriften, i. 15–27. 24 See Christia Mercer and R. C. Sleigh, Jr., ‘Metaphysics: The Early Period to the Discourse on Metaphysics’, in Nicholas Jolley, ed., The Cambridge Companion to Leibniz (Cambridge, 1995), 67–123: 76–84. 25 The requirement was loosened somewhat when it came to meteorological phenomena and phenomena such as magnetism and static electricity. See Gaukroger, Descartes’ System of Natural Philosophy, ch. 6.

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remain in a powder form when the parts are pressed together. Moreover, the ability of solid bodies to resist giving way to smaller bodies, to be reﬂected off larger bodies, and to exhibit various distinct tactile qualities, are not things that can be explained simply by reference to relative motion.26 The second ﬂaw identiﬁed by Leibniz concerned the standing of motion. For mechanists, the basic constituents of the world were matter and motion, but we can envisage a universe in which matter would be at rest, so motion is in no way part of the essence of matter, and matter could not be the source of motion either. The Epicurean tradition had treated the ultimate constituents of matter, atoms, as moving perpetually at the greatest possible speed, but seventeenthcentury atomists such as Gassendi and Hobbes needed their atoms/corpuscles to move at different speeds, since it was variation in speed, along with differences in bulk and direction of motion, that played the key role in microscopic interactions. Moreover, Gassendi, in making atomism compatible with Christianity, had made physical processes dependent on God in some ways, not least in that they received their initial motion from God. Decartes, as I have indicated, had also talked of God conferring an initial amount of motion on the universe, which was then conserved, being redistributed from instant to instant in accord with basic laws of nature. Leibniz points out that if God, and not matter, is the source of motion, then motion cannot be a property of matter.27 To make motion a property of matter we need to adopt the Aristotelian idea of inherent principles of change in bodies, something that requires us to think of bodies as things that go beyond matter, for it is bodies, not matter, that have a source of activity within themselves, and this source of activity can only be conceptualized through the notion of substance: it is because bodies are substances that they have an inherent source of activity, something lacking in matter, which is not a substance. Substances are self-sufﬁcient in that their behaviour follows from their natures, but the motion of matter does not follow from anything about the nature of matter, which consists simply in extension. Finally, there is the question of how bodies that were characterized solely by extension and impenetrability would behave in collision. Descartes had claimed that a smaller moving body striking a larger stationary one would rebound with no change of speed, leaving the larger one stationary, but Leibniz notes that unless we include the dynamic notion of resistance, the extension and impenetrability of the larger stationary body alone would not enable it to offer resistance to the motion of the smaller body, with the result that the smaller body would impart its velocity to the larger one.28 There were a number of natural philosophers in the second half of the seventeenth century who, while not wishing to abandon mechanism, considered 26 27 28

‘Confessio naturae contra atheistas’ (1669), phil. Schriften, iv. 108. Leibniz to Jacob Thomasius, 30 April 1669: phil. Schriften, i. 25–6. Discours de metaphysique, }21.

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it incomplete in some way or another. The objection in a writer like Cudworth, for example, was that although mechanism was perfectly adequate as a description of the world at the basic micro-corpuscularian level, as soon as one began to move up from this fundamental level it became clear that increasingly complex goal-directed activities were involved, activities that could not be reconciled with the inertness of matter on which mechanism rested.29 Cudworth in effect envisages three levels of activity: mechanical interactions in which collision results, presumably, in an exchange of motions, and in which there are no intrinsic forces; various vegetative, sensitive, instinctual, habitual, and other forms of activity that require intrinsic forces which guide the activity; and activities that manifest divine guidance or regulation, in which case it is a question of extrinsic causes. The option that Leibniz takes up is quite different from this. For Leibniz, mechanics is not even complete in its own right. In effect, he runs together the ﬁrst two of Cudworth’s levels, reintroducing intrinsic causes at the level of bodies that Cudworth is content to describe purely in mechanical terms. He argues for a general need ‘for something which corresponds to the soul, something which the philosophers have called substantial form, which Aristotle calls ﬁrst entelechy, and which, perhaps more intelligibly, I call primitive force, to distinguish it from secondary force which is termed moving force, and which is a limitation or accidental variation of primitive force.’30 For Leibniz, mechanics deals with discrete bodies interacting and modifying each other’s states of motion, but it does not have the conceptual resources to secure the existence of discrete bodies. This can only be achieved by going down a level, as it were, to the metaphysical underpinnings of the physical level of description. The trouble is that what we ﬁnd at this metaphysical level is an understanding of motion seemingly at odds with that offered by mechanism. What Leibniz seems to want is two complementary realms: ‘I believe that everything occurs mechanically, as Democritus and Descartes would have it . . . but that, nevertheless, everything occurs vitally and in accordance with ﬁnal causes, everything being full of life and perceptions, contrary to the views of Democriteans.’31 The question is how one keeps these realms separate in the 29 Ralph Cudworth, The True Intellectual System of the Universe (2nd edn., 2 vols., London, 1743). 30 First draft of ‘Syste`me nouveau’: phil. Schriften, iv. 473. 31 Leibniz to Thomas Burnett, 1697: phil. Schriften, iii. 217. Compare Leibniz to Des Billettes, 14 December 1696: ‘I believe that everything that occurs in nature occurs mechanically, and can be explained by efﬁcient causes, but that at the same time it also occurs morally, so to speak, and can be explained by ﬁnal causes. The two realms, the moral one of minds and the mechanical one of bodies, interpenetrate and are in perfect accord through the agency of the Author of things, who is at the same time the ﬁrst efﬁcient cause and the ﬁnal end. I claim, then, that just as there is no vacuum in bodies, so nor is there one in souls; that is, there are souls everywhere, and souls, once they exist, cannot perish. Bodies are multiplicities and souls are unities, but they are unities which express or represent the multiplicity within themselves. Every soul is a mirror of the entire world, from its own point of view. But minds are souls of the ﬁrst order or highest genus, which represent not just the world but also God in the world. Thus they are not only immortal but conserve for always their moral qualities as citizens of the Republic of the universe, which lacks nothing because it is ruled by God.’ Phil. Schriften, vii. 451–2.

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requisite domains. It might appear that Leibniz could account for the motion of bodies purely in mechanical terms, and then ask what it is that makes these bodies bodies in the ﬁrst place, keeping this as a separate form of enquiry. The problem is that the Aristotelian forms invoked at the metaphysical level are not neutral with respect to questions of motion: they offer the basic resources behind a general account of change, of which local motion is one species, and in which change is conceived and classiﬁed according to the nature of the termini from which, and to which, it progresses. In other words, the same resources that Leibniz believes allow him to offer an account of bodies, as opposed to the merely arbitrarily designated regions of matter of Cartesian natural philosophy, also place awkward constraints on how one characterizes motions. On the Aristotelian conception, for example, rest is the natural state of bodies, something that does not require a cause, whereas change generally or motion in particular, being a deviation from this natural state, is something that does require a cause. This was a characterization that was rejected in seventeenthcentury mechanics. To understand what was at issue here, we need to understand the role of matter theory in mechanism, and for this we need to distinguish mechanism from mechanics proper. Mechanism was not mechanics but a natural philosophy which, by the second half of the seventeenth century, aimed to combine mechanics and matter theory in order to provide a micro-corpuscularian reduction of physical processes. It is important to appreciate, before turning to his proposed solution, that Leibniz had put his ﬁnger on a genuine problem in mechanism, and there was signiﬁcant uncertainty on the standing of motion and rest among mechanists. On the one hand, as far as matter theory was concerned, there was nothing in the nature of matter either that produced motion or even from which the rules governing it might conceivably follow. The ultimate source of motion, at least in the wake of Descartes’ Principia, was generally taken to be something non-physical, namely God, and the laws governing motion were taken to be independent of the material constitution of bodies: typically, they were taken to be divinely instituted. Moreover, as far as mechanics was concerned, from the point of view of statics, which in the ﬁrst half of the seventeenth century had served very much as a model for dynamics, the idea of equilibrium tended to privilege rest, albeit not as the ‘natural’ state of bodies in the Aristotelian sense. But from a purely kinematic point of view, rest was simply motion that took a value of zero. Indeed, uniform rectilinear motion and rest were on a par across the kinematic tradition by the 1680s, even if there were differences over the absolute or relative nature of space. In the Cartesian relativist tradition as represented by Huygens, whether a body was undergoing uniform motion or at rest was simply a function of what reference frame one chose. Mechanism attempted to reduce all physical processes to the micro-corpuscularian level, and then to describe such processes in purely mechanical terms. In the ﬁrst half of the seventeenth century, in writers like Beeckman, Hobbes, and Descartes, the idea had been above all to mechanize matter theory by subjecting

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it to the rigours of mechanics, but once this process got under way in a serious fashion, in Huygens for example, mechanics began to usurp matter theory as the foundational discipline, something that becomes even more evident by the eighteenth century, when the tradition in rational mechanics encouraged a view of mechanics as very much self-contained, and as providing a complete description of fundamental physical processes. Matter theory came to be displaced as the foundational discipline in this way of thinking, as matter is virtually mechanized out of existence, and, to the extent to which matter theory has a role at all, it acts (often in little more than a promissory role) more as a way of connecting up basic microscopic physical processes with chemical, biological, and other ‘higher-level’ processes. In short, there were two problems. First, for the mechanist, mechanics was supposed to be grounded in some way in matter theory, but matter theory could offer no elucidation of motion, and in any case later in the century microcorpuscular matter theory lost this grounding role so that mechanics was thrown back on its own resources. Second, because the conceptual resources of mechanics had been developed out of statics (notably in the early Galileo and in Descartes) as well as in kinematics (in Galileo’s Two New Sciences and in Huygens), which approached questions of motion in very different ways, there was a residual uncertainty over the relative standing of motion and rest. The success of Leibniz’s solution to the dilemma turns on his ability to neutralize any consequences for motion that might follow from the quasiAristotelian metaphysics that grounds mechanics. His attempt to distinguish real and apparent motions is crucial here. In }18 of the Discours de metaphysique, he writes: For, taking motion in the narrow and formal sense of the term, that is, change of place, it is not something wholly real; when several bodies change position with respect to one another, it is not possible, merely by considering these changes, to determine to which of the bodies motion is to be ascribed and which should be taken to be at rest, something I could demonstrate geometrically if I wanted to dwell on this point now. But the force or immediate cause of these changes is something more real, and there is a basis on which it can be attributed to one body rather than another, and it is only in this way that we know to which body the motion should be attributed. Now this force is something different from size, shape, and motion, and from this we can conclude that not everything in a body consists solely in extension and its modiﬁcations, as moderns would have it.32

Just how we might detect real motions is not so straightforward however. It was common ground among writers on mechanics by the 1680s that rest and uniform rectilinear motion were indistinguishable, because a simple change of reference frame could indifferently allow a body to be designated at rest or in motion. However, Leibniz in this passage raises the question of there being a criterion by 32

Phil. Schriften, iv. 444.

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which one might determine whether a body is really at rest or in motion, which suggests that there might be a fact of the matter independent of our ability to recharacterize the behaviour of a body purely in relation to particular reference frames. Newton, for one, thought that there must be an absolute reference frame, absolute space, by reference to which absolute—i.e., in Leibniz’s terminology, ‘real’—motions could be distinguished from relative ones.33 But Leibniz disagreed, and probing the source of this disagreement will help us understand just what the appropriate criteria of reality were, and whether any motion at all was ultimately going to satisfy them. Newton’s defence of absolute space seems to have been, in the ﬁrst instance, a direct response to Descartes’ deﬁnition of ‘real’ motion—by contrast with ‘common usage’—as ‘the transference of matter or of one body, from the vicinity of those bodies immediately contiguous to it and considered as at rest, into the vicinity of others.’34 In elaboration, Descartes had written: ‘I have stated that this transference is effected from the vicinity, not of any contiguous bodies, but only of those which we consider to be at rest. For the transference is reciprocal; and we cannot conceive of the body AB being transported from the vicinity of the body CD without also understanding that the body CD is transported from the vicinity of the body AB, and that exactly the same force and action is required for the one transference as for the other.’35 In his De gravitatione, Newton identiﬁed numerous inconsistencies that followed from the Cartesian deﬁnition, noting in particular that, on this account, ‘no one motion can be said to be true, absolute, and proper in preference to others, but that all, whether with respect to contiguous bodies or remote ones, are equally philosophical—than which nothing more absurd can be imagined.’36 To remedy these defects, Newton tells us, ‘it is necessary that the deﬁnition of places, and hence of local motion, be referred to some motionless thing such as extension alone or space in so far as it is seen to be truly distinct from bodies.’37 Newton suggested an ingenious thought experiment to establish the existence of such an absolute framework. Because we can always adjust the frame of reference for rectilinear motions so that the body comes out as being at rest, we cannot establish an absolute reference frame here, so Newton turns to rotary motion. If we suspend a bucket of water from a twisted rope, the water being at rest and having a ﬂat surface, and then release the rope, the bucket will spin as the 33 Most notably in the Scholium to the Deﬁnitions at the beginning of the Principia: Cohen and Whitman edn., 408–15. 34 Descartes, Principia, II, art. 25: Œuvres, viiiA. 53. 35 Principia, II. art 29. 36 Unpublished Scientiﬁc Papers of Isaac Newton, 127. On the genealogy of the positive aspects of Newton’s conception of absolute space, see A. Rupert Hall, ‘Newton and the Absolutes’, in P. M. Harman and Alan E. Shapiro, eds., The Investigation of Difﬁcult Things (Cambridge, 1992), 261–86. 37 Unpublished Scientiﬁc Papers of Isaac Newton, 131.

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rope uncoils. At ﬁrst the bucket will spin with respect to the water, which remains at rest and its surface ﬂat. But as the motion of the bucket is transferred to the water, the surface of the water will gradually become concave, rising at the sides and falling in the middle, until the water is at rest relative to the wall of the bucket.38 The question now arises how we account for the concavity of the surface of the water, and Newton argues that this concavity, being due to the centrifugal forces of motion, shows that, in modern terms, the reference frame of the bucket and the water—which are no longer in motion relative to one another—is now a non-inertial one. In the relative motion that we experience just after the bucket starts rotating, the water surface is ﬂat, but now there is no relative motion, so the effect cannot be due to relative motion: it can only be due to absolute circular motion. Absolute motions are true motions and are the result of forces, whereas relative motions are not the result of forces. On the face of it, this is exactly the kind of situation that Leibniz needs to invoke in order to demonstrate the difference between true and relative motions, and exactly the right kind of basis for distinguishing them. After all, like Newton he holds that ‘motion is not the cause, but the effect or result of force’.39 But Leibniz does not count this a case of absolute motion. ‘Rotation’, he maintains, ‘arises only from the composition of rectilinear motions’, and consequently if equivalence of frames of reference ‘is saved in rectilinear motions, however they are assumed, it will also be saved in curvilinear motions.’40 The question of the composition of curves from rectilinear motions involves a number of complexities, but basically what is at issue is this.41 There are a number of ways of generating curvilinear trajectories geometrically. The standard Galilean procedure followed by Huygens and Newton is to consider them as the result of a uniform rectilinear motion and a uniformly accelerated motion. But occasionally, for example in Newton’s polygonal demonstration of Kepler’s area law, we ﬁnd a hybrid form which combines continuous and punctiform representations of the accelerating force, the latter resulting in a polygonal line which becomes a curvilinear one only at the limit.42 Leibniz generally tried to dispense with

38 It might seem that the experiment could be performed easily, and so is not merely a thought experiment. However, the situation described is envisaged to hold for a world empty of everything except a rope, bucket, and water, and, as Mach was to point out in 1883, in the real world we have to take into account the fact that centrifugal forces may be produced by the rotation relative to the earth and celestial bodies: Ernst Mach, The Science of Mechanics (6th edn., La Salle, 1960), 284. On exactly what Newton believed the bucket experiment shows, see Robert Rynasiewicz, ‘By Their Properties, Causes and Effects: Newton’s Scholium on Time, Space, Place and Motion’, Studies in History and Philosophy of Science 26 (1995), 133–53. 39 Leibniz to Jaquelot, 22 March 1703: phil. Schriften, iii. 457. 40 Leibniz, Specimen Dynamicum: Math. Schriften, vi. 253. 41 For further details and references, see Bertoloni-Meli, Equivalence and Priority, 78–84. 42 We looked at this question in the last chapter. See also the discussion in I. Bernard Cohen, ‘Newton’s Second Law and the Concept of Force in the Principia’, in Robert Palter, ed., The Annus Mirabilis of Sir Isaac Newton 1666–1966 (Cambridge, Mass., 1970), 143–85.

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accelerations and use only uniform rectilinear motions. The general principle is set out in his Dynamica of 1689: All motions are composed of rectilinear uniform ones. In fact each motion in itself is uniform and rectilinear, but each action on bodies consists in motion. Thus rectilinear motion can only be curved by the impression of another motion which is itself also rectilinear (and independent of the one it is impressed on), so that the origin of curvilinear and non-uniform motion can be understood only in terms of the compositions of rectilinear uniform motions.43

A good practical example can be found in a 1706 paper where he provides continuous and discrete analyses of a curvilinear motion, showing their equivalence.44 In Fig. 3.2, a circumference centred in C and the inﬁnitesimal arc AG, there are two ways of conceiving motion along the arc. The ﬁrst is what we might term the standard way: we think of it as a uniform rectilinear motion along the tangent AD and a uniformly accelerated motion along DG. Alternatively, we can think of it as a uniform rectilinear motion along AF, which is the prolongation of the chord EA, and along FG (equal to AH ). Because EA¼AF, the arcs EA and AG are traversed in equal times. Both alternatives give the same result for the central force because the factor ½ involved in the choice of DG rather than FG cancels out the factor of ½ resulting from the motion along DG being uniformly accelerated. Leibniz consistently preferred the latter procedure, that in which curves are constructed from rectilinear motions, and the equivalence of the two is what motivates his rejection of the Newtonian interpretation of the bucket experiment. What then is a real motion for Leibniz? Like Newton, he associates real motions with real forces. However, not only do the real forces he allows not correspond to those envisaged by Newton, but the extent to which these forces can be captured in purely physical terms is deeply problematic. Forces bridge Leibnizian metaphysics and Leibnizian physics, but given what is at times a signiﬁcant distance between the two, such bridging does not always make for clarity, and the question arises whether it could ever be any more than a promissory note.45 L E I BN I Z I A N D Y N AM I C S Newton and Leibniz each created his own system of dynamics, and Leibniz’s Tentamen de Motuum Coelestium Causis, which appeared at the beginning of 43

Math. Schriften, vi. 502. Ibid., vi. 277–8. See Richard Arthur, ‘Cohesion, Division and Harmony: Physical Aspects of Leibniz’s Continuum Problem (1671–1686)’, Perspectives on Science 6 (1998), 111–35. 45 Cf. Donald Rutherford, ‘Leibniz on Inﬁnesimals and the Reality of Force’, in Ursula Goldenbaum and Douglas Jesseph, eds., Inﬁnitesimal Differences: Controversies between Leibniz and His Contemporaries (Berlin, 2008), 255–80. 44

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1689, was a direct response to Newton’s Principia.46 Leibniz accepted Newton’s mathematical account of planetary motions, and his aim was to offer an alternative which, accepting Kepler’s laws and inverse square attraction, nevertheless went beyond Newton in providing what he considered a physically satisfactory account. What was physically unsatisfactory about the Newtonian explanation was its invocation of gravitational attraction at a distance, which Leibniz considered an occult quality, and therefore lacking in any explanatory value. In its place, he argued that the physical cause of the motion of the planets had to be accounted for in terms of a ﬂuid rotating around the sun in a vortical motion. In his marginal notes on the Principia, for example, he speculates whether the gravitation/centipetal force/void account offered by Newton might not be translated into an elasticity/centifugal force/ﬂuid vortex account: [I question] whether it may be in agreement with the nature of things, that the further a body is from a centre, so the more strongly it tends to it, and is to be regarded almost an elastic substance receding more and more from its natural state. Indeed, this operation of magnetic attraction would be contrary to such a notion, which would be strengthened if gravity arose not from the attraction of the central body but from the impulse of a vortex.47

But this was not just a question of replacing one model for another. Newton and Leibniz conceived of force differently, although they shared a commitment to the idea of the unity of force. Newton was concerned above all with external forces, which he conceived as external impacts: it is in his modelling of continuous forces on forces of impact in the polygonal proof of Kepler’s area law, as well as in 46 The most comprehensive discussion of the Tentamen is that offered in Bertoloni-Meli, Equivalence and Priority, which has an annotated translation of the text, 126–42. 47 Marginal Note 48, quoted in Bertoloni-Meli, Equivalence and Priority, 53–4.

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his treatment of the relation between impressed force and innate force in De motu and then in the Principia, that he most clearly manifests a commitment to an essential unity of force. This force can be transferred from one substance to another, and it can be manifest in a variety of forms, most notably quantity of motion, resistance, and weight. Leibnizian dynamics, by contrast, is concerned with internal forces, paradigmatically the force of a body in motion.48 Underlying this is Leibniz’s conception of the unity of force, in which unity is even more explicitly at stake than it is in Newton. If one were to conﬁne oneself to a practical level, such unity would be wholly unattainable, and it is important to bear in mind that one of the things that Leibniz’s metaphysical grounding of force seeks to achieve is a coherent and systematic rationale for the unity of force, something questionable (indeed increasingly questionable as the eighteenth century progresses) at the level of physics. Leibniz wants to provide a coherent account of force at the level of mechanics, of course, but since mechanics is not viable without a conception of body which it cannot itself provide, it is reliant on an understanding of force which bridges the metaphysical and the physical by providing both substantial unity and physical cause, and this has implications for the autonomy of mechanics. Indeed, Leibniz’s approach ends up pushing mechanics into the phenomenal realm, a phenomenal realm that, as his thinking develops, becomes distanced from what he considers to be the underlying reality. Although he had an interest in mechanics dating back to the end of the 1660s, Leibnizian mechanics effectively began with his ‘Brevis demonstratio erroris memorabilis Cartesii’ of 1686. The paper deals with the question of what quantity is conserved in physical interactions, and whether this quantity can be identiﬁed with force. Descartes had argued that ‘quantity of motion’, namely the product of the bulk of a body and its speed/velocity (usually designated mv, or more accurately m |v|, although these are a little too precise for the Cartesian notion), is what is conserved in collisions between bodies, and the Cartesian tradition had followed him in this. Leibniz sets out to show that this cannot be what is conserved. He begins with two uncontentious assumptions. The ﬁrst is that a body falling from a particular height acquires the same force necessary to lift it back to its original height, a phenomenon evident in the motion of the pendulum, and a basic tenet of seventeenth-century mechanics. The second is the Cartesian assumption that the force required to lift a body of one pound, A, through four yards is equal to that required to lift a body of four pounds, B, through one yard. By the ﬁrst premiss, A and B both acquire the force required to return them to the same height. By the second, at their lowest points, the forces of the two bodies are equal. Now if the forces were proportional to the product of weight and velocity, as Descartes 48 The contrast is explored in Westfall, Force in Newton’s Physics, chs. 6–8; and J. Christiaan Boudri, What Was Mechanical About Mechanics: The Concept of Force between Metaphysics and Mechanics from Newton to Lagrange (Dordrecht, 2002), chs. 2–3.

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maintained, the velocities at the lowest points would be in the proportion 4:1. But Galileo’s law of falling bodies shows that distance traversed in fall is proportional to the square of the resulting velocity at any point: that is, 2:1 not 4:1. The Cartesian measure of force would mean that B would rise not four feet but sixteen feet, which is a violation of the basic principles of mechanics.49 The only conclusion possible, in Leibniz’s view, is that quantity of motion is not a measure of the force involved: Of course I agree that a judgement about the force of a body is possible based on a given time or on its reciprocal, the velocity, or on other known circumstances. What I am saying is that it is neither the time nor the velocity but the effect alone that is an absolute measure of force, for when the force remains the same the effect remains the same, and neither the time nor other circumstances can vary it. Hence it is not surprising that the forces of two equal bodies are proportional not to their velocities but to the causes or effects of their velocity, that is, to the heights producing them or capable of being produced by them, or to the squares of their velocities. Consequently, it also follows that when two bodies collide, what is conserved in the wake of the collision is not the same quantity of motion or the same impetus, but the same quantity of force. It also follows that a string must be stretched by a fourfold weight to produce a tone twice as high, for the weight represents the force, and the sound represents the velocity of the vibrations of the string. The fundamental reason, however, is that motion is not something absolute and real in itself.50

In fact, Huygens had shown as early as 1669 that the product of bulk/mass and speed could not be a general measure of the force in collision as Descartes had supposed, for while Descartes had treated the motions as scalar quantities, they were conserved only if they were directed quantities, that is, where motions in opposite directions were not summed but subtracted from one another. What was conserved for Huygens was something explicitly relative to reference frames, however, rather than something in bodies themselves, and Leibniz argued that this could not be what stopped the universe running down. Rather, it had to be something ‘absolute’, namely the product of the bulk/mass and the square of the velocity. This measure of force—a force that Leibniz termed vis viva—was ‘absolute’ in the sense that one does not subtract opposite motions, so the quantity of motion is genuinely preserved, not preserved merely as a result of adjusting reference frames. It is the kind of thing that God could have ﬁxed at the creation of the world, and which could then be conserved as an absolute quantity. Indeed, it is this conservation that lies at the basis of Leibniz’s 49 The argument in fact trades on an equivocation in the notion of force, as the subsequent history of mechanics will bear out. The force acquired in falling is kinetic energy, whereas the force acquired by the body in rising to its starting point is potential energy, and the ﬁrst assumption states the equality of these two. But these are not the forces that are at issue in the second assumption: here what is at issue is work done, which is quite different. In fact both energy (1/2mv2 not mv2) and momentum (mv) are conserved, and the question hinges on whether one integrates forces with respect to distance (yielding energy) or time (yielding momentum). 50 Math. Schriften, vi. 122–3.

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rejection of Newton’s idea that an input of force is required to stop the cosmos running down. The point certainly does not settle the issue between Newton and Leibniz, however, because Newton’s claim with respect to collision was that conservation does not hold in the case of inelastic collisions, and vis viva would seem to be lost in inelastic collisions. In the ﬁfth letter to Clarke, Leibniz denies there is any loss: The Author [Clarke] objects, that two soft or un-elastick Bodies meeting together, lose some of their Force. I answer, No. ’Tis true, their Wholes lose it with respect to their total Motion; but their Parts receive it, being shaken by the Force of the Concourse. And therefore that Loss of Force is only in Appearance. The Forces are not destroyed, but scattered among the small Parts. The Bodies do not lose their Forces; but the Case here is the same, as when Men change great money into small.51

He goes on to claim that he agrees with Newton that the ‘quantity of motion’ (mv) changes, but notes he has shown elsewhere that there is a difference between quantity of motion and quantity of force (vis viva, measured by mv2). But this is hardly a satisfactory reply, since it is not as if Newton and Clarke are confusing the two: as Leibniz himself acknowledges, they explicitly argue that force is not conserved but lost. The point is that, at an empirically detectable level, ‘force’ (mv2) is not conserved in inelastic collisions. We can make a little more sense of Leibniz’s claims here if we think of his account not so much as a reaction to Newton, although that provides its context here, but in terms of its original context, as a reaction to Huygens. Leibniz had undoubtedly learned of the conservation of bulk/mass and the square of the velocity from Huygens, but Huygens had mentioned the result only in passing, according it no special signiﬁcance, whereas Leibniz wants to make it the centrepiece of his dynamics. Huygens’ antipathy to talk of forces would have disinclined him to distinguish between motion and force of motion, but this is precisely the distinction that Leibniz needs, and is what he sees as the key to the enterprise. The issues here are of importance independently of the dispute with Newton and Clarke over inelastic collisions. Huygens had in effect uncoupled general mechanics from statics: in the simple machines that statics studies, the force of the body is indeed proportional to the product of mass and velocity, but this turns out to be a special case in mechanics, not a model for the discipline. In Huygens’ view, the model for the discipline must be kinematics itself, and forces must be reduced out of kinematics as far as possible, for forces do not yield to the Cartesian criteria of clarity and distinctness that must ultimately regulate physical theory.52 Leibniz moves in the opposite direction. Noting that statical forces must be abandoned as a general model if, as it turns out, these cases lack the general application they had been thought to have, he 51 52

Clarke, Works, iv. 662 (Fifth Reply, section 99). See Gaukroger, Emergence, 420–30.

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sets out to forge a dynamics in which the forces underlying the behaviour of bodies can be examined independently of the motions to which they give rise, and he conceives this as a fundamental discipline independent of statics.53 The way in which he sets about pursuing this question, however, in effect makes dynamics not the core of mechanics, as is the case with Newton for example, but a discipline that in many respects transcends mechanics, in the end completely transcending it to the extent that mechanics no longer actually describes reality at all. Newton, as we have seen, believed that there was a difference between absolute and relative motions, even though uniform rectilinear motions were indistinguishable, because the former were the product of real forces, which one could detect in the case of rotary motion. Leibniz, by contrast, believed that our inability to distinguish between what he refers to as ‘real’ motions and apparent ones told us something profound about the nature of motion itself. If it made no sense to talk of some motions as real, then motion itself could not be a selfcontained or autonomous phenomenon. And if motion could not be an autonomous phenomenon, then the discipline that concerned itself with motion, mechanics, could not be a self-contained or autonomous discipline. Motion reﬂects dynamic interchanges, and perhaps those dynamic interchanges can be inferred from motion on occasion, but the real, absolute activity occurs at the level of forces, not at the level of motion. What then are we to make of the positive side of Leibniz’s argument? In rejecting mv as the measure of force, at the same time he appears to replace it with a new value, mv2. But if mv2 is the measure of force, a measure that directly relates motion and force, how is this compatible with the claim that motion has no reality? Leibniz wants to quantify forces, and to do this, he needs to relate forces to the magnitude of the effect that they produce. He makes this compatible with the rejection of the reality of motion by making mv2 a derivative magnitude, insisting that the effect of the force is the increase in height, the velocity being strictly secondary to this: ‘since no velocities may actually be produced, the forces are proportional to the heights which might be produced by these velocities.’54 Moreover, as he makes clear later in ‘De ipsa natura’ of 1693, what is actually conserved is not mv2 but a force measured by mv2: ‘The foundations of the laws of nature must not be sought in the conservation of the same quantity of motion, as had commonly been believed, but rather in the necessity of the same quantity of active power being conserved.’55 But as it stands this is little more than a patch, and matters become more pressing when Leibniz 53 We owe the term ‘dynamics’ to Leibniz, although he used it in a rather restricted sense: it is only in d’Alembert, Traite´ de dynamique (Paris, 1743), that we ﬁnd the term used in its full modern sense. 54 Math. Schriften, vi. 119. 55 Phil. Schriften, iv. 505–6.

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subsequently comes to differentiate forces, which he does in the ‘Specimen dynamicum’ of 1695. The ‘Specimen’ begins by setting out what force is. Leibniz tells us that it is what there is in nature besides extension, and it has a striving (conatus) or effort (nisus) ‘which exercises its full effect unless impeded by a contrary conatus’. Moreover, this force ‘constitutes the innermost nature of body’. The idea that motions might play a real role in physical processes, on the grounds that motions only ever arise from other motions already existing in the body or acting on it from outside, is dismissed on the grounds that ‘motion in its exact sense never exists, because the whole does not exist if it has no coexisting parts. Thus there is nothing real in motion itself except that instantaneous state which must consist in a force striving towards change.’56 Leibniz construes this claim as making sense of Aristotelian forms in a way that reconciles them with recent developments in physical theory, although the commitment to instantaneous states is reminiscent of Descartes’ instantaneous tendencies to motion rather than motions themselves, something that likewise derives from dynamic considerations, except that in Descartes’ case these dynamic considerations are modelled wholly on statics. Leibniz’s taxonomy of forces is far from straightforward, and it will be helpful to start with a schematic version of his classiﬁcation. There are two basic divisions: primitive/derivative and active/passive. Primitive forces act at the level of substance, whereas derivative forces are manifestations of these forces at the phenomenal level. Basic laws and principles in natural philosophy, for example, work in terms of derivative forces, not in terms of primitive ones.57 The active/ passive distinction is a little more complex but, basically, active forces have to do with motion, whereas passive forces have to do with resistance to motion. Active forces can be further subdivided into living forces and dead forces, living force giving rise to uniform motion, dead force to acceleration. This gives us a number of different kinds of force, and we can use these to explore the interface between metaphysics and physics in the Leibnizian scheme. We must bear in mind, however, that Leibniz is not just trying to set out a satisfactory physical theory. He sees his project as reconciling Aristotelian metaphysics/natural philosophy and contemporary natural philosophy, and this lies at the heart of the exercise, introducing what, from the point of view of physical theory alone, are unnecessary and unwanted ambiguities and complications. But these are part and parcel of the Leibnizian uniﬁcation of knowledge, which necessarily involved a reconciliation of Aristotelian/scholastic views with new developments in natural philosophy, and it is precisely the idea of a comprehensive uniﬁcation of knowledge—and what role natural philosophy plays in such a

56

Math. Schriften, vi. 235. On the complex standing of derivative forces, see Gueroult, Dynamique et Me´taphysique Leibniziennes, ch. 7. 57

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uniﬁcation—that interests us. Consequently, even if we could remove the ambiguities and complications engendered by the eclectic aims that accompany this project, there is much to be gained in trying to make sense of the project as a whole. In the light of this, it is important that we try to track how the various permutations capture something in the Aristotelian conception and in that of contemporary mechanics. Consider ﬁrst the contrast between primitive passive force and primitive active force. In terms of the Aristotelian/scholastic system, the analogues here are prime matter and form/soul/entelechy. In Aristotelian natural philosophy prime matter is most consistently seen as a limiting notion, namely what one has left after all the properties, attributes, etc. of a thing are removed. What is left is a substratum, a potential bearer of properties and nothing else. However, since such a substratum is not nothing—something that was literally nothing could not be a bearer of properties—there is a temptation to hypostatize prime matter into a kind of ‘stuff ’, namely the most basic kind of ‘stuff’ that can have properties. This most basic kind of stuff is not Cartesian material extension, or even pure spatial extension, but ‘what it is that brings it about that one body is not penetrated by another,’ which Leibniz explicitly equates with prime matter.58 Primitive active force, he tells us, ‘is just the ﬁrst entelechy, corresponding to the soul or substantial form’.59 The combination of these two, prime matter and ‘the ﬁrst entelechy, or generally the form of substance’, yields or constitutes ‘corporeal substance, something which is a genuine unum per se, not a mere aggregate of several substances’.60 One crucial thing here, then, is that this account of primitive forces yields genuine criteria of unity and identity for bodies, and this, as we have seen, is something which Leibniz believes that mechanics alone cannot supply. In moving from primitive forces to their derivative correlates, therefore, we are supplying mechanics with its raw materials, and using the correlates of the metaphysical forces that shape these raw materials to account for the physical behaviour of these raw materials. Of course, there remains a question as to the extent to which there can be metaphysical forces in the ﬁrst place: forces surely belong in the realm of physics. Perhaps Aristotelian forms can be seen in dynamic terms, but prime matter is an unlikely contender for this nomenclature since it was traditionally what was left once one had removed everything else. But the association of prime matter and impenetrability—something encouraged by Scotist and Ockhamist notions of matter and form, whereby they have a greater capacity for independent existence than on the Thomist conception—combined with an eclectic running together of Aristotelianism and seventeenth-century matter theory, does yield something that can be conceived in dynamic terms. Moreover, in a letter to Arnauld of 9 October 1687, Leibniz suggests that it is a

58

Math. Schriften, vi. 237.

59

Ibid., vi. 236.

60

Phil. Schriften, iv. 395.

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body’s impenetrability that is the cause of its spatial extension, thereby enhancing its dynamic aspect.61 In their manifestations in the physical realm, these forces become derivative forces. Derivative forces are the forces ‘by which bodies actually act and are acted upon’ and they are manifested in motions. In particular, derivative active forces act ‘in various ways through a limitation of the primitive force that results from the conﬂict/interaction of bodies with one another’.62 Leibniz makes it clear right from the beginning of his discussion that there are two kinds of derivative active forces.63 Dead forces, which he describes as a ‘solicitation to motion’, are actually more accurately described as a solicitation to acceleration, and he identiﬁes centrifugal and centripetal forces as dead forces, as well as the force by which a stretched elastic band restores itself. Living forces, by contrast, are associated with actual motion: ‘when we are dealing with impact, which arises from a heavy body which has already been falling for some time, or from a bow that has already been restoring its shape for some time, or from a similar cause, the force in question is living force, which arises from an inﬁnite number of continual impressions of dead force.’64 The obvious analogues for dead and living forces at the level of an Aristotelian metaphysics are potentiality and activity (in the sense of realization of this potentiality) respectively. But if this were all there was to the matter, it would be a mystery how there could be uniform motions, for the analogue of dead force is a tendency to acceleration, and a tendency to acceleration would presumably always produce just that, an acceleration. Moreover, derivative forces, as Leibniz points out on a number of occasions, lie within the subject matter of physics, which makes them subject to quantitative determination. In particular, as we saw in the discussion of Descartes’ account of the conservation of the quantity of motion, Leibniz argues that it is not quantity of motion but living forces that are conserved. But Leibniz’s metaphysical gloss makes it difﬁcult to understand how they can be conserved. In the Cartesian case, bodies interacting are supposed to simply exchange quantities of motion according to the rules of collision. Just how a body can alienate some part of its quantity of motion, especially when this is considered a mode of the body—for all intents and purposes one of its properties—remained one of the sore points of Cartesian natural philosophy. Leibniz’s Aristotelian metaphysics exacerbates the problem, for forces are very explicitly inalienable from the body. They can of course be conserved in the sense that nothing actually happens in interactions, but this would hardly be a way of providing metaphysical grounds for physical processes: there just wouldn’t be any physical processes in the world it described. Leibniz needs some way of allowing bodies to interact and inﬂuence one another’s motion without there being an actual exchange of forces. In a letter to De Volder of 20 June 1703, he 61 64

Ibid., ii. 120. Ibid., vi. 238.

62

Math. Schriften, vi. 236.

63

Ibid., vi. 238.

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writes that the force is conserved in each body in collision relative to the centre of mass of the colliding bodies.65 But this would seem to privilege particular reference frames—those in which velocities are equal and opposite before and after impact—over others: if we were to choose another reference frame, the living forces of separate substances may in fact alter.66 Passive forces offer even greater problems. In the case of primitive passive force, perhaps we might expect that it becomes translated from the power of impenetrability into the derivative force by which a body resists a change of state not merely through indifference but through the exercise of a force to maintain it in the state that it is in.67 Yet the distinction between primitive and derivative forces here is unclear. Primitive force is described in the ‘Specimen dynamicum’ as not merely the force of impenetrability but also the force of opposition to motion and the force by which that of bodies that act upon it is diminished.68 But this sounds very much like a physical force: how, we may ask, do metaphysical substances move, and how are they acted upon by other bodies? Leibniz talks of ‘the derivative force of being acted upon’ showing itself ‘to different degrees in secondary matter’,69 that is, in particular corporeal bodies. But this doesn’t help us understand how a metaphysical force becomes a physical one, or why the metaphysical force is described in such physical terms. Indeed, not only are the terms physical, they also suggest something active rather than passive, and in ‘De ipsa natura’ he characterizes a body’s resistance to changes in its state of motion in terms of perseverance in motion,70 something that, in his own terms, is due to active force, not passive force. There can be little doubt that here the attempt to incorporate the discussion of force into a comprehensive system has failed completely, and instead of grounding physical forces, the supposed metaphysical grounding in effect takes the physical forces as given and seeks to ‘metaphysicalize’ them.71 But this is the exact opposite of what should be happening: the metaphysics is supposed to reveal to us the basis for the physical manifestation of the force. A good part of the problem here seems to derive from the fact that Leibniz is working with impossible constraints. On the one hand, he cannot allow the 65

Phil. Schriften, ii. 251–2. See the discussion in Boudri, What Was Mechanical About Mechanics, 94–5. Phil. Schriften, ii. 170. 68 Math. Schriften, vi. 236–7. 69 Ibid., vi. 237 70 Phil. Schriften, iv. 510–11. 71 Compare his comment to Wolff in a 1711 letter: ‘You ask how the primitive force may be modiﬁed, for example, when a weight has its motion accelerated during fall. I reply that the modiﬁcation of the primitive force that is in the monad is best explained by explaining how the derivative force may be changed in the phenomena. What is manifest at the level of extension and mechanics in the phenomena is what is in monads in a concentrated and vital way.’ Leibniz, Briefwechsel zwischen Leibniz und Christian Wolff, ed. C. I. Gerhardt (Halle, 1860; repr. Hildesheim, 1963), 138. 66 67

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mechanical story that he wants to tell to be undermined by the underlying quasiAristotelian metaphysics, no matter what physical implications the latter may have. But on the other hand, because of the absolute priority of metaphysics, because it reveals to us the sole source of physical behaviour, he cannot use the mechanics to discover what the metaphysics must be like. Even though the metaphysics is supposed to ground the physics, it is difﬁcult to see how the two can genuinely bear on one another under these circumstances. At best, they seem to run in tandem. At worst, the one is reduced to the other, as in the brief paper on ‘the method distinguishing real from imaginary phenomena’, where we are told: ‘Concerning bodies, I can demonstrate not only that light, heat, colour, and similar qualities are apparent, but also that motion, shape, and extension are. And the only thing that is real, if anything is, is the force of acting and of being acted on, and therefore the substance of body consists in this (as it were, in matter and form).’72 This paper probably dates from the 1690s, and indeed it indicates the direction that Leibniz’s thought takes in the late 1690s, as, with the introduction of the doctrine of monads, reality becomes conﬁned to the metaphysical level, and the physical level becomes purely phenomenal, or, as Leibniz himself prefers to put it in a letter of late 1704/1705, ‘In fact I do not eliminate the physical, but rather reduce it to what it is.’73 DEMONSTRATION: GEOMETRY VERSUS ANALYSIS Leibniz’s phenomenalism was motivated by mathematical as well as physical considerations, if only because his understanding of the nature and role of mathematics played such a central role in his conception of physical theory. The application of very abstract formal algorithms to questions in physical theory, initiated by Leibniz and fostered among a group strongly inﬂuenced by Malebranche, changed its standing quite radically, and there was a sharp divide between how Newton and his British successors conceived of natural philosophy and how his continental contemporaries and successors conceived of it. The issues turn around the standing of calculus, and three sets of questions are entangled in the mathematical issues here: Newtonian versus Leibnizian notations, analytical versus synthetic methods, and limit procedures versus differential equations. When, in the course of the 1740s, dissatisfaction with the 72

Phil. Schriften, vii. 322. Ibid., ii. 275. Compare Leibniz’s remarks inscribed on the back cover of his copy of Berkeley’s Treatise Concerning the Principles of Human Knowledge. ‘There is much here that is right and agrees with my views’, he writes, but Berkeley expresses himself too paradoxically, ‘for we do not need to say that matter is nothing; rather, it sufﬁces to say that it is a phenomenon like the rainbow . . . i.e. nothing but an order of coexistences.’ Text in Willy Kabitz, ‘Leibniz und Berkeley’, Sitzunsberichte der preußischen Akademie der Wissenschaften: Philosophische-historische Klasse 24 (1932), 623–36: 636. 73

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Principia was such that it began to be signiﬁcantly revised, reworked, and rewritten, the dissatisfaction sprang from a perceived need to replace the synthetic mode of working through problems and the use of limit procedures with an analytic way of proceeding which used differential and integral calculus, employing the Leibnizian notation.74 I shall focus on Leibniz and the development of Leibnizian calculus, dealing with Newton only with regard to those respects in which he differs from Leibniz signiﬁcantly. Our primary interest is of course in natural philosophy, not mathematics, but this particular mathematical development is so important for physical theory in the wake of the Principia that some discussion of its fundamentals is necessary. With his 1684 paper, ‘Nova methodus pro maximis et minimis’, Leibniz was the ﬁrst to deal explicitly with the rules of calculus, raising a profound and longstanding problem about the requirements of mathematical demonstration, a problem that turned on the question of whether a mathematical proof should just secure the conclusion on the basis of the premisses, or whether it should also reveal to us how the conclusion is generated. Descartes, for example, in his mathematical work of the 1620s, had extolled the virtues of algebraic analysis over geometry75 on the grounds of the transparency of algebraic proofs, which revealed the path by which the conclusion was generated, by contrast with geometrical proofs, which were generally obliged to follow a very indirect path, one which took us through all kinds of auxiliary constructions needed for the demonstration of the result.76 Once inﬁnitary mathematics was introduced into the picture, matters became signiﬁcantly more complex, because inﬁnitesimal quantities did not behave like ordinary arithmetical quantities, and generated paradoxes as a result. The issues go back to ancient mathematics. The Greek and Alexandrian mathematicians had employed various heuristic devices in their attempts to deal with mathematical problems, but had always sought to present their results in formal terms. In the course of the sixteenth and seventeenth centuries, some attention began to be paid to trying to reconcile heuristic and formal methods, and various forms of demonstration had been singled out as problematic. In some cases, it was unclear just what was being recommended. The formal geometrical legitimacy of proof by superposition—where the equality of two 74 See Clifford Truesdell, ‘A Program Towards Rediscovering the Rational Mechanics of the Age of Reason’, Archive for History of Exact Sciences 1 (1960), 3–36. Newton himself was aware that his geometrical presentation might be taken as outdated as early as 1710, writing that ‘To the mathematicians of the present century, however, versed almost wholly in algebra as they are, this synthetic style of writing is less pleasing, whether because it may seem too prolix and too akin to the method of the ancients, or because it is less revealing of the manner of discovery.’ The Mathematical Papers, viii. 451. On the attitude to continental developments in calculus in Britain see Niccolo` Guicciardini, The Development of Newtonian Calculus in Britain (Cambridge, 1989). 75 In the seventeenth and eighteenth centuries, the mathematical procedure of analysis was taken to be the resolution of mathematical problems by reducing them to equations. 76 See Gaukroger, Descartes, An Intellectual Biography, 172–181.

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geometrical ﬁgures is shown by imagining one placed one over the other so that their boundaries exactly coincide—was questioned for example by Peletier in his 1557 edition of Euclid.77 Yet as Hobbes later pointed out, how else could one possibly establish equality except by such means? In other cases, however, the problems raised were genuine. For example, proofs by contradiction, where we assume the opposite of the proposition to be demonstrated and show that it leads to a contradiction, began to be questioned, and here there is a serious issue. Closely connected with the latter was the exhaustion method, which involves a double reductio: unable to prove that A¼B directly, we prove that A cannot be less than B and that A cannot be greater than B.78 The usefulness of this way of proceeding was not in doubt, but it was difﬁcult to apply and the calculations were tedious. Moreover, although seventeenth-century mathematicians did not echo Peletier’s concerns about the formal adequacy of proofs by reductio, there remained the question of whether it had the formal rigour or perspicacity required of formal geometrical proof. A signiﬁcant problem here was how one reconciled powerful heuristic techniques with the need for formal and genuinely revelatory demonstrations. It was common ground among seventeenth-century mathematicians that the ancient geometers had employed heuristic methods to discover various theorems which were quite different from the synthetic demonstrations by which they proved them. The exhaustion method is a case in point. In Proposition 8 of Book XII of Euclid’s Elements there is a straightforward proof that a prism with a triangular base can be divided into three equal pyramids with triangular bases, from which it follows directly that any pyramid is a third part of the prism which has the same base as it and is of equal height. But when, in Proposition 10, Euclid turns to what is in effect the parallel problem of showing that any cone is a third part of the cylinder which has the same base as it and is of equal height, the fact we are dealing with curvilinear ﬁgures makes direct proof impossible, so we are supplied with an exhaustion proof, that is, a double reductio. Cavalieri, in his pioneering work of the 1620s and 1630s, culminating in his Geometria indivisibilibus (1635),79 sought a method of demonstration of the cone/cylinder theorem which, unlike the method of exhaustion, provided a 77 Jacques Peletier, In Euclidis Elementa Geometrica Demonstrationum Libri XV (Basel, 1557), note appended to Proposition I.4. On Peletier’s conception of geometry, see Giovanna Cifoletti, ‘From Valla to Vie`ta: The Rhetorical Reform of Logic and its Use in the Early Modern Logic’, Early Science and Medicine 11 (2006), 390–423: 398–410. 78 On the use of exhaustion methods in seventeenth-century mathematics, see D. T. Whiteside, ‘Patterns of Mathematical Thought in the Later Seventeenth Century’, Archive for History of Exact Sciences 1 (1960), 179–388: 331–48. Whiteside argues that exhaustion methods were potentially more powerful than many seventeenth-century mathematicians realized, and that the difﬁculty and unwieldiness they experienced in trying to apply them derived in large part from the failure to develop them fully. 79 Bonaventura Cavalieri, Geometria indivisibilibus continuorum nova quadam ratione promota (Bologna, 1635).

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direct proof, one in which we can understand how the theorem emerges from the premisses, rather than just being shown that the alternatives cannot hold. One could be reasonably certain that ancient mathematicians themselves had not come by the demonstration simply by testing every possibility (the cone is half a cylinder, a third, a quarter, and so on) against the method of exhaustion. Moreover, the procedure by which it was discovered was presumably direct, not a question of systematically dismissing alternatives. Cavalieri’s solution was to develop a procedure for summing inﬁnite aggregates of lines to measure areas, and inﬁnite aggregates of planes to measure volumes. This is the procedure he employed in the demonstration that the volume of a cone is a third of that of a cylinder of the same height with which it shares a base. The method of summing was genuinely revelatory in a way that exhaustion procedures are not. In particular, Cavalieri was able to show why it is that a right triangle whose sides are the base and height of a square and whose hypotenuse is the diagonal of the square stand in the ratio of 1 to 2, yet when we rotate the triangle and the square around the height of the square, the cone and cylinder generated stand in the ratio 1 to 3.80 The trouble was that the procedure also generated paradoxes. Galileo rejected Cavalieri’s method, for example, using a reductio in which a Cavalieri-type indivisible demonstration is used to prove that the area of a cone and a bowl have equal areas, but where, in the limiting case of the last ‘indivisibles’, it turns out that the circumference of a circle, which contains inﬁnitely many points, equals a single point.81 Nevertheless, the ability of Cavalieri’s procedure to generate paradoxes was more than matched by its heuristic power, developed in a number of new areas by his younger contemporary Torricelli. The most brilliant and striking extension of the procedure was Torricelli’s 1641 demonstration, using the method of indivisibles, that an acute hyperbolic solid of inﬁnite length had the same volume as a cylinder of ﬁnite length.82 That a ﬁgure of inﬁnite length could be shown to have a ﬁnite volume was puzzling, for it was generally assumed, contra Cavalieri, that one could not establish ratios that involved inﬁnite quantities. Yet what Torricelli had done was precisely to establish a ratio between a ﬁnite quantity and an inﬁnite one. Moreover, he was able to supplement his analytic demonstration using indivisibles with a synthetic one, although he made it clear which procedure had done the real work: 80 See Paolo Mancosu, Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century (New York, 1996), 39–44, to which I am indebted here. More generally, see Kirsti Andersen, ‘Cavalieri’s Method of Indivisibles’, Archive for History of Exact Sciences 31 (1985), 291–367. 81 Galileo Galilei, Two New Sciences: Including Centers of Gravity and Force of Percussion, trans. S. Drake (Madison, 1974), 36–7. 82 Evangelista Torricelli, ‘De Solido hyperbolico acuto’, in Opera Geometrica (Florence, 1644). See Dominique Descotes, ‘Espaces inﬁnis e´gaux au ﬁni’, in A. Montandon, ed., Le Grand et le Petit (Clermont-Ferrand, 1990), 41–67.

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As for the method of demonstration, we shall prove a simple notable theorem in two ways, namely, with indivisibles and in the manner of the ancients. And this although, to tell the truth, it has been discovered with the geometry of indivisibles, which is a truly scientiﬁc method of demonstration which is direct and, so to say, natural. I feel pity for the ancient geometry which, not knowing or not allowing Indivisibles, discovered so few truths in the study of the measure of solids that a frightening paucity of ideas has continued until our times.83

Torricelli’s demonstration opened up an intense discussion of the nature of indivisibles, a discussion which entered a new phase with the 1684 publication of Leibniz’s exposition of the foundations of differential calculus in his ‘Nova methodus’,84 and a companion piece on the foundations of integral calculus, ‘De geometria recondita et analysi indivisibilium atque inﬁnitorum’,85 in 1686. Leibniz’s interest in mathematics dates from the mid-1660s, although his innovations began only with his stay in Paris in 1672, where Huygens offered him guidance on how to develop and reﬁne his rudimentary mathematical skills.86 His interest at that time was in numerical series, for example in the demonstration that the sum of consecutive odd numbers can be expressed as the difference between two squares. As he tells us in his 1714 autobiographical note (written in the third person), ‘the application of numerical truths to geometry, and the study of inﬁnite series, was at that time unknown to our young friend, and he was content with the satisfaction of having observed such things in series of numbers.’87 Huygens set him the problem of ﬁnding the sum of the reciprocals of triangular numbers: 1/1 þ 1/3 þ 1/6 þ 1/10 þ 1 /15 . . . Writing each term as the sum of two fractions, he was able to show that the value of the terms is yielded by their order in the series of triangular numbers:

2 2 t tþ1 so that substituting the ﬁrst t, 1, yields 1; the value of the second t, 2, yields 1/3, and so on. Then he provides a formula for the sum of the terms, so that in the case of sum up to n we have:

83

Torricelli, ‘De solido’, translation (emended) from Mancosu, Philosophy of Mathematics, 131. Math. Schriften, v. 220–6. 85 Ibid., 226–33. 86 Ibid., 404. See Joseph E. Hofmann, Leibniz in Paris 1672–1676. His Growth to Mathematical Maturity (Cambridge, 1974). 87 Leibniz, Math. Schriften, v. 398. 84

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t 2 ¼2 tðt þ 1Þ nþ1

As n increases, 2/(nþ1) becomes inﬁnitely small or null, and hence the sum of the inﬁnite series is 2. Examining other types of convergent and divergent inﬁnite sequences, he developed the basis of a powerful and general method of summing. On Huygens’ advice, he also turned his attention to geometry, notably to Pascal’s 1659 ‘Traite´ des sinus du quart de cercle’.88 What was at issue here was the determination of tangents, crucial to the development of kinematics because ﬁnding tangents to curves was a way of determining the velocity at any particular instant of a body moving along that curve. Traditional limit procedures had enabled one to determine tangents, for example, by the use of chords of decreasing size. If we take two points, P and Q, on the circumference of a circle and join them then we determine a unique line, the chord PQ (Fig. 3.3). But there is no such unique line passing through a single point—there are inﬁnitely many straight lines that pass through P alone—and the problem is to determine the unique one that is the tangent, i.e. the one that is at a right angle to the centre of the circle, or to the focus of a conic section. As Q approaches P, the chord PQ will provide a better and better approximation to the tangent at P. They cannot coincide, since then we would be back with the problem of determining a unique line from a single point, but if we make the distance inﬁnitesimally small, we will generate the tangent from two points. Pascal associated a triangle with inﬁnitesimal sides (dx, dy, ds) with a point on the circumference of a circle (see Fig. 3.4),89 and exploited the similarity between dx, dy, ds and the triangle y, a-x, a. Leibniz realized that the procedure could be applied to any curve if we replace the radius of the circle (a in Fig. 3.4) with the normal to the curve (n in Fig. 3.5). In short, he discovered that ﬁnding tangents to curves depended on the differences in the ordinates and abscissae, as these differences became inﬁnitely small. At the same time, he realized that the problem of areas or quadratures was simply the inverse of this, so that the areas depended on the sum of the ordinates or inﬁnitely thin rectangles making up the area. In other words, the techniques for dealing with the ﬁrst question, which turned on the relationship between rates of change of continuously varying quantities, for which Leibniz provided rules for a differential calculus, were mirrored in an inverse set of techniques for dealing with the second, namely integral calculus. These techniques take the form of simple rules, offered without demonstration, in the ‘Nova methodus’. They are introduced geometrically: consider Fig. 3.6, with the axis AX, and the curves VV, WW, YY, ZZ, whose ordinates, perpendicular to the axis, namely VX, WX, YX, and ZX, are labelled v, w, y, and z respectively, and the segment AX taken on the axis is

88 89

Blaise Pascal, Œuvres Comple`tes, ed. Henri Gouhier and Louis Lafuma (Paris, 1963), 155–8. I am indebted here to the clariﬁed ﬁgures as in Antognazza, Leibniz, 157–8.

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Q

P

Fig 3.3

ds

dy

dx

y

x

a

a–x

a

Fig 3.4

labelled x. Tangents VB, WC, YD, and ZE are drawn to the curves, cutting the axis AX at B, C, D, and E respectively. We let dx be a segment of an arbitrarily chosen line, and dv, which Leibniz deﬁnes as the ‘differentia’ of v, be a segment which is to dx as v is to XB. The rules of calculus are then set out: Let a be a given constant, da be equal to o, and dax be equal to adx. If y is equal to v (i.e. every ordinate of the curve YY is equal to the corresponding ordinate of the curve VV), then dy will be equal to dv. Now Addition and Subtraction: if z y þ w þ x is equal to v, then dz y þ w þ x or dv will equal dz dy þ dw þ dx. Multiplication: dxv is equal to xdv þ vdx, i.e. in making y equal to xv, one makes dy equal to xdv þ vdx, for we

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ds dy dx t n

y

s

k x

Fig 3.5 dx

B D

G W

K

A X

V N

C

M

L

X V

Z

W

E

B

Fig 3.6

Z

Y

Y

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may use the expression y as shorthand for xv. Note that in this calculus, x and dx are treated in the same way, as are y and dy, or any other variable letter and its differential. Note also that the inverse process, starting from the differential equation, is not always possible unless we take certain precautions which we mention elsewhere. Finally, Division: d yv or (making z equal to yv) dz is equal to vdyyyydv.90

Having set out some rules for the manipulation of signs, depending on whether the ordinates increase or decrease, Leibniz moves to the behaviour of curves, leading him to introduce second-order differentials: if, when the ordinates v increase, the same occurs with the increments or differentiae dv (i.e. if we take dv to be positive then ddv, the differentiae of the differentiae, are equally positive, or equally negative if we take them to be negative), then the convexity of the curve, or in the opposite case its concavity, turns towards the axis. But in the case where the increment is a maximum or a minimum, i.e. when the increments of decrease become increments of increase, or vice versa, there is a point of inﬂexion; concavity and convexity change into one another . . .

This then leads to rules for two further operations: Powers: dxa ¼ a:xa1 dx, for example dz3 ¼ 3x2 dx; d x1a ¼ xadx aþ1 , for example ﬃﬃﬃﬃﬃﬃﬃﬃﬃ ﬃﬃﬃﬃﬃ a p p b b 1 3dx adx a ab ﬃ¼ p ﬃﬃﬃﬃﬃﬃﬃ if w ¼ x3 , we have dw ¼ x4 . Roots: d x ¼ b dx x ; . . . d pb1ﬃﬃﬃ b aþb: xa b x

He concludes: When one knows the Algorithm, if I may call it such, of this calculus, which I term differential, one can, by means of ordinary calculation, ﬁnd all the other differential equations, and maxima and minima as well as tangents, without having to rid oneself of the fractions, irrationals, or the other peculiarities that have been a feature of methods used to date. . . . As a result, one can write the differential equation of any given equation simply by replacing each term . . . by a differential quantity. For each of the other quantities (which are not themselves terms but which contribute to forming one another), this differential quantity must be introduced in order to obtain the differential quantity of the term itself, not by means of a simple substitution, but following the algorithm that I have set out.91

Nevertheless, it should be said that the programme advocated in ‘Nova methodus’ was obscurely formulated, and the paper was so cautious in its presentation that it hardly mentioned inﬁnitesimals at all.92 Two subsequent treatises—Guillaume de l’Hoˆpital’s 1696 textbook Analyse des inﬁniment petits 93

90

Leibniz, Math. Schriften, v. 220. Ibid., 222–3. 92 See the discussion in Henck J. M. Bos, ‘Differentials, Higher-Order Differentials and the Derivative in the Leibnizian Calculus’, Archive for History of Exact Sciences 14 (1974), 1–90. 93 Guillaume de l’Hoˆpital, Analyse des inﬁniment petits pour l’intelligence des lignes courbes (Paris, 1696). 91

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and Jacob Hermann’s 1700 Responsio ad considerationes94—set out what in its origins was the Leibnizian programme with greater clarity. Hermann and l’Hoˆpital were both closely associated with Jacob and Johann Bernoulli. Jacob had written to Leibniz as early as December 1687 seeking guidance on a number of points in his calculus,95 and he and Johann quickly mastered and developed it beyond its Leibnizian origins. Hermann was from the Bernoullian stronghold of Basel, and his Phoronomia of 1716 was one of the most important early analytical treatments of dynamics. The basic mathematical ideas in l’Hoˆpital’s textbook, which were to form a statement of the approach to mathematics and mechanics associated with the Malebranche circle in Paris,96 were in large part due to Johann Bernoulli, who had visited Paris in 1691, and whose lectures on calculus during that visit to Malebranche and the Oratorians was the formative event in the setting up of Malebranche’s group of mathematicians.97 In the wake of the lectures, l’Hoˆpital paid Bernoulli to send him his mathematical results on an exclusive basis.98 The Preface to the Analyse, written by Fontenelle, was the manifesto of the group, and drew the line between ancient and modern methods sharply: ‘What we have by the ancients on these matters, above all Archimedes, is certainly worthy of admiration. But apart from the fact that they deal with very few curves, and treat these somewhat superﬁcially, the propositions are almost 94 Jacob Hermann, Jacobi Hermanni responsio ad considerationes secundas Cl. Viri Bern. Nieuventiit (Basel, 1700). 95 Leibniz, Math. Schriften, ii. 10–13. 96 See e.g. Malebranche, De la recherche de la ve´rite´, Book VI Part 1 ch 5: ‘The invention of differential and integral calculus has made analysis limitless, as it were. For these new calculi have placed inﬁnitely many mechanical ﬁgures and problems of physics under its jurisdiction.’ It was L’Hoˆpital’s reading of Malebranche’s La recherche that had been responsible for his leaving the military (he came from a family of several generations of cavalry ofﬁcers) and devoting himself to mathematics: see Fontenelle, ‘Eloge de M. le Marquis de l’Hoˆpital’: Œuvres de Monsieur de Fontenelle . . . nouvelle ´edition (10 vols, Paris, 1762), v. 79–80. As well as the works of l’Hoˆpital and Varignon, a number of textbooks issued from the Malebranche circle, notably Louis Carre´, Me´thode pour la mesure des surfaces, la dimension des solides . . . par l’application du calcul inte´gral (Paris, 1700); N. Guisne´e, Application de l’algebre a` la geometrie, ov Methode de de´monstrer par l’algebre, les theoreˆmes de geometrie, & d’en re´soudre & construire tous les probleˆmes (Paris, 1705); Charles Reyneau, Analyse demontre´e; ou, La methode de resoudre les probleˆmes des mathematiques, et d’apprendre facilement ces sciences (Paris, 1708); idem, La science du calcul, des grandeurs en general: ou, Les elemens des mathematiques (Paris, 1714). Malebranche particularly recommended the works of Reyneau, and both Maupertuis and Clairaut used Guisne´e as their initiation textbook. 97 See Pierre Costabel, ‘Introduction’; and Andre´ Robinet, ‘Les acade´miciens des sciences malebranchists’, in Malebranche, Œuvres comple`tes, xvii-2. 309–16 and xx. 162–74 respectively; Andre´ Robinet, ‘Le groupe malebranchiste introducteur du calcul inﬁnite´simal en France’, Revue d’histoire des sciences 13 (1960), 287–308; and idem, Malebranche de l’Acade´mie des sciences. L’uvre scientiﬁque, 1674–1715 (Paris, 1970); J. O. Fleckenstein, ‘Pierre Varignon und die mathematischen Wissenschaften im Zeitalter der Cartesianismus’, Archives Internationales d’Histoire des Sciences 5 (1948), 76–138. 98 Bernoulli evidently dazzled the Oratorians showing how calculus techniques could be used to determine a catenary in a straightforward way. On this, and on the transaction between l’Hoˆpital and Bernoulli, see Lenore Feigenbaum, ‘The Fragmentation of the European Mathematical Community’, in P. M. Harman and Alan E. Shapiro, eds., The Investigation of Difﬁcult Things (Cambridge, 1992), 383–98: 388–9.

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entirely particular and lack order, failing to communicate any regular and applied method.’99 It was the Bernoullis, he continues, who ‘ﬁrst perceived the beauty of the Method’.100 The Leibnizian approach, developed so fruitfully by the Bernoullis and their followers,101 explicitly defends the idea of there being inﬁnitesimal quantities whose addition to a given ﬁnite quantity does not change the value of the latter, so that two equal quantities remain equal when such a quantity is added to one of them but not the other: AþÆ¼A.102 It also depends crucially on the use of such inﬁnitesimal quantities in resolving curves into polygons with an inﬁnite number of inﬁnitesimal sides, so that inﬁnitesimal methods can be applied to curves. The geometrical interpretation provides a way to envisage in what sense differentiation and integration are the inverses of one another: determining tangents to curves (differentiation) and computing the area between the axis and the curve (integration). Guicciardini has pointed out that there were a number of basic questions on the nature of inﬁnitesimals on which Leibniz and Newton were in agreement. They agreed that actual inﬁnitesimals were useful ﬁctions and did not actually exist; that they were best deﬁned as varying quantities in a state of approaching zero; and that they can be completely avoided in favour of limit-based proofs, which provide them with a mathematically rigorous formulation.103 There is one thing that is very distinctive about Leibniz’s approach, however, and which separates him markedly from Newton on foundational questions. This is the importance he attaches to a mechanical algorithm. Although both Leibniz and 199 L’Hoˆpital, Analyse des inﬁniment petits, iv–v; also to be found in Fontenelle, Œuvres, x. 29–43: 31. 100 L’Hoˆpital, Analyse, ix; Fontenelle, Œuvres, 36. 101 See, in particular, the comprehensive account of the development of integral calculus and its applications between 1690 (Leibniz) and 1741 (Clairaut’s mature theory of the shape of the earth) in John L. Greenberg, The Problem of the Earth’s Shape from Newton to Clairaut: The Rise of Mathematical Science in Eighteenth-Century Paris and the Fall of ‘Normal’ Science (Cambridge, 1995), 225–399. 102 ‘I maintain that not only two quantities are equal whose difference is zero, but also that two quantities are equal whose difference is incomparably small’: Leibniz, ‘Responsio ad nonnullas difﬁcultates a Dn. Bernardo Niewentiit circa methodum differentialem seu inﬁnitesimalem motas’, Math. Schriften, v. 322. Leibniz is replying here to three works by Bernard Nieuwentijdt: Considerationes circa analyseos ad quantitates inﬁnite parvas applicatae principia & Calculi differntialis usum in resolvendibus problematis geometricis (Amsterdam, 1694); Analysis inﬁnitorum seu curvilineorum proprietates ex polygonorum natura deductae (Amsterdam, 1695); Considerationes secondae circa calculi differentialis principia & responsio ad Virum Noblissimum G. G. Leibnitium (Amsterdam, 1696). On the dispute with Nieuwentijdt, see Fritz Nagel, ‘Nieuwentijdt, Leibniz, and Jacob Hermann on Inﬁnitesimals’, and Douglas M. Jesseph, ‘Truth in Fiction: Origins and Consequences of Leibniz’s Doctrine of Inﬁnitesimal Magnitudes’, both in Ursula Goldenbaum and Douglas Jesseph, eds., Inﬁnitesimal Differences: Controversies between Leibniz and His Contemporaries (Berlin, 2008), 199–214 and 215–34 respectively. 103 Guicciardini, Reading the Principia, 159–63. Cf. Douglas M. Jesseph, ‘Leibniz on the Foundations of the Calculus: The Question of the Reality of Inﬁnitesimal Magnitudes’, Perspectives on Science 6 (1998), 6–40.

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Newton accept that it is limit-based proofs that provide the foundation for differential calculus, for Leibniz such proofs are a means of establishing legitimacy for procedures which differ signiﬁcantly from standard mathematical operations, but such legitimation is not required on internal grounds, and one can proceed without constant reference to limit-based proofs. Indeed, it is distinctive of the Leibnizian programme that the algorithms that make up calculus be applied without reﬂecting on the steps: the procedure is secure and, as in the case of Leibnizian logic, it is a matter of supplying the premisses and letting the algorithm generate the conclusion by ‘blind’ reasoning. Once the general legitimacy of the procedure has been established by means of a theory of limits, the calculus takes on a life of its own, as it were. In September 1691, Leibniz writes to Huygens that ‘what is better and more useful in my new calculus is that it yields truths by means of a kind of analysis, and without any effort of the imagination’,104 and in December of the same year, that ‘what I love most about my calculus is that it gives us the same advantages over the Ancients in the geometry of Archimedes that Vie`te and Descartes have given us in the geometry of Euclid or Apollonius, in freeing us from having to work with the imagination.’105 Guicciardini has argued that for Leibniz the calculus should be seen as an ars inveniendi, to be valued by its fruitfulness.106 Certainly he set great store by its problem-solving power but, as we shall see below, it would be a serious mistake to imagine that he thought of the power of calculus in purely pragmatic terms. The important point for present purposes is that, for Leibniz, its referential content has no bearing on the calculations that we are able to perform with it,ﬃ pﬃﬃﬃﬃﬃﬃ and indeed it may operate with symbols devoid of reference, such as 1, providing it is able to generate correct results.107 For Newton, by contrast, limit-based proofs were the essence of differential calculus, and the employment of calculus hinged on one’s ability to articulate it in terms of a comprehensive theory of limits. Whereas Leibniz abandons geometrical interpretation once his calculus has proceeded past the legitimatory stage, and in fact handles differential equations as algebraic objects, Newton 104

Leibniz to Huygens, 11/12 September 1691; Math. Schriften, ii. 104. Note that the Olms reprint of this edition unhelpfully includes vols. i and ii of the edition in vol. i, whereas the two parts of vol. iii of the original is spread over vols. ii and iii. I use the original division in references. 105 Leibniz to Huygens, 29 December 1691; Math. Schriften, ii. 123. 106 Guicciardini, Reading the Principia, 166. 107 We are perhaps not so worried about square roots of negative numbers appearing in the proof as seventeenth-century mathematicians were, but in our own times there have been parallel concerns about Feynman’s use of negative probabilities in calculations (an idea originally proposed by Dirac), justiﬁed on the grounds that they allow otherwise intractable calculations and do not appear in the solution: Paul Dirac, ‘The Physical Interpretation of Quantum Mechanics’, Proceedings of the Royal Society of London, A 180 (1942), 1–39; R. P. Feynman, ‘Negative Probability’, in F. David Peat, ed., Quantum Implications: Essays in Honour of David Bohm (London, 1987), 235–48. At the other end of the chronological spectrum, similar concerns about negative integers appearing in the process of calculation were expressed in pre-modern mathematics: see Jacob Klein, Greek Mathematical Thought and the Origin of Algebra (Cambridge, Mass., 1968), Part II.

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never (at least after the early 1670s) allows his calculus to transcend its original geometrical interpretation, insisting that this is what provides it with reference and meaning. Between 1670 and 1671, Newton composed a treatise on the use of inﬁnitely small quantities, ‘De methodis serierum et ﬂuxionum’,108 the central idea in which is that of the ‘ﬂuxion’. Consider a point moving at a variable speed and generating a line (e.g. a planet moving at variable speed around the sun and generating an elliptical orbit, although Newton did not realize this application in 1671).109 The distance covered in a time t is called a ‘ﬂuent’, the instantaneous speed is the ‘ﬂuxion’, and the inﬁnitely small speed acquired after an inﬁnitely small increment of time is called the ‘moment’. ‘De methodis’ provides an algorithm for calculating ﬂuxions, in which it is assumed that motion is uniform during equal intervals of time, and in which inﬁnitesimals, once they have done their work, can be cancelled (following the principle AþÆ¼A). The algorithm construes all quantities as continuous ﬂows, and enables him to reduce a vast range of particularly intractable mathematical problems to two classes: given the space traversed, to ﬁnd the speed at any time (corresponding to Leibnizian differentiation); and given the speed, to ﬁnd the space traversed at any time (corresponding to Leibnizian integration). The problems of ﬁnding tangents, extremal points, and curvatures can be reduced to the ﬁrst. The second, the class of ‘inverse’ problems, which includes the problem of determining the area under a curve, is more problematic, and Newton employed two procedures: either he changed the variable in order to reduce it to one of a catalogue of known ﬂuents which he had built up, or he used series expansion techniques.110 This part of the exercise comes under problem-solving, that is, under what was traditionally known as analysis. The demonstration of results from ﬁrst principles, synthesis, was traditionally a different kind of exercise, and was resolutely geometrical. Proponents of the ‘new analysis’ such as Descartes and Leibniz were inclined to diminish the importance of synthesis, as an unnecessary and artiﬁcial process. Descartes, as I have indicated, believed that geometrical proofs, which routinely involved detours via demonstrations of supplementary theorems needed for the ﬁnal result but not part of the actual proof, were often obscure and meandering, whereas algebraic proofs were always direct: it is simply a matter of 108 The treatise was originally untitled: Mathematical Papers, iii. 32–353. See also the treatise Tractatus de Quadratura Curvarum, in Newton, Opera, i. 333–90. There are good accounts of these questions in Guicciardini, Reading the Principia, ch. 2; and Douglas M. Jesseph, Berkeley’s Philosophy of Mathematics (Chicago, 1993), ch. 4. 109 In his entry on ‘ﬂuxion’ in the Encyclope`die, d’Alembert criticized Newton’s idea of deﬁning mathematical entities in terms of motions as introducing unnecessary extraneous considerations: Denis Diderot and Jean le Rond d’Alembert, Encyclope´die ou Dictionnaire raisonne´ des sciences, des arts et des me´tiers (40 vols., Geneva, 1777–9), xvi. 726. 110 Expansion techniques played a central role in the development of Newton’s mathematical thinking, and his ﬁrst signiﬁcant mathematical discovery, in the winter of 1664–5, was of the binomial theorem. See Guicciardini, Reading the Principia, 18–20.

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assigning symbols to known and unknown quantities, and manipulating equations that connect them so as to reveal the required relationship, a manipulation which is always completely transparent.111 Newton was committed to the virtues of the geometrical methods of the ancients as far as demonstration was concerned, however, and his model in mechanics was the rigorously geometrical Horologium of Huygens. It might seem, then, that Newtonian analysis, with its algorithm of ﬂuxions, and Newtonian synthesis, with its rigorous geometrical demonstrations, are two complementary features of the Newtonian project, one a method of discovery, the other a method of presentation. As Newton himself put it in an unpublished draft preface to the second edition of the Principia: The ancient geometers investigated by analysis what was sought [i.e. found their solutions to problems by the method of analysis], demonstrating by synthesis what had been found, and published what had been demonstrated so that it might be received into geometry. What was resolved was not immediately received into geometry; a solution by means of the composition of demonstrations was required. For all the power and glory of geometry consisted in certainty of things, and certainty consisted in demonstration clearly composed [i.e., demonstrations according to the method of synthesis, or composition]. In this science, what counts is not so much brevity as certainty. And accordingly, in the following treatise I have demonstrated by synthesis the propositions found by analysis.112

But matters are not so straightforward, for Newton was in fact unable to accept two different canons of mathematical procedure. In contrast to Leibniz, who avoided geometrical demonstration, even though he was committed to the idea that his calculus required a geometrical grounding, Newton took the other direction. In the course of the 1670s, as Whiteside has shown, he began to distance himself from his early mathematical researches, abandoning the calculus of ﬂuxions in favour of a geometry of ﬂuxions in which inﬁnitesimal quantities were not employed.113 He began criticizing modern mathematical practices, and took Descartes to task, for example, for his algebraic solution to a problem that had deﬁed the attempts of ancient geometers, Pappus’ four-line locus problem, showing that the algebraic solution did not demonstrate the unique power of analysis, as Descartes claimed, since it did in fact have a geometrical solution, which he went on to provide. What Newton appreciated in the ancient geometrical techniques (his model was Apollonius) was that they always had a deﬁnite interpretation in a geometrical construction. At no stage of a demonstration did they ever stop referring to anything. The techniques of the new analysis, by contrast, especially as developed by Leibniz and his followers, left the realm of the concrete once the problem had been presented, only to return to it at the 111 See e.g. the comparison of geometrical and algebraic solutions to the problem in Euclid’s Elements II.11 in Gaukroger, Descartes, An Intellectual Biography, 175–6. 112 Translated (with interpolations) by Cohen, ‘A Guide’, 49–50; cf. Newton, Mathematical Papers, viii. 442–59. See the discussion in Cohen, op. cit., 122–7. 113 Newton, Mathematical Papers, iii.

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solution, having proceeded via processes that eschewed all reference to the entities that the original problem (and the solution) dealt with. The success of the Leibnizian approach was palpable. As a direct result of this way of proceeding, continental mathematicians were soon exploring equations in several independent variables as well as partial differentiation, equipping them by mid-century to move mathematically, if not with ease, then at least with a great degree of facility, between rigid bodies, ﬂexible bodies, elastic bodies, and ﬂuids. But this in itself does not, and could not, confer legitimacy on them: the issues are too deep to be resolved in this way. Leibniz’s investment in ‘blind reasoning’ is not a pragmatic one: it goes to the heart of his understanding of what it means to be a philosopher. It is important here to understand in what respect Leibniz’s views emerge from a reﬂection on Pascal.114 Pascal was obsessed with the fallen nature of human beings, and with the limits that this placed on their capacity to understand: limits which he believed it was irresponsible to ignore, as he considered his contemporaries, particularly those active in natural philosophy and mathematics, were doing. The human condition, he argued, was characterized by worthlessness and despair, not egoism and optimism. The value of the true philosophy and the true religion lay in their ability to teach us the remedies for our inabilities.115 The value of mathematics lay in its ability to reveal this to us clearly, especially when the inﬁnitely large and the inﬁnitely small were considered.116 In pursuing mathematics in a serious way we are forced to recognize that inﬁnities exist, Pascal believes, but at the same time we also have to admit to our incomprehension of such inﬁnities, thereby requiring us to take stock of our limitations. Newton’s approach to inﬁnitesimals, as I have indicated, was to insist that they must remain anchored in limit procedures, and his preference was to replace algorithms employing inﬁnitesimals with geometrical demonstrations. Pascal, in sharp contrast, takes inﬁnitesimals at face value, stressing the combination of their legitimacy and their lack of intelligibility, and drawing from this a general lesson about the nature and limits of human knowledge. This lesson is one that bears directly on the persona of the philosopher, in that recognition of our cognitive limitations is an integral part of the morality of the philosopher, who must struggle against optimism and egoism, along with various contrasting faults such as scepticism and relativism. Leibniz agreed with Pascal that our unaided faculties were insufﬁcient for the kind of knowledge to which we naturally aspire, although this in itself was a widespread view motivated either by a sense of the fallen nature of human beings, or because of the kind of systematic criticism of 114 See Jones, The Good Life in the Scientiﬁc Revolution, Parts 2 and 3, on Pascal and Leibniz respectively. I am indebted to Jones’ discussion in what follows. 115 See Pense ´es, frag. 149 (Lafuma numbering): Pascal, Œuvres, 520. On Pascal’s conception of philosophy and the philosopher see Vincent Carraud, Pascal et la philosophie (Paris, 1992). 116 See, in particular, his ‘De l’esprit ge´ome´trique’, Œuvres, 348–55.

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sense perception that Descartes, and Cartesians such as Malebranche and Arnauld, among others, had mounted. Unlike those accounts that saw limitations to knowledge as a result of the Fall, the Cartesian approach had set out to undermine the reliability of sensation only to replace it with the reliability of properly tutored reason, that is, reason that could issue in ‘clear and distinct’ judgements. Leibniz was very much in this latter tradition, and mathematics acted for him very much as a model of what knowledge could be, although he believed that the limitation of knowledge claims to what we grasp clearly and distinctly (the canonical representative of which, by this stage, was Huygens, who was Newton’s model) was mistaken, for, as he points out to Conring in a letter of 1678, there are symbolic operations which we cannot grasp clearly and distinctly but which nevertheless manifestly yield the kind of knowledge that mathematicians should be seeking.117 This is clear from his attitude to one of his ﬁrst discoveries, one that would be important in his subsequent invention of the calculus, namely his quadrature of the circle. What he discovered was a means of providing the area of a circle by means of an inﬁnite series:

p 1 1 1 1 ¼ þ ... 4 1 3 5 7 It is impossible, he points out to Conring, to express the ratio between a square and a circle by a single number, but we can express the ratio in an inﬁnite series of numbers. As Jones notes, for Leibniz, series such as this offer ‘the only exact knowledge of the quadrature of a circle available to embodied human beings without divine intervention.’118 They offer a way of transcending traditional limitations which restrict mathematical knowledge to quantities and geometrical constructions, so that ‘a value can be expressed exactly, either by a quantity or by a progression of quantities whose nature and way of continuing are known.’119 For Leibniz, our native abilities do not match our native capacities, and the way to realize our full capacities is through procedures that go beyond our unaided faculties. These procedures are, paradigmatically, algebraic analysis and inﬁnitesimal algorithms, for these take us beyond the kind of pictorial geometrical representation on which our unaided faculties rely, to new and far more powerful forms of cognition, where this new power is manifested in a clear and explicit way in the novel and general results that they yield. On this view, it is not a question of appealing to unaided faculties to secure a legitimation of inﬁnitesimals (Newton), or to use their inability to provide such a legitimation as a means of criticizing unaided faculties (Pascal), but rather of using them as an extension of our reason in much the same way that we might use a microscope or 117 118 119

Leibniz to Conring, 19 March 1678: phil. Schriften, i. 199. Jones, The Good Life in the Scientiﬁc Revolution, 169–70. Leibniz, Math. Schriften, ii. 96.

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telescope as an extension of our vision. We don’t use microscopes or telescopes to show that our natural vision is fundamentally lacking, nor do we insist that their use be limited to things we can see with unaided vision. Rather, we use them to take us beyond our natural faculties. Aristotle and the Aristotelian medieval tradition had held that we have the faculties and sense organs we do so that we might know the world: nature, or God, has provided us with them for this purpose, and hence the idea that we might transcend them in any way is out of the question. This view had been rejected by seventeenth-century thinkers, a rejection often motivated by notions of diminished capacities in the wake of the Fall. There had been a widely held view in the seventeenth century that the Fall had dulled Adam’s senses, and that the use of artiﬁcial aids might effect the restoration of their pre-lapsarian acuity. But while there had also been a widespread view that reason too had been impaired in the Fall, this was diagnosed in terms of the passions triumphing over reason, the remedy being to control the passions. This was Malebranche’s strategy, for example. The application of artiﬁcial aids in solving this problem was unprecedented,120 but this is exactly what Leibniz seems to be doing. Whereas Descartes and Malebranche had focused on the inadequacy of our sense organs, Leibniz extends the criticism to our faculties. As far as the use of our faculties in mathematical reasoning is concerned, it is the fact that inﬁnitesimal algorithms cannot be grounded in ‘natural’ mathematical reasoning that means that our use of them must be ‘blind’: it is they that guide us, we do not guide them. One extreme reaction to this kind of approach was that of Berkeley. Prior to The Analyst of 1734, Berkeley’s arguments against the use of inﬁnitesimals are similar to Newton’s. Like Newton, but in contrast to Nieuwentijt for example, he has no doubt about the results achieved using inﬁnitesimals; his concerns are rather with the legitimacy of the procedure used to generate these results, and he believes that they must be translated into geometrical terms. Moreover, what motivates this position in Berkeley is the question of our being able to represent the mathematical procedures to ourselves clearly and distinctly. But the ﬂaw that Berkeley detects in the calculus is one of unintelligibility in its procedures, and the difﬁculty he isolates is one that must be traced back to his general theory of the impossibility of abstractive knowledge.121 In his Essay, Locke, discussing the abstract general idea of a triangle, struggles with the difﬁculty of forming such an abstraction in these terms:

120 It is especially unprecedented in the case of mathematics where a more usual view was that the self-evident axioms of mathematics were an example of something that had been uniquely insulated from the corrupting effects of the Fall, a view that Luther explicitly held, for example. Peter Harrison traces this position back to Luther and Melanchthon: The Fall of Man and the Foundations of Science (Cambridge, 2007), 97–103. 121 See the exemplary discussion in Jesseph, Berkeley’s Philosophy of Mathematics, ch. 1.

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Does it not require some pains and skill to form the general Idea of a Triangle, (which is yet none of the most abstract, comprehensive, and difﬁcult,) for it must be neither Oblique, nor Rectangle, neither Equilateral, Equicrural, nor Scalenon; but all and none of these at once. In effect, it is something imperfect, that cannot exist; an Idea wherein some parts of several different and non-existent Ideas are put together.122

Berkeley’s point is that if, as Locke shows, such a triangle is impossible, then it is inconceivable: If any man has the faculty of framing in his mind such an idea of a triangle as is here described, it is in vain to pretend to dispute him out of it, nor would I go about it. All I desire is, that the reader would fully and certainly inform himself whether he has an idea or no. And this, methinks, can be no hard task for any one to perform. What more easy than for any one to look into his own thoughts, and there try whether he has, or can attain to have, an idea that shall correspond with the description that is here given of the general idea of a triangle, which is, neither oblique, nor rectangle, equilateral, equicrural, nor scalenon, but all and none of these at once?123

Since geometry cannot operate with entities that are inconceivable, some way of construing its subject matter other than as abstractions must be found, and Berkeley proposes that, to secure intelligibility and conceivability, we must construe geometrical ﬁgures as objects of sense. To secure the generality of geometry, however, he devises a way of classifying particular geometrical ﬁgures in such a way that they are representative of all other lines and ﬁgures of any size. The basis of geometry then lies in the comparison of these and the ratios in which they stand to one another. This distinctive theory of what the legitimacy of geometrical operations consists in, which certainly reﬂects nothing in Newton, is then used to provide the grounds for a geometrical replacement for calculus, a replacement that is explicitly along Newtonian lines: ‘the supposition of quantitys inﬁnitely small is not essential to the great improvements of the Modern Analysis. For Mr. Leibnitz acknowledges that his Calculis differentialis might be demonstrated reductione ad absurdum after the manner of the ancients; & Sir Isaac Newton in a late treatise informs us his method can be made out a priori without the supposition of quantitys inﬁnitely small.’124 There is a signiﬁcant difference, however, between Berkeley’s approach in these writings from the ﬁrst decade of the eighteenth century, and the discussion in The Analyst, which contains his most extensive account of calculus.125 In The

122

Locke, Essay, IV. iii. 9. George Berkeley, A Treatise Concerning the Principles of Human Knowledge (Dublin, 1710), Introduction, } 15. 124 Berkeley, ‘Of Inﬁnities’, Lecture to the Dublin Philosophical Society 19 November 1707: The Works of George Berkeley, Bishop of Cloyne, ed. A. A. Luce and T. E. Jessop (9 vols., Edinburgh, 1948–57), iv. 237. 125 For the text and discussion, see George Berkeley, De Motu and The Analyst: a Modern Edition, with Introductions and Commentary, ed D. M. Jesseph (Dordrecht, 1992). 123

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Analyst, the epistemological criticisms of abstraction only come into play once he has set out independent arguments against calculus. These include the criticism that all proofs in calculus are fallacious, by standard logical criteria, and that the success of calculus is due to what he calls ‘a compensation of errors’ whereby inﬁnitesimal differences are used in a calculation but dismissed from the result. Berkeley also attacks the Newtonian method of ﬂuxions, however, on the grounds that it requires the postulation of inﬁnitesimal quantities, despite what Newton himself and his followers claimed. Berkeley’s general criticisms of the calculus were dismissed, where they were noticed, by continental mathematicians, but since The Analyst, unlike Berkeley’s earlier writings on the subject, was directed primarily against the Newtonian method of ﬂuxions, it attracted a number of responses from British mathematicians.126 There was widespread agreement in Britain that the conceptual foundations of calculus were in dire need of clariﬁcation, and to this extent Berkeley’s criticisms were not unprecedented. The problem was that mathematicians in general were increasingly convinced that calculus worked extremely well, to the extent of producing a powerful body of results that quite possibly could not be produced in some other way. That the phenomenal success of calculus was simply a question of ‘compensation of errors’ seemed unlikely at best. Berkeley himself made no effort to rewrite mathematics in his own favoured terms, and it was far from clear that it could be done. Moreover, some responses to Berkeley, notably those of Robins, Maclaurin, and Paman did succeed in providing a signiﬁcant degree of clariﬁcation while meeting Berkeley’s objections, and Maclaurin was deemed to have answered these objections decisively.127 These were speciﬁcally mathematical disputes, but it is clear that the issues here are not conﬁned to mathematical questions, and, in connection with our immediate concerns, it is important to note that they bore directly on naturalphilosophical issues. There are two natural-philosophical questions that are 126 There was a political element in the attack on ﬂuxions, for Berkeley believed that in showing that ﬂuxions were ‘incomprehensible mysteries’ he had shown that Newtonians insist upon clear points in matters of faith yet ‘do without them even in science’: A Defence of Free-Thinking in Mathematics (London, 1735), 6. See the response to Berkeley by James Jurin, Geometry no Friend to Inﬁdelity: or, a Defence of Sir Isaac Newton and the British Mathematicians (London, 1735). 127 Benjamin Robins, Discourse Concerning the Nature and Certainty of Sir Isaac Newton’s Method of Fluxions (London, 1735); Colin Maclaurin, Treatise of Fluxions (2 vols., Edinburgh, 1742); Roger Paman, Harmony of the Ancient and Modern Geometry Asserted (London, 1745). Jesseph, Berkeley’s Philosophy of Mathematics, ch. 7, provides details of these and other responses. From a mathematical point of view, the crucial development was Euler’s translation of the calculus of variable quantities and their differentials into a calculus of functions and their derivatives: see Bos, ‘Differentials, Higher-Order Differentials and the Derivative in the Leibnizian Calculus’, and A. P. Yushkevich, ‘The Concept of Function up to the Middle of the 19th Century’, Archive for History of Exact Sciences 16 (1976), 37–85. In his The´orie des fonctions analytiques (Paris, 1797), Lagrange replaced derivatives, ﬂuxions, and limits entirely with functions. See the brief account in Niccolo` Guicciardini, ‘Three Traditions in the Calculus: Newton, Leibniz and Lagrange’, in I. GrattanGuinness, ed., Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (2 vols., London, 1994), i. 308–17.

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paramount in this respect. The ﬁrst is the ability of various techniques to deal with particular parts of physical theory. Before the middle of the eighteenth century, neither Newtonian ﬂuxions nor Leibnizian differential and integral calculus were sufﬁciently developed to allow one to account mathematically for the ﬁne details of Newtonian gravitational theory such as planetary perturbations, the attraction of ellipsoids, and the tides. Newton and eighteenth-century Newtonians such as Maclaurin knew how to apply the method of ﬂuxions to some dynamical problems,128 but they had no choice but to use what were in effect qualitative geometrical constructions in dealing with the more intractable questions. Since gravitation was by far the most important physical question at stake between Newtonians and their continental rivals, the advocacy of geometrical techniques was intimately tied in with the defence of Newtonianism. The second issue concerns the question of the level of abstractness of physical theory. The Leibnizian uninterpreted calculus allows a very abstract form of mechanics, one in which mathematical demonstrations do not have to remain anchored in the physical domain. Indeed, lifting them out of the physical domain seems to be the point of the physical exercise for Leibniz; as he concludes in an essay on resistance of materials from 1684, ‘these few things having been considered, the whole matter is reduced to pure geometry, which is the single aim of physics and mechanics.’129 What is at issue here is rational mechanics, a discipline that has a problematic standing between a mathematically formulated physical theory and applied mathematics, and which became increasingly rareﬁed as the eighteenth century progressed. Newton himself describes his project as rational mechanics in the Preface to the Principia, deﬁning it as ‘the science, expressed in exact propositions and demonstrations, of the motions that result from any forces whatever and of the forces that are required for any motions whatever’.130 The Principia was not alone in this genre, and in the same year that it was published another piece of rational mechanics, Varignon’s Projet d’une Nouvelle Me´canique, also appeared. Varignon’s treatise is of minor signiﬁcance in its own right, but he was to become an important player in the Malebranche circle in the 1690s: his 1695 paper on the rectiﬁcation of curves was the ﬁrst recorded use of the Leibnizian calculus in this group,131 and his paper read to the Acade´mie in 1698, ‘Re`gle ge´ne´rale pour toutes sortes de mouvements de vitesses quelconques varie´es a` discretion’, marks the beginning of analytical mechanics in 128 See e.g. the account of Mauclarin and Simpson on the attraction of ellipsoids in Guicciardini, The Development of Newtonian Calculus, ch. 5. 129 Leibniz, Demonstrationes Novae de Resistentia Solidorum, in Math. Schriften, vi. 106–12: 112. As we have seen, this does not apply to the nature of forces, only to their effects: however, the question of the nature of forces falls outside physics for Leibniz. 130 Principia, Cohen and Whitman edn., 382. 131 But see Michel Blay, La Naissance de la me´canique analytique: La science du mouvement au tournant des XVII e et XVIII e sie`cles (Paris, 1992), 29–33, who suggests that l’Hoˆpital may have read papers on calculus to the Acade´mie in 1693, although if he did these were never transcribed.

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France.132 Yet it is worth noting that, by contrast with their contemporaries in England such as Gregory and Fatio de Duillier, this group were concerned almost exclusively with mathematical questions, and with mechanics only insofar as it could be dealt with in abstract algebraic terms. A year before the appearance of his Analyse, l’Hoˆpital was writing to Johann Bernoulli asking him to explain what centrifugal force was!133 PHENOMENALISM AND THE RISE OF RATIONAL MECHANIC S Leibniz’s attempt, in his Tentamen, to set out a dynamical system that rivalled that of Newton was a failure. He was unable to reconcile Kepler’s laws and his vortex theory, his claim that centrifugal force in orbital motion was inversely proportional to the third power of the distance was unsustainable, and Newton had delivered a serious theoretical blow to the very idea of centrifugal force in his construal of it as a reaction to forces exerted, rather than a force in its own right, in terms of his third law.134 But if the details of his physical theory were not followed up, in some respects his conception of what mechanics should be doing and how it should be doing it were. His view that gravitation had to be explained mechanically, and that the elastic properties of ﬂuids were the place to be seeking such an explanation, became common ground among continental natural philosophers and mathematicians. And the elaboration of the mathematical resources that he had provided in his calculus were widely taken as a sine qua non of further research in mechanics. There was, however, one general feature of his understanding of natural philosophy which was taken up in a way that was contrary to how Leibniz himself had intended it, but which his approach can be seen as sanctioning in some respects. Leibniz had believed that a priori knowledge of the structure of the universe was possible.135 It was possible only through metaphysics, however, and unachievable in principle without metaphysics, for all one had without metaphysics was an ungrounded phenomenal realm, which had no intelligibility, or even 132 This paper and three more from 1698 and 1699 were not published by the Acade´mie, but are reproduced in Michel Blay, ‘Quatre Me´moires ine´dites de Pierre Varignon consacre´s a` la science du mouvement’, Archives internationales d’histoire des sciences (1989), 218–48. 133 See Bertoloni-Meli, Equivalence and Priority, 201. 134 See Aiton, The Vortex Theory, ch. 6; Bertoloni-Meli, Equivalence and Priority, 186–90; and more generally on the reception of the Tentamen, ch. 9. 135 The commitment to the a priori standing of mechanics was not always a feature of Leibniz’s natural philosophy and seems to have been ﬁrst developed in the Phoranomus, written in 1689: see Franc¸ois Duchesneau, ‘Leibniz’s Theoretical Shift in the Phoranomus and Dynamica de Potentia’, Perspectives on Science 6 (1998), 77–109. I am using the term ‘a priori’ here in the modern sense (which derives from Kant). Seventeenth-century usage in particular was broader and less precise: see Adams, Leibniz, 109–10.

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reality, in its own right. Nevertheless, the investigation of this phenomenal realm reﬂected the a priori standing of the larger enterprise, particularly in the very abstract mathematical techniques that Leibniz had employed in exploring it, techniques which, as we have seen, in many respects transcended the physical situation for which they set out to account, in that considerations of geometrical picturability and physical intelligibility, so crucial to Newton’s employment of mathematics, were deliberately abandoned. The metaphysical system that Leibniz had developed was not wholly without its followers, and Wolff—who, it is worth noting, was a professor of mathematics—was to develop a trimmed-down version of it into the basic university metaphysics to replace scholasticism in the German university system.136 But those in continental Europe whose concern was with mechanics took no interest as a rule in Leibnizian metaphysics.137 Indeed, it was not just that they were not concerned to position mechanics in a more general metaphysical system, they were not even particularly concerned to position it within a more general natural-philosophical system. Their interests were in the development of mechanics as a mathematical exercise, trading on the a priori standing that Leibniz had effectively accorded it, but now this a priori standing was one that mechanics had in its own right: not something it had derivatively in virtue of reﬂecting a deeper metaphysics. The notion of mechanics as an a priori domain was reinforced by a number of developments in the discipline. If one conﬁned one’s attention to Book I and the ﬁrst half of Book II of Newton’s Principia, for example, then one could reasonably gain the impression that one was dealing with a form of mathematics, along the lines of Archimedes or Apollonius, which had physical implications that had to be drawn separately, and which were open to debate in a way that the mathematical propositions were not. It is important to remember in this context that, along with Basel, the centre for the development of mechanics in a way driven by new developments in mathematics was the Malebranche group in Paris. Malebranche’s phenomenalism complemented the idea of an a priori mechanics, and it is in the work of the Malebranche group—in Malebranche himself but also, for example, in works such as Fontenelle’s preface to l’Hoˆpital’s Analyse—that we must look if we are seeking the philosophical rationale for the new procedures. Unlike Leibniz, Malebranche had argued that the underpinnings of natural philosophy, underpinnings that made physical phenomena real in the ﬁrst place, were not in the domain of an intelligible metaphysics but in the domain of the supernatural, which was largely unintelligible to us. On the Malebranchean picture, the domain of the phenomenal is all we have access to, 136 As well as Wolff ’s own publications, there was a thriving Wolfﬁan textbook tradition between the 1820s and the 1850s. See Martin Scho¨nfeld, ‘German Philosophy after Leibniz’, in Steven Nadler, ed., A Companion to Early Modern Philosophy (Oxford, 2002), 545–61. 137 On the case of France, for example, where Leibniz had, outside mathematics, a low standing in the eighteenth century, see W. H. Barber, Leibniz in France (Oxford, 1955).

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and there is no point our seeking further elucidation. His view was that we should conﬁne ourselves to the phenomenal realm, which, provided we pay attention solely to primary qualities, can be pursued purely in mathematical— that is, effectively, a priori—terms. Such an approach risks removing mechanics from the realm of natural philosophy altogether. Throughout the Middle Ages and the Renaissance, mechanics was traditionally not regarded as part of natural philosophy, but as an essentially mathematical discipline. It was Galileo who, in his Discorsi of 1637, showed that his mechanics of falling bodies and projectiles dealt not with mathematical idealizations but with physical situations which were accessible empirically by means of carefully devised experiments. In this Galilean tradition, matter theory plays no part in the establishment of mechanics as a physical discipline, and the focus is kinematics, which Newton was able to ﬂesh out in dynamic terms (although, as we have seen, when it came to gravitation the limits of the kinematic model became evident). By contrast, on the mechanist model, mechanics was established as a physical discipline by virtue of being coupled with matter theory, in the form of micro-corpuscularianism. By the second half of the seventeenth century, however, in Huygens in particular, mechanics—in this case a blend of aerostatics, hydrostatics, and kinematics—had displaced matter theory to a large extent, although a combination of a commitment to micro-corpuscularianism, and the nature of the problems dealt with, such as orbital and pendular motions, together with the high degree of geometrical picturability of the procedures and results, meant that the physical nature of the discipline was constantly in evidence. But once we get to the continental mathematicians of the 1690s and early 1700s, there has been a signiﬁcant shift of focus. Celestial mechanics quickly stopped being an area of concern and the problems dealt with became increasingly abstract and general, as very abstract ‘blind’ mathematical techniques displaced geometrical picturability.138 This is evident in the work of Varignon, who was the ﬁrst in the Malebranche circle to apply the mathematical techniques devised by Leibniz, and being developed by the Bernoullis, to mechanical problems. Varignon did not follow Leibniz’s mechanics but Newton’s, and his work is in effect a mathematical rewriting, or rationalization as it were, of Book I of the Principia in analytical terms, rewriting the inverse square law, for example, in terms of Leibniz’s differential calculus. He assumed from the outset that the motion of bodies 138 This is matched by an almost exclusive concern with the production of accurate astronomical data, and an avoidance of astronomical theory, by astronomers and mathematicians at the Paris Observatory, exempliﬁed in their journal, Les Conaissances des Temps. The one exception is JeanDominique Cassini’s short-lived attempt to account for the rise and fall of tides in a twelve-hour cycle in terms of the impact of the lunar vortex on the earth’s celestial vortex: see J. B. Shank, The Newton Wars and the Beginning of the French Enlightenment (Chicago, 2008), 65–8. See also Anton Pannekoek, A History of Astronomy (New York, 1961), 278–9; and, more generally, Charles-Joseph-E´tienne Wolf, Histoire de l’Observatoire de Paris de sa fondation a` 1793 (Paris, 1902).

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could be mapped onto curves as described by the algorithms of the calculus, that is, in terms of summing of discrete inﬁnitesimal instants of uniform velocity, so that instead of a geometrical representation of velocity as the area of a geometrical ﬁgure, it is given in the form of a mathematical equation, v¼dx /dt, allowing any kind of motion, no matter how complex, to be captured.139 Varignon’s concern is with the full characterization of motion which has a component towards a centre, no matter how this tendency is generated, but he does not treat this, as Newton had, as a ﬁrst step, the next being to replace the central point with a body. Rather, it is an end in itself. Note also that, despite his talk of a motion towards the centre, which suggests a geometrical representation, Varignon does not work with relations between geometrical representations at all, but rather sets out to establish relations between symbols, geometrical diagrams being reduced to little more than illustrations.140 This was a tendency that was to characterize rational mechanics, so that its crowning achievement, Lagrange’s 1788 Me´canique analytique, could proceed without any geometrical diagrams. Lagrange boasts in the Preface to the ﬁrst edition that ‘no ﬁgures will be found in this work. The methods I present require neither constructions nor geometrical or mechanical arguments, but solely algebraic operations subject to a regular and uniform procedure. Those who appreciate mathematical analysis will see with pleasure mechanics becoming a new branch of it.’141 In effect, what happened with the emergence of rational mechanics was a fundamental reshaping of the relationship between mechanics and natural philosophy generally. Seventeenth-century mechanism had been the doctrine that the basic constituents of nature are inert micro-corpuscles whose interactions are restricted to collision, and are a function of their size, speed, and direction of motion. To the extent to which we can trace a mechanist tradition in the eighteenth century, one which generally speaking shares this conception, the focus of attention was no longer on the right combination of matter theory and mechanics, but on the core standing of mechanics among physical disciplines. Basically, the assumption was that all natural philosophy was mechanics, and that, as mechanics was pursued with greater and greater detail and sophistication, 139 See the texts given in Blay, ‘Quatre Me´moires ine´dites de Pierre Varignon’, and Blay’s discussion of Varignon, in his La Naissance de la me´canique analytique, 153–221. See also Pierre Costabel, ‘Pierre Varignon (1654–1722) et la diffusion en France du calcul differentiel et inte´gral’, Confe´rences du Palais de la De´couvert, ser. D., no. 108 (1965), 1–28. On the general question of geometrical versus algebraic representations in mechanics, see Michel Blay, Les Raisons de l’iniﬁni: Du monde clos a` l’univers mathe´matique (Paris, 1993). 140 See Blay, La Naissance, 161. 141 Joseph Louis de Lagrange, Analytical Mechanics, translated from the Me´canique analytique, nouvelle e´dition of 1811, ed. and trans. A. Boissonnade and V. N. Vagliente (Dordrecht, 1977), 7. A good example of a work in that tradition that stands mid-point between Varignon and Lagrange is Leonhard Euler, Introductio in analysin inﬁnitorum (Lausanne, 1748). See Niccolo` Guicciardini, ‘Dot-Age: Newton’s Mathematical Legacy in the Eighteenth Century’, Early Science and Medicine 9 (2004), 219–65: 243–6.

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the rest of natural philosophy would fall into place around it. The guiding idea, from Varignon and Hermann at the beginning of the eighteenth century, up to d’Alembert and Euler in mid-century, was that mechanics could be pursued independently of other natural-philosophical considerations, that it was the one absolutely secure physical discipline because of its mathematical (and effectively a priori) standing, and that all apparently recalcitrant physical phenomena—such as electricity, magnetism, chemical reactions, and physiological behaviour— could ultimately be reduced to mechanics. Moreover, it was taken that the way to secure this was to pursue mechanics until it was rich enough to incorporate the other disciplines, and it was assumed that such incorporation would come when the time was ripe: trying to force things prematurely would be detrimental to mechanics. There is a discrepancy in this conception, however, between what gives mechanics its foundational standing and what gives it its secure standing. What gives mechanics its foundational standing is its claim to provide a complete description of fundamental physical processes. Because these are fundamental physical processes, it can be assumed that everything else will fall into place if one gets them right. What gives mechanics its secure standing is above all its amenability to exhaustive mathematical characterization. This provides it, in effect, with an a priori status: the world must be as it claims. But this is also at the same time what pushes it into the domain of the phenomenal, and what distances it from empirical enquiry; and most problematically of all, what effectively cuts it off from other domains of natural philosophy. In the wake of the Principia, it looked brieﬂy as if the mechanist aim of modelling all natural philosophy on mechanics might be realized, but the most successful and brilliant developments in mechanics in the eighteenth century were self-contained: in isolation from, or at odds with, other developments in natural philosophy. Reduction was no more than a promissory note, and indeed little more than a bluff when it came to the development of intractable areas such as chemistry, electricity, and physiology. The collapse of mechanism as a route to a uniﬁed natural philosophy was not solely, or even primarily, the result of the change in standing of mechanics, however. The development of the notion of ‘experimental philosophy’ in the 1660s led to a questioning of mechanism’s commitment to, and ability to deliver, a micro-corpuscularian reduction of natural philosophy, and this had signiﬁcant consequences not only for explicitly reductionist programmes like mechanism, but more generally for any attempt to offer a comprehensive understanding of natural philosophy. In Locke’s hands, it was developed into a powerful and sophisticated doctrine, the central argument of which was that even an account that claimed to provide a complete description of fundamental physical processes would not thereby be a complete description of the physical realm.

4 From Experimental Philosophy to Empiricism Leibniz began reading and taking notes on Locke’s An Essay concerning Human Understanding within ﬁve years of its appearance in 1690. The publication of Pierre Coste’s French translation in 17001 enabled him to read the work with greater care, and he had completed an extensive critical commentary on it by the time of Locke’s death in November 1704. It is unlikely that Locke would have been very receptive.2 He was not impressed by the comments from Leibniz that had been passed on to him through an intermediary in the 1690s. The judgement was mutual. In 1714, while indicating his respect for Locke as a philosopher, Leibniz wrote to Re´mond of Locke’s ‘superﬁcial metaphysics’ and ignorance of ‘the mathematical method’, noting that the latter’s response was not surprising given that ‘our principles differed too widely’.3 Locke’s approach is not just at variance with that of Leibniz on particular issues, it is fundamentally antithetical to his understanding of the whole point of philosophical investigation. As we have seen, for Leibniz understanding takes the form of an essentially perspectival grasp: the aim is to expand the perspectives available to us in a 1 Essai philosophique concernant l’entendement humain, ou` l’on montre quelle est l’e´tendue de nos connoisances certaines, & la maniere dont nous y parvenons, trans. Pierre Coste (Amsterdam, 1700). This is a translation of the fourth (1700) edition of the Essay. A lengthy extract had in fact appeared in French two years before the publication of the ﬁrst English edition: ‘Extrait d’un livre anglois qui n’est pas encore publie´, intitule´ Essai philosophique concernant l’entendement, ou` l’on montre quelle est l’e´tendue¨ des nos conoissances certaines, & la manie`re dont nous y parvenons. Communique´ par Monsieur Locke’, Bibliothe`que universelle et historique 8 (1688), 49–142. On the relation between Locke and Coste, see Anne Goldgar, Impolite Learning: Conduct and Community in the Republic of Letters, 1680–1750 (New Haven, 1995), 117–21; and John Milton, ‘Pierre Coste, John Locke, and the Third Earl of Shaftesbury’, in Sarah Hutton and Paul Schuurman, eds., Studies on Locke: Sources, Contemporaries, and Legitimacy (Dordrecht, 2008), 195–224. 2 See Hans Aarsleff, ‘Leibniz on Locke on Language’, in Hans Aarsleff, From Locke to Saussure: Essays on the Study of Language and Intellectual History (London, 1982), 42–83. 3 Leibniz to Nicolas Re´mond, 14 March 1714: phil. Schriften, iii. 612. Cf. Catherine Wilson’s astute observation on Leibniz’s Nouveaux Essais: ‘Accustomed perhaps to continental subtlety, to the ignorance-as-weapon approach of writers like Pierre Bayle, Leibniz found it difﬁcult to believe that when Locke said he did not know about an issue he really did not know. He increasingly took Locke’s epistemological statements about the limits of knowledge as a cover for radical metaphysical doctrines’: Leibniz’s Metaphysics, 233.

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systematic way and to harmonize perspectives. The point of the philosophical exercise is to develop a form of intellectual grasp that reveals to us systematic connections, typically in the form of an underlying harmony, between everything at the most fundamental level. For Locke, by contrast, not only have we no reason to believe that there are any such fundamental systematic connections, we have good reason to believe that natural philosophy is pursued more successfully if such aspirations are not imposed on the enterprise. He makes his attitude to aspirations to ‘universal’ knowledge clear in the Introduction to the Essay: ‘We should not then perhaps be so forward, out of an affectation of an universal knowledge, to raise questions and perplex ourselves and others with disputes about things to which our understandings are not suited, and of which we cannot frame in our minds any clear or distinct perceptions.’4 Later on, in the body of the text, he elaborates upon the point in these terms: The Things that, as far as our Observation reaches, we constantly ﬁnd to proceed regularly, we may conclude, do act by a Law set them; but yet by a Law, that we know not: whereby, though Causes work steadily, and Effects constantly ﬂow from them, yet their Connexions and Dependancies being not discoverable in our Ideas, we can have but an experimental Knowledge of them. From all which ’tis easy to perceive, what a darkness we are involved in, how little ’tis of being, and the things that are, that we are capable to know. And therefore we shall do no injury to our Knowledge when we modestly think with our selves, that we are so far from being able to comprehend the whole nature of the Universe, and all the things contained in it, that we are not capable of philosophical Knowledge of the Bodies that are about us, and make a part of us . . . as to a perfect Science of natural Bodies, (not to mention spiritual Beings,) we are, I think, so far from being capable of any such thing that I conclude it lost labour to seek after it.5

One of the principal issues with which we shall be concerned in this chapter, which deals with the origins of empiricism in Locke, and in the next, which examines its impact on experimental natural philosophy, is the question of whether phenomenal explanations in natural philosophy have any autonomy, or whether all explanations in natural philosophy must ultimately be couched in terms of a single set of fundamental principles. On this question, Locke’s approach is as far removed from that of Leibniz as it is possible to be. Philosophical dispute had traditionally taken the form of competition between systems, and this was very much how Leibniz saw matters. Given this, it is hardly surprising that he can ﬁnd little common ground with Locke, who breaks the mould, in that his comprehensive account of human understanding is designed not to offer another system but rather shows what is wrong with the idea that phenomena have to be accommodated to a system if they are to be accounted for satisfactorily.

4

Essay, I. i. 4.

5

Ibid., IV. iii. 29.

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What is striking about Locke is not the originality of his project, but the clarity and penetration he brings to it and the success with which he accomplishes a particularly perplexing task. One of the most distinctive and disputed features of the seventeenth-century rejection of scholasticism was the questioning of systematic understanding. In the shaping of a new natural-philosophical persona, the intellectual morality of the natural philosopher that marked out the value and standing of his work was, for example, often speciﬁed in terms of independence from a system, because prior commitment to a system meant that in assessing arguments one was not assessing them with respect to the evidence but with respect to how well they ﬁt views one already held. This meant a lack of objectivity and an absence of an ability to, or willingness to, deal with arguments on their merits. We need to distinguish here between anti-system arguments of the ﬁrst half of the seventeenth century, and those from the 1660s onwards. In their early development, such arguments were at least in some respects little more than a rhetorical strategy. Both Galileo and Descartes levelled arguments against opponents along these lines, albeit for different reasons.6 Galileo was at least in part motivated by the fear that a Tychonic system was rapidly becoming the default astronomical system with increasing awareness of the faults of the Ptolemaic one, thereby pre-empting serious consideration of Copernicanism, and he responded by stressing the hypothetical nature of all astronomical systems and the ill-advisedness of attaching oneself to any single system (although he himself did in fact think that Copernicanism provided the true account).7 He was also in part motivated, however, by the desire to offer arguments without constantly having to defend them against the charge that they were incompatible with Aristotelian natural philosophy. This is clear, for example, in his attacks on Grassi in Il Saggiatore, where Grassi, in virtue of being a supporter of Aristotelianism, is presented as someone with an axe to grind, someone who is unable to argue a case on its merits and so has to rely on a philosophical system, which is treated as a form of intellectual dishonesty and a lack of objectivity. Descartes’ motivation was different, for he believed that reﬂection—guided by clear and distinct ideas—on the basic principles of natural philosophy showed that his own natural philosophy was the only true system. The principal factor obscuring this realization was prior commitment to another system—for all intents and purposes that of Aristotle—so clearing one’s mind of any prior system was a prerequisite for starting from ﬁrst principles in order to grasp the truth of the Cartesian one. By the 1660s in England, however, there began to emerge a different form of challenge to the idea of a system, one which wasn’t a holding position adopted 6

For the details, see Gaukroger, Emergence, ch. 6. See Mario Biagioli, Galileo Courtier, The Practice of Science in the Culture of Absolutism (Chicago, 1993), ch. 5. 7

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until one’s own system was accepted, but rather one in which genuine questions were raised about whether systematic understanding was always the most suitable and fruitful form of understanding in natural philosophy. The anti-system rhetoric of the Galileo/Descartes era was replaced by something that raised genuine questions as to whether there could be non-systematic forms of understanding, and indeed whether the search for systematic forms of understanding might not, on occasion, actually be an obstacle to understanding. This new questioning begins in earnest in the 1660s with the controversy over Boyle’s pneumatics, and with the controversy over Newton’s establishment of the heterogeneity of white light. I have looked at these developments in detail in The Emergence of a Scientiﬁc Culture.8 Brieﬂy, Boyle and Newton discovered that in order to account for certain phenomena in a satisfactory way they had to suspend their commitment to corpuscularianism. Because corpuscularianism had acted not merely as a form of explanation, but also as a way of organizing the explanandum into phenomena that needed explaining and those that did not, and distinguishing real and apparent properties, this meant that they needed some alternative way of organizing the phenomena under investigation other than in terms of underlying micro-corpuscularian structure. When one looks carefully at how they proceeded, it becomes clear that, for them, this organization was effectively provided by the experimental apparatus itself. The apparatus produced a certain range of phenomena which deﬁed explanation in fundamental terms, and indeed from a foundationalist mechanist perspective the results produced showed no internal coherence: they were anomalous. The way in which they were generated was therefore crucial, not just because this is what legitimated them but also because, if they were to have any coherence at all, it had something to do with the way in which they were generated, for it was this that held them together as connected phenomena, and excluded what might, on mechanist grounds, mistakenly or at least unhelpfully appear to be related phenomena. The way in which the results were generated was a function of the experimental apparatus, the way in which this apparatus was manipulated, and what one was able to do with it. Here a domain of investigation is brought into focus not through the constraints imposed by a postulated underlying structure, but by means of the experiment or instruments. For the advocate of a systematic mechanism, the ultimate explanations took the form of accounts in terms of underlying microscopic states, so that causation, and with it explanation, were always construed as vertical, as it were: causes and effects were not on the same level, because causes are always more fundamental. By contrast, Boyle and Newton postulated horizontal causal processes, those where cause and effect were on the same level, and where this was defended as a 8

Gaukroger, Emergence, ch. 10.

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genuine and independent form of explanation. What is at stake here is explanation of phenomena in terms of their systematic relations with other phenomena, not in terms of some underlying reality. Opponents of this way of proceeding were completely nonplussed by the claims of experimental philosophy, construing it as at best a merely provisional stage on the road to explanation in terms of underlying principles. Leibniz and Spinoza both thought Boyle perverse in not offering a ‘systematic’ account of his views, for example. Likewise, in criticizing Newton’s account of the production of a colour spectrum with a series of prisms, Huygens demanded that a hypothesis be offered as to how differences in motion were connected with differences in colour. But both Boyle and Newton saw the matter in a very different way. In effect, they rejected the idea that causes must be restricted to what underlies the phenomena, and in consequence that they must be located at a different level from the phenomena. Rather, their treatment implied that there is a way of understanding at least some phenomena that consists in exploring the causal connections between—as opposed to underlying—them. Putting matters in this way goes beyond any explicit statements in Boyle and Newton, who simply stand their ground, pointing to the results that they are able to achieve, rather than developing a general rationale for their practice.9 Boyle in particular was clearly torn on this issue for he was committed to mechanism as the fundamental level of explanation, and indeed was one of the greatest and most inﬂuential advocates of mechanism, yet his own experimental practice led him to reject any attempt to impose constraints driven by foundational considerations, mechanist or otherwise, if they conﬂicted with an experimental programme that was yielding a rich body of results. There are a number of ways in which one could respond to such conﬂict, and we can identify three broad directions in which one might go. First, one might conclude from the conﬂict that the problem lies with mechanism, and that it needs to be replaced by a different foundational natural philosophy, one consistent with these results. This is not Boyle’s approach but Newton can be seen as adopting such a tack in the case of gravitation, where he is prepared to seek (unsuccessfully) a non-mechanical foundational natural philosophy, albeit one that can presumably somehow coexist with mechanical explanations elsewhere. Such an approach is highly problematic in that it can easily end up in one’s seeking different foundational systems for every problematic area: there is no reason at all to think that the kind of foundations Newton sought for gravitation, for example, are going to be of any use in the case of the production of colours, and in these circumstances—where uniqueness is lost in favour of a potentially open-ended pluralism—it no longer seems appropriate to talk of the underlying systems as being foundational. Second, one could 9

Much later, with the publication of the second edition of the Principia in 1713, Newton will broach more general questions via the question of hypotheses.

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argue that the conﬂict arises because the underlying natural philosophy has not been sufﬁciently reﬁned, and that once it has been so reﬁned, we would no longer expect such conﬂicts. The guiding idea here is that the only way to account for physical phenomena, ultimately, is in terms of a fundamental underlying structure whose basic characteristics are shared not just by special classes of phenomena, as in the Boylean and Newtonian experimental cases, but by every physical phenomenon. Moreover, these characteristics shared by every physical phenomenon have a special explanatory standing because in the ﬁnal analysis they are constitutive of every physical phenomenon. Such an approach prompts a programme of developing the foundational system as an overriding priority and refusing to accept any results as deﬁnitive unless these accord with this system, on the grounds that there simply cannot be a conﬂict between the single unique underlying basic structure and particular experimental results. Third, one could argue that explanations do not have to be couched in terms of an underlying foundational system at all. This does not necessarily mean that one should abandon general natural-philosophical systems, only that explanations that take the form of making connections—causal, kinematic, or whatever—on a local level may be, and may remain, the best approach we have. The criticism that this tactic faces is that it gives up too early, avoiding fundamental issues. In what follows, I shall argue that Locke managed to devise a philosophically defensible statement of the third position, something Boyle and Newton were unable to achieve. It was only with Locke that a developed philosophical alternative began to be offered to the notion that all physical explanation must take the form of reduction to a single underlying system. The ambiguities and apparent hesitation we ﬁnd in his account reﬂect the fundamental and especially intractable nature of the task he set himself, and the radical novelty of his solution. To this end, I shall be looking at the development of Locke’s account in the Essay, for this development reveals, more clearly than an examination of his mature position alone, just what the nexus of questions was to which his novel solution was supposed to provide the answer. The issues Locke tackled were pivotal for the development of new understandings of natural philosophy, its explanatory ambitions, and its broad cultural role in the eighteenth century. To highlight these issues, I shall draw a fundamental contrast between Locke and Leibniz. But the lines on which the contrast is drawn are necessarily complex. The traditional contrast between rationalism and empiricism, while it contains some truth, harbours too many misunderstandings to be serviceable. The distinction, as it has been employed since the mid-nineteenth century, derives from the Kantian-inspired historiography of Kuno Fischer, who supplied what was until recently the deﬁnitive version of the modern account of the development of philosophy in the seventeenth and

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eighteenth centuries.10 Basically, this account sought to establish two things. First, it maintained that epistemology replaced metaphysics as the core of philosophy in the seventeenth century. Secondly, it marked out the seventeenth century as beginning a new era in philosophy: the old Platonist/Aristotelian dichotomy was replaced by a new one, reﬂecting the fact that a new beginning had been made. This new dichotomy was one between competing and mutually exclusive epistemologies, rationalism and empiricism, the former basing everything on truths of reason, the latter basing everything on experiential truths.11 But although d’Alembert comes close to such a formulation in the preliminary Discours to the Encyclope´die, as we shall see later, the dichotomy has principally served the Kantian interest of providing a genealogy of all earlier philosophy whereby certain problems irresolvable in earlier systems can be seen to be ﬁnally and deﬁnitively resolved only by adopting the Kantian project. The way in which epistemology functions in the Kantian project is, however, very different from the way in which it functions in the seventeenth and eighteenth centuries, where it often has a highly naturalistic motivation. For example, in the case of Descartes, as I have argued elsewhere,12 a philosophical programme driven primarily by natural-philosophical considerations has been distorted beyond recognition by commentators who have construed it in terms of the ‘pure’ epistemology, free from any empirical considerations, of the kind that has characterized Kantian and much post-Kantian epistemology.13 Moreover, the ‘rationalist’/‘empiricist’ grouping of Descartes-Spinoza-Leibniz versus Locke-Berkeley-Hume is wholly 10 Kuno Fischer, Geschichte der neueren Philosophie (6 vols., Berlin, 1852–77). The volume on Descartes was translated as Descartes and his School (London, 1887). See also his Metaphysik oder Wissenschaftslehre (Stuttgart, 1852). Fischer’s approach in fact draws on both Kant and Hegel: see the invaluable account in Thomas E. Willey, Back to Kant: The Revival of Kantianism in German Social and Historical Thought, 1860–1914 (Detroit, 1978). For a diametrically opposed view, in which the shift to modern philosophy is construed as one from metaphysics to anthropology, see the account of Fischer’s contemporary, Wilhelm Dilthey, in his 1904 ‘Die Funktion der Anthropologie in der Kultur des 16. und 17. Jahrhunderts’, in Wilhelm Dilthey, Gesammelte Schriften (26 vols. to date, Stuttgart/Go¨ttingen, 1957–2005), ii. 416–92. For a modern example of this kind of approach, see Harrison, The Fall of Man and the Foundations of Science. 11 On historiographical aspects of the rationalism/empiricism issue, see Louis E. Loeb, From Descartes to Hume (Ithaca, NY, 1981), ch. 1; Bruce Kuklick, ‘Seven Thinkers and How They Grew: Descartes, Spinoza, Leibniz; Locke, Berkeley, Hume; Kant’, in R. Rorty et al., eds., Philosophy in History (Cambridge, 1984), 125–40; and Knud Haakonssen, ‘The History of Eighteenth-Century Philosophy: History or Philosophy?’, in Knud Haakonssen, ed., The Cambridge History of Eighteenth-Century Philosophy, vol. ii (Cambridge, 2006), 1–25. On the historiography of philosophy in the period between Descartes and Kant, see Giovanni Santinello (gen. ed.), Storia della storie generali della ﬁlosoﬁa, ii: Dall’eta Cartesiana a Brucker (Brescia, 1982). 12 Gaukroger, Descartes, An Intellectual Biography. 13 See also Stephen Buckle, Hume’s Enlightenment Tract: The Unity and Purpose of An Enquiry Concerning Human Understanding (Oxford, 2001), ch. 2, for a detailed argument that the rationalist/ empiricist reading of Hume completely distorts his project. Cf., in the same vein, Donald W. Livingston, Hume’s Philosophy of Common Life (Chicago, 1984); and idem, Philosophical Melancholy and Delirium: Hume’s Pathology of Philosophy (Chicago, 1998). See also Eric Watkins, Kant and the Metaphysics of Causality (Cambridge, 2005), on the adverse consequences of this way of proceeding for understanding Kant.

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misleading insofar as it suggests non-existent differences and continuities. Spinoza and Leibniz rejected Descartes’ sceptically driven epistemology,14 whereas Berkeley and Hume, albeit it in rather different ways, took scepticism seriously. Locke was closer to Descartes in many respects than Spinoza and Leibniz ever were, and Berkeley owed far more to that arch-Cartesian Malebranche than he did to Locke. In looking at the development of the ideas that ﬁnally appear in Locke’s Essay, I want to bring out their thoroughly natural-philosophical origins. In particular, we shall see that making sense of an observational/empirical/experimental form of natural-philosophical practice is Locke’s starting point, and that the success of the Essay is tied in with its ability to articulate the legitimacy of a form of natural philosophy that is not grounded in, and does not require grounding in, a more fundamental underlying natural description. This is not because there exists no such foundational level. Locke’s claim is more subtle than that: it is that it is philosophically mistaken to believe that there is nothing that cannot be securely grounded at this more fundamental level. THE VINDICATION OF EXPERIMENTAL PHILOSOPHY Locke provides a statement of his ambitions in the ‘Epistle to the Reader’ at the beginning of the Essay in these terms: The Commonwealth of Learning is not at this time without Master-Builders, whose mighty Designs, in advancing the Sciences, will leave lasting monuments to the Admiration of Posterity: But every one must not hope to be a Boyle, or a Sydenham; and in an Age that produces such Masters, as the Great Huygenius, and the Incomparable Mr. Newton, with some other of that strain; ’tis Ambition enough to be imploy’d as an Under-Labourer in clearing Ground a little, and removing some of the Rubbish that lies in the Way to Knowledg.15

Locke’s concern was with the clariﬁcation and legitimation of a certain kind of natural-philosophical enquiry,16 but what exactly was he trying to clarify and 14 For a speciﬁcally historiographical treatment of the misreading of Leibniz as a rationalist, see Stuart Brown, ‘Leibniz’s Break with Cartesian “Rationalism”’, in A. J. Holland, ed., Philosophy, Its History and Historiography (Dordrecht, 1985), 195–208. 15 Locke, Works, i. p. ix. The imagery of the underlabourer clearing away rubbish was a standard trope in Royal Society apologetics: cf. e.g. Joseph Glanvill, who tells his readers that the task of his age ‘can be little more than to remove the Rubbish, lay in Materials, and put things in order for the Building’: Plus Ultra (London, 1668), 91; and Boyle writes that he is willing to ‘not only be an Underbuilder, but ev’n dig in the Quarries for Materials towards so useful a Structure, as a solid body of Natural Philosophy, than not to do something towards the erection of it.’ Certain physiological essays and other tracts (London, 1669), 18. 16 Note that Locke does not think of the Essay as being a work in ‘philosophy’ but as something preparatory to philosophy. As Aaron points out, he would have regarded Newton, Boyle, and Sydenham as more deserving of the title ‘philosopher’ than he was, and he would ‘have thought it strange had anyone identiﬁed the aim of the philosopher as such with his aim in the Essay’. Richard I. Aaron, John Locke (3rd edn., Oxford, 1971), 74–5.

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vindicate, and why did this take the form of a sensationalist doctrine that he himself seems to have had worries about? The ﬁgures he mentions are, on the face of it, quite disparate: Boyle pursued an experimentalist approach in chemistry and pneumatics, Sydenham developed elaborate procedures of record-keeping in a traditional Hippocratic form of clinical medicine, Huygens was the leading ﬁgure in mechanics in the midseventeenth century, and Newton was the author of the consummate system of mechanics. But in fact there is a stronger connection between Boyle, Sydenham, and Newton: each of them was associated with a distinctive shift to ‘experimentalist’ developments in natural philosophy.17 In Some Thoughts Concerning Education (1693), Locke sets out what should and should not be taken to be acceptable natural philosophy: But to return to the Study of Natural Philosophy: Though the World be full of Systems of it, yet I cannot say, I know any one which can be taught a young Man as a Science, wherein he may be sure to ﬁnd Truth and Certainty, which is what all Sciences give an Expectation of. I do not hence conclude, that none of them are to be read; it is necessary for a Gentleman, in this learned Age, to look into some of them to ﬁt himself for Conversation: But whether that of Des Cartes be put into his Hands, as that which is most in fashion, or it be thought ﬁt to give him a short View of that and several other also; I think the Systems of Natural Philosophy, that have obtained in this Part of the World, are to be read more to know the Hypotheses, and to understand the Terms and Ways of talking of the several Sects, than with hopes to gain thereby a comprehensive, scientiﬁcal and satisfactory Knowledge of the Works of Nature. . . . But I would not deter anyone from the study of Nature, because all Knowledge we have, or possibly can have of it, cannot be brought into a Science. There are very many things in it, that are convenient and necessary to be known by a Gentleman: And a great many other, that will abundantly reward the Pains of the Curious with Delight and Advantage. But these, I think, are rather to be found among such Writers, as have imploy’d themselves in making rational Experiments and Observations, than in starting barely speculative Systems. Such Writings therefore, as many of Mr Boyle’s are, with others that have writ of Husbandry, Planting, Gardening, and the like, may be ﬁt for a Gentleman, when he has a little acquainted himself with some of the Systems of the Natural Philosophy in fashion.18

This is a position on the standing of natural philosophy that is constant through Locke’s career. Our principal task is to discover why it becomes articulated in terms of sensationalism. We can trace a number of stages in the

17 Huygens was a staunch opponent of experimental philosophy, but he was at the same time a steadfast advocate of the doctrine that we should conﬁne our enquiries to what we can grasp clearly and distinctly (and indeed this is what drives his eschewal of any talk of force: see Gaukroger, Emergence, 420–30). 18 Some Thoughts Concerning Education }193; Works, iii. 88–9. In connection with the references to planting and gardening, it is worth remembering that Locke had been Secretary to the Council of Trade and Plantations between 1673 and 1675.

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formulation of Locke’s mature sensationalism/empiricism, as set out in the Essay. First, there is his association with Boyle while at Oxford in the 1660s, during which time he composed his Essays on the Law of Nature (1663–4). In 1667, he worked with Sydenham, and in all likelihood drafted two pieces very much in the vein of Sydenham’s work, Anatomia (1668) and De Arte Medica (1669). Then, at the beginning of 1671, he produced what was to be the ﬁrst draft of the Essay, showing the inﬂuence of Boyle and above all Sydenham, particularly in his rejection of any attempt to account for natural processes in terms of underlying causes. Later in 1671, in a second draft, while still remaining agnostic about any possibility of discovering underlying causes, he offered an argument to the best explanation for corpuscularianism, as providing the only terms in which underlying causes can be discussed. In other words, while we cannot say what the underlying causes are, we can say something decisive about what kinds of things and processes could act as underlying causes. Herein lies a far more persuasive account of the standing of experimental natural philosophy than that to be found either in Boyle, Newton, or Sydenham, or in Locke’s own earlier attempts to engage these issues. Over the next ﬁfteen years, Locke studied a number of metaphysical works which enabled him to reﬁne the position he had come to in the second draft. In 1674, Malebranche’s immensely inﬂuential revisionary Cartesian synthesis, De la recherche de la ve´rite´ was published, and it was followed in 1683 by Arnauld’s equally revisionary Cartesian response, Des vraies et des fausses ide´es. Malebranche pushed epistemology to the forefront of philosophical enquiry in a far more concerted fashion than anything we ﬁnd in Descartes, transforming the epistemologically driven metaphysics of the Meditationes into a detailed, comprehensive system which did not shirk from what he took to be the consequences of his logical, systematic approach. In particular, although an underlying causal structure was crucial to Cartesian natural philosophy, Malebranche effectively dislodged the role of underlying causes, by transferring them to the divine realm, which is unknowable, while at the same time arguing that we grasp only representations of the physical world, not the physical world itself (indeed it turns out that these representations are not even produced by the physical world). In Arnauld, Locke found a kindred spirit, although, I shall argue, he moves in a different direction from Arnauld. Malebranche treated perception as comprising sensation, a physiological process, and judgement, a completely separate mental act. Arnauld stresses that the perceptual act must be treated as uniﬁed: this is also Locke’s view, but he construes this uniﬁcation in very different terms. Uniﬁcation in Locke takes the form of the doctrine that perception is simply successful sensation. Locke and Boyle, who was ﬁve years his senior, were closely associated in the early to mid-1660s, as their correspondence and Locke’s commonplace book testiﬁes, and Locke read, and took notes on, Boyle’s books as they were

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published.19 In 1660, Boyle had published his New Experiments Physico-Mechanical, Touching the Spring of Air, and within a year his controversy with Hobbes began over whether his results, which could not be accommodated to prevailing corpuscularian accounts of the constitution of air, were to be treated as issuing from genuine natural-philosophical enquiry or whether they were merely one-off results. The controversy, which was to last more than a decade, pitted ‘speculative’ against ‘experimental’ philosophy, with Boyle having to defend the completeness of his account of the elasticity of the air, despite the fact that it made no appeal to any theory of underlying corpuscular structure, and despite the fact that there can be no doubt that Boyle himself believed that air had an underlying corpuscular structure. One way in which one might capture what is at issue here is to envisage different levels of description, and identify those levels at which we can achieve some degree of certainty, by contrast with those at which there is likely to remain signiﬁcant dispute.20 This way of thinking may well have its origins in Boyle’s irenic conception of theological understanding, whereby there is a fundamental distinction to be made between those beliefs shared by all Christians, and beliefs that go beyond these and are a cause of division among Christians. Certainly in many respects his understanding of natural philosophy mirrors this. But Boyle seems to want to say a little more: he seems to want the kind of considerations that are supposed to secure our conﬁdence in experimental philosophy to play a further role, that of guiding our thinking on those parts of natural philosophy on which there is no agreement, and where perhaps it is too much to hope for agreement. So, for example, in The Origins of Forms and Qualities, according to the Corpuscular Philosophy, written at the time when he and Locke were collaborating, and published in 1666, he writes: For the knowledge we have of the bodies without us, being for the most part fetched from the informations the mind receives by the senses, we scarce know anything else in bodies, upon whose account they can work upon our senses, save their qualities: for as to the substantial forms which some imagine to be in all natural bodies, it is not half so evident that there are such as it is, that the wisest of those that do admit them confess, that they do not well know them. And as it is by their qualities that bodies act immediately upon our senses, so it is by virtue of those attributes likewise that they act upon other bodies, and by that action produce in them, and oftentimes in themselves, those changes that sometimes we call alterations, and sometimes generation or corruption.21

19 See Jonathan Walmsley, ‘Locke’s Natural Philosophy in Draft A of the Essay’, Journal of the History of Ideas 65 (2004), 15–37: 16. More generally on this period, see J. R. Milton, ‘Locke at Oxford’, in G. A. J. Rogers, ed., Locke’s Philosophy: Content and Context (Oxford, 1994), 29–47. 20 See Jan W. Wojcik, Robert Boyle and the Limits of Reason (Cambridge, 2002). 21 Robert Boyle, The Works of the Honourable Robert Boyle, ed. Thomas Birch (6 vols., London, 1772), iii. 11.

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The idea here seems to be that we identify the requisite level of certainty— sensation—and then attempt to use this as a guide to how we might deal with other levels of description. But exactly what is being advocated is unclear. The ﬁrst sentence seems to suggest that we must restrict our enquiry to what we can observe, while the second suggests that sensory qualities are being transferred to a more fundamental unobservable level, replacing substantial forms. This is the core problem bequeathed to Locke. But except for a short manuscript note22 and a passing remark in the 1663/4 unpublished Essays on the Law of Nature, that ‘lightness and heaviness, warmth and coldness, colours and the rest of the qualities presented to the senses’, can all ‘in some way to be traced back to motion’,23 a standard Cartesian position,24 Locke wrote nothing on natural philosophy during his time with Boyle. In 1666, he came across the newly published Methodus Curandi Febres of Thomas Sydenham. Locke had been studying medicine since his graduation in 1658, and it is not surprising that he should have been drawn to the Boyle circle, which represented the cutting edge of the post-Harveian project in the physiology of respiration and circulation.25 At the beginning of 1667, Locke left Oxford to join the household of Anthony Ashley Cooper (later 1st Earl of Shaftesbury) as physician and secretary, and began a close collaboration with Sydenham.26 Although Sydenham’s interest was not in natural philosophy as such but in clinical medicine, there are striking parallels between his approach to this question and Boyle’s approach to natural philosophy, and indeed the Methodus was dedicated to Boyle. The context within which Sydenham was working was far more fraught and polemicized than that in which Boyle found himself, even in the ill-tempered dispute with Hobbes over pneumatics. Galenist clinical physicians such as Sydenham believed, with some justiﬁcation, that medicine, traditionally controlled by the College of Physicians (of which, somewhat surprisingly, Sydenham was never actually a member), was subject to takeover by apothecaries and others who eschewed clinical investigation in favour of pharmaceutical cures based on general and highly contentious natural-philosophical principles. In brief, Galenists saw disease in terms of an imbalance in humours, so that every illness is 22

The ‘morbus’ entry in Add MS 32554, written between late 1666 and early 1667. Locke, Essays on the Law of Nature, 150 [text]/151 [trans]. Locke read Descartes between 1660 and 1662: see Milton, ‘Locke at Oxford’, 37–8. Note that Boyle rejected this account of colours in his 1664 Experiments and considerations touching colours: see his criticisms of Descartes in Boyle, Works, i. 694–6. 25 On Locke’s involvement with this circle, see Robert G. Frank Jr., Harvey and the Oxford Physiologists (Berkeley, 1980). 26 On Sydenham, see especially Kenneth Dewhurst, Dr. Thomas Sydenham (1624–1689) (London, 1966), and Andrew Cunningham, ‘Thomas Sydenham: Epidemics, Experiment, and the “Good Old Cause”’, in Roger French and Andrew Wear, eds., The Medical Revolution of the Seventeenth Century (Cambridge, 1989), 164–90. On Locke’s relation to Sydenham, see Franc¸ois Duchesneau, L’Empirisme de Locke (The Hague, 1973), chs. 1–2; Jonathan Walmsley, ‘The Development of Locke’s Mechanism in the Drafts of the Essay’, British Journal for the History of Philosophy 11 (2003), 417–49; idem, ‘Locke’s Natural Philosophy’. 23 24

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essentially individual, and the remedy must be speciﬁc to the person.27 Paracelsians and Helmontians, by contrast, thought of diseases as separately classiﬁable entities with universally identiﬁable causes and anatomical effects. As a consequence, they insisted that medicines prescribed were for the illness, not the person, and could be dispensed by apothecaries. Paracelsians and Helmontians had little time for what they considered superﬁcial clinical examination. They were interested in aetiology: they sought to uncover a deeper level at which causes of illness could be recognized and treated. In fact, despite their obsession with the useless practice of blood-letting, the experienced clinical physicians of the College of Physicians had considerably more diagnostic success than the unregulated apothecaries with whom they were in competition. Sydenham believed we had no access at all to underlying causes, dismissing the study of anatomy, and maintaining that disputes over such matters were useless to medicine. The physician had to conﬁne himself to observation of the course of an illness, i.e. of its visible effects, rather than postulating underlying causes, and to keeping careful records so that the effectiveness of various remedies could be gauged. Indeed, this approach enabled Sydenham to triumph in what was the weakest area for Galenists, and the strongest for Paracelsians and their allies: epidemics and plagues. Because Galenists conceived of disease as an imbalance of humours they were constrained to see all disease in individual terms. To keep epidemics and plagues within the ambit of their skills, they had to treat them as derangements of the blood. But this was a highly problematic strategy, and at the time of the Black Death, in the fourteenth century, Galenist physicians had effectively conceded defeat and sought astrological and other causes for something that seemed to be working on a supra-individual level. Paracelsians and Helmontians, by contrast, could understand plagues in terms of the transmission of vapours or spirits through the atmosphere or through physical contact. Hence the importance for Galenist medicine of Sydenham’s invention of nosology, the systematic classiﬁcation and listing of diseases on the basis of repeated and informed clinical observation. This was something that offered a completely different approach to understanding epidemics, and provided a vindication of the general procedure of requiring detailed observation of the course of an illness rather than postulating underlying causes. Locke helped Sydenham prepare the second edition of his Methodus, and if two papers that have plausibly been ascribed to Locke, Anatomia (1668) and De arte medica (1669), are indeed by him,28 then he was a strong advocate of

27 See the discussion in Gaukroger, Emergence, ch. 9; relevant literature is cited there but see especially Andrew Wear, Knowledge and Practice in English Medicine, 1550–1680 (Cambridge, 2000), chs. 8 and 9. 28 The texts are transcribed in Dewhurst, Dr. Thomas Sydenham, 79–93. The case for Locke’s authorship is put in Guy Meynell, ‘Locke as Author of Anatomia and De arte medica’, Locke Newsletter 25 (1994), 65–73. See also, Duchesne, L’Empirisme de Locke, ch. 2.

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Sydenham’s approach in the late 1660s.29 Anatomia denies the relevance of anatomy to medicine, on the grounds that natural processes in bodies take place at such a microscopic level that they will never be observed, stressing that what the physician needs are careful and informed observation and diligent recording. Indeed, the Anatomia questions whether the search for the underlying principles of respiration—mentioning such postulated functions as cooling, fermentation, and mixing of particles—are capable of resolution, and they are dismissed as being of no relevance to medicine.30 THE ORIGINS O F LOCKE’S E SS A Y In the Epistle to the Reader, at the beginning of the Essay, Locke describes the origins of the work nearly twenty years earlier in a meeting of a group of friends, at the beginning of 1671.31 They met to discuss an unspeciﬁed philosophical matter,32 and on agreeing to focus their enquiry on a chosen question, Locke suggested the extent and limitations of human understanding, and was asked to prepare a paper on this topic. What is most likely a revised version of this paper, an extended entry in one of his commonplace books, was completed in the summer of 1671, and is the ﬁrst extant draft of the Essay, known as Draft A. Draft A shows very signiﬁcant continuities with Anatomia and De arte medica,33 and Locke generalizes the idea that one should restrict oneself to observation, replanting it, as it were, in a natural-philosophical context in which it becomes a doctrine about general sensible qualities of things and the insensible bearers of these qualities. What in the Anatomia was a doctrine about underlying principles of bodily functions is now transformed into a wholesale rejection of matter theory. All our knowledge, Locke explains in the opening sentence, ‘is founded on and ultimately derives its self from sense, or something analogous to it & may 29 Peter Anstey, who is editing the Clarendon edition of Locke’s natural-philosophical writings, has suggested to me that the inﬂuence may in fact have been predominantly the other way around: it is possible that Sydenham was in fact taking up Locke’s views on these questions. 30 On this question, see especially Walmsley, ‘The Development of Locke’s Mechanism’, 418–22. Contrary to Walmsley, who treats Boyle as a straightforward corpuscularian, I do not consider this as a rejection of Boyle’s programme so much as a statement of one horn of Boyle’s dilemma. 31 Throughout his life, Locke was an active participant in discussion groups or intellectual salons, and indeed founded some, setting out rules governing them. See Luisa Simonuti, ‘Circles of Virtuosi and “Charity under Different Opinions”: The Crucible of Locke’s Last Writings’, in Sarah Hutton and Paul Schuurman, eds., Studies on Locke: Sources, Contemporaries, and Legitimacy (Dordrecht, 2008), 177–94. 32 A marginal note against the passage in question in James Tyrrell’s copy of the Essay suggests that the questions concerned morality and revealed religion, and this has been generally accepted, although there is a dissenting view that they were medical questions: see Patrick Romanell, ‘Locke and Sydenham: A Fragment on Small-Pox’, Bulletin of the History of Medicine 32 (1958), 293–321: 319–321. See also Duchesneau, L’Empirisme de Locke, 135–9. 33 See Walmsley, ‘Locke’s Natural Philosophy’.

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be cald sensation which is donne by our senses conversant about particular objects which give us simple Ideas or Images of things’.34 The reliability of sensation derives from the fact that the understanding can noe more refuse to have these [ideas of perceived things] or alter them when in it or make new ones to its self & receive new ones into it any other way then by the senses or its owne operation then a mirror can refuse alter or change or produce in its self any other images or Ideas then the objects set before it doe there in produce, & these are properly simple apprehensions to which we apply the names that others doe which names have very undoubted & cleare signiﬁcations.35

This claim will later be articulated in terms of the idea that the mind, in considering what is presented to it by the senses, cannot be inﬂuenced by the will. Locke’s concern here, however, is rather with how the ‘immediate objects of sense . . . should subsist alone.’ We cannot understand how this can be, he argues, so we naturally suppose that ‘they rest & are united in some ﬁt & common subject which being as it were the support of those sensible qualitys he cals substance or mater, though it be certain that he hath noe other idea of that matter but what he hath barely of those sensible qualitys supposd to be inhærent in it’.36 The stress on sensation as the source of knowledge is certainly by no means novel: the Aristotelian tradition had treated it as such, and Gassendi and Hobbes had helped push the question of our reliance on sensation to the forefront of natural philosophy. Indeed, Gassendi had concluded that sense perception provided us with access not to underlying essential principles, as Aristotelians had argued, but only to surface emissions from bodies.37 But Locke is not simply taking the side of proto-empiricists in a debate over the sources of knowledge here. Gassendi and Hobbes were staunch advocates of the sole legitimacy of mechanism/corpuscularianism as the ultimate explanatory tool. In his dispute with Boyle over the air pump, for example, Hobbes refuses to accept the completeness of explanations of pneumatic phenomena which are not couched in terms of their underlying micro-corpuscularian structure.38 In Locke’s hands, the doctrine that knowledge is restricted to sensory effects must be seen in the context of the rejection of underlying structure. The most extreme form of this rejection is that of Sydenham, and it is this that he had defended two years earlier. The argument of Draft A can be seen as a philosophical vindication of this extreme view, now generalized to the whole of natural philosophy, whereby 34 John Locke, Drafts for the Essay Concerning Human Understanding, and Other Philosophical Writings i Drafts A and B, ed. Peter H. Nidditch and G. A. J. Rogers (Oxford, 1990), Draft A }1, 1. 35 Ibid., }5, 15. Locke uses the Cartesian terminology of clarity and distinctness to describe the indubitability of such simple ideas, e.g. ibid., }7, 16–17. 36 Ibid., }1, 1–2. 37 See e.g. Gassendi, Opera Omnia, ii. 462. 38 See Gaukroger, Emergence, ch. 10.

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recourse to a speculative and wholly hypothetical underlying structure—in this case matter theory—is stripped of any explanatory value. In other words, in contrast to the mainstream mechanist view that explanation in terms of underlying micro-corpuscularian structure is the only ultimately legitimate form of explanation, Locke counters with the view that such underlying structure does not in fact provide any kind of explanation at all because it falls outside the domain of what we can know. This goes far beyond anything Boyle had wanted to claim, as I have indicated. In the dispute between Galenists, such as Sydenham, and Helmontians, where diagnostic practice was what drove the issues, and where physicians often saw themselves as ﬁghting for their survival as a profession, it is not surprising that the questions occasionally took the form of a stark choice between conﬁning oneself to careful observation of the phenomena and postulating underlying non-sensible structural causes. But the move to a general natural-philosophical context imposes signiﬁcant philosophical demands. These demands are already evident in Boyle, as is the fact that he had been unable to meet the challenge. He wanted to defend the explanatory power and standing of his pneumatic results, in all their detail and complexity, against the objection that he had not explained pneumatic phenomena in terms of underlying micro-corpuscular events, and indeed his account was incompatible with available micro-corpuscular understandings of the behaviour of ﬂuid corpuscles. Consequently, it was charged, what he had offered was at best a ﬁrst attempt at describing the phenomena and not even in the realm of genuine explanation. In response, he wanted to argue that establishing systematic connections between the phenomena that his air pump linked was at least as legitimate an explanatory strategy as attempting to discover their underlying causes. But against this, he not only could not deny that there are underlying causally effective processes, he was clear also that, to the extent to which we are able to grasp such processes, they must be of a micro-corpuscularian form, by contrast with Aristotelian essential principles. Indeed, he is generally considered one of the pioneers of micro-corpuscularianism. On the face of it, it is difﬁcult to see how these two concerns might be reconciled. To stress the legitimacy of his results in pneumatics was in effect to stress their autonomy, that is, their autonomy with respect to more ‘fundamental’ levels of explanation. Of course, if one believed that there were in fact no more fundamental levels—either because they did not exist or because they were so inaccessible that there was nothing we could say about them—then there would be no issue. But if one is committed to micro-corpuscularianism as a unique and accurate description of the processes underlying the phenomena, the question arises whether any level of explanation other than this can properly be described as autonomous. If we are to have any hope of resolving these questions, we need to establish some relation between the autonomous phenomenal level and the level of microstructure. As I have indicated, Boyle seems aware of the issues here, to the extent that he takes the observational procedures employed at the phenomenal level to

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provide some kind of guide as to how we might proceed at other levels. But what kind of guide could this be? The micro-corpuscularian level is not amenable to observation, and the advent of microscopy, far from revealing a simpler world of interacting corpuscles at the microscopic level, instead revealed a world that was qualitatively more varied and complex than the macroscopic one. Moreover, it is unclear whether there are any analogues of observation at the level of the insensible. Indeed, talk of modelling the microscopic realm on procedures at the phenomenal level is misleading, in that it suggests that if such modelling were completely successful we could dispense with accounts at the phenomenal level: what conferred explanatory power on phenomenal accounts would now be transferred to the level of micro-structure. Yet that is patently not what Boyle had in mind: he wanted to retain explanatory autonomy at the phenomenal level, because he realized that—at least in the cases he was dealing with—this is where the most useful and illuminating explanatory accounts are to be found, and that reduction to a more fundamental level may not only be unnecessary but counterproductive in explanatory terms in some cases. These considerations do not undermine the idea of a relation between phenomenal and underlying levels, but they do begin to reveal some of the difﬁculty of the task of specifying just what that relation is. If, as I am suggesting, we take this to be the task of Locke’s project, and if we see Draft A as trying, in large part, to make philosophical sense of the extreme Sydenham position that he had advocated a couple of years earlier, then the transition from Draft A to Draft B can in turn be seen as a shift to a far more sophisticated approach, one which comes to terms with the dilemma that faced Boyle, and begins to deal with it in a serious way, albeit one that leads Locke into fundamental epistemological problems of an especially intractable nature. The prime concern of Draft A had been the doctrine that knowledge is restricted to sensory effects, originally advocated, as we have seen, in a natural-philosophical/ medical context. Draft B adds a complementary ingredient with a different provenance: the denial of innate ideas, a doctrine originally advocated in a moral/political/legal context. The combination allows Locke to shape a novel if, at this stage, rudimentary epistemology. Both the doctrine that the mind begins as a tabula rasa and the denial of innate ideas are mentioned brieﬂy in Draft A, although they are not explicitly associated. The former is introduced in the opening pages, and acts as a principle in his arguments for his defence of a sensationalist account of knowledge.39 The latter is introduced at the end of Draft A, and is discussed in the context of an objection to the idea that all knowledge derives from sensation, namely that we know certain truths—such as arithmetical truths—which we could not have come by via sensation and which must therefore be grasped in the form of innate 39

Drafts, Draft A, }2, 8.

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ideas. Locke’s reply is twofold. In the ﬁrst place he qualiﬁes his sensationalism, telling us: ‘I never said that the truth of all propositions was to be made out to us by our senses for this was to leave noe roome for reason at all, which I think by a right traceing of those Ideas which it hath received from Sense or Sensation may come to the knowledg of many propositions which our senses could never have discoverd.’40 The second part of the reply consists in ﬂeshing out this view that reason must work on sources of knowledge provided by sensation, and cannot provide such sources in its own right. He proceeds to provide an example of how we come by our notions of even and odd through sensation, and how we can subsequently establish by reason that all numbers are even or odd.41 It is important to note here, however, that the denial of innate ideas has quite different origins, and is introduced in the earlier Essays on the Law of Nature in the context of a discussion of moral and political authority. Here it plays a very substantial role in establishing the origins of such authority. In the third of the Essays, ﬁve arguments against innate ideas are provided: it is merely an unproven hypothesis; there is no general agreement among people as to moral rules, and where such agreement does exist it can be traced back to early education; that innate ideas would have to be universal yet ‘younger boys, illiterate people, and those primitive races which, having no institutions, laws, and knowledge, are said to live in accordance with nature’ are ignorant of morality; that ‘the foolish and insane’ have no knowledge of the supposedly innate law of nature; and that the most basic principles of the sciences, such as the law of non-contradiction, are not innate but are learned from others or discovered ‘by induction and observing particulars’.42 When the doctrine is reintroduced in Draft B, these criteria are ﬁlled out a little but remain substantially the same, and the principal discussion turns on the question of whether we have an innate idea of God or an innate idea of morality.43 Moreover, although the discussion of innate ideas is primarily focused on practical as opposed to speculative questions, when compared with the ﬁnal version of the Essay for example, the mutual reinforcement conferred by the combination of the denial of innate ideas and the further development of the doctrine of sensation as the single source of knowledge means that Locke has, in a prototypical form, a general doctrine of what can and cannot be a source of knowledge, and he can use this doctrine to probe the issue of what we can say about disputes over what causal structure underlies the physical realm. There is a sense in which Draft B involves a general account of epistemology in a way that Draft A does not. The difference is that sensationalism in Draft A, while presented as a general theory, is really a theory about how we are to proceed in enquiry. In Draft B, much the same account of the sensationalist origins of knowledge in effect becomes a theory about any possible form of knowledge. 40 42 43

41 Ibid., }43, 75. Ibid., 75–8. Locke, Essays on the Law of Nature, 136–45. Idem, Drafts, Draft B }2, 106–11.

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This shift is not explicit. Rather, what happens is that sensationalism is applied beyond particular forms of enquiry to provide an account of anything purporting to be knowledge. In Draft A, we ﬁnd not only an agnosticism about the nature of underlying causes—something that Locke is unequivocally committed to throughout his career—but a rejection of the value of any discussion of underlying causes. We cannot choose between various postulated underlying structures, whether corpuscularian or Aristotelian: they are all in the same category of things we cannot know about and hence we should not concern ourselves with them. In Draft B, by contrast, what we ﬁnd instead is an outright rejection of Aristotelian forms and an advocacy of micro-corpuscularianism. This is not because Locke has come to the view that we can know the nature of underlying causes, or because he has abandoned his commitment to the value of explanatory procedures that eschew appeal to underlying structure. Rather, whereas Draft A can be seen as providing a rationale for a Sydenham-type approach which simply dismisses talk of underlying structures, Draft B begins to engage the Boylean concern to retain the autonomy of phenomenal explanations while at the same time rendering these compatible with micro-corpuscularianism as an account of underlying structure. The move is possible because of a signiﬁcantly more general construal of sensationalism as a general theory of what is to count as knowledge. The argument is that Aristotelian forms could not possibly count as an adequate account of underlying structure because we cannot even think of something not derived from sensation and reﬂection. Micro-corpuscularianism, by contrast, does satisfy this demand in Locke’s view, and as a consequence could offer a viable understanding of underlying structure in a way that an Aristotelian account could not: ‘though in the effects we dayly see produced in the world we perceive or know very little of the ways whereby their causes operate yet I thinke I may venture to say we can hardly conceive their efﬁcacy to consist in any thing but motion.’44 What does our conﬁdence in micro-corpuscularianism here lie in? Certainly underlying structures are not knowable directly. If tradition or general consent is not a legitimate source of such understanding,45 and if some innate grasp is also ruled out, then, to the extent to which we can say anything about underlying structures, there must be some form of inference involved. Here Locke is concerned to establish that such inference cannot reveal to us the nature of matter. He makes it clear that ‘we have noe Ideas nor notion of the essence of matter, but it lies wholly in the darke.’46 In particular, he rejects the prevalent

Ibid., }138, 256. As von Leyden points out in his Introduction to Essays on the Law of Nature (62–3), tradition and general consent are discussed along with innate ideas and sensation as two of the main purported sources of knowledge in the Essays, but by the time of the Drafts they survive only in occasional phrases such as ‘reports of others’ and ‘testimony of historians’. 46 Locke, Drafts, Draft B }19, 129. 44 45

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conception of the nature of matter, namely the Cartesian view that we can establish that the essence of matter consists in extension: perhaps it comes to passe that some have made the whole essence of body to consist in extension, because their mindes were soe full of the Ideas of it, which still adhered to & was connected with all visible & tangible objects, & soe were forward to afﬁrme that the essence of body must needs be extension because we could not imagin any sensible quality of any body without extension, whereas had these men considerd their Ideas of tasts smells & sounds of hunger & thirst & other pains, they would have found that they included in them or had annexed to them noe Idea of Extension at all, which is but an affectation of body as well as the rest discoverable by our senses which have noething at all to doe with the essences of things.47

The argument that we cannot grasp real essences is in no sense an admission of human failure on Locke’s part, but rather something that helps us clarify just what human cognitive aims are. In 1676, Locke translated three essays from Nicole’s Essais de morale,48 in the second of which, ‘Discourse on the Weakness of Man’, Nicole criticizes the vanity of human intellectual pretensions, complaining that ‘philosophy is a vain amusement, and that men know almost noething’.49 As Yeo has pointed out, this is very likely a position that Locke believed he had to confront: journal entries from 1676 and 1677 show him conceiving of knowledge as a moral duty, and his interest in clearing away obstacles to knowledge seems to be a direct response to Nicole’s pessimistic view that the vast scope of knowledge and the shortness of our lives make it impossible for us to know very much at all.50 One of the prime obstacles that Locke identiﬁes in a ‘Note on Study’, in his journal for March to May 1677, is the mistaken and counter-productive assumption that we must aim for encyclopedic or universal understanding. When we can grasp this, we can begin to understand what human cognitive aims should and should not be: The essences of substantial things are beyond our ken; the manner also how Nature, in this great machine of the world, produces the several phenomena, and continues the species of things in a successive generation, &c., is what I think lies also out of the reach of our understanding. That which seems to me to be suited to the end of man, and lie level to his understanding, is the improvement of natural experiments for the conveniences of this life, and the way of ordering himself so as to attain happiness in the other.51 Ibid., }29, 139. These were published posthumously in the early eighteenth century, but the ﬁrst reliable edition was: Discourses: Translated from Nicole’s Essays, by John Locke, with important variations from the original French (London, 1828). In many respects the text constitutes a rewriting rather than a translation. Nicole’s original essays were published as Essais de morale, contenus en divers traittez sur plusiers devoirs importans (4 vols., Paris, 1672–8). 49 Locke, Discourses, 33. 50 Richard Yeo, ‘John Locke and Polite Philosophy’, in Conal Condren, Stephen Gaukroger, and Ian Hunter, eds., The Philosopher in Early Modern Europe: The Nature of a Contested Identity (Cambridge, 2006), 254–75: 265–6. 51 Peter King, The Life and Letters of John Locke with Extracts from his Journals and Common-Place Books (London, 1884; repr. New York, 1972), 106–7. 47 48

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In 1674, the ﬁrst parts of Malebranche’s De la recherche de la ve´rite´ appeared. La recherche set out a systematic, comprehensive, and highly revisionary form of Cartesianism. It was to completely dominate the philosophical landscape in the ﬁnal quarter of the seventeenth century, continuing to play a major role in philosophical thought, jostling with Locke’s Essay, up the middle of the eighteenth century. Although Locke only wrote a critical appraisal of La recherche in 1693, after the publication of the Essay, he was familiar with its contents from an early stage, and occasionalism generally played a role in shaping his own views. We know that he purchased a copy of La recherche in 1676,52 and in 1684 he was engaged in a study of Arnauld’s criticisms of Malebranche on the question of the nature of ideas. McCracken has noted that Locke mentions several occasionalist authors— Cordemoy, La Forge, and Clauberg—in a journal entry for March 1678, and he traces changes in Locke’s thinking on causation between Drafts A and B and the ﬁnal version of the Essay.53 In Drafts A and B, in line with his general sensationalist account of the source of knowledge, Locke argues that the source of our knowledge of causation is sensation, and reﬂection is mentioned only casually, although he is clear that what sensation actually reveals about causation is ‘but a grosse kinde of knowledge and noe more than this’ and that a ‘comprehensive knowledg of causes & effects . . . is I thinke out of the reach of humane understanding.’54 By the Essay, reﬂection has come to play a more signiﬁcant role, and active powers, those capable of initiating changes in something, are, we are told, most clearly understood by reﬂection.55 Moreover, in the Essay he is even more circumspect about what sensation can reveal about active powers, since even collisions between bodies do not furnish us with any clear grasp of the active power involved.56 When we come to mind/body interaction, any sensory analogy breaks down and the best way to conceive of active powers is not in sensory terms at all, but rather, we should ‘direct our Minds to the consideration of God and Spirits, for the clearest Idea of active Power’.57 As McCracken points out, while the material on causation is copied with only slight changes from Draft B, the material on powers is completely new, and shows the inﬂuence of his reading of the occasionalists: indeed, the new doctrines are all to be found in the occasionalist texts that Locke had been reading.58

52 See Gabriel Bonno, Les relations intellectuelles de Locke avec la France, d’apre`s des documents ine´dits (Berkeley, 1955), 58, and more generally 223–52. 53 Charles J. McCracken, Malebranche and British Philosophy (Oxford, 1983), 148–55. 54 55 Locke, Draft A, }15. Idem, Essay, II. xxi. 4. 56 57 Ibid., II. xxi. 4. Ibid., II. xxi. 2. 58 McCracken, Malebranche and British Philosophy, 152–3.

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In many respects La recherche is antithetical to Locke’s project. It offers a systematic ordering of knowledge on ﬁrst principles, on a par with the systems of Spinoza and Leibniz; it integrates elements of Neoplatonism through its adherence to various Augustinian doctrines, most notably that of the need for divine illumination; it treats mathematics very much as a paradigm form of reasoning, even in physical matters (and was crucial in the early stages of the development of rational mechanics); it rejects all knowledge based merely on sensation, considering sensation as wholly lacking in authority; and it denies any causality at the phenomenal level. Yet not only was it central to the British ‘empiricist’ tradition, especially to Berkeley but also to Hume, but some of Malebranche’s conclusions ﬁt in tightly with those of Locke, right down to their common denial of innate ideas. The way in which these conclusions are generated is not only unlike anything in Locke, however, but is in fact wholly contrary to Locke’s approach. As I have presented the Lockean project, one of its aims was to come to terms with the question inherited from Boyle, namely that of how one can treat the establishment of connections, including causal connections, between the phenomena under investigation as having genuine explanatory power, in need of no supplementation, while at the same time maintaining that there is a micro-corpuscularian causal structure underlying the physical realm. Malebranche by contrast argues that physical things cannot act causally on one another. On the Boylean/ Lockean view, causation can be horizontal: bodies can act on other bodies and in such cases no recourse is needed to underlying causal structure. On Malebranche’s account, there can be no horizontal causation: all causation is vertical, involving different levels. But Malebranche’s stricture against material causation is really a consequence of the mechanist doctrine of the inertness of matter, and inertness holds not merely at the phenomenal level but also at the underlying micro-corpuscularian level: the corpuscles cannot act causally upon one another, nor can they causally induce any change at the macroscopic level. Activity, encompassing causal powers, is a prerogative of the supernatural, and all causation must be traced directly back to God: It is evident, that all Bodies, great and little, have no force to move themselves: a Mountain, a House, a Stone, a Grain of Sand, the minutest and bulkiest Bodies imaginable, are alike as to that. . . . Whence we must infer, if we will follow Light and Reason, That as no Body can move it self, so no Created Spirit can be the true and principal Cause of its Motion. But when we think on the idea of God, or of a Being inﬁnitely perfect, and consequently Almighty, we are aware that there is such a Connexion betwixt his Will and the Motion of all Bodies, that it is impossible to conceive that he should will that a Body be moved, and it should not be moved. And therefore if we speak according to our Conceptions, and not according to our Sensations, we must say that nothing but his Will can move bodies. The moving force of Bodies is not then in themselves, this force being nothing but the Will of God: Bodies then have no proper Action, and when a moving Ball meets with another, and moves it, the former

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communicates nothing of its own to the latter, as not having in it self the Impression it communicates; though the former be the Natural Cause of the latter’s Motion; and therefore a natural Cause is not a true and real Cause, but only an occasional; which in such or such a Case determines the Author of Nature to act in such and such a manner.59

Malebranche’s occasionalism has a certain afﬁnity with the Lockean position at a practical level however. God’s activity is completely opaque to us, and occasionalism is a wholly descriptive account: it does not, and could not, explain the nature of causal activity. Because of this, our accounts of particular physical phenomena cannot invoke causes in any explanatory role. We can make connections between the behaviour of phenomena and we can make connections between the behaviour of microscopic corpuscles, but the latter has no priority over the former in virtue of being genuinely causal because it is not causal: at this level they are all equal. Malebranche believes that we can provide a wholly general account of physical processes at the micro-corpuscularian level whereas our understanding of the macroscopic level is thoroughly compromised by our reliance on secondary qualities which we mistakenly treat as real properties of bodies. He also believes that micro-corpuscularian behaviour falls within the domain of mechanics and is completely quantiﬁable, allowing us a mathematical grasp which answers to the canons of ‘clarity and distinctness’ that play such an important role in the Cartesian tradition. Hence it is a key part of the Malebranchean project that macroscopic processes be redescribed in terms of the behaviour of constituent micro-corpuscles. But the distinctive feature of the Malebranchean position is that this has nothing to do with the direction of causation, because there is no causation. The upshot of this is that, from the point of view of causation, the macroscopic phenomenal realm is as autonomous as the microscopic realm. Simply described in these terms, we have here an answer to Boyle’s original worry. Moreover, if we are as concerned about the plausibility of occasionalism as some of his contemporaries and successors were, there is a simple phenomenalist strategy for dealing with this: we just strip Malebranche’s account of supernatural causation and abandon talk of causation entirely. This will be Hume’s strategy, at least on the face of it.60 It is an appealing and direct way of dealing with the autonomy of phenomenal explanations. But there are other issues at stake, which act to overdetermine the question. In particular, there still remains the issue of whether the phenomenal level is better described in its own terms or in terms of 59 Malebranche, De la recherche de la ve´rite´, Book VI Part 2 ch. 3. Translation from Father Malebranche his treatise concerning the search after truth, ii. 55. 60 I shall argue in Chapter 12 that Hume’s argument here is designed to devise a paradigmatic form of metaphysical argument, with a view to uncovering something problematic and counterintuitive about metaphysical argument in general. Because of this, while we can say that ‘Malebranche minus God’, so to speak, is indeed Hume’s metaphysical understanding of causation, we cannot say that this is his understanding of causation per se, because of the limits he sees to metaphysical understanding.

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an underlying micro-corpuscularian structure for reasons that have nothing to do with the direction of causation, but have rather to do with the saturation of phenomenal descriptions with secondary qualities, which on Malebranche’s account are not real qualities of bodies and therefore cannot play a genuinely explanatory role. Locke is clearly not willing to follow the Malebranchean path on this issue. He accepts the distinction between primary and secondary qualities, but denies that we can know what primary properties of corpuscles give rise to macroscopic secondary qualities, or even whether they depend upon them at all, rather than ‘upon something yet more remote from our comprehension’.61 Because of this, we cannot know either how secondary qualities are connected with one another at a more fundamental level, or what the connection is between particular primary qualities (or conﬁgurations of primary qualities) and particular secondary qualities. In chapter 6 of Book 4 of the Essay, he launches a detailed attack on the explanatory value of conﬁning ourselves to primary qualities, and as the account progresses a strong case begins to emerge for the explanatory autonomy of phenomenal accounts: For how much the Being and Operation of particular Substances in this our Globe depend on causes utterly beyond our view, is impossible for us to determine. We see and perceive some of the Motions and grosser Operations of things here about us; but whence the Streams come that keep all these curious Machines in motion and repair, how convey’d and modify’d, is beyond our Notice and Apprehension: and the great Parts and Wheels, as I so say, of this stupendous Structure of the Universe, may, for ought we know, have such a Connection and Dependance in their Inﬂuences and Operations one upon another, that perhaps things in this our Mansion would put on quite another face, and cease to be what they are, if some one of the Stars or great Bodies incomprehensibly remote from us, should cease to be or move as it does. This is certain, Things however absolute and intire they seem in themselves, are but Retainers to other parts of Nature, for that which they are most taken notice of by us.62

In other words, the potentially inﬁnite causal complexity of the world precludes the reduction of all phenomena to their constituent primary qualities being a successful explanatory strategy. Causation, in real cases, as opposed to the hypothetical idealized cases describable purely in mechanical terms, is typically a mixture of ‘horizontal’ and ‘vertical’ causation, and in the medical cases, as well as those of Boylean pneumatics and Newtonian chromatics, it is the ‘horizontal’ ones, that is, the causal relations between phenomena, that are doing the real explanatory work. Malebranche’s aim had been to redescribe the phenomena in terms of primary qualities, which characterized the micro-corpuscularian level and which provided this level with its explanatory priority. Relations, whether between phenomena, 61

Locke, Essay, IV. iii. 11.

62

Ibid., IV. vi. 11 (Works, i. 274).

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micro-corpuscles, or micro-corpuscles and phenomena, were not causal. There was a complete absence of any kind of power, and this meant that relations between bodies could be described in mathematical terms without residue. Physics was reduced to kinematics, a goal of the Cartesian tradition in mechanics, represented most notably in Huygens, and the beneﬁt of this was that everything could be presented ‘clearly and distinctly’. I showed in The Emergence of a Scientiﬁc Culture how, if we examine such a reductive strategy in the case of colour, we ﬁnd that not only did Descartes’ attempt to account for the behaviour of refracted light in terms of underlying structure mark a move away from quantiﬁcation, to one in the direction of a purely qualitative and speculative matter-theoretical approach, but that the explicitly non-reductive approach of Newton, in which phenomenal comparisons did the work, allowed a fully quantiﬁed account.63 Locke is on the Newton/Boyle side of the fence here and indeed the passage that I have just quoted from him provides a rationale for such an approach. What marks out Locke’s explicitly philosophical treatment from the ways in which Sydenham, Boyle, and Newton had touched on this question, is his attempt to provide an account of sense perception that underpins the coherence of the explanatory autonomy of phenomenal explanation. A good deal hinges on just how well his account of sensation and its role holds up. At ﬁrst sight, the prospects do not look good, for there seems to be a fundamental ambiguity in Locke’s treatment of the representational nature of perception. The problem is broached in the Essay in these terms: ’Tis evident, the Mind knows not Things immediately, but only by the intervention of the Ideas it has of them. Our Knowledg therefore is real, only so far as there is a conformity between our Ideas and the Reality of Things. But what shall be here the Criterion? How shall the Mind, when it perceives nothing but its own Ideas, know that they agree with Things themselves?64

But if, as Locke maintains, the mind only perceives its own ideas, then it would seem that the criticism he will make of Malebranche in his unpublished 1693 critique of Malebranche’s doctrine that we see all things in God will surely count against his own view. This objection is that, if when we believe we see the sun what we in fact see is not the sun at all but an image that God has caused to be in our mind, then because we cannot compare this image with the real sun, we are in no position to say that it is an image of the sun at all.65 The point seems generally applicable to any theory that holds that what we grasp in perception is a representation and not the thing represented.

63

Gaukroger, Emergence, ch. 10. Locke, Essay, IV. iv. 3 (Works, i. 262). Idem, ‘An Examination of P. Malebranche’s Opinion of Seeing all Things in God’, Works, iii. 429–50: }20, 434. 64 65

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The ﬁrst question we need to ask here is what the relation is between a representation and what it represents, and for this we need to be clear about what it is that is represented. Descartes, and with him the Cartesian tradition, had rejected the idea that perceptual representations are in any sense pictures of what they represent, and in Le Monde Descartes had suggested a linguistic model for visual perception, so that grasping something in virtue of seeing it is not like grasping it in virtue of seeing a picture of it, but rather like grasping something in virtue of understanding a statement about it.66 There are two issues here. First, the stress on representation rather than resemblance is a very strong theme in Descartes and it is developed not only in the context of visual cognition but also in that of memory recall, where he rejects the idea that memory traces must be stored in a way that resembles the content that is brought to mind when we remember.67 Cognitive representation never works via resemblance in Descartes. Malebranche qualiﬁes the representation doctrine in the case of primary qualities, but otherwise it was held generally by Cartesians. Second, Descartes held that God has provided us with sense organs not so that they might reveal to us the true nature of the world but in order that we might protect our bodies from harm.68 This second theory, about the function of sense perception, was universally held in the Cartesian tradition, and it was defended in detail, for example, both by Malebranche (who devotes the whole of Book I of La recherche to this and related questions) and Arnauld, who were otherwise diametrically opposed on questions of the nature of sense perception. Malebranche, for example, points out that if we experienced sensations as modiﬁcations of our mind, which is what they really are, then we would have to make a conscious inference from the state of our bodies, thereby failing to attend to the body’s needs immediately. Our false belief that pains are in our body is crucial if we are to remove our body from something harmful to it.69 Colours, likewise, we are told, enable us to pick out distant bodies—such as predators—much more easily than uncoloured bodies would.70 In a classic statement of the Cartesian account, Arnauld compares colour perception to the use of auxiliary patterns by tapestry workers. Where tapestry workers are faced with an area involving many only slightly varying shades of a colour, they routinely work from an auxiliary pattern ‘where the various shades of the same colour are indicated by completely different colours, so that they are less liable to mistake them’.71 66

Descartes, Le Monde, ch. 1. Œuvres, xi. 4. Traite´ de l’homme: Œuvres, xi. 177–9. See the discussion in Gaukroger, Descartes, 273–4; and, more generally, John Sutton, Philosophy and Memory Traces: Descartes to Connectionism (Cambridge, 1998). 68 Œuvres, vii. 83 (Sixth Meditation). 69 See e.g. De la recherche, I. x. }v. 70 This was at least the prevalent view among Cartesians. In fact matters are not so straightforward, as black and white vision offers a higher degree of deﬁnition than colour vision. 71 Antoine Arnauld, Des vrayes et des fausses ide´es contre ce q’enseigne l’auteur de la recherche de la verite´ (Cologne, 1683), 165; translation from Arnauld, On True and False Ideas (Manchester, 1990), 131–2. 67

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This doctrine must be borne in mind in considering Locke’s response to the question how the mind, when it perceives nothing but its own ideas, knows that they agree with things themselves. There are, he tells us, two sorts of ideas, namely simple ideas and complex ideas. The issue does not arise in the case of complex ideas, which are—with qualiﬁcations in the case of substances— combinations of simple ideas ‘which the Mind, by its free Choice, puts together’. These are ‘Archetypes of the Mind’s own making, not intended to be Copies of any thing’, and ‘that which is not design’d to represent any thing but it self, can never be capable of a wrong representation.’72 This leaves us with simple ideas: The ﬁrst are simple Ideas, which since the Mind, as has been shew’d, can by no means make hto iti self, must necessarily be the Product of Things operating on the Mind in a natural way, and producing therein those Perceptions which by the Wisdom and Will of our Maker they are ordain’d and adapted to. From whence it follows, that simple Ideas are not Fictions of our fancies, but the natural and regular Productions of Things without us, really operating upon us, and so carry with them all the Conformity which is intended, or which our State requires: for they represent to us Things under those Appearances which they are ﬁtted to produce in us, whereby we are enabled to distinguish the sorts of particular Substances, to discern the states they are in, and so to take them for our Necessities, and apply them to our Uses. Thus the Idea of Whiteness, or Bitterness, as it is in the Mind, exactly answering that Power which is in any Body to produce it there, has all the real Conformity it can, or ought to have, with things without us. And this conformity between our simple Ideas, and the Existence of Things, is sufﬁcient for real Knowledg.73

What is it that makes simple ideas true ideas here? Locke seems to be advocating a Cartesian view about what work ideas do. He talks of them being produced in the mind by things in a manner that accords with the way in which God, in his wisdom, wills them to be produced. The suggestion seems to be that God has made our minds in such a way that they respond to things by producing the requisite ideas, where what is requisite is something that God has determined, not something that we can settle by examining the relation between what is represented and the representation of it. To understand the difference between Locke and the Cartesian tradition here, consider the Aristotelian account of the veridicality of ideas. Aristotle did not think that we establish the veridicality of ideas by comparing them with what they represent. Rather, he argued that nature has provided us with the sense organs we have so that we might know the world. On this approach, only once we have answered the question why we have the sense organs we do, can we ask what their veridicality consists in, and Aristotle’s answer is that our sense organs are veridical, in the canonical case, when they are perceiving special sensibles 72 73

Locke, Essay, IV. iv. 5 (Works, i. 262–3). Ibid., IV. iv. 4 (Works, i. 262).

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under optimal conditions.74 For example, colour is the special sensible of vision, because it is that quality peculiar to vision: it can be perceived visually and it is not something that is common to vision and another sense (such as roundness, which, because it can be perceived by vision and touch, is a not a special sensible but a common sensible). When I perceive that something is white, and I perceive this under optimal conditions—I am healthy, the lighting is excellent, there is no intervening medium, etc.—then my perception is veridical, not because I can compare my white perception with the whiteness in the object, but because I have satisﬁed all the conditions for determining whether something is white. There are no other conditions to be satisﬁed. Compare this with Malebranche’s Cartesian account. Here again, a functional understanding of sense perception is prior to the question of veridicality. Our sense organs are designed to enable us to preserve our bodies, not to enable us to know what the world is like. Malebranche provides numerous examples to show that the senses systematically mislead us as to the nature of the world, but he is adamant that the error does not lie in the senses: rather it lies in our mistaken judgement that the role of the senses is to reveal the nature of the world to us.75 If we want to understand the nature of the world, then we must turn to natural philosophy, at its core (a mechanics puriﬁed of talk of forces) purely the work of reason, but aided by tightly controlled sense perception (that is, sense perception tightly controlled by reason) in the experimental realm. But can the Malebranchean account bypass veridicality by comparison in the way that Aristotle’s can? Aristotle’s is what might be called functional veridicality as opposed to comparative veridicality. The representation of the world is veridical to the extent that it completely satisﬁes a function, to the extent that it does exactly what it is supposed to do. The functional understanding offered in the Cartesian account is different: satisfaction of the function does not yield veridicality, but recognition of certain kinds of bodily needs and how they might be satisﬁed. Such recognition is cognitive and representational, but not of a kind that involves veridicality. Of course, one direction that one might go in here is to say that we can do without veridicality. Two centuries later, this will be the path taken by evolutionary and pragmatist forms of epistemology, but I do not know of any seventeenth- or eighteenth-century thinkers who considered this to be an option, and it is certainly not the path that Malebranche follows. There are two issues in Malebranche’s account. One is the mistaking of secondary qualities for real qualities in our perception, with the result that we believe we see something in the world (e.g. colour) which is actually something in 74 See e.g. De anima, 428b27–8. The issues are discussed in detail in Irving Block, ‘Truth and Error in Aristotle’s Theory of Perception’, Philosophical Quarterly 11 (1961), 1–9; and Stephen Gaukroger, ‘Aristotle on the Function of Sense Perception’, Studies in History and Philosophy of Science 12 (1981), 75–89. 75 See the discussion in Gaukroger, Emergence, 333–5.

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the mind. When we perceive primary qualities—paradigmatically shapes—however, we are seeing something that resembles what there is in the world. The importance of this for present purposes is that sensory veridicality consists in resemblance for Malebranche. The other issue is the occasionalist view that when we turn our eyes towards some object in the world, what we see (secondary qualities aside) resembles the object, but the object itself is not the cause of our veridical perception. Objects lack causal powers, so cannot be the cause of anything. Only God can cause things, so he causes us to have a veridical image (in the case of primary qualities76 ) of the object whenever we look at the object. The problem here is how we can say that what God causes us to see is a veridical image of something which does not stand in a causal relation either to God’s activity (because it lacks any causal powers) or to our perception. The role of the real object here appeared mysterious to Malebranche’s critics. In particular, it seemed to be redundant, with lack of any causal connection seeming to rule out any connection at all, and certainly anything strong enough to support verisimilitude. The problem for Malebranche, in short, is this. He has a functional account of what perception does, an account that has nothing to do with veridicality. But (unlike later evolutionary epistemologists, for example) he is also concerned to establish that there is such a thing as a veridical account of the world, namely that provided by the right natural philosophy. His functional understanding of perception is irrelevant for these purposes. In particular, it does not yield functional veridicality of an Aristotelian kind, because its function is different from that postulated by Aristotle: we have the perceptual faculties we do so that we might protect our bodies, not so that we might know the world. But if functional veridicality is not available, how is veridicality to be established? It would seem that all that is left for Malebranche to appeal to is comparative veridicality, yet this is ruled out by his doctrine that we see all things in God, which denies any causal connection, direct or indirect, between the object to which we direct our sensory faculties and the perceptual representation that we have as a result of (i.e. that is ‘occasioned’ by) this. Representation is, then, a genuine problem for Malebranche. Locke also wants to establish veridicality, but he wants to establish it for sensation, which Malebranche has ruled out as too contaminated by secondary qualities, and wholly incapable of the clear and distinct grasp required for genuine knowledge. Locke’s objection to Malebranche that I quoted above is a legitimate one because it shows how Malebranche is not entitled to comparative veridicality, and we have seen that he cannot establish veridicality on functional grounds, i.e. on the grounds of 76 Malebranche in fact denies that the senses are trustworthy guides to the discovery of such primary qualities of objects as size, shape, motion, and location; but we are not completely deceived about the characteristics of bodies, for we are right in believing that bodies have some size, shape, location, speed and direction of movement, even if we are wrong in supposing them to have the ones they appear to our senses to have.

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satisfying the function of sense perception. Locke, by contrast, does not attempt to establish comparative veridicality, so the objection to Malebranche does not apply to his own efforts. Instead, in Locke’s case, everything rests on his ability to establish functional veridicality, and this is what he sets out to provide in his account of sensation. He needs something on a par with the Aristotelian approach, along the lines that we know that our sensory ideas represent the world not because we are able to compare them with the world but because the reason we have them in the ﬁrst place is so that we might know the world, and, given this, their proper exercise secures such knowledge. Such an approach assumes that the function of our sense organs is indeed to reveal the nature of the world to us, i.e. to provide us with a veridical representation of the world. This is of course precisely what the Cartesian tradition denies, so it is important that we understand the claims of the Cartesian case in the context of what Locke needs to establish. There are two kinds of reasons that lie behind the Cartesian denial: one turns on the failure of the traditional Aristotelian version of the function of sense perception, while the second has to do with the claims of a foundational natural philosophy—mechanism, which reduces phenomena to the effects of an underlying structure—to provide the sole veridical representation of the world. On the ﬁrst point, Aristotle’s subordination of questions of how vision works to what it is meant to achieve rested on a profound misunderstanding of ocular anatomy and physiology, and it made little sense in terms of geometrical optics. Aristotle had argued that the form of the object is transmitted through the medium and causes an impression of the object upon the sense organ. This impression resembles the object perceived because the properties it has are caused by the same thing that causes the original object to have these properties, namely its form. In vision, for example, the quality of the object is actually assumed by what he considered to be the seeing part of the eye: when a white object is seen, the watery substance (the crystalline humour) constituting the seeing part of the eye becomes white.77 Aristotle had in effect laid down that perception, given its function, had to yield an exact resemblance of the world, and then offered details of how this was achieved in the perceptual process. Worries about this account were not conﬁned to critics of Aristotle. Sixteenth- and early seventeenth-century scholastic Aristotelians had questioned whether we do in fact grasp essences in sense perception, and began to distinguish both degrees of certainty relative to subject matter, and degrees of certainty relative to evidence and reasons.78 Here the kind of automatic veridicality that Aristotle had sought was no longer available. At the same time, outside scholastic circles, there was criticism that the species or forms supposedly transmitted through the medium were undetectable, and the very mechanism postulated by Aristotle for transmission of visual 77 78

De sensu, 438b19–20. I looked at these developments in Emergence, 241–3, q.v.

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species began to look beside the point as the importance of refraction in vision came to be appreciated. Aristotelian veridicality was a refractionless one: were there any interference with the visual species, veridicality would be undermined. It was not that Aristotle got the optics wrong, but rather that optics played no part in his account: species are not light rays, but there was an increasing sense that vision is about the refraction of light rays, and Kepler’s work on the formation of the retinal image, Ad Vitellionem paralipomena (1604), showed deﬁnitively that the kind of resemblance intended by Aristotle was optically impossible.79 On the second point, the optical theories of Descartes can be seen as a response to optical considerations in vision. His ﬁrst project was to develop an understanding of the geometry of refraction, and by the mid-1620s he had discovered the sine law of refraction, and used this in the project of grinding aspherical lenses for telescopes. At the same time he explored the physical question of why light behaves in particular geometrically deﬁned ways in reﬂection and refraction, a physical question which, he believed, turned on an understanding of the corpuscular interactions and pressures that were generated at the level of the underlying microscopic structure.80 Colour, in particular, was to be explained in a reductive way. There were no colours at the micro-corpuscularian level, but a light ray—actually a line of pressure, conceived on the analogy of a stream of light particles by Descartes for these purposes—on being reﬂected off a microtextured surface, is given a spin as a result of the oblique interaction at the surface, and our minds are naturally ﬁtted to respond to such spins by perceiving colours. Colours, then, are a paradigm case of non-resemblance. Locke manifestly could not have denied the inadequacy of the Aristotelian account of the transmission of species and the formation of an image on the crystalline humour, he was resolutely opposed to the Aristotelian idea that we grasp essences in sense perception, and he certainly did not wish to deny that colour is a function of micro-corpuscular structure. How, then, could he defend functional veridicality? In particular, what of his claim, in the passage from the Essay quoted above, that ‘the Idea of Whiteness, or Bitterness, as it is in the Mind, exactly answering that Power which is in any Body to produce it there, has all the real Conformity it can, or ought to have, with things without us’?81 How could one establish this conformity on a non-comparative basis? The answer is that we go through tests—whether through reason, evidence, or a combination of the two—to satisfy ourselves. The procedure is not unlike that in legal trials, natural history, and civil history, but also in some respects like 79

See David C. Lindberg, Theories of Vision from al-Kindi to Kepler (Chicago, 1976), ch. 9. On these developments, see Gaukroger, Descartes, chs. 5 and 6. Cf. Essay, II. xxxi. 2: ‘Because being nothing but the effects of certain Powers in Things . . . to produce such Sensations in us, they cannot but be correspondent, and adequate to those Powers: And we are sure they agree to the reality of Things.’ 80 81

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astronomy, where we test claims against the evidence, and establish, where we can, one account as being the true one. The difference is that in such cases the evidence may be virtually limitless, allowing only a degree of probability, whereas in the case of sensation the evidence is conﬁned within a very narrow range: it is in effect just a question of securing optimal conditions for observation. Notice that Locke does not say that the idea conforms to the thing, but rather that it has all the conformity it can have, or all the conformity it ought to have. There is a scale or continuum, as it were, and sensation comes at the limit of the scale. The judgement we make is not one relative to how things are independently of our ideas of them, for that is impossible, but how things are relative to evidence and reasons. Bearing this in mind, consider what is at issue between Malebranche and Locke in the case of colour. Like Malebranche, Locke thinks of light in microcorpuscularian terms, and of colour as a secondary quality. In Malebranche’s case, this means that there are no colours in the world, only corpuscles with various forms of motion, so that what we see when we see colour is not something resembling anything in the world. Locke is more circumspect in his treatment. Boyle had shown the inadequacy of a wholly reductive account of colour in his Experiments and considerations touching colours (1664), drawing attention to many kinds of colour phenomena that could not be accounted for reductively: the fact that pressure on the eye and exposure to very bright sources of illumination can generate coloured images, and that we can perceive colours in dreams; the fact that many animals and plants regularly change colour, presumably as a result of physiological processes and in some cases exposure to varying degrees of illumination; and the fact that exposure to heat causes substances to change colour, and liquids often change colour when mixed. Locke would have learned from Boyle’s account of the phenomenology of colour that far more than micro-corpuscularian activity is involved in the physical production of colours. Moreover, although he does not explictly mention Newton’s prism experiments, the high-proﬁle 1673 dispute between Newton and Huygens in Philosophical Transactions82 over Newton’s spectacular results on the production of an elongated spectrum through prisms makes it unlikely that Locke would have been unfamiliar with this work,83 which showed that one can learn a great deal about colour phenomena in way that makes no reference whatsoever to micro-corpuscularian structure. While Boyle had doubts about whether a microcorpuscular account of colour was true, preferring the traditional account of colours as a mixture of light and dark, Locke says nothing that would lead us to doubt that he assumed that micro-corpuscularian activity played a role in the process of colour production, but at the same time nor would he have had any 82

See especially Philosophical Transactions, vol. viii (1673), 6109. On Locke’s acquaintance with Newton, see G. A. J. Rogers, ‘Locke’s Essay and Newton’s Principia’, Journal of the History of Ideas 39 (1978), 217–32. 83

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reason to doubt that it was merely a part of the story: and not the part that plays the key role in the explanation of colour phenomena. A crucial ingredient in Locke’s strategy is a construal of sense perception on which it has a degree of cognitive authority which Cartesians, and Malebranche in particular, denied to it. As we have seen, in the Cartesian tradition, perceptual cognition consisted of two processes: sensation and an attendant judgement. This latter should not be confused with the judgement that we might term postperceptual reﬂection, or intellectual reﬂection, which is not at issue here, being accepted by both the Cartesians and Locke, albeit construed somewhat differently in the two cases. What we are concerned with here is something which is indispensible to perception itself. This turned out to be a very complex tangle of issues, and it cannot be said that all of these were resolved, but it is in this context that Locke in effect forges a new conception of the role of judgement in sense perception, a conception that vindicates phenomenal explanation. If, on Locke’s account of the veridicality of sensations of bodies and their qualities, there is no comparative judgement of the kind that Malebranche requires to establish veridicality, then the question of just what kind of judgement is involved in sensation must be raised. Malebranche treated perception as comprising sensation, a physiological process, and judgement, a completely separate mental act. Arnauld, in Des vrayes et des fausses ide´es, in effect objected that Malebranche had confused seeing by means of representations and seeing representations: having a visual representation of the world and seeing the world are not two stages of, or two separate parts of, the one process, but rather just two ways of describing exactly the same thing, one in physiological terms and the other in mental terms. One way in which we might describe Arnauld’s criticism, is to say that Malebranche has illegitimately broken a single act up into two parts, and then proceeded to treat each part separately, enabling him to hypostatize sensory representations, so that it looks as if the mental process is being applied to an independent physiological item. At the basis of Arnauld’s criticism is the claim that the perceptual act must be uniﬁed, and this is exactly the conclusion that Locke seems to draw from Arnauld. What exactly Locke believed about the representational nature of ideas is obscure,84 but this is not so relevant to our present concerns, for the crucial conclusion is that of the unity of perception. Arnauld used this to probe the nature of perceptual representation, but Locke moved in another direction. For Locke, the issues turn on whether there are separate ingredients in perception which we might label ‘seeing’ and ‘judgement’. His own take on uniﬁcation emerges in the doctrine that perception is simply 84 See John W. Yolton, Perceptual Acquaintance from Descartes to Reid (Oxford, 1984), ch. 5; Michael Ayers, Locke: Epistemology and Ontology (2 vols., London, 1991), i, ch. 6; Vere Chappell, ‘Locke’s Theory of Ideas’, in Vere Chappell, ed., The Cambridge Companion to Locke (Cambridge, 1994), 26–55; and Martha Brandt Bolton, ‘Locke on the Semantic and Epistemic Role of Simple Ideas in Sensation’, Paciﬁc Philosophical Quarterly 85 (2004), 301–21.

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successful sensation. The act of perception is single because it is identical with sensation. There is no separate or separable act of judgement involved in seeing the world: there is just one thing, sensation. It is above all Locke’s understanding of the functional veridicality of sensation that enables him to incorporate judgement into the very act of sense perception. For the Cartesian tradition, the physiological and physical details of what occurs in sense perception are absolutely crucial to our assessment of it as a source of knowledge, and this is what effectively makes sense perception an unsuccessful competitor to a micro-corpuscularian natural philosophy. But this is not how Locke construes the matter: to the extent that his aim is to vindicate the experimental philosophy programme, the whole point is that sense perception and natural philosophy are not in competition. How the action of bodies affects our sense organs is something that, Locke believes, we do not understand and may never fully understand: sense perception cannot reveal to us the nature of whiteness, nor the role that primary qualities play in its production. The point is rather that, whatever the physical mechanisms by which sense perception occurs, these cannot cause our idea of whiteness to fail to conform to whatever it is in nature that causes us to have that idea.85 To secure the credentials of sense perception in this way against the claim that it might be replaceable by something else, is ipso facto to defend the credentials of phenomenal explanation against the claim that it might be replaceable by something else. As he explains towards the end of the Essay: In the Knowledge of Bodies, we must be content to glean, what we can, from particular Experiments: since we cannot from a Discovery of their real Essences, grasp at a time whole Sheaves; and in bundles, comprehend the Nature and Properties of whole Species together. Where our Enquiry is concerning Co-existence, or Repugnancy to co-exist, which by Contemplation of our Ideas, we cannot discover; there Experience, Observation, and natural History, must give us by our Senses, and by retail, an insight into corporeal Substances.86

Locke’s attempts to give philosophical substance, ﬁrst to the Sydenham defence of what, at the generalized level that Locke engages it in Draft A, is the autonomy of the phenomenal level, and then to the far more nuanced Boylean defence of this autonomy beginning with Draft B, came to a head in his subsequent encounter with Malebranche’s philosophy, because what Malebranche provided was a comprehensive vindication of the sole legitimacy of micro-corpuscularian explanation. If Malebranche were right, the phenomenal level could not possibly have any explanatory autonomy, and the realm of sensation, by contrast with that of a theoretical and wholly reductionist natural philosophy, had to be bypassed if 85 Cf. G. A. J. Rogers, ‘Locke and the Objects of Perception’, Paciﬁc Philosophical Quarterly 85 (2004), 245–54. 86 Essay, IV. xii. 12.

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understanding was to be achieved.87 At one level, this was not a new divide. The Cartesian conception was in many ways continuous with the Aristotelian understanding of natural philosophy as a discourse that sought to explain wholly in terms of underlying principles, by contrast with the ‘experimental’ natural philosophy that focused the phenomena around a speciﬁc experiment or apparatus constructed because of its power to generate a particularly revealing set of facts or events.88 But to have lifted these questions out of the realm of simply a conﬂict of styles of doing natural philosophy into the realm of an explicit epistemological defence of the autonomy of phenomenal explanation, and to have established the general philosophical legitimacy of non-reductive, and indeed non-systematic, explanation in natural philosophy, is Locke’s achievement.

LOCKE AND THE DEFENCE OF NEWTON In the eighteenth century, the rejection of the idea that any (complete or ﬁnal) explanation in natural philosophy had to invoke micro-structure was associated with a form of Lockeanized Newtonianism, one of a number of various Newtonian trajectories,89 and the one best represented in the ﬁrst editions of the Principia and the Opticks, before the addition of the speculative General Scholium and the Queries. As a general cultural phenomenon, its standing was far greater than that of other versions of Newtonianism. In 1698, the Francophobe dramatist and critic John Dennis, writes: ‘What Proﬁcients have we in Philosophy? What in mathematicks? Let all Europe reply, who had read, and reading, admir’d them. I shall content myself with mentioning Two of the living Glories of England, Mr. Newton, and Mr. Lock; the one of which has not his Equal in Europe, and neither of them has his Superior.’90 By the middle of the eighteenth century the idea of an unsurpassable Newton/Locke partnership was widespread. It continued well into the nineteenth century, despite a decline in the fortunes of

87 It is interesting that when attacks on Locke’s work began to appear in France around 1735, it was from Malebrancheans: see John W. Yolton, Locke and French Materialism (Oxford, 1991), 5; and, for details, Jørn Schøsler, La Bibliotheque raisone´e (1728–1753): Les Re´actions d’un pe´riodique franc¸ais a` la philosophie de Locke au XVIII e siecle (Odense, 1985). 88 See Gaukroger, Emergence, ch. 10. 89 On the varieties of Newtonianism in the eighteenth century, see Robert E. Schoﬁeld, ‘An Evolutionary Taxonomy of Eighteenth-Century Newtonianisms’, Studies in Eighteenth Century Culture 7 (1978), 175–92; and, more generally, Patricia Fara, Newton: The Making of Genius (London, 2002). 90 The Critical Works of John Dennis, ed. Edward N. Hooker (2 vols., Baltimore, 1939), i. 161: quoted in Mordechai Feingold, ‘Partnership in Glory: Newton and Locke Through the Enlightenment and Beyond’, in P. B. Scheuer and G. Debrock, eds., Newton’s Scientiﬁc and Philosophical Legacy (Dordrecht, 1988), 291–308: 297.

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Lockeanism,91 with Coleridge telling his audience that ‘one great man has overthrown the physical parts and another the metaphysical part and to that circumstance we owe entirely the custom of talking of Locke and Newton’.92 That Lockeanism and Newtonianism should come to be associated in the eighteenth century is not surprising. In 1715, in his anonymous review, ‘An Account of the Book entituled Commercium Epistolicum’, Newton set out what he took to be the experimental standing of his own natural philosophy: ‘The Philosophy which Mr. Newton in his Principles and Optiques has pursued is Experimental; and it is not the Business of Experimental Philosophy to teach the Causes of things any further than they can be proved by Experiments. We are not to ﬁll this Philosophy with Opinions which cannot be proved by Phenomena.’93 Just as the Principia is resolutely agnostic on the nature of gravity, the only hint coming in the General Scholium added to the second edition, so too the ﬁrst edition of the Opticks is resolutely agnostic on the nature of light, the only hint— this time a longer one, covering the optical, thermal, sensory, and gravitational aether—coming in the Queries added to the second edition. Moreover, as we have seen, even these additions are far from unequivocal, and in a draft of the ‘General Scholium’ in the Principia, composed around 1712, Newton writes: ‘We do not know the substances of things. We have no idea of them. We gather only their properties from the phenomena, and from the properties [we infer] what substances may be. . . . And we ought not rashly to assert that which cannot be inferred from the phenomena.’94 This certainly has a Lockean ﬂavour, and Newtonianism in England has a strongly Lockean reading right through to at least mid-century. This is evident in Newton’s greatest advocate in eighteenth-century England, Colin Maclaurin, who writes in 1748 that the derivation of natural-philosophical results from ﬁrst principles, in the Cartesian and Leibnizian style, ‘ﬂatters human vanity so much, and sets out in so pompous a manner, that they who attend not to the unexhaustible variety of nature, and consider not how unequal the human powers are to so ardous an undertaking, are deluded by its promises: it may be doubted if such a philosophy lies within the reach of any created being; and it seems to be very plain that it far surpasses the reach of men.’95 Maclaurin’s defence of Newtonianism was, moreover, not conﬁned just to its natural philosophy but also covered its role in natural religion and moral philosophy. Natural philosophy, 91 On the changing fortunes of Lockeanism, see Hans Aarsleff, ‘Locke’s Inﬂuence’, in Vere Chappell, eds., The Cambridge Companion to Locke (Cambridge, 1994), 252–89. 92 Quoted in Feingold, ‘Partnership in Glory’, 300. 93 Isaac Newton, ‘An Account of the Book entituled Commercium Epistolicum’, Philosophical Transactions 29 (1714–15), 173–224: 222. The Commercium was a Royal Society report which Newton, as President, had in fact written himself, vindicating him in the priority dispute with Leibniz over the invention of the calculus. 94 Newton, Unpublished Scientiﬁc Papers, 360. 95 Colin Maclaurin, An Account of Sir Isaac Newton’s Philosophical Discoveries, in Four Books (London, 1748), 14. Cf. the criticisms of ‘systems founded on abstract speculations’ (24).

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he writes, ‘is subservient to purposes of a higher kind, and is chieﬂy to be valued as it lays a sure foundation for natural religion and moral philosophy.’96 The association of Locke and Newton was almost immediate in England, and in France it was established by the 1730s, when Voltaire tied their fortunes together so intimately. In the Netherlands, ’sGravesande, from his appointment at Leiden as Professor of Natural Philosophy in 1717, effectively translated the Principia into experimental terms, offering popular public experimental demonstrations of Newton’s theories on collision, ﬂuid motion, magnetism, optics, and gravitation. His Mathematical Elements of Natural Philosophy, conﬁrmed by Experiments (1719), which was translated by Desaguliers, quickly became the standard experimental reference work for Newtonianism. When ’sGravesande became a convert to a Leibnizian notion of force in 1722, it was on suitably Newtonian ‘experimental philosophy’ grounds, not metaphysical grounds, and throughout his career he was committed to the notion of not ‘feigning hypotheses’. He effectively established an experimental reading of Newtonianism in the Netherlands, a reading consolidated in the work of Pieter van Musschenbroek, an indefatigable experimenter and author of a number of widely used and widely translated textbooks.97 At the same time, the association of Locke and Newton in Italian thinking was such that Newtonianism took on a radical political edge, principally because of Toland’s favourable references to Locke, so that Locke, and by extension Newton, came to be associated with deism, and indeed Locke’s Essay was put on the Index of Prohibited Books in 1734. The leader of the proNewton movement in natural philosophy in Italy, Celestino Galiani, read Coste’s translation of the Essay soon after it appeared, and his own Newtonianism was of a thoroughly Lockean variety.98 Locke’s inﬂuence was at its height between the 1730s and the 1760s, and when, in the 1760s, there began a decline in his fortunes, Newton and Locke were so interconnected that the pressing question, was, as Feingold puts it, ‘How could Lockean epistemology be discarded without affecting Newtonian science?’,99 a question with which Kant, in particular, struggled. Indeed, Kant’s resolution of this question signiﬁcantly redirected Western philosophical culture, a culture that, between the early decades of the eighteenth century and the 1760s, was dominated by a Newtonian-Lockean conception of Enlightenment. This culture was central to mid-eighteenth-century understandings of the standing of philosophy in general and natural philosophy in particular, in both the French and Scottish Enlightenments. 96

Ibid., 3. Later he remarks that to ‘all such as have just notions of the great author of the universe and his admirable workmanship, Sir Isaac Newton’s caution and modesty will recommend his philosophy; and even the avowed imperfection of some parts of it will, to them, rather appear a consequence of its conformity with nature’ (11). 97 Petrus van Musschenbroek, Epitome elementorum physico-mathematicorum conscripta in usus academico (Leiden, 1726), Elementa physicae (Leiden, 1734), Institutiones physicae (Leiden, 1748), and the posthumous Introductio ad philosophiam naturalem (2 vols., Leiden, 1762). 98 See Vincenzo Ferrone, The Intellectual Roots of the Italian Enlightenment: Newtonian Science, Religion, and Politics in the Early Eighteenth Century (Amherst, 1995), 122–82. 99 Feingold, ‘Partnership in Glory’, 302.

5 Explaining the Phenomena Locke’s defence of phenomenal explanation was part of a programme of providing a philosophical vindication of experimental natural philosophy, a vindication that allowed that phenomenal explanations were not subordinate to micro-corpuscularian accounts. The defence worked on two levels: it denied that observational procedures are reliable only if and until judged satisfactory by the lights of a foundational micro-corpuscularian account of fundamental natural processes; and it showed that, from an explanatory point of view, it is an open question what kinds of considerations are going to be of fundamental explanatory signiﬁcance, a question that may be decided in favour of phenomenal explanations in many cases. This conception of natural philosophy is compatible with a good deal in Hume, as we shall see later, but there is no continuous ‘empiricist’ tradition in British thought. Berkeley, in particular, is a systematic metaphysician indebted primarily to Malebranche, and his project, despite its concern with sensation as the sole appropriate source of natural knowledge, is antithetical to the Lockean understanding of just what role sensation plays in natural philosophy. By the 1730s, as we shall see in Part III, Lockean conceptions had come to play an explicit role in the anti-system rhetoric of French natural philosophy in particular, but a broadly Lockean conception of experimental philosophy is in evidence in a more subtle way in three developments in natural philosophy in the decades between the publication of the Essay and the 1730s. The ﬁrst of these, Ray’s botanical taxonomy of the 1690s, confronts an entrenched view of underlying essential botanical structure, replacing it with a classiﬁcation that bypasses notions of underlying essential structure and opts instead for a procedure in which observed similarities and differences may be used to provide a basis for classiﬁcation in their own right. The second is Gray’s 1720 discovery of electrical conductivity, in which a traditional and de facto universally held approach to electricity, one which construed the aim of the exercise as being to provide an understanding of the underlying mechanisms that produce the electrical properties of ‘electrics’ (i.e. electrically charged bodies), was replaced by one that conﬁned itself to the phenomenological level of ‘electrical communication’, recording how bodies acquired and transmitted electricity. The third is Geoffroy’s rejection of attempts to understand chemical reactions in terms of underlying micro-corpuscularian structure, replacing these with a project of drawing up tables of chemical afﬁnities, recording the degree to which various substances

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are able to displace one another in chemical reactions, and in effect organizing relations between substances on a purely phenomenal basis. THE ‘ NATURE’ OF SPECIES The ﬁrst case I want to look at is that of botany, where what was at issue was essentialism rather than reductionism. Interest in botany in the early modern era had been focused on its pharmaceutical applications and on taxonomy. The ﬁrst was a practical matter, although with the rise of Paracelsianism—whereby disease was conceived no longer in terms of imbalances of the bodily humours but as separately identiﬁable entities, so that medicines could be prescribed by an apothecary rather than a physician—pharmaceutical botany was caught up in a dispute that went beyond practical matters to some degree, and bore on its natural-philosophical standing. The second was a question on which the naturalphilosophical standing of botany hinged. Botanical classiﬁcations were often just alphabetical listings, and as such had no claim to the title of ‘natural philosophy’. To provide it with the kind of explanatory power that was associated with natural-philosophical disciplines, botanical taxonomy had to concern itself with capturing a classiﬁcation that was ‘natural’, one that mirrored the natural order rather than simply reﬂecting pragmatic or conventional considerations. This raised the questions of what characteristics of the plant should be selected as the basis of classiﬁcation, and what relations these characteristics should stand in to those not chosen: in particular, whether resemblance in respect of a single characteristic could or should override overall similarity.1 The prevailing view from the sixteenth century onwards was that classiﬁcation was to be based on a single structure, namely the reproductive apparatus of the plant. Andrea Cesalpino offered what was in effect the canonical statement of and rationale for this principle in his De plantiis of 1583. Cesalpino was professor of medicine at the University of Pisa, and in 1571 he had published an extensive treatise on ‘Aristotelian questions’, dealing in detail with natural-philosophical issues in astronomy, biology, and anatomy.2 This work was in no sense a mere commentary on Aristotle and Cesalpino does not hesitate to advance revisions in the light 1 I am indebted in this discussion particularly to Phillip R. Sloane, ‘John Locke, John Ray, and the Problem of the Natural System’, Journal of the History of Biology 5 (1972), 1–53; and Charles E. Raven, John Ray Naturalist: His Life and Works (Cambridge, 1950). On the history of taxonomy in medieval and Renaissance natural history, see Charles E. Raven, English Naturalists from Neckam to Ray (Cambridge, 1947); Karen Reeds, ‘Renaissance Humanism and Botany’, Annals of Science 33 (1976), 519–42; Barbara Shapiro and Robert G. Frank, Jr., English Scientiﬁc Virtuosi in the Sixteenth and Seventeenth Centuries (Los Angeles, 1979); and Joseph M. Levine, ‘Natural History and the Scientiﬁc Revolution’, Clio 13 (1983), 57–73. 2 Andrea Cesalpino, Quaestionum Peripateticarum libri V (Venice, 1571). See the discussion in Lynn Thorndike, A History of Magic and Experimental Science (8 vols., New York, 1923–58), vi. 325–38.

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of new empirical ﬁndings. It is this approach that he brings to botany.3 Aristotle’s own view, in De partibus animalium, had been that biological subject matter in general was so complex and varied that the application of basic classiﬁcatory principles was not possible, leaving biology outside the kind of theoretical understanding to which natural philosophy aspired.4 Ancient botany (established by Aristotle’s successor at the Lyceum, Theophrastus, whom Cesalpino follows in a number of respects) was pretty much the core discipline of natural history, a discipline that fell outside ‘the theoretical sciences’ because it did not derive the natural properties of things from their essential characteristics. There had been attempts to apply Aristotle’s method of division to plants, and in 1623 Caspar Bauhin described over 6,000 species by generic name and essential differentiae on this basis,5 without providing anything other than nominal deﬁnitions in strictly Aristotelian terms, however. Such classiﬁcations did not solve what Sloane terms the ‘Aristotle problem’, namely ‘the seeming impossibility of determining the assumed essential characters in organisms in a way which permitted the subordination of characters as required by the method of division and the canons of traditional logic.’6 This was the problem to which Cesalpino directed himself. He believed that there was a way to incorporate botany into natural philosophy, by providing a new rationale for botanical taxonomy. The essential feature of plants was that they possessed a ‘vegetative soul’, marking them out from inanimate things, which did not possess a soul of any kind, and from animals, which as well as a vegetative soul also possessed a sensitive soul, responsible for sensation, which plants lacked. The deﬁning features of the vegetative soul as set out in De anima were self-nutrition and reproduction, so it is these that were chosen by Cesalpino as the basis for taxonomy.7 Self-nutrition is a function of the root of the plant on the Aristotelian view, but Cesalpino rejects shape of the root as unsuitable as a basis for classiﬁcation, and he settles on a basic dichotomy between plants with hard and medullary substance (Arbores) and those with soft and ﬂeshy matter (Herbae). All subsequent divisions depend on variations in the reproductive features of plants, namely the number, shape, location, and structure of the reproductive parts,8 so that their fruits and ﬂowers become the basis for taxonomy.

3 The Northern Italian universities, Pisa, Padua, and Bologna, had notably well-stocked gardens in the mid-sixteenth century: see Paula Findlen, ‘Sites of Anatomy, Botany, and Natural History’, in Katherine Park and Lorraine Daston, eds., The Cambridge History of Science, iii. Early Modern Science (Cambridge, 2006), 272–89: 282. 4 See Sloane, ‘John Locke, John Ray, and the Problem of the Natural System’, 6; and more generally G. E. R. Lloyd, ‘The Development of Aristotle’s Theory of Classiﬁcation’, Phronesis 6 (1961), 59–85. 5 Caspar Bauhin, Pinax theatri botanici (Paris, 1623). 6 Sloane, ‘John Locke, John Ray, and the Problem of the Natural System’, 9. 7 Andrea Cesalpino, De plantiis libri XVI (Florence, 1583), 1–2. 8 Ibid., 29.

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Cartesian mechanism, the dominant natural philosophy of the second half of the seventeenth century, explicitly rejected the very idea of vegetative and sensible souls, and indeed this rejection had been one of the basic tenets of Cartesian biomechanics. Descartes himself took some interest in botany, and was exchanging seeds from the Leiden botanical gardens with Mersenne in Paris in 1639,9 and he kept a garden for botanical experiments as well as a vegetable garden at his house at Sandpoort in the 1640s. He points out to Mersenne that the plant ‘l’herbe sensitive’ (Mimosa pudica), which is extremely sensitive to touch, the leaﬂets of the bipinnate leaves folding together at the slightest contact with the ﬁngers, is manifestly capable of sensation.10 This is impossible on the Aristotelian account, but no problem for Descartes’ own biomechanics, where sensation of this reﬂex kind simply requires a circulatory system, whether of blood or sap (thought to circulate on the model of the circulation of the blood). Yet the question of the consequences of rejection of the idea of a vegetative soul for the ability of botanical taxonomy to capture a natural differentiation of plants was not raised. Mechanism seems to have left taxonomic questions untouched. This is perhaps not so surprising, given that the notion of a species was so problematic in mechanist terms that botanical taxonomy was far more marginal to mechanist natural philosophy than it had been to Aristotelian natural philosophy. Those who took a more fundamental interest in botany found the issues harder to ignore however. Locke delved far more deeply into the subject than Descartes had, and he was engaged in botanical work during the whole period in which he was working on the Essay.11 His own response to the core problem was characteristically hesitant however. He does not accept Aristotelian vegetative souls any more than Descartes does. On the other hand, someone who regularly traded in seeds as Locke did at the very least faced practical difﬁculties in adopting a nominalist view of plant species.12 He had kept a carefully documented herbarium of 973 plant type specimens in the mid-1660s and continued to trade in seeds for many years after that. Yet in Book III of the Essay, Locke comes very close to species nominalism, telling us that ‘the boundaries of species are as men, and not as Nature makes 9

See Gaukroger, Descartes, 405. Descartes to Mersenne, 23 August 1638: Descartes, Œuvres, ii. 329. See Peter R. Anstey and Stephen A. Harris, ‘Locke and Botany’, Studies in the History and Philosophy of the Biological and Biomedical Sciences 37 (2006), 151–71. It is perhaps also worth noting that Sydenham had used botanical classiﬁcation as a model in his classiﬁcation of diseases: see Erik Nordenskio¨ld, The History of Biology (New York, 1928), 175. On the importance of horticulture to the Royal Society’s conception of its scientiﬁc mission, see Sarah Irving, Natural Science and the Origins of the British Empire (London, 2008), who also looks speciﬁcally at Locke’s interests in natural history, 120–5. The ﬁrst work of Hans Sloane, a friend of Locke’s who was later to become President of the Royal Society, was a ﬂora of Jamaica—Catalogus Plantarum quae in Insula Jamaica Sponte Proveniunt (London, 1696)—and he built up an extensive herbarium in the course of his life. 12 See Anstey and Harris, ‘Locke and Botany’, 166–9. 10 11

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them . . . I cannot see how it can properly be said, that nature sets the boundaries of the species of things.’13 He draws back when Molyneux accuses him of claiming that there are ‘no such species as birds’, telling Molyneux that he has never said this, which ‘is both contrary to truth and to my opinion’, continuing that ‘there are real constitutions in things’ and that ‘there are real distinctions and differences in those real constitutions one from another; whereby they are distinguished one from another, whether we think of them or name them or no.’14 But if one rejects botanical essentialism yet accepts that there are in fact different species, quite independently of what philosophical views we may have, how does this work in the case of taxonomy? Locke’s Essay did not provide any clear-cut guidance on this matter: coming, as it does, dangerously close to species nominalism, it might seem to point to a dead end, as mechanism had done. But once we turn from the metaphysics of the Essay to its vindication of phenomenal explanation, we can begin to understand how a very different kind of guidance might provide a different tack on the problem. The crucial ﬁgure here is the botanist John Ray. It is the legitimacy of proceeding at the phenomenal level, eschewing reference to underlying essential structures, not species-nominalism, that, I suggest, guides Ray’s programme in the wake of the publication of Locke’s Essay. This programme is the result of a series of twists and turns on Ray’s part. His ﬁrst classiﬁcation of plants, the Catalogus Cantabrigiam of 1660, follows the standard pattern of herbals in providing an alphabetical listing.15 In 1668 he contributed the sections on botanical classiﬁcation to Wilkins’ An Essay towards a Real Character.16 Wilkins’ project was to provide a universal language of transparent grammatical structure as an alternative to Latin. The aim of the various chapters that dealt with speciﬁc parts of the natural realm was simply to supply an ordering of the material consonant with his own general classiﬁcatory schemes, which were highly formalistic but also comprehensive, so that plants for example have to follow a pre-given sixfold classiﬁcation and are further distinguished by colour, taste, habitat, and so on. Ray’s contribution was attacked by the King’s physician Robert Morison,17 who set out a classiﬁcation based solely on form and structure of fruits, giving the (false) impression that Ray knew nothing of such systems. Ray put matters right in his Methodus plantarum nova (London, 1682), in which he acknowledges the indebtedness of the scheme set out there to 13 Essay, III. vi. 30. What is at issue here is not just the question of nominalism, however, but also that of indistinguishability of, and continuity between, species: ‘that the several Species are linked together, and differ but in almost insensible degrees’ (Essay, III. iv. 12). 14 Locke to Molyneux, 20 January 1693: Locke, Correspondence, iv. 626. 15 John Ray, Catalogus plantarum circa Cantabrigiam nascentium (Cambridge, 1660); see Raven, John Ray, ch. 4. 16 John Wilkins, An Essay towards a Real Character, And a Philosophical Language (London, 1668), Part II ch. 4. 17 Robert Morison, Praeludia botanica (London, 1669).

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Cesalpino. However, he does deviate from him on some speciﬁc taxonomic matters, treating a number of variations in reproductive parts of the ﬂower that are ignored by Cesalpino as being of taxonomic relevance, for instance.18 Even more important, he does not follow Cesalpino’s Aristotelian procedure of using a single basis for division, offering a far more ﬂexible set of differentiae.19 It was on this last question that a new controversy arose, not in the context of the Methodus but with the publication of the ﬁrst volume of his Historia plantarum in 1686, which incorporated the same ﬂexible methodological maxims.20 It was just this ﬂexibility that was at issue in the disputes of the 1690s between Ray and continental botanists such as August Rivinus and J. Pitton de Tournefort. Rivinus’ Introductio generalis in rem herbarium of 1690 offered a compact, elegant alternative to Ray’s complicated schemas, its simplicity, not to mention its adherence to strict norms of division, deriving from its taking structural variations in the corolla as the basis of the main taxonomic divisions. By conﬁning the basis of taxonomy exclusively to reproductive parts, however, Rivinus comes up with a signiﬁcantly different classiﬁcation from Ray. In his 1694 handbook of European plants, Ray objects that while the subalternate genera can usefully be discriminated by the structure of reproductive parts, these are not to be used for the primary divisions, where the total aspect and division of the plant are what is relevant.21 Ray’s criticism here is primarily practical. Rivinus’ narrow basis for taxonomy results in manifestly natural groups being split between different genera, and manifestly different groups being classed together. The problem is the converse of that which Locke faced. Locke’s apparent advocacy of species nominalism had the consequence of denying that birds were a natural species. Rivinus’ advocacy of essentialist taxonomy had the consequence of denying that Daffodils and Tulips were in the same group, contrary to the consensus among horticulturalists. Locke would certainly have seconded Ray’s criticisms here, and, ironically, 18

See Sloane, ‘John Locke, John Ray’, 29–32. It is worth noting that Ray had also been concerned with zoological classiﬁcation during the 1670s. In the early 1660s he had travelled extensively with Francis Willughby, including a twoyear natural-history excursion in Europe, Ray working on botany and Willughby on animals. At his death in 1673, Willughby left detailed notes for works on ornithology and ichthyology. Ray worked these up into books, and although these books were published under Willughby’s name— Ornithologiæ libri tres (London, 1676) and De historia piscium libri quatuor (Oxford, 1686)—they were largely Ray’s work, and employed his methods of classiﬁcation. Curiously, not only was Linnaeus also later to divide his interest in the living realm with a friend, Peter Artedi, but he too completed his friend’s work (which was left in a far more complete state) on the classiﬁcation of ﬁsh for publication: Ichthyologia (Leiden, 1738). 20 The Historia was Ray’s masterwork, but he was unable to ﬁnd sponsors for engravings, which meant that the work appeared without illustrations, by contrast with the lavishly illustrated Willughby books or Hooke’s Micrographia, and there can be little doubt that this was an obstacle to wider recognition. 21 John Ray, Stiripium Europeanarum extra Brittannias nascentium sylloge (London, 1694), Praefatio. 19

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Locke’s rejection of the idea that propagation by seeds in plants or sexual reproduction in animals provides some unambiguous test for discerning the real limits of natural species may well have been directed against Ray’s earlier advocacy of something along these lines in his 1670 Catalogus Angliae, which we know Locke owned.22 In the course of the 1690s—that is, in the wake of the publication of Locke’s Essay—we ﬁnd a fundamental shift in Ray’s approach, from practical concerns over a particular form of species essentialism to a paradigmatically Lockean rejection of species essentialism in general. In the 1695 Appendix to his Synopsis methodica, he writes that the ‘correct and philosophical division of any genus into species is by essential differences. But the essences of things are unknown to us. Therefore, in place of these essential characters, some characteristic accidents should be used, which are present in only some species and in all the individuals contained in these.’23 The point is repeated in De variis plantarum of 1696: ‘Since the essences of things are unknown to us, certainly the essential generic characters could not be known to us. However, it is probable that those plants which agree in several attributes, conform in their natures. Therefore, it cannot be properly said that the ﬂower or fruit in plants are essential parts.’24 As Sloane points out, Ray has ﬁnally come to the view that no character is ‘essential’ in the traditional sense, and that the multi-criterial classiﬁcation he has devised is perfectly justiﬁed.25 It was a shared assumption among taxonomists that the aim was to capture naturally perceived afﬁnities, and both species essentialism and species nominalism failed in this regard. Ray has no objection to using a single structure for classiﬁcatory purposes where there is no good reason for not doing so, but he now has a justiﬁcation for using any kind of similarity when there is reason not to proceed in terms of single structures.26 The problem that confronted Locke explicitly was that of nominalism: what Ray shows is that essentialism is just as problematic on the question of capturing natural divisions. One thing that this means is that the debate cannot be seen in terms of an all-or-nothing metaphysical choice between species nominalism and species essentialism or, to put it in the non-metaphysical terms which capture the Lockean project more helpfully, between phenomenal explanation 22

See Sloane, ‘John Locke, John Ray’, 25 n. 25. John Ray, Synopsis methodica stiripium brittanicarum (2nd edn., London, 1696), Appendix, 30. 24 Idem, De variis plantarum methodis dissertatio brevis (London, 1696), 5. 25 Sloane, ‘John Locke, John Ray’, 37–8. 26 See e.g. John Ray, Methodus plantarum emendata et aucta (Amsterdam, 1703), 6–7. This is a very Lockean position. Locke himself was not averse to fundamental explanations in those cases where he believed they were genuinely available. In his late unﬁnished Of the Conduct of the Understanding, begun in 1697, he talks of Newton’s discovery of the workings of gravity as something ‘which may be counted as the basis of Natural Philosophy’. Of the Conduct of the Understanding, }42: Works, iii. 425. Cf. Paul Schuurman, ‘Willem Jacob ’sGravesande’s Philosophical Defence of Newtonian Physics: On the Various Uses of Locke’, in Peter R. Anstey, ed., The Philosophy of John Locke (London, 2003), 43–57. 23

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and explanation in terms of underlying structure. Some complex negotiation between the two is required, a negotiation that varies from case to case, and in which phenomenal explanation may carry most if not all of the explanatory load. The debates that pitted Ray against Rivinus and Tournefort are mirrored ﬁfty years later in Buffon’s Lockean criticisms of Linnaeus’ system of botanical classiﬁcation, which had been set out in the numerous editions of his Systema naturae that had appeared since the ﬁrst edition of 1735. Linnaeus had aimed to tighten up the principles of classiﬁcation by restricting the classiﬁcation algorithm for all living things to ﬁve categories in each of the ‘kingdoms’: class, order, genus, species, and variety. The aim of classiﬁcation was to gather together similar things and separate dissimiliar ones, and the issue for Buffon, as it had been for Ray, was whether such similarities and dissimilarities could be deemed natural, or whether they were merely conventional. There were two issues here. The ﬁrst was that of whether any system of classiﬁcation could capture a natural grouping. The second was whether natural groupings could be reﬁned beyond the level of families. On the ﬁrst question, Linnaeus took the traditional view of Rivinus and Tournefort that there were ‘natural families’ of plants united by a number of characteristics. He focused on the reproductive parts, in which he identiﬁed sexual differentiation, as in animals: namely ‘male’ stamens and ‘female’ pistils, and these, together with the ﬂower, formed the basis of his taxonomy.27 Nevertheless, he recognized the impossibility of establishing such families directly. There being no available method by which ‘natural families’ could be discovered, one had to fall back upon an ‘artiﬁcial’ method whereby a particular characteristic was chosen which was present in all species of the same genus and absent in those of neighbouring genera.28 But, inevitably, a characteristic that was deemed particularly successful in this regard effectively took on the standing of an essential characteristic, and this is how Linnaeus treated such characteristics. On the second question, there was widespread agreement among those who followed this path that families were natural, in the sense that they were deemed to have a real basis in nature, but they were immense categories and ideally the botanist was seeking something more ﬁne-tuned. Tournefort and Linnaeus both sought a natural basis for genera, considering them as marked out in nature.29 27 More speciﬁcally, he divided plants into classes according to the number of stamens, and further subdivided them into orders on the basis of seven parts: four of the ﬂower—calyx, corolla, stamen, and pistil—and three of the fruit—ovary, receptacle, and seed. 28 See the discussion in Jacques Roger, Buffon: A Life in Natural History (Ithaca, NY, 1997), ch. 19; and, more generally Henri Daudin, De Linne´ a` Lamarck. Me´thodes de la classiﬁcation et ide´e de se´rie en botanique et en zoologie (1740–1790) (Paris, 1926). 29 This is reﬂected in the Linnaean classiﬁcatory nomenclature, where a plant or an animal is identiﬁed via a capitalized noun, indicating the genus, followed by an uncapitalized adjective, indicating the species: such as Mimosa pudica or Homo sapiens. The idea behind this was that the noun picked out a natural kind, whereas the adjective designated a particular modiﬁcation or attribute of this kind.

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Buffon stresses that classiﬁcation cannot conﬁne itself to unique characteristics but must take into account all features, and for this we need some way of organizing the domain that we are dealing with. The crucial realization, for Buffon, is that there is no natural system. Among other things, the idea that there are natural groupings presupposes discrete entities, whereas in fact in nature there is a continuous shading of features: It is clear that it is impossible to provide a general system, a perfect method, not only for the whole of natural history, but even for a single one of its branches: for in order to have a system, an arrangement, in a word a general method, it is necessary that it include everything; and this whole must be divided into different classes, which must be separated into genera, and the genera sub-divided into species, and all this according to an ordering which is necessarily arbitrary. But nature proceeds by indistinguishable gradations, and consequently it cannot lend itself wholly to these divisions, since it passes from one species to another, and often from one genus to another, by means of imperceptible nuances, in such a way that there are a great number of intermediate species and things that would ﬁt equally in to species, so that one does not know where to place them, and this of necessity undermines the project of a general system.30

The limits of the attempt to impose a rigid system of classiﬁcation can be seen, he argues, in the bizarre groupings that the Linnaean classiﬁcations yield in the case of animals: sloths and scaly lizards are put in the same group as humans, the hippopotamus in with the shrew, and so on.31 If there is to be classiﬁcation, as there must be for natural history to proceed, one has to give up ideas of natural groupings and instead think of classiﬁcation as relative to human interests. As Roger has put it, Buffon organized ‘his discovery of the living world in concentric circles, starting from what was closest and the most familiar to him’.32 It is these human interests that determine what we pick out as salient to distinguishing and grouping things.33 So, in the case of identiﬁcation of species, for example, we pick out interfertility as the criterion, a criterion that is no more, or less, ‘natural’ than any others, but one that matches human interests in explaining the relations between animals, or between plants.34 In other words, 30

George Louis Leclerc, Comte de Buffon, Œuvres completes de Buffon (34 vols., Paris, 1827), i. 63–4. 31 Linnaeus’ zoological classiﬁcations never had anything like the success of his botanical ones, and his criteria do indeed seem somewhat arbitrary: mammals are grouped by toes and teeth; ﬁsh by ﬁn bones; birds by feet and beaks; and molluscs, starﬁsh, zoophytes, and crustaceans are grouped together under Vermes. 32 Roger, Buffon, 151. 33 Cf. the article ‘Botanique’ in the Encyclope´die, written by Buffon’s assistant at the Jardin du Roi and collaborator on his Histoire Naturelle, Louis-Jean-Marie Daubenton, where a call is made for less attention to nomenclature and classiﬁcation and more to knowledge of cultivation and the properties of natural productions. 34 Cf. Spary: ‘In much of his writing Buffon imported the moral world and social concerns which he shared with many of his readers into the natural world, and there converted them into prescriptive claims about human appropriation of nature which were faithfully represented in the natural history collections of the Jardin du Roi, with their emphasis on the human value of

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we use ability to interbreed as a criterion of species inclusion not because it is the manifestation of some natural essence, but simply because it provides us with a good secure means of grouping animals into things of the same kind in an especially useful and economical way, one that overrides the various and inﬁnitely shaded differences between things.35 T H E ‘ N A T UR E ’ O F E L E C T R I C I T Y The issues in botanical taxonomy that concerned Ray and Buffon were not ones that engaged questions of the micro-corpuscularian underpinnings of natural philosophy.36 At least in the case of Ray, they could be presented, with some degree of simpliﬁcation, as a dispute between Aristotelian essentialists and those advocating a commitment to the idea that the observational realm may provide its own taxonomies, explanations, and causes, and that these are not automatically inferior to accounts that invoke more ‘fundamental’ levels of explanation and causation, or essences. Mechanists would have been happy to draw the negative consequences for Aristotelian essentialism from this, but would have been unlikely to endorse any more general lessons for how natural philosophy should be pursued. This is because mechanists were as committed to the uniqueness of explanation in terms of underlying structure as Aristotelians were to demonstration from underlying principles. They might draw conclusions on metaphysical questions of realism and nominalism, but not on the more intractable question of the nature of explanation. In particular, as I have indicated, the rejection of vegetative souls by mechanists was not accompanied by anything that might guide taxonomy, and the more general problems that mechanism faced, but failed to confront, on questions of unity and identity were well highlighted by Leibniz, as we saw in Chapter 3. But Leibniz highlighted these in metaphysical terms, which tended to force the issues into an allor-nothing dispute, which is disastrous, for, as the case of Ray shows, what is

specimens’; Emma C. Spary, Utopia’s Garden: French Natural History from the Old Regime to the Revolution (Chicago, 2000), 32. Keith Thomas draws attention—in his Man and the Natural World: Changing Attitudes in England 1500–1800 (London, 1983), 66—to Linnaean anthropomorphism as presented in its late eighteenth-century English version: the vegetable ‘kingdom’ is divided into ‘tribes’ and ‘nations’; grasses are described as ‘plebeians’ as ‘the more they are taxed and trod upon, the more they multiply’; lilies are ‘patricians’ as ‘they amuse the eye and adorn the vegetable kingdom with the splendour of courts’; mosses are ‘servants’, ﬂags ‘slaves’, and funguses ‘vagabonds’. A System of Vegetables . . . translated from the 13th edition . . . of the Systema Vegetabilium of the late Professor Linneus and from the Supplementum Plantarum of the present Professor Linneus . . . by a Botanical Society at Lichﬁeld (2 vols., Lichﬁeld, 1782), i. 3–5. 35 Perhaps ironically, the subsequent persistence of the Linnaean classiﬁcation in botany has been due to the fact that it is the most useful and practical system of classiﬁcation, able to be employed by specialists and novices alike. His zoological classiﬁcation, by contrast, was not a success. 36 Contra Sloane, ‘John Locke, John Ray’, 44.

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actually needed is a much more subtle negotiation between different levels. We need to confront these issues, but in explanatory, as opposed to metaphysical, terms. For the mechanist, botanical taxonomy would be considered an area too remote from the core activity of natural philosophy for it to yield compelling lessons. This will change as we move into the eighteenth century, and Buffon will play a key role in this change, as we shall see, but for the moment I want to keep our focus on a context in which mechanism was still dominant, so that we might see exactly how a Lockean construal of ‘experimental natural philosophy’ shifts the ground from under micro-corpuscularian explanation. As the earlier disputes over Boylean pneumatics and Newtonian chromatics made evident, mechanists were inclined to construe purely phenomenal accounts, in those cases where they offered challenging new empirical results, as being merely an initial step on the path to the only kind of explanation they deemed appropriate, namely one in terms of underlying micro-corpuscular structure.37 More generally, it was a maxim of mechanist procedure that whatever the empirical context of one’s investigations, one should always seek fundamental explanations because these will always override any other accounts. This sounds innocuous: after all, why would we prefer an explanation in less fundamental terms to one in more fundamental terms? But the issue is whether seeking explanations in fundamental terms cuts off appropriate avenues of research, avenues that offer very signiﬁcant explanatory power that is wholly lacking in attempts to offer ‘fundamental’ explanations. One clear example of the beneﬁts of refusing to seek ‘fundamental’ explanations was Newton’s establishment of the heterogeneity of white light. Newton eschewed the mechanist goal, which Descartes had attempted to realize, of trying to understand why light behaved in particular geometrically deﬁned ways when reﬂected off surfaces or refracted through transparent materials, in terms of the micro-corpuscularian physical structure of light.38 Descartes had taken a macroscopic geometrical description of the angle ranges at which white light passing through a water droplet would be refracted in such a way as to generate a spectrum, and sought to understand in physical terms just why the spectrum was generated at these angles, ingeniously reducing the phenomenon to a single refraction through a prism, and offering an account of the modiﬁcation of the light ray in refraction in terms of the motion of the corpuscles making up the light ray. Newton, by contrast, produces a spectrum through a series of prisms and focuses on something that a mechanist such as Descartes, preoccupied with the fundamental constitution of light, has no interest in, namely the elongation of the spectrum: its stretched lozenge shape. Because this falls neither under the part of the exercise dealing with geometrical optics, nor that which comes under the physical understanding of the nature of light, it falls outside the 37 38

See Gaukroger, Emergence, ch. 10. See the full discussion, ibid., 379–97.

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concerns of someone aiming at a ‘fundamental’ explanation. Newton, by contrast, in a paradigm case of ‘experimental’ natural philosophy, focuses exclusively on the manipulation of the phenomena that his arrangements of boards, prisms, and screen allows and is intrigued by unexpected correlations. Indeed, it is just such an unexpected correlation that enables him to establish that sunlight is in fact heterogeneous. Mechanists, on the other hand, had assumed that white light must be homogeneous on the grounds that the postulated physical interference with light corpuscles at the refracting surface, causing their differential rotation as a function of the angle of contact, answered perfectly to the canons of mechanist explanation: it had recourse to nothing other than contact action involving transfer of motion/momentum. In the case of the production of spectral colours, foundationalist concerns were directly responsible for mechanists overlooking the phenomena that provided the key to understanding: a concern with the ‘nature’ of light seriously inhibited its comprehension. A similar case occurs in late seventeenth- and early eighteenthcentury studies of electrical phenomena, where a concern with the underlying ‘nature’ of electricity completely obscured what was to turn out to be the key to the grasp of electrical phenomena: electrical conductivity. It was Gilbert, in his De magnete (1600), who distinguished magnetism and electricity as separate phenomena, showing that magnetic attraction was a mutual attraction whereby one body was drawn to another as if by force, whereas there are other forms of attraction that are quite different in nature from this. He was particularly concerned to distinguish magnetism from amber attraction, which required the amber to be rubbed, and he designated substances which, like amber, when rubbed exhibit an attractive power, ‘electrics’. He speculates that they must be made up from ﬂuid and humid matter which never completely solidiﬁes, and rubbing acts on this, releasing an efﬂuvium that captures small particles and pulls them inwards.39 There were efforts in the corpuscularian tradition to account for magnetism, notably by Mersenne40 and Gassendi,41 but it was Descartes’ account in Part IV of his Principia (1644) that provided a model for a mechanist account of magnetism and electricity. He relied heavily on Gilbert’s accounts of magnetic and electrical phenomena, however, and these were far less copious in the latter case, so his discussion is correspondingly brief. For Descartes, the only way to deal with magnetism was to mechanize it, because that is the only way we can understand any material process. At the end of his discussion in Part IV he tells us that he has shown that magnets have ‘no qualities so occult, nor effects of sympathy and antipathy so marvellous as to 39 William Gilbert, De magnete, magnetisque corporibus, et de magno magnete tellure: Physiologia nova plurimis et argumentis et experimentis demonstrata (London, 1600), Part II, ch. 2. 40 See the discussions of magnetism in Marin Mersenne, Quaestiones in Genesim (Paris, 1623), cols. 548 and 552, and La Verite´ des Sciences (Paris, 1625), 910–21. 41 Gassendi returns to the Epicurean doctrine of hooked particles: Opera Omnia, i. 345 col. 2–346 col. 1; ii. 122 col. 1–135 col. 2.

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render them inexplicable by the principles of magnitude, size, position, and motion’.42 Descartes was not alone in pressing this view, but his was the ﬁrst detailed and remotely plausible mechanistic account. At its core was the postulated existence of long threaded pores or channels in lodestone which admitted grooved particles, depending on whether the particle had a right-hand screw or a left-hand one. These pores are aligned along the polar axes of the lodestone and one set admits grooved particles in one polar direction, the other grooved particles in the opposite polar direction. Their grooves derive from the fact that the particles have been formed by being squeezed through the interstices of contiguous spherical globules. As a result of this squeezing they end up as cylinders having three or four concave sides joined by rims, depending on whether they are squeezed through three or four contiguous globules (see Fig. 5.1). Moreover, because they rotate on being squeezed through these interstices, the channels or grooves are rotated, forming a stream of diagonally grooved, cylindrical fragments, some of which will have a left-hand screw, some a right-hand screw, according to the direction of the twist. This, in mechanical terms, is what lies at the basis of the different polarities. The account of electricity follows on naturally from that of magnetism in Descartes’ view since, just as magnetism exhibits a force of attraction, so too do ‘amber, wax, resin, and other similar things’.43 Moreover, the aim in both cases is to provide an account of the phenomena in terms of mechanics and matter theory, on the model of what he has just offered in the case of magnetism. He conﬁnes his treatment to the behaviour of glass, and the account of the structure of glass he offers conﬂicted with a theory of static electricity that had been advocated by the English natural philosophers Kenelm Digby, Thomas White, and Thomas Browne.44 Descartes writes that: some men, seeing that this force occurs in amber, in wax, in resin, and in practically all oily substances, will perhaps think it consists in the fact that certain slender and branching particles of these bodies have been moved by friction (for friction is usually required to arouse this force), scatter themselves through the nearby air, and, adhering to one another, immediately return and bring with them the tiny bodies that they strike on their way. Just as we see that a drop of liquiﬁed fats of this kind, suspended from a rod, can be shaken by slight movements in such a way that one part of the drop still adheres to the rod, while another part descends for some distance and immediately returns and also brings with it the tiny straws or other minute bodies which it has encountered. For no such thing can be imagined in glass, at least if its nature is as we described it above; and therefore another cause of this attraction in it must be indicated.45

42

Principia IV art. 187: Œuvres viiA. 314–15. Principia, IV art. 184. See J. L. Heilbron, Electricity in the Seventeenth and Eighteenth Centuries (Mineola, NY, 1999), 193–5. The theory is set out in Kenelm Digby, Two Treatises (Paris, 1644), 172–5. 45 Principia, IV art. 184. 43 44

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Fig 5.1

On Descartes’ account, the structural difference between glass and oily substances is that the latter have interlinking branching parts, whereas glass has large smoothly joined constituents. The explanation for the behaviour of glass is to be found in the mechanical arrangement of its constituent matter rather than in some chemical property of this matter. As with magnetism, Descartes sees the solution in the distinctive pores of glass. The heating process through which glass is formed, he argues, has produced long thin channels which run from one end of the glass to the other and which are ﬁlled with subtle matter, which forms itself into long thin ribbons. These ribbons, being formed of subtle matter, are highly agitated, but are conﬁned within the pores of the glass because their shapes have been ﬁxed in the cooling of the glass and they cannot accommodate themselves to the pores of neighbouring bodies and the surrounding air. Rubbing of the glass agitates these ribbons to such an extent that they escape into the nearby air and the pores of nearby bodies, picking up material from these as it adheres to them, but returning in the end to the glass for this is the only thing that can accommodate their shape.46 Neither of the two great defenders of ‘experimental natural philosophy’ drew any conclusions from their advocacy of experimental philosophy for the study of electricity. Newton has almost nothing to say about magnetism or electricity except in respect of the difﬁculty in characterizing their behaviour: he did not consider that the inverse square law applied to magnetism,47 for example, and he complains bitterly about the chaotic nature of triboelectrical phenomena.48 Boyle accepted that what was at issue was the nature of electrics, that the answer lay in understanding the emission of the ‘material efﬂuvium’ from the electric and its return to the electric, and that this needed to be accounted for in terms of

46 The Cartesian programme was developed, with signiﬁcant revisions, in Huygens’ various works on magnetism, collected in volume 19 of his Œuvres. 47 Newton, Principia, Part II, prop. 8, coroll. 5 (810 of Cohen edn.). 48 The Correspondence of Isaac Newton, i. 364–5.

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mechanist matter theory.49 The basic assumption was that some bodies were electrics and some were not, and that the electrical power was released by rubbing, so attention—theoretical and experimental—was focused on the phenomenon of attrition, which in mechanist terms could only be the effect of friction, and it was such friction that imparted motion to the particles making up the efﬂuvium in the requisite way.50 The canonical version of this mechanist account of the nature of electrical bodies was provided by Francis Hauksbee’s Physico-Mechanical Experiments of Various Subjects, the ﬁrst edition of which appeared in 1709. The audiences for which Hauksbee, in his role as Curator of Experiments at the Royal Society, had to prepare experimental demonstrations tended to be large ones, and the devices that demonstrated the effects were correspondingly as large as was feasible.51 For triboelectrical demonstrations, he devised a large generator worked by two pulley wheels whose powerful attrition effects were evident in a glass globe which was rotated at speed by the action of the pulleys, generating the required friction (see Fig. 5.2). The straw, chaff, and paper scraps of earlier devices were replaced by brass leaves, and the experimental conditions varied in different ways, not least by linking the machine to an air pump so that the effects at different air pressures could be exhibited. The aim, as with Boyle’s pneumatic experiments of the 1660s, was to vary the circumstances experimentally so that the phenomenon could be studied exhaustively. But whereas Boyle used the range of phenomena that he could generate and control using his air pump, instead of a micro-corpuscularian model of the behaviour of gas, to guide the connections that he made between the experimentally induced phenomena (because he realized at an early stage that the two were in fundamental conﬂict), Hauksbee used his experimental apparatus to reconcile the apparently chaotic electrical effects with a theory of the fundamental nature of electrically charged bodies. The rationale behind the experiments was to vary the circumstances in which the electrically charged body exhibited its effects. As the Physico-Mechanical Experiments makes clear, it was built into the experiments and their variation of

49 Robert Boyle, Experiments and Notes about the Mechanical Origins or Production of Electricity (London, 1675), 1–2. Much of his experimental research on electricity was tied in with his investigation of the properties of glass: see idem, A Discovery of the Perviousness of Glass to the Ponderable Parts of the Flame (London, 1673); idem, Of the Great efﬁcacy of Efﬂuviums (London, 1673). 50 See Michael Ben-Chaim, ‘Social Mobility and Scientiﬁc Change: Stephen Gray’s Contribution to Electrical Research’, British Journal for the History of Science 23 (1990), 3–24; Gideon Freudenthal, ‘Early Electricity between Chemistry and Physics: The Simultaneous Itineraries of Francis Hauksbee, Samuel Wall and Pierre Polinie`re’, Historical Studies in the Physical Sciences 9 (1981), 203–29; D. W. Corson, ‘Pierre Polinie`re, Francis Hauksbee, and Electroluminescence: A Case of Simultaneous Discovery’, Isis 58 (1968), 402–13. 51 Hauksbee originally made a name for himself building an improved air pump. See Terje Brundtland, ‘From Medicine to Natural Philosophy: Francis Hauksbee’s Way to the Air Pump’, British Journal for the History of Science 41 (2008), 209–40.

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Fig 5.2

parameters that electricity was a property of bodies such as glass that depended on their material constitution, and that it was only when acted upon by frictioninduced attrition (the only mechanically acceptable form of action) that their material constitution was affected in such a way that they emitted an efﬂuvium of subtle particles from the pores of the glass, which, once emitted, generated a material efﬂuvium around the electric. This material efﬂuvium then acted to induce non-electrics to turn, via a centripetal force, to the centre, that is, to the electric. The problem was that Hauksbee soon started obtaining some very peculiar results with his generator. He assumed that the luminosity and electricity that had been generated in the glass tube were functions of the internal pressure in the tube, which he was able to vary with the air pump. Indeed, the luminosity did vary with pressure, glowing more brightly the lower the pressure, but the electricity decreased in power as the tube was evacuated. One of the electrical effects that was particularly impressive for public demonstration purposes was the tickling effect on the forehead or the back of the hand as one faced the rotating glass sphere, caused by the attractive pull on the hairs of the demonstrator’s hand. The obvious explanation for this, given his theoretical assumptions, was that the hand was in direct contact with efﬂuvia, which were static or ﬂowed in a regular manner. To test this he constructed a large glass cylinder and surrounded it with a wooden hoop supporting threads at equal intervals. As expected, when he spun and rubbed the cylinder, the threads extended themselves radially outwards towards an axial point determined by the location

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of his hand.52 But when he moved his ﬁnger towards the pointing ends of the threads they shrank from his touch,53 and placing the threads within the glass, he found their behaviour even more peculiar, the efﬂuvia apparently not moving in the kind of vortical motion that one might expect from a ﬂuid, but rather ‘it seems very much to resemble or emulate a Solid, since Motion may be given to a Body, by pushing the efﬂuvia at some distance from it’. Even more surprising, ‘this Body (I presume to call it so) altho’ so subtil as seemingly to perviate Glass, will not . . . affect a light Body thro’ a piece of Muslin: Now whether the Muslin absorbs the efﬂuvium, or what other laws it may be subject to, I cannot tell, but sure I am ’tis very amazing.’54 The possibility that was effectively ruled out by Hauksbee’s experimental setup and the theory behind it was that electricity was not a property of bodies at all, and hence not something that fell within the domain of the kind of mechanized matter theory that had routinely been invoked to explain a range of macroscopic physical phenomena. There was no available plausible theoretical context in which such a possibility could be given substance, and there was no opportunity to follow up such a line of reasoning within the context of mechanism. When the move came, therefore, it was within a wholly experimental context. Stephen Gray, a dyer by profession and an amateur naturalist by inclination,55 had been experimenting with optical instruments since the 1690s, and, stimulated by reading the accounts of Hauksbee’s experiments in the Philosophical Transactions, which began appearing in 1705, he started experimenting on electrical phenomena with a view to examining the electrical efﬂuvium.56 In 1708 Gray sent a letter to Hans Sloane, an active Fellow of the Royal Society (subsequently its President) dealing with Hauksbee’s experiments.57 Gray’s apparatus was more primitive than that of Hauskbee. In place of the elaborate brass leaves he used a down feather, and he rubbed the glass tube not with a system of pulleys but with his bare hand. What is distinctive is not his experimental apparatus, but the way he approaches the experiment. His approach is much closer to the ethos of Boyle’s air pump experiment than Hauskbee’s, because his concern is with the phenomena in their own right, not as expressions of underlying micro-corpuscular activity. He does not treat attrition of electrics as the key to understanding the generation of electricity, and he is explicit that the emission of a subtle efﬂuvium 52

See the account in Heilbron, Electricity, 233–4, to which I am indebted here. Francis Hauksbee, ‘A Continuation of the Experiments on the Attrition of Glass’, Philosophical Transactions 25 (1706), 2332–5. 54 Idem, ‘Several Experiments showing the strange Effects of the Efﬂuvia of Glass’, Philosophical Transactions 25 (1707), 2372–7: 2374. 55 This artisan background was not at all unique: Hauksbee had been a draper turned instrument maker and, like Gray, lacked formal education. 56 On Gray’s life, see D. H. Clark and L. Murdin, ‘The Enigma of Stephen Gray Astronomer and Scientist (1666–1736)’, Vistas in Astronomy 23 (1979), 351–404. 57 See R. A. Chipman, ‘An Unpublished Letter of Stephen Gray on Electrical Experiments, 1707–1708’, Isis 45 (1954), 33–50. 53

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by means of attrition is not a basic assumption of the whole experiment but a hypothesis. Indeed, the experiment that had so surprised Hauksbee, in which the brass leaf (a feather in Gray’s version of the experiment) is repelled by the hand, is treated by Gray as showing that it cannot be a question of electrics emitting efﬂuvia because all bodies, not just electrics, ‘Emitt soe they receive part of the Efﬂuvia of all other bodies that Inviron them’.58 Generally, he does not talk in causal terms of attraction at all, conﬁning himself rather to describing the motions relative to the electric. Commentators have misunderstood what is at issue here, taking Gray’s refusal to articulate his results in terms of a theory of the nature of electricity as a failure to make any contribution to electrical theory, his discoveries being essentially accidental.59 The exception is Ben-Chaim, who grasps the novelty of Gray’s procedure when he points out that simply to label Gray an empiricist, as if this explains his distinctive approach, is to beg the question. The point, he notes, is rather that he ‘refrained from using the more philosophical terminology and conﬁned himself to conventional tokens of representing the events. Gray was not more accurate than Hauksbee in his observational reports; rather, while the latter laboured to demonstrate a philosophical doctrine of electrical effects, the former was playfully attentive to the unforeseeable outcome of occurrences.’60 Heilbron has accused Hauksbee of appropriating what he found valuable in Gray’s paper and suppressing or glossing over what conﬂicted with his own ideas, including misrepresenting the experiment with the feather.61 But I think it more likely that Hauksbee simply did not know what to make of Gray’s communication. What exactly was Gray claiming? Since he did not actually reject either emission or efﬂuvia theories, or engage current theories at the level of their failure to solve problems, then, as Ben-Chaim points out,62 all that seemed to be in dispute was whether electrics emitted their own efﬂuvia, but for Hauksbee this was exactly what electricity meant. The emission of efﬂuvia by electrics was precisely what one studied when one studied electricity, yet Gray was offering no redeﬁnition of the theoretical ﬁeld: he wasn’t even engaging the theoretical issues. The situation has exact parallels with the reaction to Boyle’s original air pump experiment. Apparently one-off results seemed to be being held up as making some profound natural-philosophical point, yet there was no engagement with theoretical discussion of the issues, no suggestion of alternatives: indeed there was, it would seem, no appreciation of the intellectual capital on which current understandings of the phenomena were based. Newton’s prism experiment received the same

58

Ibid., 36. See e.g. I. Bernard Cohen, Franklin and Newton (Philadelphia, 1956), 295; Roderick W. Home, The Efﬂuvial Theory of Electricity (New York, 1981), 42, 46–7; Heilbron, Electricity, 247. 60 Ben-Chaim, ‘Social Mobility and Scientiﬁc Change’, 10. 61 Heilbron, Electricity, 236. 62 Ben-Chaim, ‘Social Mobility and Scientiﬁc Change’, 10–11. 59

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kind of reaction: there was signiﬁcant difﬁculty grasping the standing of the results. In 1716, Gray moved to London and did some experimental work with Hauksbee’s successor at the Royal Society, Desaguliers, as a result of which he was able to set up electrical experimental apparatus at the level of sophistication of Hauksbee’s. In 1720, he published his results in a paper on ‘electrical communication’ in the Philosophical Transactions.63 The actual items in the experiment are much the same as were Hauksbee’s. What is different is their arrangement, and what motivates this is a difference of focus. Because Hauskbee had set out to investigate how electrics emit the efﬂuvium that causes the electrical effects, the means of generation—attrition—was central to the experimental set-up, as was the position of the electric at the centre of the experiment. Gray must have rubbed the glass to generate the effects in the ﬁrst place, but he doesn’t even mention this, concerning himself instead exclusively with what happens once the electrical phenomena have been generated. In doing so, he effectively brackets off one set of causal questions. Moreover, Hauksbee had moved the electric around to test its effects on the various non-electrics in the experiment, because it was the electric that was the causal agent, the non-electrics being on a par with passive recipients: the hierarchy was ﬁxed in advance, as it were. Here again, Gray brackets off questions of causality: just as an account of how the electric gains its potency is missing, so this potency also loses its guiding role in what is manipulated and how. Gray doesn’t set up the experiment around the electric, keeping non-electrics at rest and changing the setting of the electric, but keeps the electric ﬁxed and devotes all his attention to the behaviour of the non-electrics. A network of effects was now the focus of attention, an ‘electrical communication’, not a centrally produced electrical ‘vertue’ which worked by means by attractions and repulsions. Gray had pared the discussion back to a very basic phenomenal level, not only discarding talk of causes, but also the Newtonian matter theory that had underlain the current theory of electricity, and which required an efﬂuvium because otherwise—since it was known since Boyle that electrical effects could occur in a vacuum—there would be action at a distance.64 What Hauskbee had provided was not just one theory among others but an account that went to the core of a Newtonian model for physical phenomena generally. Gray’s notion of electrical communication, silent as it was on what many considered the fundamental questions, in that it provided no new clues as to the nature of electricity, was treated not as revolutionary but as anomalous, and as a result was ignored. The situation changed only in 1729, when Desaguliers gave these anomalous results a new airing as something that might excite public 63 Stephen Gray, ‘An Account of Some New Electrical Experiments’, Philosophical Transactions 31 (1720), 140–8. 64 See the exemplary account in Ben-Chaim, ‘Social Mobility and Scientiﬁc Change’, 13–15, to which I am indebted here.

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interest (they were chosen as an entertainment for the Prince of Wales). Gray himself published a new report on electrical communication in 1731,65 and his demonstration that electricity could be communicated over long distances—in which, with his neighbour and electrical experimenter Granville Wheler, he had managed to carry electricity 650 feet along a heavy string suspended from silk cords mounted on poles in Wheler’s orchard—not to mention his dangling of an electriﬁed child from silk strings, which proved to be an exceptionally popular experiment over the next twenty or thirty years (see Fig. 5.3, from Nollet’s 1749 Recherches sur les causes particulie`res des phe´nome`nes ´ele´ctriques), made sure that electrical experiments came to the fore in the public domain.66 Over the next decade there was very signiﬁcant growth in experimental and theoretical interest in electrical communication, not just in England but more notably in France and the Netherlands, beginning with the systematic experimental work of Dufay in 1733, and culminating in the discovery of the Leyden jar in 1745. THE ‘NATURE’ OF METALS In introducing Ray and Gray, I said that their work was at the margins of natural philosophy, construed as mechanist matter theory. Botanical classiﬁcation fell wholly outside such concerns, while the phenomenon of electrical conductivity had a more substantial relation with matter theory, although its very intractability made this a particularly problematic relation. There was one area in which one might expect mechanist matter theory to be very much at home, however, and this was in the domain of chemical properties of substances. If mechanist matter theory, and micro-corpuscularianism more generally, worked at all as a general foundation for physical phenomena, then it should work here. It failed, however, just as it had failed in pneumatics, physical optics, and electrical conductivity. Moreover, just as in these cases, its failure was made evident by the emergence of a manifestly successful account of a different kind, one that sought to explain the phenomena in terms of ‘horizontal’ rather than ‘vertical’ relations. One of the most formative events in the development of chemistry was the publication by E´tienne Franc¸ois Geoffroy in 1718 of a table of chemical afﬁnities, that is, a table indicating, in the form of a ranking, the degrees to which different substances are found to combine with one another.67 This was a 65 Stephen Gray, ‘A Letter to Cromwell Mortimer, M.D. Secretary of the Royal Society containing several experiments concerning Electricity’, Philosophical Transactions 37 (1731), 18–44. 66 See Heilbron, Electricity, 245–9. 67 ´ Etienne Franc¸ois Geoffroy, ‘Tables des diffe´rens rapports observe´s en chymie entre diffe´rentes substances’, Me´moires de l’Acade´mie royale des sciences (1718), 202–12. Generally, see A. M. Duncan, ‘Some Theoretical Aspects of Eighteenth-Century Tables of Afﬁnity’, Annals of Science 18 (1962), 177–96 and 217–232; and F. L. Holmes, ‘The Communal Context for Etienne-Franc¸ois Geoffroy’s “Table des rapports”’, Science in Context 9 (1996), 289–311.

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Fig 5.3

striking case of a refusal to order enquiry around notions of underlying structure, and instead to pursue a phenomenological investigation. In Geoffroy’s table (Fig. 5.4), different substances are represented symbolically by their alchemical symbols. The top line contains a number of chemical reagents, and under each of these is a list of substances by order of afﬁnity, the ones nearest the top being those with the greatest degree of afﬁnity: such substances might be able to displace substances lower down the list, but could never themselves be displaced

208

Esprits acides. Acide du sel marin. Acide nitreux. Acide vitriolique. Sel alcali fixe. Sel alcali volatil.

Explaining the Phenomena

Terre absorbante. Substances metalliques. Mercure. Regule d’Antimoine. Or. Argent.

Cuivre. Fer. Plomb. Etain. Zinc Pierre Calaminaire.

Soufre mineral. [Principe. Principe huileux ou Soufro Esprit de vinaigre. Eau. Sel. [dents. Esprit de vin et Esprits ar

Fig 5.4

by those substances. So, for example, the ﬁrst column lists, from the top, acid spirits, ﬁxed alkali salt, volatile alkali salt, absorbent earth, and metallic substances, and it records the information gleaned from experiments that ﬁxed alkali salts react most favourably with acid spirits and will displace all the substances listed below it from their existing combination with acid spirits, but the reverse never occurs. The aim of the table was both to discover what happened in various chemical reactions, and to predict what would result from various combinations.68 The importance of the prescriptive function of the table is evident from the responses to it from other chemists, and Geoffroy replied to these in 1722.69 Note that the classiﬁcation is a purely empirical or phenomenological one: it is an economical compendium of a body of experimental results. Geoffroy is especially keen to avoid importing any theoretical assumptions into the presentation, to such an extent that he does not even use the term ‘afﬁnity’ because this had 68 He used the example of a corrosive sublimate in this latter respect: see the account in Mi Gyung Kim, Afﬁnity, That Elusive Dream: A Genealogy of the Chemical Revolution (Cambridge, Mass., 2003), 137–9. 69 ´ Etienne Franc¸ois Geoffroy, ‘E´claircissements sur la table insere´e dans les me´moires de 1718, concernant les rapports observe´s entre diffe´rentes substances’, Me´moires de l’Acade´mie royale des sciences (1722), 20–34.

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associations with a particular kind of account of the relation between the supposed constituents of chemical substances, just as the term ‘attraction’ did. He himself used the neutral term ‘relations’ (rapports) in labelling the table. What is so important about Geoffroy’s table is that, by classifying substances in this way by degree of afﬁnity, the table pushes the question of chemical composition to the fore. Chemical composition was not one of the traditional questions posed by matter theory, whether, for example, in an Aristotelian element version or in a corpuscularian version. Geoffroy’s table transforms the nature of chemical enquiry: indeed, it institutes a practice that breaks signiﬁcantly with traditional matter theory and has a genealogical relation to modern analytical chemistry.70 Before looking at just what is involved in Geoffroy’s table, however, it is important to note that the shift to ‘horizontal’ relations can be motivated either by Lockean considerations or by phenomenalist ones of a Malebranchean kind. For Locke, causation is not restricted to vertical relations, in that things on the same level can causally interact with one another, and I have argued that such an approach rationalizes Boylean and Newtonian procedures. For Malebranche, by contrast, all causation must necessarily cross levels because only God can genuinely act as cause. Consequently, there are no causal relations between macroscopic objects, or between these objects and their micro-corpuscularian constituents. But lack of causal relations does not mean lack of relations per se for Malebranche. Quite the contrary, provided we grasp relations clearly and distinctly, then it is in the exploration of such relations that natural-philosophical enquiry, and indeed enquiry generally (for the model, as always with Malebranche, is mathematics), consists: ‘All the mind’s action and attention towards objects, is then, only an attempt to discover their relations (rapports).’71 Consequently, although Malebranche saw the micro-corpuscularian level as that of primary qualities, by contrast with the macroscopic level of sense perception, it was the clarity and distinctness of grasp that drove the Malebranchean reduction programme, not causal direction, so if there were cases where such clarity and distinctness could be achieved at a macroscopic level then such forms of investigation were legitimate. This account effectively sanctions exploration at the phenomenal level as a legitimate way of proceeding in natural philosophy, just as (for wholly different reasons) Locke’s does, by contrast with more traditional 70 See, in particular, Ursula Klein, ‘E. F. Geoffroy’s Table of Different “Rapports” Observed Between Different Chemical Substances—A Reinterpretation’, Ambix 42 (1995), 251–87; idem, ‘Origin of the Concept of Chemical Compound’, Science in Context 7 (1994), 163–204. Geoffroy’s importance lies in the systematizing of the relations, not in their discovery. All the operations recorded in Geoffroy’s table are to be found in seventeenth-century books of metallurgical and pharmaceutical chemistry, as Klein notes elsewehere: idem, ‘The Chemical Workshop Tradition and the Experimental Practice: Discontinuities within Continuities’, Science in Context 9 (1996), 251–87. 71 Malebranche, De la recherche de la ve´rite´, Book VI Part 2 ch. 10. The theme is ubiquitous. Cf. loc. cit. Book I chs. 2 and 6; Book II Part 3 ch. 1; Book III Part I ch. 4; Book III Part 2 chs. 6 and 10; Book V ch. 5; Book VI Part 1 chs. 1, 4, and 5; Book VI Part 2 chs. 1, 4, and 7.

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mechanist reductionist understandings of natural philosophy. Indeed, for different reasons again, this is also the case on the Leibnizian account, as we have seen. These three streams have completely different motivations, of course, but they converge, for whatever different reasons, on a project that places a value on capturing horizontal relations, and it is this that I want to use Geoffroy’s account to highlight. Geoffroy came from a practical pharmacy and medical background, and it is unlikely that Leibniz exercised any inﬂuence on him, since those mathematicians who took up the new Leibnizian inﬁnitesimal calculus in the Acade´mie des Sciences had no interest in Leibnizian metaphysics as such: the fact that its upshot, in the case of the questions that concerned them, was the same as that of Malebrancheanism, was sufﬁcient. Locke is a different matter, for Geoffroy had good connections with the Royal Society and translated the ﬁrst edition of the Opticks, the most Lockean in tenor of Newton’s works. But we must also consider Malebranche seriously in this respect. The Malebranche circle members were elected to the Acade´mie en masse with the reforms of 1699, making them a signiﬁcant force in the natural-philosophical aspirations of the Acade´mie.72 Fontenelle, the Acade´mie’s Permanent Secretary and its most powerful representative, gives a good statement of the Malebranchean position in his enormously inﬂuential Pre´face sur l’utilite´ des mathe´matiques (1699): Geometry, and algebra even more, are the key to any study that can be made of magnitude. These sciences, which deal exclusively with abstract rapports and simple ideas, might seem unproductive in that they never leave the intellectual realm, so to speak; but the mixed mathematical sciences, which descend to the material realm and deal with the motion of the stars, the increase in motive forces, the different paths taken by light rays in different media, the different sounds produced by the vibration of strings, and in short all the sciences that discover the particular rapports between sensible magnitudes, advance further, and more convincingly, to the extent that the art of discovering rapports in general is perfected.73

Geoffroy’s explicitly neutral terminology of rapports might also have been a consciously natural-philosophical reﬂection of Malebranchean strictures,74 and Fontenelle, in his report on the table for the Acade´mie des Sciences, certainly describes it in explicitly Malebranchean terms: The more chemistry is perfected, the more M. Geoffroy’s table will be perfected as well, either by the increased number of substances that it will contain or by the increased exactitude in the arrangement of the rapports. If physics can never achieve the exactitude of mathematics, it can at least imitate the order of it. And a chemical table is by itself an 72 Other than Fontenelle, Varignon and L’Hoˆpital were the only members of the group who were already members of the Acade´mie. 73 Fontenelle, Œuvres, v. 7. 74 But not his occasionalism, which, so far as I can tell, not even members of the Malebranche circle adhered to.

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agreeable spectacle to the human mind, just like a table of numbers ordered according to certain properties or rapports.75

It does not matter for our immediate purposes whether Geoffroy is indebted to Locke or Malebranche, or to a combination of the two, because he makes no attempt to articulate his commitment to a neutral, phenomenal, ‘horizontal’ level in methodological and epistemological terms. We cannot say whether, if pressed, he would regard such explanation as genuinely causal, as Locke would, or whether it is actually just a clear illuminating description, as Malebranche would conceive it, remembering that for Malebranche this is all that any physical account could hope to offer. What is clear is that his commitment, as was typical in the experimental philosophy tradition, was resolutely practical, taking seriously the idea of connections between phenomena having explanatory power, and focusing on these much to the exclusion of all else. The question of whether such explanatory power proceeds via causation, or bypasses it, is not, and need not be, raised. What is important is the commitment to the legitimacy of explanations through horizontal relations, and the anti-reductionist consequences of this. Although absent from matter theory, the question of chemical composition had been of some relevance in two practical chemical disciplines, pharmacy and metallurgy. Pharmacists and metallurgists needed to know what quantities of ‘simple’ substances (i.e. those effective in their own right) had to be mixed together to make a successful product, they needed to know which substances reacted with one another and which did not, and they employed two traditional tried and tested experimental means: distillation in the case of pharmacy and selective dissolution of metals in acids in the case of metallurgy.76 Geoffroy came from a family that had been pharmacists for four generations, and he himself trained in pharmacy at Montpellier and Paris, becoming fully qualiﬁed in 1694. He soon turned to the study of medicine, however, and in 1698 he travelled to England as personal physician (despite still being only a medical student) to the French ambassadeur extraordinaire, the Comte de Tallard; while there, he participated in the activities of the Royal Society, performing a number of chemical 75 Histoire de l’Acade´mie Royale des Science. Avec les me´moires de mathematiques et de physique . . . tire´e des registres de cette acade´mie (92 vols., Paris, 1702–97): 1718: Histoires, 37. Quoted J. B. Shank, ‘Before Voltaire: Newtonianism and the Origins of the Enlightenment in France, 1687–1734’ (PhD thesis, Stanford University, 2000), 410–12. It is noteworthy in this connection that d’Alembert, in his 1751 ‘Discours pre´liminaire’ to the Encyclope`die, expresses the Lockean view to which he is otherwise committed in very Malebranchean terms, again employing the terminology of rapports: ‘The usefulness of mathematical knowledge is no less great in the examination of the terrestrial bodies that surround us. All the properties that we observe in these bodies have rapports to one another which are more or less accessible to us. The knowledge or discovery of these rapports is almost always all that we are able to attain, and consequently the only one that we should propose for ourselves.’ Diderot and d’Alembert, Encyclope´die, i. p. xii. 76 Kim, Afﬁnity, 5–6. I am particularly indebted to the early chapters of Kim’s book in what follows, as well as to He´le`ne Metzger, Les Doctrines Chimiques en France du de´but du XVIIe a` la ﬁn du XVIIIe Sie`cle (Paris, 1969).

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demonstrations. He was elected a member of the Royal Society, on Hans Sloane’s recommendation, in the same year.77 In 1704, he graduated in medicine, and began preparing a French translation/pre´cis of the ﬁrst edition of Newton’s Opticks: between August 1706 and June 1707, he read sections to members of the Acade´mie, the audience including Malebranche, Varignon, and Fontenelle.78 In 1707, Geoffroy started lecturing at the Jardin du Roi, a particularly signiﬁcant institution in the development of pharmacy in France.79 It had been established in 1635 for the supplemental education of medical students, and was a source not only of teaching and experimentation in pharmaceutical medicine, but also the principal source of textbooks in this area. The Jardin was dominated by Huguenots who had strong ties with Montpellier—a Protestant medical faculty with a commitment to chemical remedies80 and the University of Paris’ great rival—as well as with the Protestant medical community in Paris, and it was Paracelsian in orientation, in direct competition (as in England) with the reigning Galenism of the medical community. In contrast to Aristotle’s four elements—earth, air, ﬁre, and water—Paracelsians had argued that the fundamental constituents of all material things were mercury, sulphur, and salt, subsequently expanded into ﬁve ‘principles’: spirit, oil, salt, water, and earth. It was never clear however whether, or to what extent, these were to replace the Aristotelian elements or to supplement them. The teachers at the Jardin, in an effort to provide a philosophical basis for their teachings, attempted to ground Paracelsian principles in Aristotelian natural philosophy, but it was crucial that any such grounding was consonant with the process central to laboratory investigations, namely distillation. By the middle of the seventeenth century, Aristotelian elements and Paracelsian principles had been matched up with the ﬁve products of distillation.81 This is particularly clear in De Clave’s textbooks from the 1640s. In his Nouvelle lumie`re philosophique, he tells the reader that ‘there are ﬁve bodies called elements, not because they are simple, otherwise the sky and the air would be elements, but only because they compose all mixed bodies’,82 and these elements are identiﬁed as distillation products. It is heating 77

See Jean Jacquot, Le naturaliste Sir Hans Sloane (1660–1753) et les ´echanges scientiﬁques entre la France et l’Angleterre (Paris, 1953) on scientiﬁc relations between the Royal Society and the Acade´mie des Sciences (to which Sloane was elected as a corresponding member at the beginning of 1699). 78 See A. Rupert Hall, ‘Newton in France: A New View’, History of Science 13 (1975), 233–50; and Henri Guerlac, Newton on the Continent (Ithaca, NY, 1981), 102–7. 79 See Jean-Paul Contant, Enseignment de la chimie au Jardin Royal des Plantes de Paris (Cahors, 1952). 80 On Montpellier, see Elizabeth A. Williams, A Cultural History of Medical Vitalism in Enlightenment Montpellier (Aldershot, 2003). As Williams notes (9), Montpellier was nurtured through a shared Protestant medical culture formed through an epistolary network linking it with Uppsala, London, Halle, Geneva, and Lyons. 81 See Metzger, Les Doctrines Chimiques, ch. 1. 82 Estienne De Clave, Nouvelle lumie`re philosophique des vrais principes et elemen de nature, & qualite´ d’iceux (Paris, 1641), ‘Au lecteur’.

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that resolves substances into their elements,83 namely water, spirit or mercury, oil or sulphur, salt, and earth. Not only did De Clave’s approach indicate that only experiments could teach the number and properties of elements, he brought together two previously separate criteria: that elements should be the building blocks of substances, and that they should be revealed by chemical analysis.84 In fact, the experimenters of the Jardin were particularly well placed in this respect, for while distillation products of minerals were very limited, the distillation products of plants were of great variety and should reveal all ﬁve elements if anything could. As a result, ‘vegetable analysis’ became the key to understanding the simples from which substances were composed. There were, however, two outstanding problems with the identiﬁcation of simples or elements by means of distillation products. The ﬁrst was the assumption that heating broke up products into their simple constituents. An alternative view was that the ‘principles’ separated out by distillation had not in fact existed in the body before the analysis, but may well have been created by it. Second, there were procedures other than distillation known to chemical experimenters that yielded products of analytical value at least equal to that of distillation, namely the combining of and extraction of substances in solution, which were not blunt instruments like heating, and were capable of greater ﬁne-tuning. Both these criticisms were associated particularly with van Helmont, and they had also been urged by Boyle for example.85 They were taken up by Du Clos, one of the two founding members of the Acade´mie in the area of chemistry. Like Boyle, Du Clos saw the ultimate solution in terms of the Helmontian ‘alkahest’, a liquid capable of resolving any substance into its constitutive parts,86 but in the absence of such an alkahest, it was considered that various acids and alkalis could be substituted. The natural-philosophical standing of chemistry was a matter of dispute in the Acade´mie, however, and Perrault and Mariotte rejected what they considered to be outdated ‘principles’ and ‘elements’ and urged the formulation of chemistry in micro-corpuscularian terms.87 In the 1670s, Nicolas Le´mery combined Du Clos’ commitment to solvent, as opposed to distillation, methods with a micro-corpuscular vocabulary. Although Metzger has credited Le´mery with reforming the French didactic chemical tradition by reformulating it in terms of mechanism,88 matters are a little more complex for, as Kim points out, while the use of corpuscular language may well have been responsible for the unprecedented success of Le´mery’s lectures on

83

Estienne De Clave, Cours de chimie (Paris, 1646), 4. As pointed out by Kim, Afﬁnity, 29–30. 85 Robert Boyle, The Sceptical Chymist (London, 1661), 286–7. 86 See Metzger, Les Doctrines Chimiques, 266–72. 87 Generally, see Alice Stroup, A Company of Scientists: Botany, Patronage, and Community at the Seventeenth-Century Parisian Royal Academy of Sciences (Berkeley, 1990). 88 Metzger, Les Doctrines Chimiques, 281–338. 84

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chemistry in the fashionable Parisian salon culture, it did not signiﬁcantly alter the content of the chemistry that he taught. What did the real work was the displacement of distillation in favour of solvent procedures in mineral and vegetable chemistry.89 Nevertheless, the appointment of Fontenelle—the greatest popularizer of Cartesian cosmology90—as permanent secretary of the Acade´mie in 1697, and the reorganization of the Acade´mie in 1699 which he supervised, meant that the theme of a uniﬁed natural philosophy along Cartesian lines became very much a general desideratum.91 The revision of the underpinnings of chemical reactions on a micro-corpuscular basis was an important ingredient in the legitimation of chemistry as a serious natural-philosophical discipline, something needed if it was to be lifted decisively out of the domain of ‘sooty empirics’ and incorporated into an integrated project of understanding the world, of the kind offered by Cartesian natural philosophy. But this is different from the demand that such micro-corpuscular reduction make a contribution to the understanding of speciﬁc chemical reactions. One of the problems with the Cartesian uniﬁcation programme was that the very different kinds of contribution made by the replacement of Paracelsian principles by Cartesian microcorpuscles, for example, and the replacement of analysis of distillation products with the analysis of the behaviour of substances in various acids and alkalis, were liable to become blurred. Nevertheless, in recognizing the great difference between the two, we must not be led to underestimate the importance of the project of incorporating chemistry into natural philosophy, not just for its theoretical claims to be taken seriously, but for it to issue in theoretical claims in the ﬁrst place. That is to say, for the shift to solvent methods to have any theoretical standing, chemical analysis had to be seen as part of a general naturalphilosophical project in which the basic constituents of substances are identiﬁed, and being considered as part of a micro-corpuscularian general project in natural philosophy meant that it could trade on the legitimacy, standing, and successes of this project. The key player in this enterprise was Wilhelm Homberg, trained as an experimental natural philosopher rather than in pharmacy or medicine as his contemporaries were, and the Acade´mie chemist most concerned to establish connections between chemistry and general physical theory, most notably in a series of ‘Essais de Chimie’ published in the Acade´mie Me´moires between 1702

89

Kim, Afﬁnity, 53. Bernard le Bovier de Fontenelle, Entretiens sur la pluralite´ des mondes (Paris, 1686); and idem, Digressions sur les anciens et les modernes (Paris, 1688). 91 Within limits, that is. An outspoken Cartesian such as Rohault was never admitted to the Acade´mie, despite the central place of his textbook in the conception of natural philosophy fostered there: see Roger Hahn, The Anatomy of a Scientiﬁc Institution: The Paris Academy of Sciences, 1666–1803 (Berkeley, 1971), 9. Cordemoy likewise was never admitted, and Re´gis only at the end of his life. 90

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and 1709.92 When we look at how Homberg went about this task, it becomes clear that it is his experimentalist background, rather than his basic naturalphilosophical commitments, that shapes his work. His approach to distillation is typical. Although he had no theoretical commitment to distillation procedures, he did not simply abandon them but rather used an aerometer in an attempt to measure the ﬁve ‘principles’, and set out to provide a corpuscular account of ﬁre in which it was a tangible substance able to enter into chemical reactions. In other words, he did not attempt simply to replace the basic categories that pharmacists, metallurgists, and others had found useful in chemical analysis, with a microcorpuscularian ontology, for the latter, which was largely speculative and a priori, simply had no purchase in terms of procedures and analysis. Instead, he took the categories that chemists generally had found useful and gradually assimilated them to techniques associated with the new micro-corpuscularian natural philosophy.93 At the reorganization of the Acade´mie in 1699, Homberg brought in Le´mery as an associate, and Geoffroy as a student. One of Homberg’s main concerns was a quantitative determination of acids in their reaction with alkalis, for which classiﬁcation of salts was crucial, and Geoffroy’s research proposal was to work on essential salts. Yet despite their collaboration, there was a signiﬁcant difference in their approaches.94 One of Homberg’s core concerns was the sulphur principle, which was active, in that it could act alone or activate three other principles: namely salt, mercury, and water, with earth being unable to be activated. It was also universal, but it was especially difﬁcult to isolate, because sulphurs and salts were always joined to a third principle which acted as a vehicle. In the case of salts, Homberg studied the reactions of acids and alkalis. For sulphur analysis he used a three-foot diameter convex burning glass designed by Tschirnhaus, enabling him (weather permitting) to subject substances to intense heat in a more controlled and efﬁcient way than was possible with the traditional chemical furnaces. The aim was to establish the true sulphur principle in fundamental micro-corpuscular terms, and then to connect this to the intermediate level, characterized by the much greater variety of distillation products. Homberg subjected what he considered to be the three sulphurous acid salts—metallic 92 Wilhelm Homberg, ‘Essays de Chimie. Article Premier: Des Principes de la Chimie en general’, Me´moires de l’Acade´mie royale des sciences (1702), 33–52; idem, ‘Essay de l’analyse du Souffre commun’, loc. cit. (1703), 31–40; idem, ‘Suite de Essays de chimie. Article Troisie`me. Du Souphre Principe’, loc. cit. (1705), 88–96; idem, ‘Suite de l’article trois des Essais de chimie’, loc. cit. (1706), 260–72; idem, ‘Suite des essais de chimie. Art. IV. Du Mercure’, loc. cit. (1709), 106–17. There is an especially good discussion of Homberg’s contribution in Kim, Afﬁnity, ch. 2, on which I draw in what follows. 93 Note however that this does not means that the language of corpuscularianism was doing no real work at all. As Kim notes, it allowed Homberg to establish connections between the results of different analytical methods and thereby to form a uniform terrain of chemical theory: Kim, Afﬁnity, 81. 94 See ibid., 84–103.

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sulphur, vegetable sulphur, and bituminous sulphur—to analysis, but although he extracted a dense red oil which he believed to be ‘true’ sulphur, further analysis did not reveal a sulphur principle, and he ends up suggesting it might be ‘the matter of light’ (which in effect also makes it the matter of heat), which would also explain why, if the true sulphur principle were in fact the source of all activity in matter, it would nevertheless be inaccessible by means of chemical analysis. This also takes the question directly back to Cartesian micro-corpuscularianism, where light was associated with a particularly small size of corpuscle, and indeed Homberg speculates that light, being the smallest of all bodies at the corpuscular level, can pass freely through the pores of other bodies, ﬁlling the pores of inﬂammable bodies and transforming them into ﬂames.95 He notes that this prompts the question of how this ‘matter of light’ acts on bodies so as to produce the sulphurous matters recognized by chemists, although he does not follow this up, and indeed it is unclear how, on an experimental level, one could proceed. Geoffroy, by contrast, was reluctant to leave the level of chemical analysis for that of micro-corpuscularian natural philosophy, and took the dense red oil itself to be the sulphur principle, concentrating on experiments in which he decomposed and recomposed common sulphur from its ‘principles’.96 Having achieved this, he generalizes not by attempting to move to a more fundamental level but by working outwards to the composition of ‘metals’ in general, trying to show that iron was also a compound of the sulphur principle, a vitriolic principle, and an earth, differing from common sulphur only in the last respect, something that should be experimentally demonstrable. It is not that Homberg did not endorse this move, for he did; rather, it is that such investigation had for him a merely evidential as opposed to an explanatory role. Geoffroy, by contrast, endows it with explanatory signiﬁcance in its own right. Geoffroy moved decisively in this direction after Homberg’s death in 1715, when he took charge of the chemistry section at the Acade´mie. By this time, the use of solvents had become the dominant form of chemical analysis, and the selectivity of chemical reactions— what reacted with what, and what could displace what in solution—became the leading question in theoretical chemistry, partly due to the efforts of Le´mery’s son Louis, and partly due to Geoffroy. The Acade´mie chemists other than Geoffroy had seen the problem of selectivity as being that of discovering the causes of selectivity, however, something to be explored by postulating microcorpuscularian mechanisms. Geoffroy by contrast saw the central problem as being that of imposing a comparative and numerical ordering on the various chemical interactions. The principle of organization that lies behind Geoffroy’s table is that of displacement, and indeed he and Louis Le´mery had used displacement as a measure of the relations of afﬁnities between substances. Le´mery pursued the 95 96

Homberg, ‘Suite de Essays de chimie. Article Troisie`me. Du Souphre Principe’. See Kim, Afﬁnity, 96–8.

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question in ‘vertical’ terms, asking what underlying micro-corpuscularian mechanism could be invoked to account for the production of such displacements. Geoffroy not only did not consider such questions, but devised a terminology that was explicitly neutral with respect to them. His interest was in exploring the horizontal relations, staying at the level of the phenomena, ignoring everything except the relations themselves, and seeking to characterize these relations in terms of ratios (the French term ‘rapport’, which Geoffroy uses, also has the mathematical meaning of ratio). The table not only offers description, explanation, and prediction, but as Kim notes, it also allows dissent within a comprehensive framework.97 It is helped in this last respect by the fact that the description and explanation it offers are relative to available levels of chemical analysis, not to some assumed ﬁxed and absolute underlying micro-corpuscular structure. Because of this, it is able to—and did—offer guiding structure and a set of aims for further research, setting out precisely the tasks of chemical analysis within a purely experimental context, one that focused on metals in acid-alkali solution. CAUSATION AND EXPLANATION The genre in which Ray pursued his botanical classiﬁcation, that in which Gray pursued his study of electrical conductivity, and that in which Geoffroy pursued the understanding of chemical afﬁnities, is the same as that in which Boyle pursued his pneumatics and that in which Newton pursued his work on the refraction of light through prisms. It is the genre that was originally rationalized in the Royal Society in terms of ‘experimental philosophy’, and which received a refurbished and far more sophisticated rationale in the hands of Locke. Its most distinctive feature is that it looks for explanations in ‘horizontal’ rather than ‘vertical’ relations. It is worth reiterating here that the Lockean position, as I have described it, does not say that we must prefer horizontal to vertical explanations tout court: its claim is rather that there may be cases of horizontal explanation which are sufﬁcient in their own right, which do not need to be replaced by vertical ones to yield ‘ultimate’ explanations. It does not deny that there may well be a micro-structural level underlying natural phenomena, but it does not restrict causal explanations to those that invoke such a structure, and it does not allow considerations of micro-structure automatically to override phenomenal accounts. That is to say, what is at issue is not reduction per se, but uniﬁcation through reduction. The Lockean view goes against the tenor of the project of uniﬁcation that drives much of the new natural-philosophical programme from the 1620s onwards. But its success lies in the fact that, in the cases we have 97

Ibid., 139.

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explored, for example, it is able to open up and provide structure for remarkably successful research programmes, in each case able to generate results in areas where reductionist strategies had been able to offer nothing. Geoffroy and Gray offer compelling examples of the beneﬁts to be gained from formulating projects that eschew micro-corpuscularian reduction in favour of investigating ‘phenomenal’ correlations. This prompts the question whether we can establish any broad guidelines on phenomenal versus micro-reductive explanations. In particular, it is worth taking the opportunity at this point to explore the relationship between mechanics, considered as offering non-reductive forms of explanation, and matter theory, as the canonical form of micro-reduction. From classical antiquity, but particularly in the wake of Aristotle’s deﬁnition of the theoretical sciences, there had been a distinction drawn between the kinds of account offered in the practical-mathematical disciplines such as mechanics and astronomy, and those offered in natural philosophy proper. Only in the latter were physical phenomena deemed to be explained in terms of their essential features, which left the former with a lesser standing that only began to be questioned from the end of the sixteenth century. The distinctive characteristic of explanation in terms of essential features was its claim to have uncovered a deeper level than that of the merely phenomenal. When, with the development of mechanism, micro-corpuscularian explanations replaced essential ones, this feature was retained. Nevertheless, the standing of mechanical explanations, which recognized no differentiation between levels any more than did geometry, was reassessed in the wake of Galileo’s defence of the law of falling bodies as genuinely physical (as opposed to being a mathematical idealization), so that ‘horizontal’ explanations were rehabilitated in the case of mechanics. What I am calling explanations in terms of ‘horizontal’ relations here are simply those that do not require us to move from one level to another in explanation, but some clariﬁcation of the distinction between such horizontal and vertical explanations is needed. Vertical explanation is distinctive of matter theory, and while natural philosophy was conceived as being essentially matter theory—as it was from antiquity to the seventeenth century—it was taken as axiomatic that explanations would take the form of penetrating beyond the phenomena, as it were, to discover what made them behave as they did. Vertical explanations account for the phenomena in terms of something deemed more fundamental, by contrast with horizontal explanation, where the issue of being more or less fundamental does not arise: this latter is something distinctive of the practical-mathematical disciplines, especially mechanics, which Aristotle had excluded from natural philosophy. These practical-mathematical disciplines provided mathematical accounts of their subject matter, not physical ones, and Aristotle had drawn a very sharp distinction between the two. To some extent, despite the acceptance of mechanics as a physical discipline in the course of the seventeenth century, the idea remained that matter theory was what physical explanation consisted in. In the mechanism of Descartes, Gassendi, Hobbes, and

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Boyle for example, mechanics was a way of enhancing matter theory. It provided the resources for a quantitative description of a microscopic level which matter theory had identiﬁed as being the fundamental level of explanation. But the Galilean model that Newton developed in the Principia was quite different from this, as I have indicated. Indeed, as we shall see in Chapter 8, the rational mechanics tradition, which took its bearings in part from Book I of the Principia, treated natural philosophy as mechanics. The question that arises in the experimental philosophy tradition is not that of an all-or-nothing choice between the matter-theoretical and mechanical modes, but rather one of how one tackles phenomena that do not ﬁt neatly into either of these traditional categories. Because of the traditional conception of natural philosophy as matter theory, vertical explanations are invariably the default position, so that if one can provide a vertical explanation this is treated as requiring no justiﬁcation, whereas horizontal explanations are treated as being intrinsically problematic, and indeed as having at best diminished explanatory power. Essentialism and reductionism are paradigm forms of vertical explanation, and the two familiar forms of vertical explanations that I have focused on in this chapter are Aristotelian essentialism and mechanist micro-corpuscularianism: both work on the assumption that understanding natural phenomena is a question of ‘lifting the lid’, as it were, and seeing what is going on inside/ underneath. The ﬁrst requires that explanations take the form of demonstrations from ‘natures’ or essences of bodies that ‘underlie’ the forms of behaviour of the body that arise from these essences. Such essences are not of a different order of magnitude from the behaviour to which they give rise, because they are not of any order of magnitude: they are immaterial. The micro-corpuscularian explanations offered by mechanism are also vertical, but here the crossing of level is not a qualitative one, but rather one of scale, and the idea of the realm of the explanans ‘underlying’ that of the macroscopic phenomenal realm is taken more literally. Although the levels between which we move are quite different kinds of thing, in both cases the controlling idea is that change of level is necessary for explanation. In mechanics, as I’ve indicated, all explanations are necessarily horizontal: there is no stratiﬁcation into more and less fundamental levels, corresponding to the microscopic and the macroscopic in matter theory. There is no difference between the microscopic and macroscopic realms, and the notion of invoking the one to explain the other therefore has no purchase. Mechanists combined mechanics with micro-corpuscularianism, to render its explanations vertical, by invoking microscopic events to explain macroscopic ones. But mechanics itself neither contains nor indeed recognizes different levels, and hence it always offers ‘horizontal’ accounts.98 98 As we saw when discussing Book II of Newton’s Principia in Chapter 2, and will see further when we look at the rational mechanics of ﬂuids in Chapter 8, there are of ways of building up complex structures, such as elastic and ﬂuid bodies, from the behaviour of their constituent mass

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Note that mechanics is being used here as a resource that matter theory employs, not the other way around. The reason for this is the deeply entrenched view that vertical explanations are complete and that they are causal, by contrast with horizontal explanations, which are incomplete, and unable to provide causes. Consideration of mechanics indicates just what is wrong with this view of the explanatory priority of matter theory. Consider the question of causation, as we move from Aristotelian essentialist matter theory to mechanist reductive matter theory. Causes did indeed reside at the level of essences in the former, because it was essences that completely determined the natural behaviour of the body having that essence. The situation with mechanist matter theory is more complicated, however. Mechanist micro-reduction means that physical activities are always traced to the level of micro-corpuscles, but this in itself does not mean that causation is traced to this level. On the Malebranchean occasionalist account, there is no natural causation of any kind, whether at the macro- or at the micro-levels: as we have seen, all causation is supernatural. So on this construal, matter theory is not an account of causation at all. Alternatively, there is the view that natural causation does indeed exist, and that all causation takes place in virtue of causation at the micro-level. But again this does not mean that such causation is to be traced to material properties of the micro-corpuscles. The rules governing collision, for example, to the extent that they invoke any interaction of forces, i.e. to the extent to which they invoke causation,99 invoke mechanical forces, and I am unaware of any attempt in the mechanist tradition to explain the nature of such contact forces in terms of the nature of matter (Leibniz leaves behind the mechanist programme as soon as he embarks on consideration of this

points: building up multiple processes from single ones. Is not this, one might ask, a paradigmatic form of micro-reductive, and hence vertical, explanation? The answer is that it is not, for these are exercises in mechanics, not in mechanist micro-corpuscularianism. The form of mechanics within which they are pursued, like all forms of mechanics, makes no attempt to incorporate matter theory at a fundamental level, and the microscopic and the macroscopic are no longer different ‘realms’ in these projects, because there is no mechanically signiﬁcant distinction between the microscopic and the macroscopic in mechanics. 99 The issues I have raised here merely touch on some difﬁcult and profound questions about the relation between causation and explanation, and reduction and explanation. Even the very idea of force as a paradigmatic form of cause in this context is problematic. There were cases in late seventeenth-century mechanics where it was generally assumed that one thing was doing something to another in their interaction, for example transferring motion or momentum to another body in collision, but where it turned out, as Huygens showed, that the situation could be analysed simply in terms of reference frames, in which case the bodies no longer seemed to be doing anything to one another. Even where apparently straightforward accelerative forces are involved there were problems. As we have seen, Leibniz and Newton differed fundamentally on whether an accelerative force was responsible for the change of shape in the surface of water in a rotating bucket, and more generally there are some physical forces such as Coriolis forces that can be considered equally either as fundamental forces, or as purely phenomenological and relative to other factors: see Ian Hacking, ‘Why Motion is Only a Well-Founded Phenomenon’, in Kathleen Okruhlik and James Robert Brown, eds., The Natural Philosophy of Leibniz (Dordrecht, 1985), 131–50. It would take us too far from our present concerns to pursue these questions further here.

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question). Such notions as rigidity and elasticity are resolutely mechanical, and no micro-reduction is going to throw any light on them. Once we leave the realm of essentialism for that of mechanism, what causal claims matter theory makes are largely parasitic on the causal role of forces that fall under the purview of mechanics, not under that of matter theory. On the question of completeness, a comparison between matter-theoretical and geometrical explanation can be used to illustrate what is at issue. We can explain why a square peg won’t ﬁt into a smaller round hole in two ways: using a vertical matter-theoretical explanation and using a horizontal geometrical one. In the ﬁrst case, we appeal to the material constitution: we note when we attempt to push the peg into the hole, a particular region of matter at the corners of the peg comes into contact with a particular piece of matter at the boundaries of the hole, and the latter halts the progress of the former. We then change the position of the peg, and ﬁnd the same kind of thing happens. In such a case, we are able to generate a potentially inﬁnite number of accounts, each of which deals with a particular conﬁguration of the constituent corpuscles/atoms of the peg and the matter encompassing the hole. Alternatively, we can offer a geometrical explanation, noting that the diagonal length of the peg is greater than the diameter of the hole, and conclude that this explains why the peg will never enter the hole. On the face of it, the material constitution explanation looks complete in itself, whereas the geometrical explanation does not, because the geometrical explanation assumes that the peg is made of a particular kind of material. But it could hardly be maintained that the geometrical explanation needs to be supplemented with a matter-theoretical account on the grounds that if the peg were made of sponge we could squeeze it into the hole. The geometrical argument is an argument about shapes and sizes: the only way in which a sponge peg can be forced into the hole is by changing its shape. If its material constitution allows it to be reshaped into a cylinder as it enters the hole, then from a geometrical point of view all this means is that a round peg of a given diameter will enter a hole of the same diameter. It is because geometry picks out shapes—by contrast with theories about the material constitution of bodies, which ignore them—that it is able to offer a single explanation for a situation in which a theory of the material constitution of bodies requires an inﬁnite number of such explanations. By showing how a geometrical notion of ‘ﬁt’ is what we need, not a physical notion, the geometrical account tells us why the situation is as it is, in a way that indicates why a survey of each of the inﬁnite number of particular material conﬁgurations is irrelevant, and hence why the explanation that relies on the theory of material constitution misses the point. Note that the geometrical explanation invokes no underlying structure, whereas the matter-theory account does, so what we have here is a case where we prefer a horizontal to a vertical explanation. Nevertheless, there is still a sense in which the geometrical explanation is not a complete explanation. For even though the geometrical explanation does not have to assume any particular kind of matter, it does assume that the boundaries

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are rigid. Some non-geometrical assumptions about the nature of the peg and the boundaries of the hole are being made. If matter were not as it is, if it did not have particular fundamental properties, then shapes might simply pass through one another, like holograms. In other words, we must supplement the geometrical account if we are to provide something that explains why rigid structures do not pass through one another in those cases where the geometry shows that they each extend beyond the other’s boundaries in places. But as I have indicated, in asking for the explanation of rigidity, there is no point appealing to the material constitution of the bodies. The account of structure that we need to understand a phenomenon like rigidity is mechanics, not some reduction to material constituents.100 Rigidity is an issue that falls outside the realm of matter theory as much as it does that of geometry. What makes a structure rigid is a question for mechanics, not matter theory. Moreover, not only do we look to mechanics to tell us what structures are rigid, but we also look to it to tell us why they are rigid: when we explain why suspension bridges hold up while those of identical material but of a slightly different shape collapse, why chairs with four legs are stable and why those with two legs are not, why bolts and screws are so effective in securing rigid structures, what we need to understand is the distribution of macroscopic forces. In response to this, it might be countered here that, whatever role rigidity plays, the crucial property is that of impenetrability, and that impenetrability is a matter-theoretical notion. But the situation is not so straightforward. Certainly the impenetrability of corpuscles or atoms can be regarded as a question of matter theory, but the reason why we can successfully push a peg through air, but are unsuccessful when we attempt to insert it into solid wood, is not that in the former case we manage to penetrate the atoms making up air, whereas in the latter case we are unable to penetrate the atoms making up wood. In neither case do we penetrate atoms. The impenetrability of atoms and the impenetrability or penetrability of macroscopic substances are quite different. Carbon gas and diamond are each made up of the same carbon atoms, for example, yet one is penetrable and the other not. The reason one can be penetrated but not the other is not that we are able to penetrate the atoms in the one case but not in the other, but nor is it a question of the atoms being closer together in the latter than in the former, any more than it is in the case where a peg cannot penetrate wood but can penetrate far denser mercury. What is at issue is a structural question, namely 100 There is no simple answer to the question why some molecular structures are rigid: they may comprise particularly tight ﬁtting molecules or potentially huge structures such as polymers, and one only needs to think of the allotropic varieties of carbon (amorphous carbon, graphite, diamond, fullerenes, lonsdaleite, and carbon nanofoam, among others) to realize that the answer lies not in sub-atomic constituents but, insofar as we are concerned with atomic structure, the spatial relations between these constitutents and the distribution of forces that this allows. The same material constituents may result in wholly different structural properties, and wholly different material constituents may have exactly the same structural properties.

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the distribution of forces, and this is a question for mechanics. The penetrability of a substance—consider the case of sawdust as opposed to solid wood—might simply have nothing to do with microscopic constituents. It might be argued, however, that, if atoms were not impenetrable, then the structures formed from them could not be impenetrable. But this does not follow. The move from micro- to macro- is typically a move to collective rather than distributive properties, and there is nothing to prevent structures built of penetrable microscopic constituents being constructed in such a way that the resulting macroscopic structure is impenetrable. Of course, the mechanics that we invoke to explain the (degree of) impenetrability of the macroscopic structure may show us that (and how) this impenetrability trades on the impenetrability of the microscopic constituents. But it might just as easily show us that it is independent of the impenetrability of the microscopic constituents. In short, there are three possibilities. Matter theory may be of no relevance, of marginal relevance, or of signiﬁcant relevance in explaining the properties of a resisting material. The point is simply that matter theory does not, and could not, supply all we need, so matter-theoretical explanation is not a complete explanation in this case. What we have in the cases of geometry and mechanics are horizontal explanations which focus on different aspects of the situation under investigation. They take some factors as ﬁxed or given, and indicate the contribution of those they identify as carrying the explanatory weight. They ask speciﬁc questions in accord with the explanatory resources they have to offer, and the answers they give to these questions are complete. But completeness here is relative to the question asked, not to some absolute standard. This prompts us to ask whether there could be such thing as completeness per se. If there could not, then a matter-reductive approach that rejected the single geometrical explanation on the grounds that only a micro-reductive account was complete in its own right, maintaining that any other forms of explanation lack such completeness because they focus on particular aspects of the situation at the expense of others, would be misconceived. Misconceived and impossibly uneconomical: for the purportedly ‘complete’ account, which eschews geometrical, mechanical, and other considerations that are autonomous with respect to matter theory, redescribing the phenomena in terms of the conﬁguration of their microscopic constituents, requires us to provide a different explanation in each case, since each conﬁguration will be different. By contrast, the ‘incomplete’ and, it should be said, potentially openended alternative requires us to pick out what is pertinent from consideration of the phenomena, invoking autonomous domains as necessary: geometry, mechanics, and perhaps matter theory, as the occasion dictates, and depending on just what it is one speciﬁcally deems in need of explanation. In sum, horizontal explanation does not suffer in comparison with vertical explanation either in respect of completeness or causation. Mechanical, mattertheoretical, and geometrical explanations are each potentially legitimate (and

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potentially compatible) forms of explanation. Whether they are actually legitimate depends on the particular case, that is, on the skills one can bring to bear to identify and deploy the appropriate resources. So long as one does not assume from the outset that matter-theoretical explanations will trump other kinds—on the spurious grounds of completeness for example—then they will be one important resource that one can choose where appropriate. It is also perhaps worth noting here the importance of the fact that completeness of an explanation is relative to what one wants the explanation to achieve, and that there is no completeness per se. This has consequences not just for the respective merits of matter-theoretical explanations vis-a`-vis other forms of explanation, but also for matter-theoretical explanation in its own terms: the fact that one might be able to identify smaller or smallest constituents of bodies, does not in itself mean that matter-theoretical explanations must ultimately be formulated in terms of these smaller or smallest constituents. An eighteenth-century chemist, for example, may be committed to micro-corpuscularianism, but may consider this to be irrelevant when it comes to explaining chemical reactions in terms of the constituents of substances.101 Here a meso-reduction to identiﬁable constituents identiﬁed by separation methods such as distillation may be what does the explanatory work, and an attempt to move from the meso-level to the microlevel might well be not merely useless but counter-productive. To enable us to consider some general questions, I have focused on two familiar forms of non-reductive horizontal explanation, namely geometry and mechanics. The issues in mechanics and geometry do not carry over exactly when we consider areas outside traditional matter theory in which there is a commitment to phenomenal explanations, but the general questions that I have just raised should be enough to alert us to some misconceptions that might prevent our taking such phenomenal explanations on their merits. At issue here are not just questions of reduction, but also the question of the legitimacy of appeal to systems. The former are effectively conﬁned to naturalphilosophical disputes, but the latter question is part of, and helps shape, a broad cultural context which is explicitly indebted to Locke. The latter in fact increases in importance as reduction to micro-corpuscles tends to be displaced in canonical areas of physics in the eighteenth century by assimilation to mechanics, as we shall see in Chapter 8. The core issues that carry over are those that centre around the question of systematic versus non-systematic forms of understanding, for reduction and assimilation are in effect different forms of incorporation of material into a context of systematic understanding. It is to the eighteenth-century disputes over the legitimacy of systematic understanding that we shall now be turning, and what will quickly become evident is that it is the insertion of Lockean/Newtonian-inspired rejection of ‘systems’ into a 101

See e.g. the long entry on ‘Chymie’ by Gabriel-Franc¸ois Venel in the Encyclope´die, in which the irrelevance of the laws of matter in motion to chemistry is spelled out.

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political and intellectual culture in which natural philosophy is allowed to move to centre stage that is largely responsible for the emergence of a dominant mideighteenth-century form of Enlightenment thought (and, it turns out, counterEnlightenment thought), namely the rejection of the claims of systematic understanding.

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PART III

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6 Natural Philosophy and the Republic of Letters Commenting on the transition from the intellectual culture of Louis XIV at the turn of the eighteenth century to that of the philosophes in mid-century, J. G. A. Pocock writes that ‘there came to be recognised, and to exist, what we have come to call “the” Enlightenment, a movement at once cosmopolitan and Francocentric, with the result that the Paris of the philosophes continued to assert the claim to intellectual and cultural leadership in “Europe” already put forward by the court culture of the grand sie`cle, and European history was written in terms of the transition from grand sie`cle to sie`cle des lumie`res, the latter both rebelling against and continuing the former.’1 In this chapter and the next, I want to examine this transition, and to establish that the vehicle by which it was effected was natural philosophy. Up to this point, we have have conﬁned our attention largely to developments in natural philosophy. We can now introduce another variable, so to speak, enriching our picture by considering how natural philosophy comes to interact with a particular culture, that of Paris between the late seventeenth and the middle of the eighteenth century. If this is to be done fruitfully, some detail is necessary. In this chapter, I shall be concentrating on the way in which natural philosophy as conceived within the Parisian Acade´mie des Sciences was promoted through the Republic of Letters, how this transformed its standing, and how the diffusion of a Lockean-inspired version of Newtonianism, which traded on a widespread rejection of systems, played a role in the emergence of a new cultural standing of natural philosophy. This new standing is manifest in a number of ways, not least in the tradition of ´eloges, in which academicians are treated in terms previously reserved for monarchs and generals, and marks a crucial turning point in the national assessment of character and worth. In the next chapter, I shall focus on the consolidation of this cultural standing in Voltaire and in the Encyclope´die. In the course of the eighteenth century, natural philosophy began to take on an unprecedented public presence in Parisian culture. Our concern in what

1

J. G. A. Pocock, Barbarism and Religion (4 vols., Cambridge, 1999–2008), i. 138.

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follows is with what this standing was and how it was consolidated, but these are not questions that we can consider in isolation. It is, for example, unlikely that natural philosophy could have taken on such a new role simply by installing itself at the centre of an already constituted culture. The question is therefore not just what was displaced in this process and how it was affected as a result. We also need to examine whether or not natural philosophy was able to achieve its new standing because the culture itself had been transformed in a way that imposed on it a new structure conducive to natural philosophy, and to what extent natural philosophy played a role in this change, or was simply a beneﬁciary of it. Above all, we must discover what more general effects this realignment/transformation had. Speciﬁcally, if, as I have suggested in earlier chapters, the new standing of natural philosophy turned largely on its ability to shape cognitive standards, did this shaping beneﬁt or hinder forms of cognitive enquiry that traditionally lay outside natural philosophy? Here we need to consider those who, while neither primarily natural philosophers nor theologians, were engaged in what we might broadly call philosophical speculation about moral, political, and educational questions in the context of general considerations about the place of human beings in the natural order of things. Such considerations are particularly important in the period under examination because of the emergence of deism in England, a movement whose advocates were not usually clergymen or natural philosophers, and the emergence in France of a new kind of cultural ﬁgure, the philosophe, epitomized in Voltaire, who was not a natural philosopher yet was able to bind the identity of the philosophe to the new standing of natural philosophy. We saw in Chapter 1 that, from the 1680s, there was a concerted effort, in the form of physico-theology, to combine the resources of natural philosophy and natural theology, and that this transformed the cultural standing of natural philosophy from a set of technical disciplines into an indispensable partner in a far more ambitious uniﬁed project, in which natural philosophy shared in some of the traditional aspirations of theology, notably that of understanding the world and our place in it. But to enter into this partnership, natural theology had to be construed exclusively in terms of its cognitive content. By the end of the seventeenth century, the criteria for assessing cognitive content, whether generally or in the more contentious speciﬁc case of physico-theology, were not ﬁxed, either by natural philosophy or by natural theology. As we have seen, in the case of theories of the formation of the earth, there was a series of different compromises between natural-historical and various theological considerations. In the circumstances, one might expect that it would be in English physicotheology that the move to ﬁx cognitive standards would come ﬁrst, for it was an especially pressing problem in this context. It did not come here, however, but rather in a context where there were no internally generated pressures for uniform cognitive standards, but where this pressure was external, and indeed politically

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motivated: namely, in the general reorganization of French culture under the absolutist aspirations of Louis XIV and his ministers. Accordingly, our ﬁrst task will be to examine how this process occurs up to the 1730s, focusing on the establishment and reform of the Paris Acade´mie des Sciences. What was distinctive about the programme of the Acade´mie was the institutionalization of natural philosophy and the shaping of a new persona for its practitioners, and these produced a distinctive form of authority, as the Acade´mie gradually assumed the role of guardian of cognitive standards in natural philosophy. In his Lettres philosophiques of 1734, Voltaire, steeped in Lockean liberalism and English deist thought, introduced a set of distinctively English themes into French culture. The issues of freedom of speech and thought were not especially radical, or indeed novel, and they were part and parcel of the Republic of Letters, characterized by Bayle in his Dictionaire Historique et Critique of 1696–7 as a State extremely free. The Empire of Truth and Reason is only acknowledged in it; and under their Protection an innocent War is waged against any one whatsoever, Friends ought to be on their Guard, there, against their Friends, Fathers against their Children, Fathers in-law against their Sons-in-law, as in the Iron Age. . . . Everybody, there, is both Sovereign and under every-body’s Jurisdiction.2

A number of works, most notably Montesquieu’s Lettres persanes of 1721, had exploited this freedom. But in bypassing the highly developed notions of expertise then prevailing in the several Parisian Acade´mies, and pursuing his criticisms in a popular genre which might otherwise be considered inappropriate for consideration of such questions, Voltaire redirected the Republic of Letters in an uncontrollable way: uncontrollable, that is, by the Acade´mie des Sciences, which, under Fontenelle, had carefully cultivated this domain and indeed had had some early success in making it its own. Coming to terms with such developments means that, as well as the questions of how cognitive standards were shaped and what their authority lay in, we also need to ask how this authority was manifest in those who claimed to exercise it. We need to engage the question of the persona of the natural philosopher and how it is connected to the persona of the philosophe. Locke played a crucial role here, for his full-scale defence of an unprecedented form of sensibilist epistemology opened up the question of the sources of our beliefs in a way that was to prove pivotal for the subsequent development of Enlightenment thought generally. In particular, when we turn—as we shall in Chapter 11—to the development of French Lockeanism proper, beginning with Condillac’s Essai sur l’origine 2 Pierre Bayle, The Dictionary Historical and Critical (2nd edn., 5 vols., London, 1725), ii. 389 note D col. 1 (entry on Catius). On the contemporary understandings of the Republic of Letters, see Franc¸oise Waquet, ‘Qu’est ce que la Re´publique des Lettres? Essai de se´mantique historique’, Bibliothe`que de l’E´cole des Chartes 147 (1989), 473–502; and more generally Hans Bots and Franc¸oise Waquet, La Re´publique des Lettres (Paris, 1997), and Daniel Roche, Les Republicains des lettres: Gens de culture et lumie`res au XVII e sie`cle (Paris, 1988).

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des connaissances humaines (1746), we can see how Lockean sensibilism takes on very distinctive social and political connotations, which are used to create a persona for the responsible citizen. My argument will be that we can trace a trajectory from the persona of the natural philosopher as shaped in the Acade´mie des Sciences, to the persona of the philosophe as this developed in Parisian literary culture in the 1730s and 1740s, to the persona of the responsible citizen in French sensibilists such as Diderot. However, in tracing this trajectory, what we discover as its outcome is not a new consensus on the role of reason, but a radically contested domain in which reason and sensibility are played off against one another. T H E AC AD E´ MIE DES SCIENCES AND THE REPUBLIC OF LETTERS Amateur scientiﬁc societies had ﬂourished in Paris before the formation of the Paris Acade´mie des Sciences, which ﬁrst met in December 1666, and they had among their aims the abandonment of verbal dispute and its replacement with visual demonstrations, as well as the creation of a class of practitioners who could devote all of their time to natural philosophy and related activities.3 The Acade´mie was a rationalization and consolidation of these aims: it incorporated them into the culture of French absolutism, whereby the state funded salaries, buildings, and equipment, in exchange for natural philosophers giving up their dilettantism and devoting their activities towards the national beneﬁt, as decided by the king and his ministers. But the model by which this incorporation might be achieved was not at all obvious, and two main proposals were being considered seriously in the mid-1660s by Colbert, the minister responsible.4 The models answered respectively to the demands of self-interest and self-gloriﬁcation that characterized French absolutism. The ﬁrst proposal was for a Compagnie des Sciences et Arts, on a Baconian model of control over nature and natural processes with a view to gainful production. As well as natural philosophers, the Compagnie would include investors and those who had skills relevant to trade, such as travellers and linguists. Its focus was on the practical arts, and the core of its membership was to be made up of those from the natural-philosophical disciplines that excelled in matters of practical interest. What was envisaged was an army of 3 On these societies, see Harcourt Brown, Scientiﬁc Organizations in Seventeenth Century France, 1620–1680 (New York, 1967). 4 In my discussion of the Acade´mie I am indebted above all to Hahn, The Anatomy of a Scientiﬁc Institution. See also Franc¸ois-Jean-Marie Olivier-Martin, L’Organisation Corporative de la France d’Ancien Re´gime (Paris, 1938); and Rene´ Taton, Les Origines de l’Acade´mie Royale des Sciences (Paris, 1966). Speciﬁcally on Colbert, see James E. King, Science and Rationalism in the Government of Louis XIV, 1661–1683 (Baltimore, 1949).

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technical experts, free of their own political agendas. Colbert was certainly attracted by this, and as naval secretary he was concerned to build up the French navy and transform it into the technically most advanced in the world. The second proposal, primarily the work of Charles Perrault, was for an altogether different kind of enterprise. Perrault had been appointed by Colbert as secretary of the Acade´mie des Inscriptions et Belles-lettres at its formation in 1663.5 Although he had supervised the building of the Royal Observatory in 1667, he was not a natural philosopher but a writer of ﬁction (known especially for his fairy tales) and, as we shall see below, he was a notable defender of modern literature and the initiator of the ‘quarrel’ between the ancients and the moderns. The Acade´mie des Inscriptions had consolidated and centralized the work of historians, philologists, and others, and Perrault’s plan for a general academy, proposed in 1666, was in many ways a grand expansion of this, suggesting a further level of consolidation and centralization. This general academy was to encompass sections on belles-lettres, history, philosophy, and mathematics, and it was breath of knowledge and skills, rather than narrowly deﬁned technical expertise, that formed the basis for membership. As Hahn notes, despite his practical naval concerns, Colbert was tempted by Perrault’s proposal, which effectively involved the reorganization of the Republic of Letters on a rational basis under the direct and single control of the Crown, but its realization was impossible in the face of ﬁerce resistance from cultural groups that already had their own organizational structures and were not prepared to have their prerogatives diminished.6 Colbert faced a dilemma here, for he demanded both practical and theoretical returns on the King’s investments.7 As Fontenelle put it in his ´eloge of Gallois: M. Colbert supported the study of letters, not just from natural inclination, but from sound political judgement. He knew that the sciences and arts alone sufﬁce to bring glory to a reign; that they spread the language of a nation perhaps even more than do its conquests; that they give the reign control over knowledge and industry, which is just as

5 On the Acade´mie des Inscriptions et Belles-lettres, see Blandine Barret-Kriegel, Les historiens et la monarchie (4 vols., Paris, 1988–9), iii. Part II. 6 Hahn, Anatomy of a Scientiﬁc Institution, 13–14. More generally, see Robin Briggs, ‘The Acade´mie Royal des Sciences and the Pursuit of Utility’, Past and Present 131 (1991), 38–88; John Milton Hirschfeld, ‘The Acade´mie Royale des Sciences (1666–1683): Inauguration and Initial Problems of Method’ (PhD thesis, University of Chicago, 1957); E. S. Saunders, ‘The Decline and Reform of the Acade´mie des Sciences a` Paris, 1676–1699’ (PhD thesis, The Ohio State University, 1980); Shank, ‘Before Voltaire’; Harold T. Parker, ‘French Administrators and French Scientists during the Old Regime and the Early Years of the Revolution’, in R. Herr and H. T. Parker, eds., Ideas in History (Durham, NC, 1965), 85–109. Resistance from the University of Paris Faculty of Medicine successfully prevented the formation of a Parisian academy devoted to medicine, proposals for which were made from 1718 onwards: see Paul Delaunay, Le monde me´dical parisien au XVIII e sie`cle (Paris, 1906), 309–10. 7 See Stroup, A Company of Scientists, 51.

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prestigious as it is useful; that they attract to the country many foreigners who enrich it by their talents, adopt its character, and associate themselves with its interests.8

It is not surprising, in the light of Colbert’s aims, that what resulted was a compromise: what is perhaps surprising is just how successful the compromise was. The Acade´mie des Sciences was in effect an elite civil service, with residence requirements, legal privileges, and generous stipends. It was to focus on natural philosophers, excluding some of the more purely utilitarian occupations, but it was also to exclude practitioners of the Republic of Letters more generally, who had their own academies. It was a consultative assembly designed to answer the Crown’s queries on technological problems, but its role was certainly not conﬁned to that: rather, it was primarily a means of glorifying the Crown through the advancement of natural philosophy, broadly conceived.9 Accordingly, the ﬁfteen original members of the Acade´mie included, as well as natural philosophers of the ﬁrst rank, such as Huygens,10 men of considerable cultural attainments chosen not simply for their contribution to natural philosophy. Among those excluded were Cartesians and Jesuits, as well as many of the amateurs who had graced the pre-Acade´mie groups. Cartesians and Jesuits were considered too partisan to share in the open-minded kinds of research that were envisaged for the Acade´mie. There was in fact a Baconian-inspired culture of communal work, manifested in the anonymity of its publications. In time, this communality and anonymity were found to be counter-productive in the case of promoting discoveries, but there was another aspect, in which they were central to the tasks of the Acade´mie. The distinctive function of the Paris Acade´mies—the Acade´mie Franc¸aise, the Acade´mie Royale des Beaux-Arts, the Acade´mie des Inscriptions et Belles-lettres, the Acade´mie des Peinture et Sculpture, the Acade´mie des Arts, the Acade´mie d’Architecture, the Acade´mie des Jeux Floraux, and others—was that of ultimate judge and arbiter in their ﬁelds of expertise: they were guardians of standards.11 Adjudication of claims in the scientiﬁc realm was a key role of the Acade´mie des Sciences immediately on its formation, and remained so, reinforced by the inauguration in 1720 of regular prize competitions, open exclusively to non-academicians and judged exclusively by academicians. In accord with this role as ultimate arbiter, the publications of academicians themselves did not require the approval of the royal board of censors (who had gradually taken over this role from the University of Paris): the Acade´mie set its own standards and was responsible only to itself, and

8

Fontenelle, Œuvres, v. 183–4. In this respect, it was in fact not unlike the more localized patronage networks of the sixteenthand early seventeenth-century Italian states: see Biagioli, Galileo Courtier. 10 The attempts to attract natural philosophers of ﬁrst rank to the Acade´mie continued after this initial recruitment, and it seems reasonably certain, for example, that Jacques Cassini travelled to England to offer Newton such a position in 1698: see Westfall, Never at Rest, 587. 11 See Hahn, Anatomy of a Scientiﬁc Institution, 21–33. 9

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extended its rights in this respect to prize-winning essays from outside its ranks. Moreover, scientiﬁc journals gradually came under its control: the astronomical almanac, Connaissance des Temps, was taken over by the Acade´mie in 1679, and Fontenelle’s assumption of the editorship of the Journal des Sc¸avants in 1702 effectively put it under the Acade´mie’s control. Inventions also came under its exclusive purview, since it was now the Acade´mie that carried out tests for awards of patents—the royal privile`ge—in the case of scientiﬁc and technological inventions, and it exercised this power in a very directive way.12 It not only required full disclosure of the workings of the invention in the form of drawings and models, thereby jeopardizing the proﬁts of the inventor, but adopted an explicit programme of rationalizing the various trades along the lines of a scientiﬁc method that realized the canons of objectivity, testing, and public scrutiny. Such a role was associated with a particular persona: above all, the academician was a member of the Republic of Letters, and elite group which conceived itself to have a civilizing mission.13 Those elected to the Acade´mie des Sciences were ‘savants’ in the sense of men of learning, and this was as much a source of their authority as was their particular expertise. Freedom of opinion was crucial to this role, and the exclusion of Cartesians and Jesuits from membership in 1666, as well as the later condemnation of Linnaeans,14 was on the grounds that commitment to dogmas was antithetical to the standing of the academicians. D’Alembert, in his 1753 Essai sur la socie´te´ des gens de lettres et des grands, makes it very clear that meritocracy rather than birth provides the only viable criterion for membership of the Acade´mie, and he draws a strong link between the strength of the Republic of Letters generally and its democratic form.15 The qualities of members, as set out in the 69 ´eloges of members of the Acade´mie that Fontenelle composed over his forty-four years as Secretary, were not conﬁned to, and indeed in many cases did not even focus on, scientiﬁc expertise and achievements, but rather on the way in which the members had exempliﬁed various moral, cultural, intellectual, and personal values: the life of science inevitably produced someone of exemplary life and character, and with exemplary independence of mind. 12

See ibid., 66–70. Ibid., ch. 2. 14 Ibid., 114. 15 The Essai was ﬁrst published in Paris under a false Berlin imprint. It can be found in d’Alembert, Œuvres (5 vols., Paris, 1721–2), iv. 335–72. The theme of lack of democracy was, needless to say, a constant refrain in those whose work the Acade´mie refused to sanction. See e.g. Bertrand de la Coste, Le reveil matin fait par Monsieur Bertrand pour reveller les pretendus sc¸avans matematiciens de l’Academie Royale de Paris (Hamburg, 1674); Guillaume Roberger de Vausenville, Essai Physico-ge´ome´trique (Paris, 1778); Jacques-Pierre Brissot de Warville, De la verite´, ou me´ditations sur les moyens de parvenir a` la verite´ dans toutes les conaissances humaines (Neufchaˆtel, 1782). There is a good discussion in Jeff Loveland, ‘Panckouck and the Circle Squarers’, EighteenthCentury Studies 37 (2004), 215–36. See also Hahn, Anatomy of a Scientiﬁc Institution, 140–58; and Keith Michael Baker, Condorcet: From Natural Philosophy to Social Mathematics (Chicago, 1975), 13–16. See also Robert Darnton, The Literary Underground of the Old Re´gime (Cambridge, Mass., 1982). 13

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In his ´eloge of Maraldi, he writes: ‘His character was that which the sciences form ordinarily in those who make it their sole occupation: seriousness, simplicity, righteousness’; on Du Hamel: ‘One easily saw that his humility was not a pose but a feeling founded on science itself ’; and on Varignon: ‘His character was as simple as his superiority of mind could require. I have already given this same praise to so many persons in this academy that one would believe their merit to pertain rather more to our sciences than to our savants.’16 In Fontenelle’s ‘Discours’ addressed to the Acade´mie Franc¸aise in 1741, he tells his audience that in the 1699 reform of the Acade´mie des Sciences, the minister, the Abbe´ Jean-Paul Bignon, ‘had wanted to see the taste for science spread in society. As in ancient Egypt, science had been using a certain sacred language which was understood by its priests alone. The new minister wanted it to speak the common language, as far as was possible, and he did me the honour of making me its interpreter.’17 This was in fact not a new direction in the Acade´mie, however, so much as a renewal of a strategy that had not been carried out successfully. As Fontenelle makes clear in his ´eloge of Du Hamel, the ﬁrst Secretary of the Acade´mie, in 1666 Colbert had chosen Du Hamel as someone ‘who understood and could speak the languages of the different savants—that of chemistry for example, and that of astronomy—who would be their common interpreter to the public, who would be able to offer clariﬁcation of all thorny and abstract matters, . . . and ﬁnally someone with a character free of partiality, and able to provide a disinterested account of academic disputes.’18 Fontenelle ﬁtted this description perfectly, and the characterization sums up how he saw his own task. He came not from a natural-philosophical background19 but from a literary one, nephew of Corneille, a member of the Acade´mie Franc¸aise from 1691, a regular contributor to the popular journal/magazine Mercure galant, and 16 Quoted in L. M. Marsak, ‘Bernard de Fontenelle: The Idea of Science in the French Enlightenment’, Transactions of the American Philosophical Society 49 Part 7 (1959), 1–64: 43. See also Suzanne Delorme, ‘La vie scientiﬁque a` l’e´poque de Fontenelle d’a`pres les “Eloges des Savants”’, Archeion 19 (1937), 217–35. The tradition of ´eloges marks a crucial turning point in the national assessment of character and worth, and it will be continued mid-century in d’Alembert’s ´eloges for the Acade´mie Franc¸aise, and later in the century by Condorcet. Indeed, the composition of ´eloges was one of the principal duties of the Permanent Secretary of the Acade´mie des Sciences, and in the bitter struggle for the secretariat in the 1770s, Condorcet (d’Alembert’s candidate) secured a great advantage through his sketch of an ´eloge of the mathematician Alexis Fontaine: see Baker, Condorcet, 36–7. More generally, see Charles B. Paul, Science and Immortality: The E´loges of the Paris Academy of Sciences (Berkeley, 1980); George A. Kelly, Moral Politics in Eighteenth-Century France (Waterloo, Ontario, 1986), ch. 3; Georges Gusdorf, De l’histoire des sciences a` l’histoire de la pense´e (Paris, 1966); Judith Shklar, ‘Jean d’Alembert and the Rehabilitation of History’, Journal of the History of Ideas 42 (1981), 643–64. 17 Fontenelle, Œuvres, iii. 381–2. It is worth nothing in this context that in 1694, the Dictionnaire of the Acade´mie Franc¸aise had called for the expunging of all scientiﬁc terms from the language: see Marsak, ‘Bernard de Fontenelle’, 44. 18 Fontenelle, Œuvres, v. 131. 19 It is worth remembering in this context that Sprat, Royal Society apologist par excellence, was not a natural philosopher either but a poet and preacher.

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favourite of salon circles, his contributions ranging from poetry, journalism, and an opera libretto to what can be considered the ﬁrst piece of ‘popular science’. This latter was indeed one of the best-selling books of the eighteenth century: the Entretiens sur la pluralite´ des mondes was an instant success, necessitating an updating and the addition of a sixth chapter within a year of its publication in 1686, and going through thirty-three editions and numerous translations during his lifetime.20 Descartes’ account of the formation of the planets from encrusted suns, and his defence of the idea that there are an indeﬁnite number of solar systems, had opened up the possibility of there being other inhabited worlds, although this possibility had been followed up exclusively outside the Cartesian tradition.21 Fontenelle’s account is Cartesian (the added sixth chapter provided an explicitly Cartesian explanation of the mechanisms behind planetary motions), directly linking a topic that had hitherto existed only at the margins of natural-philosophical discussion (Bruno being the favourite source) to the prevailing natural-philosophical system. Moreover he does this using a popular literary genre, an after-dinner dialogue with a Marquise set in the garden of her grand house, in which the universe is portrayed as an opera theatre and the mechanism behind planetary and stellar motions compared to the hidden wheels, counterweights, and ropes that lay behind stage effects (see Fig. 6.1). One of the most striking features of the Entretiens was the way in which it picked out women as part of its target audience.22 Women had been excluded from the Acade´mies and the universities, but had carved out an intellectually lively salon culture, one in which Fontenelle was in his element, and his 1699 reforms of the Acade´mie, within two years of his appointment, which instituted a publishing programme as well as one of holding public assemblies, transformed it from a largely self-contained organization into one that could engage with the 20 See Lyliane Mathieu-Kerns and Michel Alexandre Nusimovici, ‘1686–1687. L’Odysse´e de l’espace, Fontenelle ou le ge´nie de la vulgarisation scientiﬁque’, in Alain Niderst, ed., Fontenelle: Actes du colloque tenu a` Rouen du 6 au 10 Octobre 1987 (Paris, 1989), 87–103. 21 There are two main discussions of the idea before Fontenelle: Henry More, Democritus Platonissans, or an Essay upon the Inﬁnity of Worlds out of Platonick Principles (Cambridge, 1646); and Pierre Borel, Discours nouveau prouvant la pluralite´ des mondes, que les astres sont des terres habite´es, & la terre un estoile, qu’elle est hors du centre du monde dans le troisie`me ciel, & se torne´ devant le soleil qui est ﬁxe, & autres choses tres-curieuses (Geneva, 1657). There was a notable attack on the idea of a plurality of worlds in the anti-Cartesian writer Gerhard de Vries, Dissertio academica de lunicolis, appendix to Daniel Voet, Physiologia, sive, de natura rerum libri sex (Utrecht, 1694). See the discussion in Steven J. Dick, Plurality of Worlds: The Origins of the Extraterrestrial Life Debate from Democritus to Kant (Cambridge, 1982), ch. 5. 22 As Erica Harth notes in her Cartesian Women: Versions and Subversions of Rational Discourse in the Old Regime (Ithaca, NY, 1992), 139–40, there was a tradition of such works that targeted women, from Louis de Lesclache, Avantages que les femmes peuvent recevoir de la philosophie, et principalment de la morale (Paris, 1667) to Je´roˆme de Lalande, Astronomie des dames (Paris, 1786), which was frequently bound with Fontenelle in the nineteenth century. Cf. J. B. Shank, ‘Neither Natural Philosophy, Nor Science, Nor Literature: Gender and Natural Knowledge in Fontenelle’s Entretiens sur la pluralite´ des mondes’, in Judith Zinsser, ed., Men, Women, and the Birthing of Modern Science (DeKalb, 2005), 86–110.

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newly emerging intellectual sphere outside the Acade´mies, which the salons had played a signiﬁcant role in creating.23 There was a delicate balancing act needed here, and as Shank points out, it was Fontenelle’s ability to preserve his identity as an independent man of letters, while simultaneously wedding the interests of the state with those of the literary public, that largely accounted for the success of the new public academy after 1699.24 Crucial to Fontenelle’s success in this respect was his ability to place natural philosophy in the Republic of Letters, a placing that transformed both the standing of natural philosophy and its aspirations.25 Such an understanding deﬁnes French Enlightenment natural philosophy, and more than ﬁfty years later, in the entry on ‘science’ in the Encyclope´die, we are told that ‘The principle of the sciences would be tedious without the charms of belles lettres. Truths are more easily perceived by means of clear style, agreeable images, and all the clever

23 On salon culture at the time, see Roger Picard, Les salons litte´raires et la socie´te´ franc¸aise, 1610– 1789 (New York, 1943). On the idea of science as an entertaining intellectual pastime in French eighteenth-century culture, see Barbara Stafford, Artful Science: Enlightenment Entertainment and the Eclipse of Visual Education (Cambridge, Mass., 1994). Salon culture was opposed strongly by Sorbie`re in particular, and he urged that natural philosophy be pursued in the kind of highly structured and disciplined organization that the Acade´mie was to become, at least after the 1699 reforms. However, it had become a powerful force in countering the very exclusionary nature of the Acade´mie by the end of the century: see Joan DeJean, Ancients against Moderns: Culture Wars and the Making of a Fin de Sie`cle (Chicago, 1997). On the importance of the role of women in salon culture, see Harth, Cartesian Women; DeJean, Ancients against Moderns; and Dena Goodman, ‘Enlightenment Salons: The Convergence of Female and Philosophic Ambitions’, EighteenthCentury Studies 22 (1989), 329–50. See also Mordechai Feingold, The Newtonian Moment: Isaac Newton and the Making of Modern Culture (New York/Oxford, 2004), ch. 5. 24 Shank, ‘Before Voltaire’, 128. 25 Over the last couple of decades, these questions have been dealt with by historians predominantly in terms of Habermas’ notion of the ‘public domain’. The key text in this respect is Ju¨rgen Habermas, The Structural Transformation of the Public Sphere: An Inquiry into a Category of ¨ ffentlichkeit Bourgeois Society (Cambridge, Mass., 1989), which ﬁrst appeared as Strukurwandel der O (Darmstadt/Neuwied am Rhein, 1962). See e.g. James Van Horn Melton, The Rise of the Public in Enlightenment Europe (Cambridge, 2001); T. C. W. Blanning, The Culture of Power and the Power of Culture: Old Regime Europe 1660–1789 (Oxford, 2002); Joan Landes, Women and the Public Sphere in the Age of the French Revolution (Ithaca, NY, 1988); and, speciﬁcally on the impact of Habermas for studies of the French Revolutionary period, Keith Michael Baker, ‘Deﬁning the Public Sphere in Eighteenth-Century France: Variations on a Theme by Habermas’, in Craig Calhoun, ed., Habermas and the Public Sphere (Cambridge, Mass., 1999), 181–211. But the idea of applying the notion of the public sphere to political and social developments before the emergence of modern liberal notions, of the kind that Habermas wishes to develop—that is, ideas deriving essentially from Kant (by contrast with Locke for example) at the end of the eighteenth century—is an inherently problematic exercise: see e.g. Condren, Argument and Authority in EarlyModern England, 77; and idem, ‘Public, Private and the Idea of the “Public Sphere” in Early Modern England’, Intellectual History Review 19 (2009), 15–28. The Habermasian notion of the public sphere provides a genealogy which extrapolates back from modern notions: such a genealogy takes us back to Kant, but it becomes extremely problematic once one encounters French midcentury Enlightenment culture. In particular, it operates in terms of a contrast between reason and authority, but, as I shall argue in Chapter 12, the key contrast at stake—one that turned on Lockean, not proto-Kantian, notions—was that between reason and sensibility.

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devices by which they are presented to the mind.’26 Consideration of how Fontenelle’s placement of natural philosophy in the Republic of Letters occurs not only helps us make sense of the genre that he uses to legitimate the standing of natural philosophy, but also allows us to grasp the rise of an interest in particular aspects of natural philosophy on the part of an audience that would not, up to this point, have considered such questions of any signiﬁcance to them. There were two distinct characteristics of the literary culture that emerged at this time: there was a change in what literature did and how it did it; and there was a change in the audience for whom literature was written, and who was to assess its value. In the ﬁrst respect, the traditional prose and poetic forms that had dominated literary culture as those best suited to conveying the moral and other qualities that literature fostered and displayed were replaced by a new literary form, what would subsequently develop into the novel, which displayed very different kinds of values, and displayed them in a very different way. Second, the works in this new literary form were often written by, and were largely directed at, a very broad audience, who were invited to offer judgements on the work—to act as arbiters of literary taste—in a way that had traditionally been reserved for expert critics. This bears on the issue of the prerequisites for literary judgement, and it is in the salons, reading groups, and periodicals such as Mercure galant, where readers, men and women alike, are invited to comment on the latest literary works, that the value of new works, and engagement with the moral and social issues they raise, are discussed. More generally, the emergence of journals, especially in the wake of the appearance of Bayle’s immensely inﬂuential Nouvelles de la Re´publique des Lettres in 1684, redirected Francophone culture in particular by providing reports on the latest scientiﬁc work, as well as philosophical, theological, literary, and other matters. The journal contained reviews, pre´cis, and discussions of books that were in effect alternatives to the books themselves. Not everyone was happy with this. Daniel Huet complained in 1698 about the ‘decadence that letters have fallen into in France’, writing that he could not help himself speaking out ‘against the barbarousness of this century, of which all these abridgements of books people are publishing in Paris, in Rotterdam, in Leipzig, are the indubitable proofs’. Baillet concurred: ‘Many love and seek out these abridgements’, he writes, ‘because they are appropriate to their laziness, because they want to skim over the surface of things, because they consider themselves skillful when they know the general deﬁnitions, and the divisions and terms of the arts.’27 As might be expected, what some perceived as a defect, others argued were a beneﬁt. Bayle tells his readers that the Nouvelles de la Re´publique des Lettres ‘are not so much for doctors, and savants by profession, as for an inﬁnite number of people in the world whose natural laziness, or the strains of a heavy job, prevents them 26 27

Diderot et al., Encyclope´die, xxx. 306. Both quoted in Goldgar, Impolite Learning, 54–5.

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from reading a great deal, although they would be very glad to learn.’28 But however the merits of the journals were construed, one thing was clear: while the readers for these journals included active, productive researchers who followed up the information they had gleaned, they also included passive readers who did not read, and would never have read, the books reviewed and discussed. Yet somehow such readers were now part of an audience that had some degree of entitlement to have an opinion on the material discussed, whether they wished to exercise that entitlement or not. Moreover, the reviewers themselves often had no particular expertise, yet they had no hesitation in offering judgements. As the publishers of the Bibliothe`que raisonne´e put it: But people might say, . . . is it absolutely necessary for a journalist to decide on the value of works? . . . Let him limit himself to giving faithful Extraits; let him tell us how many pages, Books, and Chapters are in the volume; let him tell us generally the plan, and the goal of it. No one asks more from him and when he charges himself with the ofﬁce of biasing the public, either for good or for bad, he leaves his sphere, and arrogates to himself, in the Republic of Letters, a despotism, which is insufferable. . . . Messieurs, when we dig up a journalist of the sort you require, who can go through a boring work without showing disgust, who never sees anything but good in books, who pardons a thousand false reasonings in favour of one good thought, who reads the writings of others with the eyes of the author, who absolutely never gives in to his prejudices, and who can never fall into error, when, we say, we dig up such a journalist, we promise to give him to you, however much he costs. In the meantime, content yourselves with those that we are giving you, in the persuasion that if we had been able to choose better we would not have failed to do so.29

The cultural impact of these developments is evident in the French ‘quarrel between the ancients and the moderns’, initiated by the reading of a lengthy narrative poem by Charles Perrault, Le Sie`cle de Louis le Grand, to the Acade´mie Franc¸aise on 22 January 1687. The reading unleashed a literary storm that lasted for nearly thirty years. Perrault had defended the moderns, but he was not the ﬁrst to do so and, polemical as his piece was, there had been more violent polemical defences, notably in the work of Desmarets early in the previous decade.30 Yet by 1687 the new literary genres, and their new readership, had become far better established—the Mercure galant had been pressing them on public attention during 1677 and 1678 for example—and the issues at stake were correspondingly more urgent, not to mention the extent to which debates over such issues were no longer centred exclusively on the Acade´mie Franc¸aise, although the violence of the reaction to Perrault’s defence on the part of some academicians was in large part instrumental in opening up the question as one of 28

Quoted ibid., 62. Quoted ibid., 112. See, in particular, Jean Desmarets de Saint-Sorlin, La Comparaison de la langue et de poe´sie franc¸aise avec la grec et la latine, et des poe`tes grecs, latins, et franc¸aises (Paris, 1670). 29 30

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broader public concern. Perrault identiﬁes Homer as the dominant ﬁgure in antiquity and proceeds to single out his defects—such as using too many digressions and making his heroes too brutal—while noting that this was all one could expect, since Homer was a product of his age, whereas had he lived in the age of Louis XIV he could have avoided these defects. Moreover, Perrault argued, the poets that the ancients valued often do not correspond to those that we value: tastes have changed and so it cannot deﬁnitively be said that certain ancient authors have had, or will continue to have, a universal standing.31 The debate was intense, and two years later Perrault spelled out the case for the moderns in detail and, perhaps more appropriately, in prose form.32 These developments are of particular signiﬁcance for us, for we are now at a point where we can ask what happens when natural philosophy is taken out of the culture of the Acade´mie and brought into a public domain that has been shaped by a different set of critical values. As conceived by Colbert, natural philosophy was pursued for the glory of the crown and for its public utility to the state. Now something else comes into play, and questions of public proﬁle arise which have a far less certain, and a far less homogeneous, audience, as the standing of natural philosophy as a worthwhile form of pursuit was defended in terms of a broader range of values.33 Consider the new 1699 regulations engineered by Fontenelle. These stressed the constitution of the Acade´mie as a meritocratic association of peers, and as a vehicle for consensus produced by rational deliberation: members were explicitly instructed to speak with circumspection and to avoid expressions of anger. The move to a more open, public institution meant that disputes which had been internal matters could now adopt a more public face, however, and in 1701 the minister of State responsible for oversight of the Acade´mies, Bignon, drew attention to the Rule XXVI on the proper conduct of members, and instructed that future discussion of inﬁnitesimal analysis be conﬁned to purely mathematical questions.34 As we saw in Chapter 3, there were profound difﬁculties with the use of inﬁnitesimals, in that they were supposed to behave on some occasions like numbers and on others not. Varignon’s use of inﬁnitesimals had been publicized in the Mercure galant in 1699, and in 1700 the academician Michel Rolle had 31 On these questions, see the discussion in Noe´mi Hepp, Home`re en France au XVII e sie`cle (Paris, 1968). 32 See Charles Perrault, Paralelle des anciens et des modernes, en ce qui regarde les arts et les sciences. Dialogves. Avec le poe¨me du Siecle de Louis le Grand, et une epistre en vers sur le genie (Paris, 1688). 33 The issues will come to a head with the publication of the Encyclope´die. The anonymous author of the Lettre a` un ami contenant quelques observations sur le discours de M. d’Alembert (1754), for example, complains that d’Alembert’s preliminary Discours is written by a scientist of renown and a fashionable author, and this makes the piece ‘dangerous for both literature and morality . . . I say “dangerous” because the more famous an author is, the more easily is his authority imposed on the masses.’ Quoted in Ronald Grimsley, Jean D’Alembert (1717–83) (Oxford, 1963), 82. I have been unable to trace the original, which is not listed in the Catalogue collectif de France or WorldCat. 34 See Shank, ‘Before Voltaire’, ch. 5.

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rejected Varignon’s use of inﬁnitesimals on these grounds, but he had also argued that it led to provably fallacious results, which was not something earlier critics such as Newton and Nieuwentijt had maintained, and it was to this question that Varignon responded, the dispute subsequently being expanded to include Abbe´ Jean Gallois, a founding editor of the Journal des Sc¸avants, on Rolle’s side, and l’Hoˆpital on Varignon’s. Bignon’s attempt to keep the issue an internal, technical one was confounded by the appearance in 1701 of a new journal, the Journal de Tre´voux.35 The Journal, which appeared monthly, was published by Jesuits at the Colle`ge Louisle-Grand in Paris; it published reviews, extracts, and critical pieces for a broad audience, with a special focus on natural philosophy and mathematics. The Journal de Tre´voux acted as a forum for all those engaged in scientiﬁc subjects outside the Acade´mie, and was in effect a competitor.36 It made claims to objectivity in all but one area, religion, where it carried extensive attacks on the heterodox, singling out Le Clerc for special attention. There were also some questions in which religion and natural philosophy overlapped, and another area in which polemics predominated was Cartesianism, following a long and very active tradition of anti-Cartesianism in French Jesuit thought. The Journal was resolutely opposed to mechanism—which was seen as antithetical to the notion of design in nature and not conducive to an orthodox understanding of transubstantiation—but its editors also kept up a concerted campaign (on largely Aristotelian grounds) against the principle of inertia. They targeted Malebranche, not just for his advocacy of Cartesian mechanism, but for his occasionalism, which was treated as a form of scepticism about the physical world, where scepticism in turn was treated as a road to atheism. In the third issue of the Journal, inﬁnitesimal analysis came under attack, the anonymous Jesuit author arguing—in direct contradiction with Descartes’ defence of analysis over 35

Its actual title was Me´moires pour l’histoire des sciences et beaux arts. It was founded under the patronage of Louis, Duc de Maine, and printed at his presses at Tre´voux: hence the name by which it came to be known. On the journal, see Gustave Dumas, Histoire du Journal de Tre´voux depuis 1701 jusqu’en 1762 (Paris, 1936); and particularly George R. Healy, ‘Mechanistic Science and the French Jesuits: A Study of the Responses of the Journal de Trevoux (1701–1762) to Descartes and Newton’ (PhD thesis, University of Minnesota, 1956). 36 See Alfred R. Desautels, Les Me´moires de Trevoux: le mouvement des ide´es au XVIII e sie`cle, 1701–1734 (Rome, 1956); Catherine M. Northeast, The Parisian Jesuits and the Enlightenment, 1700–1762 (Oxford, 1991); and Donald Schier, Louis Bertrand Castel: Anti-Newtonian Scientist (Cedar Rapids, Ia., 1941). Jansenism was also a Catholic competitor, though as much of the Jesuits as of the Acade´mie. Its impact, which peaked in the 1730s, was less signiﬁcant, however, partly because its literature—most notably its journal, Nouvelles eccle´siastiques—was proscribed in France and so was available only as underground literature (a market it ignominiously shared with radical books and pamphlets, and pornography), and partly because its ﬁdeist programme was directed towards an uneducated urban population, and was rejected by the educated elite. See Israel, Enlightenment Contested, 702–11; and more generally, B. Robert Kreiser, Miracles, Convulsions, and Ecclesiastical Politics in Early Eighteenth-Century Paris (Princeton, 1978); Monique Cottret, Janse´nismes et Lumie`res: pour un autre XVIII e sie`cle (Paris, 1998); and Didier Masseau, Les Ennemis des philosophes: l’antiphilosophie au temps des Lumie`res (Paris, 2000).

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geometry on the grounds of the clarity and distinctness of its operations—that in geometry one can see how the conclusion is generated, whereas, because this is not the case in analysis, one can easily take a wrong path. The front on which the Journal fought was, then, a very broad one, and one antithetical to the Acade´mie’s sense of itself as the ultimate arbiter of scientiﬁc questions. One of the more remarkable aspects of the attacks on various forms of ‘modernist’ natural philosophy and mathematics in the Journal was the attack on them as ‘systems’, mirroring the Acade´mie’s own rejection of preconceived systems.37 Mathematics was a particular problem here, for it was the ambitious claim of mathematics, in the form of analysis, to offer a comprehensive grasp of the whole physical realm that most irked the Jesuits. They could not attack mathematics directly of course, and indeed included distinguished mathematicians in their ranks, but what they saw as the delusions of grandeur of analysis, delusions encouraged by the lack of concrete guidance evident in inﬁnitesimal calculus, were compared with the methodologically secure modesty of geometry. More generally, their attack on ‘systems’ was not merely a disingenuous attempt to pre-empt their own system being replaced by another, for by this stage they were aware that scholastic Aristotelian natural philosophy was not something they could have plausibly defended. Their concern was with what they perceived to be a godless mechanism, one that left one with no sense of the wonder of creation. While natural philosophy was based on sense perception and preserved a sense of wonder about nature, the Jesuits had no objections, but once an abstract system was introduced, dispelling reverence for and astonishment at nature, they were alarmed, and the new analysis being advocated by Leibniz, Varignon, l’Hoˆpital, and the Bernoullis was just such an abstract system.38 The response of the Journal here was in keeping with a broad development within the Society of Jesus. At the end of the seventeenth century, the Jesuit Cardinal Tolomei urged Catholic philosophers to abandon the path of medieval philosophy, which he maintained had ruined Aristotelian philosophy,39 and his own eclecticism, evident for example in his Philosophia mentis of 1698,40 so impressed Leibniz that he recommended to Des Bosses that Tolomei be elected General of the Society of Jesus.41 Eclecticism was in fact to be a feature that was to characterize Catholic thought generally until the late nineteenth century.42 37 It is this anti-system stand that led to the works of Condillac being reviewed in such a favourable manner: see Journal de Tre´voux (¼ Me´moires de Tre´voux), May 1747, 800–8; September 1749, 1836–53; March 1755, 641–9; December 1755, 2911–37. 38 The point is well made in Shank, ‘Before Voltaire’, 237. 39 See Hellyer, Catholic Physics, 194. 40 Giovanni Battista Tolomei, Philosophia mentis et sensuum secundum utramque Aristotelis methodum pertracta metaphysice, et empirice (Augsburg, 1698). 41 Leibniz to Des Bosses, 2 February 1706: Leibniz, phil. Schriften, ii. 294. 42 In 1879, Pope Leo XIII’s encyclical Aeterni Patris urged a return to Thomism as the perennial philosophy of the Church, although there had in fact been moves in this direction as early as the 1860s. The stimulus seems to have been, at least in part, Kantianism, which offered a very

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In the case of natural philosophy, the General Congregation of the Society of Jesus ofﬁcially proclaimed the fundamental compatibility between Aristotelian and experimental philosophy in 1731 and again in 1751.43 On the face of it, there was nothing Lockean in the advocacy of experimental philosophy, and indeed Locke’s Essay was placed on the Index of Prohibited Books in 1734. However, the situation was more complicated than it seems, and it has recently come to light that there was subsequently a struggle in the Vatican, in the 1740s and 1750s, over the acceptability of the Lockean/Newtonian programme, with Pope Benedict XIV sympathetic to aspects of Voltaire’s defence of the programme and the Holy Ofﬁce unsympathetic.44 Nevertheless, it seems reasonably clear that, at least as far as the Jesuits were concerned, the pursuit of natural philosophy in terms of particular experimental results precluded its systematization, but this was not because of concerns about systematic approaches per se: rather it was a way of protecting a systematic theology against competitors, for in effect the Jesuit view was that theology was the only systematic enterprise. By mid-century the anti-medieval tendency in Jesuit natural philosophy had become transformed into nothing short of a rewriting of history. The Jesuit Professor at the University of Vienna, Josef Redlhamer, in his 1755 textbook Philosophiae Naturalis, provides a genealogy for Jesuit physics, in which he does not even mention the Latin medieval philosophers, conﬁning his attention to Averroes, who he complains substituted contentious abstract metaphysical questions for physical ones, and completely ignored experiments,45 contrary to the Jesuit approach, which develops the tradition of such ﬁgures as Descartes, Gassendi, Boyle, Galileo, Torricelli, Newton, and (selected) Jesuit natural philosophers such as Kircher, Schott, and Fabri. Unexpectedly taking a stand on the ancients versus moderns question (at least on this issue), Redlhamer tells the reader that, had Aristotle been alive in the modern era, he would have completely revised what he had written.46 As Hellyer points out, ‘aside from the erroneous detour provided by the Arabs, the course of the history of science followed the straight comprehensive metaphysical system with clear moral and theological consequences, consequences that Catholics found very antithetical, but to which eclecticism provided no response. Criticism of Catholic eclecticism, especially that advocated by Victor Cousin, had been mounted from the 1830s by Rosmini, but his alternative had been condemned by the Church. So far as I have been able to tell, the question of the ninteenth-century abandonment of eclecticism and the revival of Thomism as a response to Kantianism has remained unexplored. For a brief sketch of philosophical developments in nineteenth-century Catholicism, see P. J. Fitzgerald, ‘Neoscholasticism’, in Norman Kretzman, Anthony Kenny, and Jan Pinborg, eds., The Cambridge History of Later Medieval Philosophy (Cambridge, 1982), 818–52. 43 Hellyer, Catholic Physics, 178. 44 See Peter Godman, Die geheime Inquisition: Aus der verboten Archiven des Vaticans (Munich, 2001), 248–68. There was a similar quarrel over whether or not to ban Montesquieu’s L’Esprit des Lois : see ibid., 239–47. 45 Josef Redlhamer, Philosophiae Naturalis. Pars prima, seu Physica generalis ad praeﬁxam in scholis nostris normam concinnata (Vienna, 1755), 7. 46 Ibid., 13.

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path of the development of experimental science. The Jesuits, in Redlhamer’s telling, were integral to this process. His readers could be forgiven for supposing that the Jesuits had never done any other kind of natural philosophy.’47 Fontenelle’s view of natural philosophy and analysis was diametrically opposed to the Jesuit defence of the clarity and distinctness of geometry over the reckless procedures of analysis, and the associated defence of modest experimental natural philosophy. Analytical mathematics has not only produced inﬁnitely many truths, he writes, but ‘more generally, has produced in the minds of men a soundness [justesse] more precious perhaps than all these truths’.48 His Pre´face sur l’utilite´ des mathe´matiques et de la physique et sur les travaux de l’Acade´mie des Sciences (1699) is the fullest statement in this regard. Even when arithmetic and geometry lead to nothing, he tells us, we at least know that what they offer is our only hope of certain knowledge attainable by natural reason. They train our mind and offer it a glimpse of truth. ‘They teach us how to operate upon truths’, he writes, ‘and how to grasp their threads, which are often so delicate and imperceptible, and to follow where they lead us.’49 The mind automatically wishes to know everything it can, and its desire for truth is manifest in our ability to appreciate algebra, despite its dryness and difﬁculty.50 What is being offered here is clearly not just an apology for the arcane activities of the members of the Acade´mie. As Shank points out, ‘descriptions such as these appealed to the noncourtly public because these elites used intellectual comportment as a means of challenging status criteria rooted in rank, title and birth. Fontenelle understood this psychology well, and here he connects abstract mathematical work with the kind of intellectual comportment worthy of a person of quality.’51 Fontenelle opened up an intellectual space in which mathematics, natural philosophy, and the Republic of Letters were intimately connected. His efforts in this direction were acknowledged by his successors even when they disagreed with his conception of natural philosophy, as in the case of Voltaire. What Fontenelle wanted to achieve in this intellectual space was to establish the virtues of an abstract rational mechanics as a model of natural philosophy, ﬂeshed out in physical terms via vortex theory, which, by restricting the transmission of physical action to surface contact, embodied the values of clarity and distinctness by supplying picturable micro-mechanisms to account for physical behaviour. In this latter respect, it was clear by the early 1730s that he had failed. By the 1720s, the ﬁrst generation of natural philosophers and mathematicians in the Acade´mie was being replaced. This generation had come up through the Malebranche circle and was committed to a highly abstract notion of rational mechanics. To the 47 48 49 50 51

Hellyer, Catholic Physics, 194–5. Fontenelle, ‘Pre´face de l’histoire de l’Acade´mie des Sciences’, Œuvres, x. 3. Œuvres, v. 12. Ibid., 13. Shank, ‘Before Voltaire’, 260.

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extent to which there was an explicit commitment to a physical theory, it was to vortices. The new generation that replaced them in the 1720s and 1730s had no such agenda. There were fewer appointments in the ﬁeld of rational mechanics, and those who did pursue it were neither committed to vortex theory nor necessarily hostile to Newtonianism: indeed, in 1732 rational mechanics was Newtonianized by Maupertuis, and a group committed to a Newtonian interpretation of rational mechanics began to form around him.52 This is a development that will prove crucial to the cultural standing of natural philosophy in France after the 1730s, and it turned on the question of the shape of the earth. VORTICES, ATTRACTION, AND THE SH APE OF T HE EAR TH In 1707, an updated version of vortex theory appeared in which the author, the Lyon Jesuit Philippe Villemot, attempted to iron out a number of problems in existing treatments.53 Villemot became aware of Newton’s Principia only shortly before publication, but noted that he had found nothing in it that caused him to alter what he had written. Although Newton’s criticisms of vortex theory in Book II of the Principia were becoming more widely known in France by this time, his own gravitational account was regarded as appealing to occult qualities, and consequently as having no explanatory value. The Principia was in effect treated as comprising two different exercises, the ﬁrst offering a new and powerful mathematical treatment of motion, one in which the importance of centripetal force had been established, while the second offered a physical account of celestial mechanics which was decidedly retrogressive by mechanist standards. Villemot was concerned exclusively with the latter type of question. His approach was highly problematic however: his grasp of mathematics was extremely elementary, and he appeared ignorant of Kepler’s ﬁrst two laws, surely crucial to any serious attempt to develop a theory of the stability of planetary orbits. The gulf between the mathematical and the physical programmes in French natural philosophy in the early decades of the eighteenth century was immense.54 52 Generally, see Franc¸ois de Gandt, ‘Qu’est-ce qu’eˆtre newtonien en 1740?’, in Franc¸ois de Gandt, ed., Cirey dans la vie intellectuelle: la re´ception de Newton en France (Oxford, 2001), 126–47; Pierre Brunet, L’Introduction des the´ories de Newton en France au XVIII e sie`cle: I Avant 1738 (Paris 1931); idem, Les physiciens hollandais et la me´thode expe´rimentale en France au XVIII e sie`cle (Paris, 1926). 53 Philippe Villemot, Nouveau syste`me ou nouvelle explication du mouvement des plane`tes (Lyon, 1707). 54 The contrast between French and English culture here is a sharp one and is evident midcentury in textbooks of Newtonian natural philosophy. One of the most popular works in English, John Rowning’s A Compendious System of Natural Philosophy (4 Parts, 1737–43), uses only simple geometry and generally avoids mathematics, but has many illustrations, especially of machines. In complete contrast, the equivalent introductory text in French, Pierre Sigorgne’s Institutions

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As I have already indicated, l’Hoˆpital seems to have had no understanding of the basics of physical theory, and Varignon studiously avoided it. Varignon’s principal concern was with the question of motion under the action of a central force, that is, a centripetal force.55 As Newton himself had been well aware, however, at the level of a mathematical mechanics and astronomy, one could ﬂesh out the physics in such as way as to account for a centripetal effect in terms of centrifugal forces. Varignon, like Newton in Book I of the Principia, is non-committal on this issue. His concern is to expand the examination of the curves described under central forces to include not just circles and conic sections but any kind of curve. On the other side of the divide, the interests of those concerned to develop vortex theory into a viable physical account of planetary stability were resolutely physical, and mathematical considerations were secondary, even in the dispute between the mathematically sophisticated Saurin and Malebranche in the 1710s.56 In each of these cases, a high premium was placed on picturability. What was at stake in the choice between Newtonian gravitation and Cartesian vortices was a contrast between occult qualities and the identiﬁcation of a clear and distinct underlying mechanism, where clarity and distinctness were manifested paradigmatically in terms of picturability. We can picture a planet being carried along in the motion of a dense ﬂuid just as we can picture a heavy boat being carried along by the ﬂow of a river; and we can picture corpuscles of ﬂuid matter being forced out from a rapidly spinning centre, and so acting to push an orbiting body outwards, being exactly balanced by corpuscles squeezed inwards from the periphery because of their size and motion, with the result that the planet on which these two forces act does not deviate from a route along a curve. Despite the fact that, in some sense, all these authors are concerned with celestial mechanics, it would seem that we have two quite incommensurable projects here, directed toward very different kinds of questions.57 Varignon was interested in extending the treatment of motion under central forces to any shape of orbit, oblivious to physical questions, while Villemot was concerned to provide a physically compelling picture of what happens in orbital motion. Yet Fontenelle not only took Villemot’s book seriously, he goes so far as to present it along with Varignon’s research as part of the same project. Leibniz complained to Johann Bernoulli that the book was devoid of demonstrations, and he was certainly not the only mathematician puzzled that Fontenelle could praise

Newtoniennes (Paris, 1747), is full of quite advanced mathematics and contains no illustrations of machines at all. 55 See Blay, La Naissance de la me´canique, 153–221. 56 See Aiton, Vortex Theory, 170–80. Cf. J. Morton Briggs, ‘Aurora and Enlightenment’, Isis 58 (1967), 498–515. 57 Compare e.g. Aiton, Vortex Theory; and Blay, La Naissance de la me´canique. Both deal with mechanics in France in the late seventeenth and early eighteenth centuries, yet there is hardly any overlap in the kinds of questions that they look at.

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Villemot’s work,58 but although he would be a lifelong supporter of vortex theory, it is unlikely that Fontenelle’s interest derives from this, for he would not have discovered anything novel or especially enlightening in Villemot’s book. What was at issue for Fontenelle was something rather different. It was crucial for his understanding of the kind of natural-philosophical project that the Acade´mie was concerned to pursue that it could be presented as something that connected with reality, let alone have a practical interpretation. Given this, he could not have construed analytical mechanics as constitutive of natural philosophy, as Varignon and the Bernoullis were in effect inclined to do. His conﬂation of Varignon’s and Villemot’s very different projects was an attempt to present a uniﬁed account of something that demonstrated the cutting edge in the mathematical treatment of mechanics, while at the same time satisfying the requirement of clarity and distinctness in terms of picturability of the underlying processes envisaged. In one sense, the incompatibilities did not matter as much as it might at ﬁrst seem, for the general programme to which he assimilates them was very much work in progress. And it was what it was in progress towards that shaped how it should be construed. The problem is that there is a slippage here between explanatory models and explanatory resources. As explanatory resources, both analytical mechanics and the provision of a physically satisfying account of how vortices operate by means of a picturable representation of micro-corpuscularian processes were simply different kinds of techniques on which one could draw. But as explanatory models—that is, as conceptions of the explanatory aims of the discipline—these two were quite incompatible with one another, for they demanded quite different things of explanation. We shall return to this question of explanatory resources versus explanatory models in Chapter 8. For the moment, I want to stress that the problem for Fontenelle here is that powerful analytical procedures are being employed even though they transcend anything that can be legitimated in terms of traditional understandings of clarity and distinctness. As I have indicated, this mismatch between the principles in terms of which one captures one’s sense of what the certainty of mathematics consists in—a certainty that allows it to act as a general cognitive model—and the principles underlying advanced mathematical techniques goes back to Descartes. Leibniz bites the bullet: for him, the advanced mathematical techniques provide us with new and powerful forms of understanding that will only be held back if we attempt to subject them to the picturability requirements imposed by mechanist and geometrical understandings of clarity and distinctness. But for Fontenelle, it is crucial that the projects operating with these different criteria are ultimately reconciled. It is not just a question of particular results that was at stake here, but more generally the

58

See the account of Villemot in Aiton, Vortex Theory, 152–72.

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standing of a highly mathematical form of natural philosophy which was beginning to emerge as a general and unique model for natural understanding. The difﬁculties were compounded with the appearance of the second edition of Newton’s Principia in 1713. The General Scholium that was added to this edition singled out vortex theory for attack, listing the fundamental physical problems to which the theory was subject. At the same time, Cotes’ Preface to the new edition focused on the methodological rationale behind Cartesianism. He distinguishes classes of natural philosopher, which correspond to Aristotelians, Cartesians, and Newtonians. First there are those who have ‘endowed the individual species of things with speciﬁc occult qualities, on which—they have then alleged—the operations of individual bodies depend’.59 Cotes then turns the tables on the Cartesians, accusing them of being the true inheritors of these Aristotelians on occult qualities: Therefore, others have hoped to gain praise for greater carefulness by rejecting this useless hodgepodge of words. And so they have held that all matter is homogeneous, and that the variety of forms that is discerned in bodies arises from certain very simple and easily comprehensible attributes of the component particles. And indeed they are right to set up a progression from simpler things to compounded ones, so long as they do not give those primary attributes of the particles any characteristics other than those given by nature itself. But when they take the liberty of imagining that the unknown shapes and sizes of the particles are whatever they please, and of assuming their uncertain positions and motions, and even further of feigning certain occult ﬂuids that permeate the pores of bodies very freely, since they are endowed with an omnipotent subtlety and are acted on by occult motions: when they do this, they are drifting off into dreams, ignoring the true constitution of things, which is obviously to be sought in vain from false conjectures, when it can scarcely be found out even by the most certain observations. Those who take the foundation of their speculations from hypotheses, even if they then proceed most rigorously according to mechanical laws, are merely putting together a romance, elegant perhaps and charming, but nevertheless a romance.60

By contrast, the Newtonian position is presented as an approach in which ‘natural philosophy is based on experiment’, in which ‘nothing is assumed as a principle that has not been thoroughly proved from phenomena.’61 The reaction to this in France was muted at ﬁrst, and in 1714, for example, we ﬁnd Fontenelle praising new vortical theories of the tides and of weight.62 At the same time, the Journal de Tre´voux, whose stock response to natural-philosophical systems that made any claim to completeness was that they were mere ‘systematizing’, denied that Newton had framed no hypotheses, accusing him of illegitimately assuming premisses and building a system on them.63 59 60 61 62 63

Newton, Principia, Cohen and Whitman edn., 385. Ibid., 385–6. Ibid., 386. See Shank, ‘Before Voltaire’, 367–76. See Healy, ‘Mechanistic Science and the French Jesuits’, 108–15.

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Nevertheless, we can detect the beginnings of a shift in the focus in the Acade´mie, especially after the death of Louis XIV in 1715: the powerful position of the mathematicians was replaced to some extent by the more practical concerns centred on Re´aumur and Mairan. Re´aumur joined the Acade´mie as an assistant (e´le`ve) of Varignon in 1708, and his ﬁrst work was on the analytical derivation of curves, but, as well as being a major contributor to natural history, notably entomology, he also developed an interest in mineral extraction, the transformation of iron into steel, and the cooling of molten iron.64 Moreover, most of the generation of Malebranchean analysts had passed away by 1720, Varignon himself dying in 1722, and the new generation of mathematicians that replaced them did not have the commitment to the same kind of issues represented in Varignon and Fontenelle.65 Mairan, who joined the Acade´mie in 1718, is of particular interest in this regard, as he explicitly challenged Malebranche’s phenomenalism in some detail, and with it the idea that it was legitimate to pursue the study of nature at a high level of abstraction: he explicitly pitted clear and distinct mechanical explanations of the traditional kind against abstractions which, he believed, potentially reopened the door to occult qualities.66 Among other projects, Mairan was concerned to defend the vortex theory, but his rejection of analytic methods—thereby prizing open the two components of French natural philosophy that Fontenelle had attempted to bind together—and his commitment to empirical and astronomical research meant that, when the inadequacy of vortex theory began to come to light, it was no longer protected by association with superior French analytical techniques. In this respect, it is important to remember that Newton’s commitment to a universal attractive gravitational force was not conﬁned to the Principia. The theory of light offered in the Opticks had also invoked this force. Newton had construed light in corpuscular terms, which French natural philosophers had great sympathy for, and he had accounted for the different refractive indices of media in terms of their different densities, the denser the medium the greater the gravitational attraction it exercises on the light corpuscles passing through it. This put the phenomenon of gravitational attraction in a signiﬁcantly different 64 As Shank notes, ‘it is clear that Re´aumur’s deﬁnition of academic science was far more appealing to Bignon than that of the analysts. For example, Re´aumur’s work was directly and obviously utilitarian while Fontenelle needed to perform rhetorical gymnastics to convince readers that analytical mechanics was something other than a jeux d’esprit.’ ‘Before Voltaire’, 342. His work on metallurgy occupied Re´aumur through his career, culminating in L’art de convertir le fer forge´ en acier et l’art d’adoucir le fer fondu ou de faire des ouvrages de fer fondu aussis ﬁnis que de fer forge´ (Paris, 1762). 65 In any case, the standard of work in mathematics in Paris had declined radically by the 1720s, much to the annoyance of Johann Bernoulli: see Greenberg, The Problem of the Earth’s Shape, 246. 66 See Shank, The Newton Wars, 94–104; and, for more detail, Abby Rose Kleinbaum, ‘Jean Jacques Dortous de Mairan (1678–1771): A Study of an Enlightenment Scientist’ (PhD thesis, Columbia University, 1970). Shank also draws attention to the rise in prominence of the Observatoire, where observational work was close to constitutive of the activity of the astronomers.

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context: it was no longer a question of bodies being attracted over huge distances by a completely mysterious force, but rather an issue about microscopic bodies, which chemists had traditionally thought of in terms of various combinations of attractive and repulsive forces. There was also a range of other phenomena with which matter theory had traditionally been concerned, such as capillary rise, which completely deﬁed any mechanical explanation. It was a chemist, Geoffroy, who, as we have seen, brought the Opticks to the attention of the Acade´mie in 1705/6 in his reading of his translation to Fontenelle and others. The matter theory tradition will be our concern in Chapters 9 and 10, so I shall reserve treatment of these questions until then, except to note here that, in matter theory, repulsive and attractive forces had a much more intuitive feel to them, by contrast with mechanics, where it was unclear how the basic resources could generate such forces. The general situation was, then, far more complex than Fontenelle allowed. Chemists had no objection in principle to attractive forces, but nor did those whose concern with rational mechanics was primarily mathematical. When matters came to a head over the shape of the earth in 1732, it was the mathematicians who took the merits of the Newtonian theory of gravitation seriously.67 That it was on the question of the shape of the earth that the issues turned was not something that could have been predicted. Although the French reaction to the Leibniz/Clarke debate by the late 1720s, as evidenced by the discussions in the Journal des Sc¸avants and the Journal de Tre´voux,68 shifted the issues to some extent away from theological questions and the priority dispute over the calculus towards the issue of universal gravitation, the shape of the earth was not an issue that straightforwardly divided Cartesians and Newtonians, for example along vortex theory/gravitational attraction lines. What was in contention was whether the earth was ﬂattened at the poles—an oblate spheroid—or whether it was elongated at the poles—a prolate spheroid. Huygens and Newton had both argued for the former, assuming that a stationary earth would be spherical, and that rotation would cause it to bulge at the axis of rotation (the equator). This ﬁtted with the measurements that had been made at the time: in 1672 and 1673, the French astronomer Jean Richer had carried out experiments with seconds pendulums in French Guyana and found that they had a shorter length than those in Paris. Newton, using the value of a degree of latitude calculated by Picard in 1669–70 to determine the radius of an earth assumed to be spherical, 67 See the detailed account of these questions in Greenberg, The Problem of the Earth’s Shape, chs. 1–5; and Mary Terrall, The Man Who Flattened the Earth: Maupertuis and the Sciences in the Enlightenment (Chicago, 2002), ch. 3. 68 See Shank, ‘Before Voltaire’, ch. 10. What was offered was discussion and reviews of a French translation of the Leibniz/Clarke letters with an extensive collection of related pieces, collected and introduced by Pierre Des Maizeaux: Recueil de diverses pieces, sur la philosophie, la religion naturelle, l’histoire, les mathematiques, & c par Mrs Leibniz, Clarke, Newton et autres auteurs cele´bres (2 vols., Amsterdam, 1720).

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and knowing the earth’s sidereal rate of diurnal rotation, calculated the centrifugal force per unit of mass at the equator of a spherical earth. Using the results of experiments with seconds pendulums and falling bodies performed in Paris he was then able to determine the effective gravitational force per unit of mass there. The magnitude of attraction at the equator, on the assumption of a spherical earth, should be the same as that in Paris, that is, it should equal the magnitude of the effective gravity (more precisely, the magnitude of the component of gravitational attraction perpendicular to the earth’s surface) plus the magnitude of centrifugal force per unit of mass (more precisely, the magnitude of the component of centrifugal force perpendicular to the earth’s surface) in Paris. But there was a discrepancy of 1/289. Huygens obtained the same result but within the context of a vortex theory rather than one of gravitational attraction: mathematically, both worked from a central force of attraction, Newton assuming an inverse square reciprocal attraction, while Huygens assumed that the centre of force was in the attracted body. Subsequent and seemingly more accurate measurements, however, suggested a prolate shape. In 1713, Jacques Cassini measured the arc of the meridian from Dunkirk to Perpignan, and found that lengths of eight consecutive degrees decreased slightly from south to north: extrapolating to the shape of the earth, using basic astronomical geometrical techniques of triangulation along the Paris meridian, he calculated that the earth must be ﬂattened at the centre. He announced his results to the Acade´mie in 1718, and published his account in 1720.69 Cassini was an extremely distinguished and careful astronomer: born and raised in the Observatoire, where his father was director, he was admitted to the Acade´mie at the age of 17, and elected a Fellow of the Royal Society at 19. His results had to be taken seriously, and while it was difﬁcult to see how a Newtonian theory of gravitational attraction could be reconciled with them, vortex theory was a different matter. Mairan, for example, tried to account for the prolate shape by reworking the vortex theory that Huygens had assumed. He did not deny that the centrifugal forces arising from rotation would cause the centre to bulge, but argued that the earth in a non-rotational form was forced into a prolate shape under the force of a celestial vortex: the effect of the bulge caused by the rotation was simply to make the shape less prolate.70 It is also worth noting that Johann Bernoulli was linking vortex theory to the elongation of the earth by 1734, arguing that the observed inclination of the earth’s orbit, accounted for on the basis of a version of Descartes’ vortex theory, conﬁrmed that the planet was elongated at the poles and not at the equator, thus supporting the results of Cassini’s geodesic surveys.71 69

Jacques Cassini, Traite´ de la grandeur et de la ﬁgure de la terre (Paris, 1720). Jean-Jacques Dortous de Mairan, ‘Recherches ge´ometriques sur la diminution des degre´s terrestres en allant de l’e´quateur vers les poˆles’, Me´moires de l’Acade´mie Royale des Sciences 1720, 231–77. See the account in Greenberg, The Problem of the Earth’s Shape, ch. 2. 71 See Aiton, Vortex Theory, 228–35. 70

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The question of the shape of the earth acted as the platform on which Newtonianism became introduced into continental mechanics, and the person who introduced it was Maupertuis. He was elected to the Acade´mie in 1723, to the mechanics section as a geometer, despite having applied under natural history and having produced nothing in mathematics. Though not an outstanding mathematician, compared with the Bernoullis or Clairaut for example, he was very conscientious one, and was able to rely on continuous tutelage from Johann Bernoulli, who was resident in Basel. He built up his mathematical skills throughout the 1720s, working particularly on the application of integral calculus to the exploration of the properties of curves. Maupertuis’ original aim was to clarify Newton’s treatment of dynamics for a French audience, and the problem he ﬁxed on for these purposes was the shape of the earth. He found Mairan’s geometry wanting and set out to apply analytic techniques to the question. It was a basic assumption of mechanical treatments of the shape of the earth that it could be treated as a ﬂuid body, this being a prerequisite for the understanding of the distortion of its shape caused by rotation. Refusing to limit his analysis to the inverse square law, Maupertuis calculated that any such body subject to attractive forces varying as a power of distance would bulge at the centre. In exploring the relationship between weight and centrifugal force, however, he began to take the idea of gravitational attraction seriously,72 even though its nature and mode of action were not understood, starting to go beyond the purely mathematical questions that had occupied him up to this point and to speculate on the physical consequences of his results. Maupertuis was up for election to a pensionable position in the Acade´mie in early 1731, and did not want to alienate senior members, so he sent a paper surreptitiously to the Royal Society for publication, at the same time considering how he might separate the work into three parts, comprising a mathematical solution to the rotating body problem, speculation about Saturn’s rings, and a defence of the idea of attraction. The ﬁrst of these was eventually published by the Royal Society, but had little impact, and Maupertuis decided to publish the whole work, in its less technical aspects, as a book, which appeared as Discours sur les different ﬁgures des astres avec une exposition des syste`mes de MM. Descartes et Newton (Paris, 1732). As the title of the book indicates, Maupertuis did not hold back from raising the physical question of attraction versus vortices, and in fact he clearly came down on the side of the former, albeit without explicitly attacking proponents of vortex theory. The defence of attraction proceeded via the argument that it was in fact no more mysterious than the force of impulsion, so to argue that attraction was somehow unacceptable while impulsion was ﬁne was to adopt double 72 Maupertuis had spent three months in England in 1728, consulting with Newtonian natural philosophers and mathematicians, but there is no evidence of Newtonian sympathies as a result of the trip. The ﬁrst signs of an acceptance of the Newtonian account are in 1731. See Terrall, The Man Who Flattened the Earth, 41–3.

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standards. Moreover, he claims, not only had Newton treated gravitation as a lawlike effect rather than as a cause, but gravitational attraction is not in conﬂict with any other accepted physical property. He notes that perhaps Kepler’s laws could be reconciled with Cartesian vortex theory—along the lines of Johann Bernoulli’s prize-winning 1730 essay defending the view that the layers of vortices do in fact follow Kepler’s area law—but the question nevertheless remained an open one, whereas the Newtonian theory of gravitation was manifestly consistent with the laws. Maupertuis’ Discours, by contrast with his technical treatment of rotating ﬂuids, adopted a conversational tone, and, as Terrall notes, its chief target was Fontenelle, who in his e´loge of Newton had championed vortex theory over attraction in much the same way, and with the same wide audience in mind, that Maupertuis was now championing attraction over vortex theory.73 For his colleagues in the Acade´mie, his strategy was to translate Newton into the analytic notation they were employing, concerning himself not with the consequences of inverse forces but rather with demonstrating propositions on how such forces acted according to any power of the distance between attracting bodies.74 There remained an outstanding problem for the defence of Newtonian attraction, however: Cassini’s measurements of the shape of the earth. If Cassini were right, then it would seem that the Newtonian account of gravitational attraction must be mistaken. Maupertuis and his circle found it difﬁcult to believe that Newton’s account could be wrong on this question. There were a number of possible lines of attack: both the measurement procedures, and the calculations performed on the measurements, were open to re-examination. Cassini’s account had remained largely uncontested, but there had been a couple of isolated doubts raised about the procedures that he had used in his calculations as early as the 1720s. Both the Italian astronomer Giovanni Poleni and the French astronomer Joseph-Nicolas Delisle had independently argued that degrees of latitude along the Paris meridian were so small as to be within the margin of error of the measuring instruments. Consequently, they recommended instead measuring the length of a degree of longitude, then comparing this to the length calculated for a perfect sphere.75 Maupertuis took up this idea, deriving equations for relating the axes of the spheroid, longitudes, and latitudes.76 Clairaut also put his prodigious mathematical talents to work on the question, showing that Cassini’s calculations were based on spherical geometry, whereas the geometry 73

See ibid., 72–83. Maupertuis, ‘Sur les loix d’attraction’, Me´moires de l’Acade´mie royale des sciences (1732), 343–62. 75 See John L. Greenberg, ‘Geodesy in Paris in the 1730s and the Paduan Connection’, Historical Studies in the Physical Sciences 13 (1983), 239–60; and idem, ‘Degrees of Longitude and the Earth’s Shape: The Diffusion of a Scientiﬁc Idea in Paris in the 1730s’, Annals of Science 41 (1984), 151–8. 76 Terrall, The Man Who Flattened the Earth, 91–2. 74

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of the spheroid is more complicated: indeed, it was Clairaut who was to develop the complex mathematics of coping with the earth’s curvature in a detailed way over the next eleven years.77 The measurements themselves were also at issue however, and the Acade´mie decided that new measurements had to be made. The idea was to measure the length of an arc of latitude at the equator and at the pole, or as near to the pole as possible: an oblate spheroid would show a shorter arc of latitude at the equator than nearer the poles, a prolate spheroid a larger one at the equator. In 1735, an expedition under the leadership of Godin, La Condamine, and Bouguer set out for Peru,78 and Maupertuis argued for a parallel expedition to the Arctic: he headed this expedition, to Lapland, in 1736. The expeditions not only established deﬁnitively that the earth was an oblate spheroid, but the gloss put on the expedition to Lapland by Maupertuis in his 1738 La ﬁgure de la terre,79 at the same time personal and heroic, was a very successful public relations exercise. As Terrall notes, his account ‘makes the reader acutely aware of the bodies of the academicians, as they freeze or sweat or bleed in the service of science. However difﬁcult it might have been to imagine such sensations, the physical suffering of these men made the accomplishments real and substantial to a genteel audience with little direct experience of climates beyond the boundaries of the French provinces. The measurements themselves emerged pristine from this trying process when the results were revealed: two teams measuring the same distance independently came up with numbers that differed by no more than a few inches.’80 Such an exercise was worthy of Fontenelle, but in what was, for all intents and purposes, a defence of Newtonian attraction, it was the opposite of what Fontenelle had sought to demonstrate. And as Voltaire was about to show, more than physics was at stake. 77

See Greenberg, The Problem of the Earth’s Shape, chs. 6 and 9. Given the observations had to be made at the equator, and given that Africa was largely unexplored and the islands of south-east Asia too far, a double chain of mountains in the viceroy of Peru (in present day Ecuador) was identiﬁed as the ideal observation point. There is a full acount of the expedition in Antonio Lafuente and Antonio Mazuecos, Los Caballeros del Punto Fijo: Cienca, polı´tica y aventura en la expedicı´on geode´sica hispanofranco al Virreinato del Peru´ en el siglo XVIII (Barcelona, 1987). 79 Pierre-Louis Moreau de Maupertuis, La ﬁgure de la terre determine´e par les observations de MM. de Maupertuis, Clairaut, Camus, Le Monnier, Outhier, Celsuis au cercle polaire (Paris, 1738). 80 Terrall, The Man Who Flattened the Earth, 123. By contrast with Maupertuis’ portrayal of events, the expedition to Peru was evidently marred by constant quarrels between Bouguer and La Condamine, who found their separate ways home, and were unable to agree on a joint publication of their works, pursuing their quarrel in a series of memoirs which ended only with the death of Bouguer in 1758. Their separate accounts appeared as [Pierre] Bouguer, La ﬁgure de la terre, de´termine´ par les observations de Messieurs Bouguer & de la Condamine, de l’Acade´mie royale des sciences, envoyes par ordre du roy au Pe´rou, pour observer aux environs de, l’e´quateur (Paris, 1749), and Charles-Marie de la Condamine, Journal du voyage fait par ordre du roi, a l’e´quateur, servant d’introduction historique a la Mesure des trois premiers degre´s du me´ridien (Paris, 1751). 78

7 The Realm of Reason When Newtonianism was introduced into French natural philosophy in the 1730s, the timing of its introduction meant that it effectively came as part of a package. The other ingredient in this package was a radicalized form of Lockeanism, which was taken as its natural complement. This second ingredient was crucial in promoting natural philosophy as something of central cultural standing. In this chapter, I shall be examining how Newtonianism and radicalized Lockeanism interacted, building on the discussion of the last chapter with a view to constructing a more detailed picture of how natural philosophy could assume the dominant cultural role that it played in mid-eighteenth-century Paris. THE B IRTH OF THE PHILOSOPHE The publication of Voltaire’s Lettres philosophiques in 1734 transformed Parisian intellectual culture, playing a formative role in the shaping of a new philosophical persona—the philosophe—and reinforcing the standing of natural philosophy at the centre of the Republic of Letters. In the process, natural philosophy took on a new social and political signiﬁcance, quite different from anything it had had either in Great Britain or in France. Voltaire linked what he considered an especially successful form of English scientiﬁc practice with what he considered a particularly successful English political culture, contrasting both with what he found in France.1 This linkage, combined with a heavily ironic and condescending tone, an airing of a materialist theory of mind, a frontal assault on Pascal’s defence of religion, and the rather unique circumstances of publication of the book, which added considerable drama to its appearance, propelled the Lettres philosophiques to the centre of the Republic of Letters. Materialism, 1 Associations between Newtonianism and the British form of constitutional monarchy were common in England. The title of Desaguliers’ very popular The Newtonian System of the World, the Best Model of Government: An Allegorical Poem (London, 1728), for example, says it all, and the prefatory remarks spell out just what feature of the Newtonian system is responsible: ‘The limited Monarchy, whereby our Liberties, Rights, and Privileges are so well secured to us, as to make us happier than all the nations round about us, seems to be a lively Image of our System; and the Happiness that we enjoy under His present MAJESTY’s Government, makes us sensible, that ATTRACTION is now as universal in the Political, as the Philosophical World’ (v).

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atheism, a defence of the virtues of English political life over French absolutism, and a bypassing of French censorship laws formed the context for the defence of Newtonianism. Voltaire’s Newtonianism was a Lockean variety, however, and it was this that held these themes together: his political aspirations and his notion of religious toleration were shaped by Lockeanism, and his attack on Cartesian epistemology—crucial for the Cartesian notion of clarity and distinctness—was based largely on the Lockean rejection of innate ideas. The extent to which Lockeanism had permeated Parisian culture by the 1720s is evident from a piece by Nicolas Fre´ret, ‘Sur l’e´tude des anciennes Histoires, & sur le degre´ de certitude de leurs preuves’, delivered on 17 March 1724 to the Acade´mie des Inscriptions, of which Fre´ret would become secretary in 1742. There is nothing more attractive than the idea of a system, he writes, but the limits that nature has prescribed are so restricted that we should not ﬂatter ourselves to hope that we could ever accumulate enough knowledge to form a general and complete system on anything at all. We know hardly anything beyond particular facts, which are almost always not connected with one another, and experience has all too often persuaded us of the falsity of all those ingenious systems constructed in criticism, politics, and philosophy in the last few centuries. . . . I do not mean, in what I say here, to confuse the love of systems with the methodical mind, which the study of the exact sciences has brought to the fore in our own age. . . . The spirit of philosophy is very different from the spirit of system, the ﬁrst being as necessary as the second is dangerous.2

As we have seen, the attack on systems was widespread by this time, part of the polemics of both the Acade´mie des Sciences and that of its rival the Journal de Tre´voux, but the explicitly Lockean tone of Fre´ret’s defence is distinctive. The task of the Acade´mie des Inscriptions was the philological and historical reconstruction of the ancient and medieval worlds, and it might be expected that its legitimatory programme (which had been restructured and refocused in 1701, two years after the reorganization of the Acade´mie des Sciences) would reﬂect the piecemeal nature of much of its work. This lent itself to a Lockean rationale, and this is exactly what Fre´ret provides. ‘True criticism’, he writes, ‘is just philosophical enquiry’—of the kind he has just outlined—‘applied to the study of facts; it follows that, in its examination of them, it uses the same procedures that [natural] philosophers employ in seeking natural truths.’3 Nevertheless, while this indicates that Voltaire’s readers may not have been unaware of Lockean ideas, there were also native French currents that, being more pervasive, would have prepared the ground to an even greater extent. Although English thought in general and Locke in particular play a key role in the Lettres philosophiques, and indeed in Voltaire’s intellectual development more

2 Me´moires de litte´rature tire´s des registres de l’Acade´mie Royale des inscriptions et Belles-Lettres, 8 (1731), 235–6. 3 Ibid., 239.

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generally, there were two formative Francophone precedents: Fontenelle’s Histoires des oracles (1686) and the various writings of Bayle. We shall be looking at the Histoires des oracles in Chapter 12. Here we need only note that its theme is how one can rationally reconstruct superstition, and he offers a naturalistic reconstruction of ancients shrines and oracles. Although not an especially original work, it was written for a broad reading public in an elegant and engaging French, just as his Entretiens had been a few months earlier, and it was a very successful attempt to open up questions of religion and superstition that successfully steered around French censorship on these delicate questions. The delicacy of such questions is evident from the fact that, although Fontenelle was cautious enough in his formulations and sufﬁciently well connected to stave off censorship and criticism at the time, when matters came to head in 1707, a defence of the work by his follower Du Marsais was denied a licence to publish, and personally prohibited by Louis XIV.4 If Fontenelle’s Histoires offered an example of the triumph of reason over superstition, this was even more manifest in Pierre Bayle, whose Francophone journal Nouvelles de la Re´publique des Lettres took full advantage of the comparative lack of censorship in the Netherlands5 to supply members of the Republic of Letters with news of views, books, and events with which they might be otherwise unfamiliar, because of censorship or simple inability to access recent books. Bayle was born and raised in France as a Protestant, converting to Catholicism in 1669 at the age of 21, soon to become disillusioned with the Jesuits with whom he had then studied and he converted back to Protestantism, moving to Geneva and brieﬂy back to France before he joined other Huguenot refugees in the Netherlands in 1681.6 In his Pense´es diverses sur la come`te (1682), he took up the themes of idolatry and superstition, starting not from a consideration of pagan religion but with the appearance of comets observed in the winter of 1680–1, and widely believed to portend difﬁcult or evil times ahead. By this stage, Bayle had become a Cartesian, and it is worth remembering that Descartes had picked out meteorology as something destructive of superstition and wonder, replacing these with a reasoned, mathematical account of meteorological phenomena.7 What is at issue for Bayle, as for Descartes, is not merely superstition but wonder at nature, exactly the thing the Jesuits who edited the Journal de Tre´voux would pick out as being undermined by Cartesian natural philosophy and mechanism more generally. But not only is a sense of wonder being attacked, the idea of the authority of the Church in such matters, defended in writers like the very inﬂuential Catholic 4

See Israel, Radical Enlightenment, 368–9. Compared with France for example, but by no means absolute. On Bayle’s subjection to local censorship, see Israel, Enlightenment Contested, 264–8. 6 On Bayle’s intellectual development, see Elizabeth Labrousse, Pierre Bayle, i: Du Pays de Foix a` la Cite´ d’Erasme (The Hague, 1963); and idem, Pierre Bayle, ii: He´te´rodoxie et Rigorisme (The Hague, 1964). 7 See Gaukroger, Descartes, An Intellectual Biography, 219. 5

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theologian Jacques-Be´nigne Bossuet in terms of its unbroken chain of tradition, is ridiculed as a basis for belief.8 Neither continuity of tradition nor general consent of peoples throughout history could possibly constitute a basis for the truth of Christianity, Bayle argues, and he then mounts not only a defence of the possibility of a virtuous atheist, but identiﬁes Spinoza and Vanini as such, noting, in connection with the latter—who had his tongue cut out, was strangled, and had his body burned at the stake for atheism—that atheism has its martyrs just as do revealed religions. Moreover he identiﬁes a whole culture, that of China, which is virtuous, politically stable, and culturally rich, on the one hand, and yet atheist, not just in the negative sense in which primitive peoples lacked a belief in God, but in a positive sense, so that Confucius and Mencius for example could offer a highly developed naturalistic metaphysics that compared favourably with a religious one.9 In his Commentaire philosophique (1686), he mounted a fullscale defence of religious toleration which went well beyond earlier defences in its lack of exclusions, and he begins by arguing that ‘natural reason’ is the only instrument that can guide us.10 This was far more radical than anything possible in France without a signiﬁcant change of French culture, and the work that— seemingly unwittingly—effected that change in crucial respects was Voltaire’s Lettres philosophiques, one novelty of which lay in its association of ‘natural reason’ with a particular form of English natural philosophy. Voltaire established a reputation for himself as a caustic wit during the early years of the Regency, earning himself a couple of spells in the Bastille, and as a man of letters with the publication of his Oedipe in 1718.11 An important inﬂuence on him in these years was the Tory libertine, Lord Bolingbroke, who was exiled in France from 1715 to 1723. Closely associated with English deism, Bolingbroke represented an urbane, cosmopolitan, literary and political ﬁgure, and, it is doubtless from him that Voltaire’s early Anglophilia derived.12 During 8

The importance of an unbroken chain of tradition will also be the main weapon in the arsenal of ‘Enlightened’ Christian apologists: see e.g. Jean Denyse, La ve´rite´ de la religion chre´tienne de´montre´e par ordre ge´ometrique (Paris, 1717), and Alexandre Claude-Franc¸ois Houtteville, La religion chre´tienne prouve´e par les faits (Paris, 1721). 9 For example, Bayle, Continuation des Pense´es diverses sur la come`te (2 vols., Rotterdam, 1705), ii. 537–40, 728–30; and Reponse aux questions d’un provincial (5 vols., Rotterdam, 1704–7), iv. 139–41. Bayle’s critics found such claims particularly galling: see e.g. Jean-Pierre de Crousaz, Examen du Pyrrhonisme ancien et moderne (The Hague, 1733), 410–11. More generally, see Israel, Enlightenment Contested, 640–62; and Virgile Pinot, La Chine et la formation de l’esprit philosophique en France (1640–1740) (2 vols., Paris, 1932). 10 Nevertheless, there was still a role for the state in the enforcement of morals: see Ian Harris, ‘Toleration and its Place: A Study of Pierre Bayle in his Commentaire Philosophique’, in Sarah Hutton and Paul Schuurman, eds., Studies on Locke: Sources, Contemporaries, and Legitimacy (Dordrecht, 2008), 225–44. 11 On Voltaire’s early career, see Ira O. Wade, The Intellectual Development of Voltaire (Princeton, 1969), Parts I and II; and Rene´ Pomeau, D’Arouet a` Voltaire (Oxford, 1985). 12 Bolingbroke is covered in more detail than anyone else, for example, in John Leland, A View of the Principal Deistical Writers (3rd edn., 3 vols., London, 1756–7). His writings were collected posthumously as The Philosophical Works of the Late Right Honorable Lord Viscount Bolingbroke

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Voltaire’s stay in England from 1726–9, Bolingbroke was his chief contact and host, and while there he developed an appreciation of Newtonianism, both through his London contacts, notably Clarke, with whom he had several meetings, and through connections such as ’sGravesande, whom he ﬁrst met on a trip to Holland at this time.13 On his return from England, he exploited a loophole noticed by the young mathematician Charles Marie de la Condamine (later to lead the expedition to Peru to determine the shape of the earth) in the new National Lottery, and the returns on this investment provided him with independent means from that time onwards.14 The Lettres philosophiques began very much as a witty comparison between London and Paris. There were a number of models for this, most notably Montesquieu’s Lettres persanes (1721), a satire based on the imaginary correspondence of an Oriental visitor to Paris, pointing out the absurdities of contemporary society.15 Whereas in Montesquieu’s case it is exclusively the country visited (5 vols., London, 1754–77). Voltaire wrote a number of pieces on Bolingbroke: see e.g. The Complete Works of Voltaire/Œuvres comple`tes de Voltaire (150 vols., Oxford/Paris, 1968–), xxxiiB and lxii. On the extent of Bolingbroke’s inﬂuence on Voltaire, see J. H. Brumﬁtt, Voltaire Historian (Oxford, 1958), 40–5. On Anglophilia in France generally, see Israel, Enlightenment Contested, 344–71. 13 On his third trip to Holland in 1737, Voltaire sat in on ’sGravesande’s lectures: see Jeroom Vercruysse, Voltaire et la Holland (Geneva, 1966), 36–7, 127. 14 The lottery was devised to regularize state ﬁnances. The proposal was that holders of government bonds be entitled to buy lottery tickets against the nominal value of the bonds. Since the real value of the bonds had declined to such an extent that they were virtually worthless, this was an attractive offer to the holders of the bonds, while the government could extinguish state debt and could excuse avoiding payment of the nominal value of the bond. The bond holder was entitled to purchase a ticket proportional to his holding: if one held a 1,000 livre bond one was entitled to a 1 livre ticket, which if one won meant a prize of 1,000 livres (less taxes), whereas if one held a 10,000 livre bond one bought a 10 livre ticket, standing to win a prize of 10,000 livres. To encourage bond holders to participate in the lottery, extra money was added to the draw so that the prize money exceeded the total value of the tickets by a signiﬁcant amount. Condamine realized that, in these circumstances, purchasing all tickets, or failing that as many as one could, would yield a large proﬁt. However, the lottery was only open to bond holders, and one was only entitled to purchase tickets against the value of one’s bonds, which one forfeited at purchase. How then does one take advantage of the potential yield delivered by buying extra tickets? What probably happened—and I am grateful to John Hambly for this suggestion—is that Condamine et al. offered to buy tickets from ticket holders for a marginally greater price than the ticket holders had paid for them (as far as these ticket holders were concerned it would be risk-free money for nothing). Having accumulated a great number of tickets in this way, they then registered them with various invented names: Voltaire evidently showed particular skill in this respect. On discovery of the arrangement—and this is the only arrangement that I have been able to imagine that ﬁts all the facts and would yield the beneﬁts—the Lottery was closed down and its Controller-General sacked for incompetence. In his defence, he argued that the practice followed was illegal, but the Royal Council found that it was in fact not prohibited. Voltaire is thought to have netted around half a million livres (about four million pounds sterling in current values), which he then very proﬁtably invested. 15 Charles de Secondat, Baron de Montesquieu, Lettres persanes (‘Cologne’ [Amsterdam], 1721). There was also, as might be expected, celebration of the difference by English writers. The ﬁrst issue of the Independent Whig, 20 January 1720, for example, highlighted the divide between France and England, and rejoiced in English liberties. The difference was such that someone regarded as a conservative in liberal England could be admired by philosophes in reactionary France. Bishop

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that is satirized, however, Voltaire’s satire is primarily directed at his own country, and although there is some gentle ridicule of the Quakers, the freedom of worship they enjoy is praised. ‘England is a country of sectarists’, he writes: ‘As an Englishman, one to whom liberty is natural, one may go to heaven his own way.’16 Moreover, he draws a conclusion about social harmony from this, telling us that ‘if only one religion were allowed in England, the government would very possibly become arbitrary; if there were but two, the people wou’d cut one another’s throats; but as there are such a multitude, they all live happily, and in peace.’17 Morality is also at stake, and the contrast he draws between the Church of England and the French Catholic church is a moral one: With regard to the morals of the English clergy, they are more regular than those of France, and for this reason: All the clergy (a very few excepted) are educated in the universities of Oxford and Cambridge, far from the depravity and corruption which reign in the capital. . . . That fable mix’d kind of mortal (not to be deﬁn’d) who is neither of the clergy nor of the laity; in a word, the thing call’d Abbe´ in France, is a species quite unknown in England. All the clergy here are very much upon the reserve, and most of them pedants. When these are told, that in France, young fellows famous for their dissoluteness, and rais’d to the highest dignities of the church by female intrigues, address the fair publickly in an amorous way, amuse themselves in writing tender love-songs, entertain their friends very splendidly every night at their own houses, and after the banquest is ended, withdraw to invoke the assistance of the Holy Ghost, and call themselves boldly the successors of the apostles, they bless God for their being Protestants.18 William Warburton was an example of such a case—see Frank E. Manuel, The Eighteenth Century Confronts the Gods (Cambridge, Mass., 1959), 72–3—and the philosophes were particularly taken by his material on hieroglyphics in his The Divine Legation of Moses Demonstrated (4 vols., London, 1738–41). This was translated into French by M. A. Le´onard des Malpeines, Essai sur les hie´roglyphes des Egyptians, traduit de l’Anglois par M. Warburton (2 vols., Paris, 1744), and a signiﬁcant amount of material from it was incorporated into the Encyclope´die. 16 I quote from the ﬁrst full English version of the Lettres philosophiques: Letters Concerning the English Nation. . . . The second edition, with large additions (London, 1741), 28. It has traditionally been thought that Voltaire originally wrote many of the letters in English, himself translating them into French, but recent research shows that they were in fact originally written in French and translated into English by a John Lockman: see J. Patrick Lee, ‘The Unexamined Premise: Voltaire, John Lockman and the Myth of the English Letters’, Studies on Voltaire and the Eighteenth Century 10 (2001), 240–70. 17 Letters Concerning the English Nation, 37. The ‘multitude’ of sects increased in the course of the eighteenth century, as the 1807 list compiled by Robert Southey indicates: ‘The heretical sects in this country are so numerous, that an explanatory dictionary of their names has been published. They form a curious list! Armininians, Socinians, Baxterians, Presbyterians, New Americans, Sabellians, Lutherans, Moravians, Swedenborgians, Athanasians, Episcopalians, Arians, Sublapsarians, Antinomians, Hutchinsonians, Sandemanians, Muggletonians, Baptists, Anabaptists, Paedobaptists, Methodists, Papists, Universalists, Calvinists, materialists, Destructionists, Brownists, Independants, Protestants, Huguenots, Nonjurors, Seceders, Hernhutters, Dunkers, Jumpers, Shakers, and Quakers, &c. &c. &c.’ Robert Southey, Letters From England by Don Manuel Alvarez Espriella (Gloucester, 1984), 159. 18 Letters Concerning the English Nation, 31–3. The French abbe´, neither monk nor priest but an ecclestiastical scholar, was generally treated as an oddity outside France. Compare the account of the German travel writer Joachim Christoph Nemeitz: ‘I had always assumed that those in France who

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This was certainly not likely to endear Voltaire to the French censors, yet if these letters, which is what he had composed by 1729,19 were all that was at issue, it is unlikely that the work would have attracted great attention. Between 1732 and 1733, however, Voltaire added letters on Locke, Newton, a comparison of Newtonianism and Cartesianism, a letter defending and recommending the English practice of smallpox inoculation,20 and, at the last minute, a ﬁerce attack on Pascal’s defence of religion. While Voltaire was waiting for royal permission, two pirated English editions appeared, forcing him to bypass the censorship process and publish an authentic edition.21 As a consequence of publishing without permission, a warrant was issued for his arrest, his publisher was thrown into the Bastille, the book itself was publicly burned by the hangman, and it quickly became a best-seller. The introduction of Newtonian themes seems to have been stimulated largely by his reading of Maupertuis’ Discours. Voltaire was in continuous contact with Maupertuis, sending him various materials he was composing on Newton, including drafts of the letters on Newtonianism. Moreover, in the spring of 1733, Voltaire began a long intimate collaboration with Emilie du Chaˆtelet (it was to her chateau at Cirey that he escaped following the issue of the arrest warrant in May 1734), whose grasp of the technicalities in Newton was superior to Voltaire’s:22 as well as preparing the ﬁrst French translation of the Principia, she was, as Voltaire acknowledged, in effect co-author with him of his 1738 Ele´mens de la philosophie de Neuton.23

wore little collars and short mantles were men of the Church. Consequently, I was sure that these men were prostituting their character when I saw an abbe´ playing cards in company with ladies and others.’ Sejour de Paris, c’est a` dire, Instructions de ﬁde`les pour les voiageurs de conditions, comment ils se doivent conduire, s’ils veulent faire un bon usage de leur tempts & argent, durant leur Se´jour a` Paris (Leiden, 1727), 139. 19 On the composition of the letters, see Pomeau, D’Arouet a` Voltaire, ch. 19; and Rene´ Vaillot, Avec Mme Du Chaˆtelet (Oxford, 1988), ch. 1. 20 There was a political dimension to the issue of inoculation in France. By the 1750s it had become a central plank in the philosophes’ campaign for the reform of society, and the opposition it faced had an explicitly theological dimension: see Arnold Rowbotham, ‘The Philosophes and the Propaganda for Inoculation of Smallpox in Eighteenth-Century France’, University of California Publications in Modern Philology 18 (1935), 265–90. 21 Franc¸ois-Marie Arouet de Voltaire, Lettres ecrit de Londres sur les Anglois (Paris, 1734). Actually, Voltaire manipulated the process of publication to a signiﬁcant degree, albeit ultimately without success: see Roger Pearson, Voltaire Almighty: A Life in Pursuit of Freedom (London, 2005), 115–20. 22 See e.g. her lucid account of the vis viva controversy in her Institutions de physique (Paris, 1740). Mme du Chaˆtelet was not as uncritical an advocate of Newtonianism as was Voltaire: she rejected not only the Newtonian idea of attraction but also that of the absoluteness of space and time. 23 The Ele´mens was more conciliatory than the Lettres and was instrumental in introducing Newtonianism to a wide audience, including the Jesuits: see e.g. the review of the second edition in the Journal de Tre´voux 44 (1744), 1008–28. See also C. B. O’Keefe, Contemporary Reactions to the Enlightenment (1728–1762) (Paris, 1974), 522–3.

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In the ﬁnal version of the Lettres, Newton emerges as the upshot of a tradition of experimental philosophy, and the exploration of the limits of our reasoning powers, in the work of Bacon (Letter XII) and Locke (Letter XIII) respectively. Locke is defended over the prevailing Cartesian view on two issues. Voltaire ridicules the notion of innate ideas, following Locke in the view that we build up our ideas through sense experience. Far more contentiously, he draws attention to and defends what was in effect a passing remark in Locke, namely that our understanding of mind and of God’s powers is so limited that for all we know it would have been possible for God to endow matter with the power to think. The ﬁrst point would have been widely thought to be a part of any defence of a ‘Newtonian’ natural philosophy by the 1730s, but the latter, with its intimations of materialism and, by implication, mortalism, was a different matter. At one level, Voltaire’s argument is simply directed against the idea that a pre-given system can provide grounds for believing something which one cannot defend in its own right. What is at stake here is what Voltaire refers to as ‘modesty’. The contrast is between a pre-given system, in which all gaps are ﬁlled in dogmatically, and a comprehensive and reasoned understanding of the limits of human knowledge of the kind offered by Locke. Here of course the pre-given system is not merely Cartesianism but a Cartesian articulation of basic Christian doctrine, and what Voltaire is in effect setting out to establish are theological credentials of a philosophy uninformed by any prior theological commitments: But why may not God, if he pleases, communicate to our more delicate organs that faculty of feeling, perceiving, and thinking, which we call human reason? To whatever side you turn, you are forced to acknowledge your own ignorance, and the boundless power of the Creator. Exclaim therefore no more against the sage, the modest philosophy of Mr. Locke, which, so far from interfering with religion, would be of use to demonstrate the truth of it, in case religion wanted any such support. For what philosophy can be of a more religious nature than that, which afﬁrming nothing but what it conceives clearly, and conscious of its own weakness, declares that we must always have recourse to God in our examining of the ﬁrst principles.24

In a context informed by physico-theology, as the English one was, this would not be such a radical argument, but in France matters were different. The notion that philosophy could correct theology in any way was far more controversial. The idea of the limits of reason had not been without its defenders in France, but the most famous of these, Pascal, had drawn a very different conclusion for the standing of religion, construing the limits of reason as indicating the point of submission to religion. Pascal’s view in the Pense´es, for example, had been (in Voltaire’s summary) that we must ‘acknowledge the truth of religion even in the gloom and obscurity of it; in the very light we have in it; and in the indifference which we shew with regard to gaining light into it’. Voltaire replies: ‘What odd 24

Letters Concerning the English Nation, 86–7.

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characteristics of truth are here brought us by Pascal? Which then are the characteristics of falshood? How! wou’d it be enough for a man, who was desirous of being believed, to say, I am obscure, I am unintelligible?’25 For Voltaire, the limits of intelligibility and the limits of systematic understanding were two quite different things, and the latter did not mark the limits of reason. A ‘modest’ form of nonsystematic understanding of a Lockean kind, pursued for example by means of empirical enquiry, was still a genuine form of understanding. The crucial point for Voltaire is the Lockean one that lack of systematic understanding is not lack of understanding per se. This Lockean view is associated with Newton in the letter comparing Descartes and Newton, and those looking at the Newtonian accounts of attraction and optics. In the former, Descartes is considered as someone who cleared the path for Newton by removing the scholastic rubbish that had lain in the way of natural philosophy, but it is Newton who has actually made all the advances, not Descartes. In the letter on attraction, Voltaire summarizes the Newtonian criticisms of Cartesian vortex theory: notably, the earth would lose its motion in a vortex, for example, and the orbits produced by such vortical motions do not accord with Kepler’s laws. He concludes with Newton’s establishment of the oblate shape of the earth, against the Cartesian view that it is prolate. Attraction is defended against the notion of impulsion, allowing Voltaire to explore the idea of the limits of knowledge in a natural-philosophical context. Vortices and the impulsion they would create were postulated by an all-inclusive systematic natural philosophy as something well understood. But rather than ﬁlling in gaps in our knowledge and making it complete, by contrast with Newtonian attraction whose nature Newton admits he does not understand, the reverse is actually the case: ‘Vortices may be call’d an occult quality because their existence was never prov’d: Attraction on the contrary is a real thing, because its effects are demonstrated, and the propositions of it are calculated.’26 But of course Voltaire’s target is greater than natural philosophy. The technical credentials of Newtonianism are blended in with, and indeed seem an integral part of, more general social, religious, and political questions. This is evident in the discussion of Newton and Clarke. Voltaire praises them as great thinkers while at the same time drawing attention to their Arianism, and comparing English freedom of thought (actually a somewhat problematic comparison in the case of Arianism) favourably with the situation in France. This kind of connection between politics, religion, and natural philosophy is not wholly unprecedented. As we have seen, the views of Leibniz and Locke on 25 Ibid., 221. In fact, Pascal’s Pense´es had been largely forgotten in French culture, even by religious writers such as Bossuet, and Voltaire helped revive an interest in him: see J. S. Spink, French Free-Thought from Gassendi to Voltaire (London, 1960), 312. More generally, on the image of Pascal in the Enlightenment, see Mara Vamos, ‘Pascal’s Pense´es and the Enlightenment’, Studies on Voltaire and the Eighteenth Century 97 (1972), 17–145; and John Barker, Strange Contraries: Pascal in England During the Age of Reason (Montreal, 1975). 26 Letters, 113.

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the questions of a single foundation for natural philosophy were reﬂected in their understandings of politico-theology. Leibniz believed that there was ultimately a single metaphysical doctrine in which to ground all of natural philosophy, and a single metaphysical understanding in which to ground and resolve all theological disputes. There was a single, coherent set of truths from which each derived. The Lockean view, by contrast, was that there was no reason to assume such grounding in either case, and that there was reason to believe that such an assumption was actually harmful to progress. In the case of natural philosophy, as the experimental natural philosophy tradition showed, what resulted from assumptions of this kind was an unwarranted cutting-off of possibilities, possibilities which in fact turned out to be very productive, opening up new areas of enquiry and reforming our understanding of key phenomena. In the case of politico-theology, there was, in the wake of the Thirty Years War, a general awareness of the dangers of proceeding on the assumption that there was a right doctrine, so that even Leibniz recommended a form of eclectic reconciliation in practice. But there was still a bifurcation into those, such as Leibniz, who could not accept that there was no ultimate fact of the matter, to be revealed in Leibniz’s case by the appropriate metaphysics, and those, such as Locke, who construed the issue in terms of toleration, where the question of the objective truth of a doctrine is not what was at issue, at least beyond certain minimal and generally accepted basic tenets of Christianity. In other words, there is a fundamental divide between uniﬁcatory and pluralist conceptions. In the former, at least in its Leibnizian version, what is at stake is much the same in the case of natural philosophy and that of politico-theology: there is a single underlying realm of truth, to be explored by the conceptual and a priori methods of metaphysics. In the latter, there is a difference between the pluralism appropriate to the politico-theological case and that appropriate to the natural-philosophical one. For Locke, once the basic tenets of Christianity had been ﬁxed, there was no way that we could deﬁnitively decide between various competing theological claims that fell outside these tenets, and they could no longer provide a basis for political organization (for example by providing a moral basis for a political system), or be dictated by such a political organization. Locke himself nevertheless continued to believe that there was a cognitive dimension to religious belief, and his own ‘reasonable Christianity’ was an attempt to develop a form of religious belief grounded in reason. Moreover, because he believed that the pursuit of religious truth could not be delegated to the state, or some other authority, once we have left the state of nature, he rejected forms of religious belief dictated by conciliar and papal dogma, which meant that Catholics were excluded (along with atheists) from toleration. But this is not the reading Voltaire puts on the Lockean doctrine.27 Voltaire is 27 Voltaire was not alone in this conﬂation of what Locke was advocating with absolute liberty: such a conﬂation would seem to have been there from the beginning. For example, in the section ‘To the Reader’ that prefaces A Letter concerning Toleration, which was originally composed by

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actually closer to Bayle (and to Thomasius in Germany), who effectively removes religious belief from the cognitive realm. This puts Voltaire’s reading of Locke at odds with the tradition of physico-theology, for example, for it was a premiss of physico-theology that any reconciliation would be on cognitive grounds. But if theology has no cognitive standing in its own right, then there could be no ‘reconciliation’ of theology and natural philosophy of this kind. What is distinctive in Voltaire is the combination of what in his hands becomes a radical doctrine, namely a version of Lockeanism which, by contrast with Locke’s own account, has now become incompatible with the very idea of physico-theology, and a doctrine that, at least in its origins, is a conservative one, namely the idea that there should be a guardian of cognitive standards. Freedom of opinion—of a wholly general Baylean kind, no longer with the restrictions that Locke had advocated—effectively acts as a premiss of the whole argument, not just in a politico-theological context, but in an epistemological and metaphysical context as well. In this way, Voltaire ties his radicalized Lockeanism into the ideology of the Acade´mie, at once both elitist, in that academicians are the only competent judges on a range of matters, and democratic, in that, among academicians, there is complete openness and no distinction of rank. The ‘vindication’ of Newtonianism acted in its turn as a vindication of Lockeanism for Voltaire, in that the latter provided the conditions of possibility of the kind of culture in which Newtonianism could thrive. On the question of cognitive standards, the Acade´mie des Sciences had set itself up (on behalf of the monarch) as a guardian of these in the case of natural philosophy. On Voltaire’s reading it had failed in this regard, and even though it was an academician, Maupertuis, who had brought this failure to light, the Acade´mie’s claims to uniqueness as guardian of cognitive standards in natural philosophy began to look somewhat questionable. Note that it was not Voltaire who took these issues outside the Acade´mie: in effect Fontenelle had done this right from the start, in his placing of natural-philosophical questions within the Republic of Letters, as a way of generating public support for natural philosophy as practised in the Acade´mie. But Fontenelle had been selective in what he opened up for public discussion, and he had used the Republic of Letters as a medium in which to display and advertise the achievements of natural philosophy as pursued in the Acade´mie. Voltaire effectively threw everything open to public discussion, however, and in his comparison between England and France maintained not only that the achievements of British natural philosophy far outshone those of France,28 but Locke in Latin, the English translator, William Popple, offers unqualiﬁed support for what he evidently assumes to be Locke’s defence of ‘absolute liberty’. 28 Voltaire makes one exception to the superiority of English over French culture. In Letter XXIV he points out that in Paris being a mathematician or a chemist can mean being paid a small fortune as a member of the Acade´mie, whereas in England one has to pay to join the Royal Society. The difference between the Royal Society and the Acade´mie is perhaps most evident in their publications. The Philosophical Transactions were an unfocused collection of largely amateur

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that the social and cultural conditions under which these natural philosophies were pursued were instrumental in the success of the one over the other.29 He made the issues turn on competing understandings of natural philosophy, where one of the core issues was how we secure rational agreement on cognitive matters. In the process, not only did natural philosophy come to be the bearer of these rational values, in a way that had no precedent in English or in French culture, but the philosopher regained the role of social critic: a role that was there at the origins of philosophy, in Socrates and Plato, but which had been excised from French philosophy and was wholly absent, for example, from Descartes’ conception of the persona of the philosopher. What is even more striking, the regaining of the role of social critic is effected, at least in large part, through natural philosophy, albeit not by natural philosophers claiming this role for themselves but rather by someone from outside claiming this role for natural philosophy. Indeed, what is being advocated is the philosophe, deﬁned in the entry of that name in the Encyclope`die—which was in effect the culmination of the project initiated in the Lettres philosophiques—in these terms: The character we ascribe to the philosophe is as follows. Whereas others are determined to act without feeling, and without knowing—or even dreaming—of the causes that move them, the philosophe by contrast discerns the causes as far as he is able, often even anticipating them and knowingly giving himself up to them: he is, as it were, a watch that winds itself up on its own. In this way he avoids sensations which neither agree with one another nor are appropriate for a rational being, seeking instead those which excite in him affections suitable to the state in which he ﬁnds himself. Reason is for the philosophe what grace is for the Christian. Grace determines the actions of the Christian, reason that of the philosophe. Whereas other men are moved by their passions, without their actions being preceded by reﬂection, and walk in the shadows, the philosophe acts not on his passions but on reﬂection. He travels by night, but with a ﬂame in front of him. The philosophe bases his principles on innumerable particular observations. Whereas other people adopt a principle without thinking of the observations that produce it, believing that the maxim exists by itself as it were, the philosophe takes the maxim back to its source, examining its origins; he knows its proper value, and uses it only as he sees ﬁt. For the philosophe, truth is not a mistress who corrupts his imagination and which he takes to be present everywhere: he is prepared to uncover it where he can perceive it. He does not confuse probability and

contributions, many from the landed gentry, and there does not seem to have been any signiﬁcant level of editorial oversight. The Histoires et Me´moires by contrast contained only communications from natural philosophers and mathematicians, the annual volumes being prefaced by an analysis of the most important work produced during that year. But central control had its drawbacks. When the workload of the permanent secretary of the Acade´mie proved too onorous, as it did under Grandjean de Fouchy from 1743 onwards, publication of the Histoires et Me´moires came to be subject to very long delays, much to the anger of the Academicians. 29 This view won widespread acceptance, not least in Britain. Compare Hume: ‘however other nations may rival us in poetry, and excel us in some other agreeable arts, the improvements in reason and philosophy can only be owing to a land of tolerations and liberty.’ A Treatise of Human Nature, ed. L A. Selby-Bigge (Oxford, 1898), xxi.

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truth: he takes to be true what actually is true, and to be false what is false, as doubtful what is doubtful, and as probable what is only probable. Moreover—and this is his real strength—when the philosophe lacks a basis on which to come to a judgement on something, he remains undecided.30

T H E ENCYCLOPE´ D I E The culmination of the efforts of Fontenelle and Voltaire to link natural philosophy with the Republic of Letters came with the publication of the Encyclope´die, the ﬁrst volume of which appeared in 1751, its frontispiece showing a coy truth (radiating rays of light) having her veils removed by assembled philosophes (Fig. 7.1). Its task was nothing less than a whole reform of the Republic of Letters.31 The two most distinctive features of the Encyclope´die are its alphabetical arrangement of topics and its coverage. It proceeds alphabetically rather than thematically, by contrast with Renaissance encyclopedias, where the ordering of the material is a sine qua non of the whole project. In both the Aristotelian and (albeit in a rather different way) the Platonist traditions, scientia was construed as a systematic and comprehensive grasp of the phenomena in terms of their underlying principles, and as a consequence the aim of the exercise was demonstration of the phenomena from such principles. The appropriate ordering of material was not a matter of account-keeping but a prerequisite for the explanatory power of the system. The thrust of early eighteenth-century developments in natural philosophy, ﬁrmly reinforced once Lockean considerations entered the picture, was one in which the idea that natural philosophy was a question of building a system was rejected, however, and a presentation of a comprehensive understanding of the world could no longer take the form of something in which everything was generated from ﬁrst principles. In the book-length entry on encyclopedias, Diderot sets out the organizational principles in these terms: There is ﬁrst a general order, which is what distinguishes this dictionary from every other work in which the material is likewise subjected to alphabetical order, this being why it is called an encyclopedia. We will say only one thing about this ordering, considered in relation to the whole of the encyclopedic material, which is that an architect of the most fertile genius could not introduce as much variety into the construction of a large ediﬁce, into the decoration of its fac¸ades, the combination of its orders, in short into all its parts, as the encyclopedic order allows. It might be created either by relating our different kinds of knowledge to the various faculties of the soul (this is the system we have used), or by relating them to the entities they take as their object; and this object may be one of pure curiosity, or a luxury, or a necessity. Science in general may be divided into science of things and of signs, or into concrete or abstract sciences. The two most general causes, art

30 31

Diderot et al., Encyclope´die, xxv. 667–9. The author of this article is Diderot. Cf. Dena Goodman, The Republic of Letters (New York, 1994), 27–8.

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and nature, also yield an elegant and broad distribution. Others will be found in the distinction between the physical and the moral, the actual and the possible, the material and the spiritual, the real and the intelligible. Does not all we know derive from the use of our senses and our reason? Is it not either natural or revealed? Is it not either words, or things, or facts? It is therefore impossible to banish arbitrariness from this broad primary distribution. The universe offers us only individual beings, inﬁnite in number, and virtually lacking any ﬁxed and deﬁnitive division; there is none which one can call either the ﬁrst or the last; everything is connected and progresses by imperceptible shadings; and if throughout this uniform immensity of objects, some appear, which like the tips of rocks seem to break through the surface and rise above it, they owe this prerogative only to particular systems, vague conventions, certain unrelated events, and not to the physical arrangement of beings and to nature’s intention.32

He continues: In general, the description of a machine can begin with any of its parts whatsoever. The larger and more complex the machine, the more connections there are between its parts, the less we know these connections, and the greater the number of different perspectives for description there will be. What then if the machine is in every sense inﬁnite; if we are speaking of the real universe and the intelligible universe, or a work which is like the imprint of both? Both the real and the intelligible universe have inﬁnite points of view from which they can be represented, and the possible systems of human knowledge are as numerous as those points of view.33

A signiﬁcant advantage of alphabetical listing, then, is that it does not ﬁx subject matter in a systematic way: it is relative to the present state of knowledge, allowing new additions as this progresses.34 Diderot still ﬁnds it necessary to present a general schematic representation of the structure of knowledge at the beginning of the Encyclope´die (Fig. 7.2), a representation heavily indebted to Bacon, but the crucial point is that it does not guide its organization. The second distinctive feature of the Encyclope´die is its coverage. There were three kinds of alphabetical dictionary by the beginning of the eighteenth century: language dictionaries, biographical and historical dictionaries or encyclopedias, and dictionaries or encyclopedias of the arts and sciences. To understand what the editors of the Encyclope´die conceived its task to be, we need to consider the development of each of these genres brieﬂy. One of the most important works in the ﬁrst category was Furetie`re’s Dictionnaire Universel, published in 1690, two years after the author’s death, with a preface by Bayle.35 What was especially signiﬁcant about the Furetie`re

32

Encyclope´die, xii. 381. Ibid., xii. 381–2. 34 More generally, see Hugh M. Davidson, ‘The Problem of Scientiﬁc Order versus Alphabetic Order in the Encyclope´die’, American Society for Eighteenth Century Studies 2 (1972), 33–49. 35 Antoine Furetie`re, Dictionnaire Universel, contenant generalment tous les Mots Francais . . . et les termes de toutes les Sciences et des Arts (3 vols., Rotterdam, 1690). 33

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Fig 7.2

Dictionnaire was the fact that it was produced outside the ofﬁcial Acade´mie structure and as a result was located very much within the broader Republic of Letters. Its signiﬁcance is indicated by the fact that it formed the (unacknowledged) basis, cleansed of perceived Protestant bias and invested with a Catholic

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one, for the Dictionnaire produced by Tre´voux Jesuits in 1704.36 The Acade´mie Franc¸aise also had its own plans for a dictionary of the French language, and on learning of Furetie`re’s plans—which went beyond the standard listing of equivalent words, and included descriptions, theories, and principles drawn from various arts and sciences—it expelled him from its membership.37 Bayle defends Furetie`re’s project in his preface to the work, and two years later, in his ‘Projet d’un Dictionaire critique’, he had come to the conclusion that the most useful form of dictionary on this scale, something that would be ‘an insurance exchange for the Republic of Letters’,38 was one in which, in the course of scholarly and succinct abridgements of great works, errors could be highlighted and identiﬁed to help the reader through otherwise intractable scholarly polemics. This paved the way for the key work in the second category, Bayle’s own Dictionnaire, which appeared in 1697. It began very much as an attempt to correct the errors in the standard biographical and historical dictionary, the popular and inﬂuential Grand Dictionnaire Historique of Louis Mo´reri,39 which appeared in 1674 and in an expanded second edition in 1681. Bayle realized that not all scholarly disputes were simply matters of truth and falsity, but by focusing on questions of evidence he was to champion a radical form of independent rational enquiry into everything that fell within the domain of the Republic of Letters—as he himself had shaped it over a decade earlier in his Nouvelles de la Re´publique des Lettres—including natural philosophy and religion. Voltaire, in particular, had devoted many hours to poring over the Dictionnaire, annotating and reacting to the articles, and there can be little doubt that its inﬂuence on him was formative.40 In one respect Furetie`re’s Dictionnaire was a pioneer in the third category, since it included arts and sciences, but works in the third category proper— which will be that of the Encyclope´die—excluded biographical and historical entries except as a purely incidental part of an entry: they were concerned, as the entry on encyclopedias in the Encyclope´die makes clear, to set out the present state of knowledge.41 Here there are two predecessors of the Encyclope´die: John Harris’ Lexicon Technicum (London, 1704), and Ephraim Chambers’ Cyclopaedia: or, an

36 Dictionnaire Universel franc¸ais et latin Contenant la signiﬁcation et la de´ﬁnition tant des Mots de l’une et l’autre Langue, avec leurs diffe´rents usages . . . ; la description de toutes les choses . . . ; l’explication de tout ce que renferment les Sciences et les Arts. . . . Avec des remarques d’e´rudition et de critique (3 vols., Tre´voux, 1704). See Jean Macary, ‘Les dictionnaires universels de Furetie`re et de Tre´voux, et l’esprit encyclope´dique moderne avant l’Encyclope´die’, Diderot Studies 16 (1973), 145–58. 37 See Richard Yeo, Encyclopedic Visions: Scientiﬁc Dictionaries and Enlightenment Culture (Cambridge, 2001), 45. 38 Pierre Bayle, Projet et fragmens d’un Dictionaire critique (Rotterdam, 1692), sig. [*8] recto. 39 Louis Mo´reri, Grand Dictionnaire Historique, ou me´lange curieux de l’histoire sacre´ et profane (Lyon, 1674). 40 See Haydn T. Mason, Pierre Bayle and Voltaire (Oxford, 1963). 41 See the discussion in Yeo, Encyclopedic Visions, 12–22.

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Universal Dictionary of Arts and Sciences (2 vols., London, 1728). Harris’ Lexicon makes clear in its subtitle that it contains ‘not only the terms of the arts, but the arts themselves’. In other words, it was not simply a question of deﬁnitions of terms, but of using these deﬁnitions as a route to the subject matter of the discipline, which could be set out as expansively under an alphabetical arrangement as it could under a thematic one. Harris, a Low-Church clergyman, was one of the most active exponents of Newtonianism in England, a public lecturer on and apologist for Newtonianism, with an eye to practical problems, especially navigation.42 Chambers’ Cyclopedia, inspired by Harris’ Lexicon and designed to provide something even more comprehensive, was similarly a work within the tradition of Newtonian apologetics (Fig. 7.3, the frontispiece, depicts knowledge outside the academy). Chambers believed that the chief objections to the Newtonian system turned on misunderstandings of the term ‘attraction’, despite what he considered to be Newton’s clear and unambiguous account of it.43 Chambers’ solution lay in the explicit and wholesale advocacy of a Lockean theory of language, and the long entry on ‘knowledge’ sets out this Lockean account in some detail. Diderot, who between 1741 and 1745 translated Temple Stanyan’s Grecian History, Shaftesbury’s An Inquiry Concerning Virtue and Merit, and Robert James’ comprehensive English medical dictionary, was employed in 1745 to assist with a French translation and modest expansion of the Cyclopedia. This project experienced some signiﬁcant teething problems however, and in 1747 Diderot and d’Alembert were appointed to edit the work, with d’Alembert—who had less commitment to the project44 but higher standing because of his recent publications on dynamics and on wind pressure, and his membership of the Acade´mie des Sciences—taking responsibility for mathematics and astronomy. Diderot was soon envisaging something far more ambitious than a modest expansion of the Cyclopedia, to the extent that the revised project required a new licence, which was granted in April 1748. In 1749 Diderot was incarcerated at Vincennes for publishing works, including his Lettre sur les aveugles, which had just appeared, without licence. It quickly became evident that he was the driving force behind the project, for without him things effectively came to a halt. On his release, he continued working frantically on a huge number of entries on the arts and trades.45 Because d’Alembert was a member of the 42 On Harris, see Larry Stewart, The Rise of Public Science: Rhetoric, Technology, and Natural Philosophy in Newtonian Britain, 1660–1750 (Cambridge, 1992), 108–19. 43 Cyclopaedia, i. xvii. 44 As early as 1749, he told the Wolfﬁan apologist Formey (whose papers had formed the basis for the Encyclope`die entry on ‘athe´ism’) that he ‘had no intention of condemning himself to ten years of boredom editing seven or eight volumes’: see Johann Heinrich Samuel Formey, Souvenirs d’un citoyen (2 vols., Berlin, 1789), ii. 366. 45 In the 1750 ‘Prospectus’ for the Encyclope`die, Diderot takes great pride in pointing out to potential subscribers that he has ‘taken the trouble to go into the workshops [of the workmen], questioning them, taking down what they dictated, developing their thoughts, eliciting from them the terms of their profession, compiling tables of such terms, deﬁning them, and conversing with those persons from whom we obtained memoranda.’

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Fig 7.3

Acade´mie des Sciences, the Berlin Acade´mie Royale des Sciences, and the Royal Society, he was better placed than Diderot, who was elected an honorary member of the Berlin Academy only in 1751 (and then only at the urging of d’Argent and Voltaire who wanted to strengthen Diderot’s hand in defending the Encyclope´die46), to engage the various experts—around 160 of them—needed to write for the project, although both d’Alembert and Diderot were engaged on this from the beginning, coopting Voltaire (after some initial hesitation on his part),47 Turgot, and Rousseau among others, but failing to attract Condillac48 and Montesquieu (except for a minor entry on taste) for example. It was Diderot, however, who did the bulk of the 46

See Israel, Enlightenment Contested, 854. Diderot was politically astute enough to realize that Voltaire could be a loose cannon, and, much to the latter’s annoyance, allocated him uncontentious subjects such as ‘elegance’, ‘esprit’, ‘fantasie’, and ‘galant’. Voltaire also completed Montesquieu’s article on taste (subsequently added to by d’Alembert). 48 The Encyclope´die entries on ‘divination’ and ‘syste`mes’ were taken verbatim from Condillac’s Traite´ des syste`mes, but they are unsigned, and I have been unable to determine whether Condillac approved their use. 47

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work over the twenty-one-year period that it took to complete the seventeen volumes of text and eleven volumes of plates of the Encyclope´die.49 The sheer size of the Encyclope´die gave it a structure that was in some ways unwieldy. This could occasionally lead to errors and carelessness, as Diderot was well aware. Comparing his venture with Chambers’ Cyclopedia, he asks: Why is the encyclopedic order so perfect and regular in the English author? Because he limited himself to compilation from dictionaries and from the analysis of a small number of works, inventing nothing, and sticking strictly to what was known, everything being equally interesting or indifferent to him, since he had neither a preference for any topic, nor favourable or unfavourable time for work, save that of a migraine or spleen, he was a labourer who plowed his furrow, shallow, but even and straight. Such is not the case with our work: we have our pride; we want our set-pieces. Such is perhaps my vanity at this moment. One person’s example attracts another. The editors object, but in vain. Their own mistakes are held up to them, and everything inclines to excess. Chambers’ articles are fairly regularly distributed; but they are empty. Ours are full, but irregular. If Chambers had ﬁlled his up, I have no doubt his organization would have suffered.50

Moreover, the unwieldiness was in keeping with the eclecticism that lay behind the project, and its very unwieldiness allowed it to express radical views which could be buried in a mass of detail. On the question of eclecticism, the long entry on eclecticism—probably drafted by d’Alembert—sets out a strong defence of an eclectic approach, associating this closely with the moral integrity of the eclectic, that is, in a contemporary context, the philosophe: The eclectic is a philosopher who, riding roughshod over prejudice, tradition, antiquity, universal consent, authority, in a word, everything that subjugates the mass of minds, dares to think for himself, goes back to the most clear and general principles, examines them, discusses them, allowing only that which can be demonstrated from his experience and his reason; and having analyzed all philosophical systems without any deference or partiality, he constructs a personal and domestic one that belongs to him. I say a personal and domestic philosophy because the ambition of the eclectic is not so much to be the instructor of the human race as its disciple; not so much to reform others as to reform himself; to know the truth rather than to teach the truth. He is not a man who plants and sows; he is a man who reaps and sifts. He would quietly enjoy the harvest he has reaped, live happily and die uncelebrated, if enthusiasm, vanity, or perhaps a more noble sentiment, did not prevent him from acting in character. The sectarian is a man who embraces the doctrine of a philosopher; the eclectic, by contrast, is a man who recognizes no master.51 49 Diderot did the bulk of the editorial and prooﬁng work throughout, but these duties, especially once the preparation of the volumes of plates began, took up an inceasing amount of his time, so that although he contributed more entries than anyone else in the ﬁrst seven volumes, by vol. viii he was contributing very few entries, and the most proliﬁc contributor by far was now Louis de Jaucourt: see Jean Haechler, L’Encyclope´die de Diderot et de Jaucourt: Essai biographique sur le chevalier Louis de Jaucourt (Paris, 1995). 50 Diderot et al., Encyclope´die, xii. 384 (art. ‘encyclope´die’). 51 Ibid., xi. 670–1. The defence of eclecticism is indebted to the German Protestant tradition of eclecticism particularly as represented in Jacob Brucker’s very inﬂuential Historia critica philosophiae

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The moral—indeed one might say self-righteous—tone here is unmistakable, but the eclecticism of the enterprise, especially in respect of the question of precipitate judgement, also accounts for the otherwise odd inclusion of entries on topics on which there is virtually no information, reﬂecting the Baconianinspired sense—evident in his Sylva Sylvarum—in which it is not for the authors to preclude entries on questions which they ﬁnd uninteresting or bizarre. The entry on the ‘aco’ describes its subject as: ‘a ﬁsh mentioned in Aldrovandi, which he states is common in Egypt, Lombardy, Lake Como, and is very nourishing. Now ﬁnd out what an aco is.’52 An Amphiphon is ‘a cake made in honour of Diana, which was surrounded by small ﬂames. This is all we know.’53 In this case, however, the author (without doubt Diderot himself) follows up the comment with a complaint on how compilers of dictionaries have not provided enough information in the past. The entry on ‘aguaxima’ is hilarious on the uselessness of the information to be found in traditional dictionaries. There is an element of parody here, but in other entries the parody is far more subtle. The theological entries are particularly interesting in this respect. They were compiled largely by the Abbe´ Edme-Franc¸ois Mallet, Royal Professor of Theology at Navarre, and seemingly the epitome of orthodoxy, if somewhat long-winded and inclined to go into immense detail on the most minor points. Yet perhaps not all is as it seems in the case of Mallet. His sheer thoroughness has the effect of naturalizing and contextualizing his subjects, embedding the sacred in such a thoroughly mundane context that differences between the sacred and the profane tend to become levelled. In the entry on hell,54 for example, the detailed discussion of views on its location—Australia, the suburbs of Rome, the sun, a comet, etc.—is at best odd and at worst suggests that he is not taking the theological questions too seriously. In the entry on the gospels, the thirtynine apocryphal gospels that he identiﬁes are given four times as much discussion as the four authentic ones, and their contents described in varying detail.55 The entry on Noah’s ark56 is especially odd, and it is difﬁcult to know what to make of its pages of detail on the disputes over exact speciﬁcations of size, type of wood used, the insufﬁciency of the dimensions given in the Bible to accommodate the animals, the units of measurement, the number of species on board, the amount of fodder needed, the amount of fresh water required as ballast, and so on. In the context of late seventeenth-century British physico-theological disputes over the universality of the deluge, where it was assumed that there was a convergence (5 vols., Leipzig, 1742–4): see Gregorio Piaia, ‘Jacob Bruckers Wirkungsgeschichte in Frankreich und Italien’, in Wilhelm Schmidt-Biggemann and Theo Stammen, eds., Jacob Brucker (1696– 1700): Philosoph und Historiker der europa¨ischen Aufkla¨rung (Berlin, 1998), 218–37. 52 Encyclope´die, i. 432. 53 Ibid., ii. 426. 54 ‘Enfer’, Encyclope´die, xii. 441–53. 55 ´ ‘Evangile’, ibid., xiii. 351–60. 56 ‘Arche de Noe´’, ibid., iii. 228–35.

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between natural history and Christian theology, such calculations were appropriate, and had occupied the time of Wilkins and others. But no one in Catholic Paris of the 1750s was working on such assumptions,57 and the article removes the account of Noah’s ark from a religious context and treats it in a wholly naturalized way as a problem in the logistics of ship-building.58 In effect, it refuses to deal with any question that cannot be posed in broad natural-philosophical terms. In the context of physico-theology, this would not have been an anti-religious move, but in the French context, where there is a separation between religious and naturalphilosophical argument on such issues, it could easily have been taken as such. Indeed, the strategy, if that is what it was, is at least as damaging as anti-religious polemics and far more difﬁcult to counter—for example, by censorship.59 Attempts at censorship and suppression plagued the Encyclope´die from the beginning, but a number of factors militated against the latter, not least economic ones.60 Censorship, however, did in fact get the better of the Encyclope´die in some respects in the end. D’Alembert, encouraged by Voltaire, had composed a long entry on ‘Gene`ve’ for volume vii, published in November 1757. Although it 57 Physico-theology was represented in France—for all intents and purposes single-handedly— in Noe¨l-Antoine Pluche, Le spectacle de la Nature (8 vols., Paris, 1732–51), the early volumes of which achieved signiﬁcant popularity, but it never gave rise to a movement remotely on a par with that in England. By mid-century, it was the most popular natural history book in France in terms of ownership in private libraries, yet it had no signiﬁcant impact in natural history debates, and was effectively marginalized. The Jesuits, for example, condemned Pluche’s anti-intellectualism and his hostility to curiosity about the natural world—Journal de Tre´voux (March 1733), 416—and Voltaire ridiculed his theories in Candide (e.g. the passage on stockings in ch. 1). In his Enlightenment Contested, Jonathan Israel counts Re´aumur as a supporter of physico-theology, but he points out that Re´aumur, unlike Pluche, ‘insisted on adhering strictly to natural evidence, discarding the biblical Flood as an authoritative explanation’ (743). In other words, Re´aumur is not a physico-theologian in the sense in which I am using the term, that is, someone who attempts to make theology and natural philosophy converge on shared truths, but rather just someone who thinks that religion and natural philosophy should be compatible, which includes almost everyone in the period we are concerned with, Catholic and Protestant alike. 58 Philipp Blom—Encyclope´die: The Triumph of Reason in an Unreasonable Age (London, 2004), 114—points out that Mallet shared accommodation with Abbe´ Claude Yvon, another contributor to the Encyclope´die, and Abbe´ Martin des Prades, whose highly naturalistic Lockean-inspired dissertation submitted to the Sorbonne Theology Faculty in 1752 caused a scandal which brieﬂy put the future of the Encyclope´die itself in jeopardy. The company he kept in itself suggests there may be more than meets the eye to Mallet. 59 Nevertheless, it should be noted that censorship was nowhere near ﬁne-tuned enough for the task, and ploys such as cross-referencing, whereby the entry on cannabilism refers the reader to ‘eucharist’ for example, and that on freedom of thought refers to ‘Intolerance and Jesus Christ’, not only got past the censor, but Diderot made no secret of the procedure and its aims. See Blom, Encyclope´die, 154–6. 60 Subscriptions had built up quite rapidly from the publication of the ﬁrst volume, numbering over 4,000 by 1752, and Lamoignon de Malesherbes, who in his capacity as ‘directeur de la librairie’ had ultimate responsibility for the Encyclope´die at a state level, feared the economic consequences of supression: see his Me´moire sur la librairie et sur la liberte´ de la presse (Paris, 1814), 60. The Encyclope´die was one of the best-selling books of the second half of the eighteenth century in France: see Daniel Mornet, ‘Les Enseignements des bibliothe`ques prive´es, 1750–1780’, Revue d’histoire litte´raire de la France 17 (1910), 449–96.

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was intended to draw a favourable comparison between what d’Alembert saw as the liberalism of Calvinist Geneva and the dogmatism of France, his enthusiasm got the better of him (or, perhaps, Voltaire’s enthusiasm got the better of him since Voltaire seems to have been behind the article), and he ends up ascribing a form of Socinianism and deism to the Genevians, which caused great offence. This was one of very few non-mathematical/natural-philosophical entries he contributed, and, despite Diderot’s efforts to smooth things over, the self-righteous unapologetic response of d’Alembert had jeopardized the future of the enterprise. The Encyclope´die’s ‘privilege’ was revoked on 8 March 1759, and only the volumes of plates were allowed to proceed, although the remaining text volumes were compiled, with Diderot devoting the bulk of his time to the volumes of plates, and contributing very few entries to the remaining ten volumes of text. When these text volumes were ﬁnally allowed to be published— they appeared together at the end of 1764—it turned out that they had been extensively censored by the publisher, Le Breton, who, wanting to protect his investment, not only secretly removed material offensive to the Church and the State, but also announced that he had burnt the originals.61 But in fact the ﬁrst seven volumes had already done their work in establishing the Encyclope´die, and in any case Le Breton missed a good deal in expurgating the later volumes, so that its reputation was secure. This reputation actually rested largely on a few selected entries, and particularly on ‘Discours pre´liminaire des e´diteurs’, drafted largely by d’Alembert.62 The impact of Locke on the project is very explicit here in the opening statement on the basis of knowledge: There is nothing more certain than the Existence of our Sensations; and to prove that they are the foundation of all our Knowledge, we need only shew that they may possibly be so: for in sound Philosophy, Deductions, founded on Facts and acknowledg’d Truths, are preferable to what rests only upon Hypotheses, though ever so ingenious. Why then should we imagine that Man has pure intellectual Ideas born with him, when he need only reﬂect upon his own Sensations in order to form them? The following Particulars will shew, in fact, that our Intellectual Ideas have no other origin than Reﬂection.63

61 It turns out that Le Breton did keep a copy of at least some, and possibly all, of the excised material, however, for this was found pasted in an additional volume of blank pages in a copy of the set sold at auction in Berlin in 1933. The set had belonged to a member of the Tsar’s general staff, although its earlier provenance is uncertain. See Douglas H. Gordon and N. L. Torrey, The Censoring of Diderot’s Encyclope´die and the Reestablished Text (New York, 1947). Modern English translations now routinely include the excised passages. 62 As regards the work of drafting, d’Alembert was responsible for roughly the ﬁrst two-thirds of the ‘Discours’ (Encyclope´die, i. v–liii), and Diderot for the rest (Encyclope´die, i. liii–lxxiv), which is a reworking of the original prospectus. Both authors took responsibility for the ﬁnal version. 63 Diderot and d’Alembert, Encyclope´die, i. vi. I have used the English translation that appeared within a year of the French version: The Plan of the French Encyclopædia, or Universal Dictionary of Arts, Sciences, Trades and Manufactures. Being an Account of the Origin, Design, Conduct, and Execution of that Work (London, 1752), 4.

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Indeed it turns out to be Locke who provides the general rationale for Newtonian natural philosophy: Metaphysics were not entirely neglected by Newton. He was too great a philosopher not to be sensible that this science is the Foundation of all our Knowledge; and that it is hence alone that we must derive precise and accurate Notions of Things. . . .What Newton would not attempt, and perhaps could not have executed, Locke undertook, and successfully performed. He may be said to have invented Metaphysics, as Newton invented Physics. He judged that Abstractions, and ridiculous Questions controverted before his Time, and mistaken for the Substance of Philosophy, were the Principal Part to be rejected. He examined into these Abstractions, and the Abuse of Words, and found them the Primary Causes of our Errors.64

The theme is pursued in a number of entries, not least that on ‘colle`ge’, drafted by d’Alembert, which offered a scathing criticism of Jesuit teaching (without mentioning the Jesuits by name). Here we are told that, in the teaching of philosophy, ‘logic should be conﬁned to a few lines, metaphysics to a summary of Locke, purely philosophical ethics to the works of Seneca and Epitectus, Christian morals to the sermon on the mount, and physics to experiments and geometry, which, of all the physics and logics, is the best.’65 The Encyclope´die was always an explicitly eclectic enterprise, as we have seen, and, despite various attempts at presenting a uniﬁed face, Diderot and d’Alembert had rather different conceptions of what natural philosophy should comprise and what its role should be. I shall turn to some of these differences in Chapter 11, but because of its special standing I want to concentrate for the moment on the ‘Discours’, which was an attempt to establish a general programme that encapsulated the aims of both d’Alembert and Diderot, even though it was drafted by d’Alembert and in some respects reﬂects views of which Diderot was critical. Voltaire considered the ‘Discours’ superior to Descartes’ Discours de la me´thode and on a par with the works of Bacon,66 and its standing as a statement of what might be termed a Voltairean strand of Enlightenment thought was unequalled, even in Voltaire’s own writings. D’Alembert’s general proposal for the reform of knowledge, as set out in the ‘Discours’, begins by defending the sensationalist basis of all knowledge, and this is effected by substituting a Lockean for a Cartesian epistemology. In fact, Locke’s epistemology did not and could never have stood in a one-to-one relation with that set out in Descartes’ Meditationes, for example, yet this is exactly how it is presented. D’Alembert takes the shell of the systematic metaphysics of the Meditationes and provides it with a sensationalist content, thereby producing a hybrid which, while it might 64 Plan, 89–90; Encyclope´die, i. xlv. The praise of Locke was singled out for attack by a number of critics of the project: see e.g. the review in the Journal des sc¸avants (October 1751), 197–233. 65 Encyclope´die, vii. 499. 66 See Grimsley, Jean D’Alembert, 19.

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be attractive at the programmatic level, could not possibly stand up to philosophical scrutiny. ‘The ﬁrst thing taught us by our Sensations’, he tells us, ‘is our own Existence, which cannot be distinguished from them.’67 Locke never made any such claim, or attempted to provide an alternative starting point for an essentially Cartesian project, for which the obvious question would be what we could say about the bearer of these sensations independently of the sensations themselves. But d’Alembert brusquely dismisses such concerns, maintaining that ‘that thinking Principle which constitutes our Nature’ is just the same thing as ourselves. The ‘ourselves’ in question is not our bodies, which are part of the realm of external objects, for our bodies ‘are, in a certain Sense, external to us, even before we distinguish the separate Nature of the thinking Principle within us’.68 This looks contradictory, in that, even though our sensations, which require corporeal organs and hence bodies, are indistinguishable from ‘our own existence’, i.e. ourselves, these differ from the ‘thinking principle’ within us. But indistinguishability does not mean identity: We need not examine far into the Nature of our own Bodies, and the Ideas we have of them, to discover that they are not [the Principle that wills and conceives]; because the Properties found in Bodies have nothing in common with the Faculty of Willing and Thinking; consequently the Beings, call’d Us, consist of two Principles, different in their Nature; but so united, that the Motions of the one have a certain Correspondence with the Affections of the other, which we have no Power either to suspend or Alter.69

The revamped Cartesian programme is continued with an equally brief account of the basis of sense certainty, in which epistemological worries are dismissed: The Multiplicity of these Sensations, the concurring Agreement of their Evidence, the Degrees we observe them in, the involuntary Affections they excite in us, compar’d with the voluntary Controul we have over our Ideas of Reﬂection, which operate only upon our sensations; all this, we ﬁnd, produces in us an irresistible Impulse to ascertain the real Existence of external Objects; and to regard them as the Cause of our Sensations. Many philosophers have held this Impulse to be the Effect of a Supreme being, and the most convincing Argument of the real Existence of an external World. But as there is no relation, that we know of, betwixt any single Sensation, and the Object thus suppos’d to occasion it, we cannot reason from the one to the other: and nothing but a kind of Instinct, more certain than reasoning itself, could oblige us to draw so remote a Conclusion.70

What has happened here is that a profound and complex epistemological question about sense certainty has been translated into a simple choice between 67 68 69 70

Plan, 5; Encyclope´die, i. vi–vii. Plan, 5; Encyclope´die, i. vii. Plan, 10; Encyclope´die, i. ix. Plan, 5–6; Encyclope´die, i. vii.

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divine guarantee versus what might be termed psychological certainty. One element in Descartes’ elaborate epistemological argument is held up as if it were the issue on which everything else hinged (which it certainly is not for Descartes), so that what is now at stake is a choice between religion and reason: a choice made easier by the fact that whatever epistemological rationale the divine guarantee may have had in the original Cartesian argument, its removal from the context of this argument robs it of any epistemological rationale, so that it now appears as devoid of epistemological function, and hence wholly gratuitous as a means of securing the veridicality of sense perception. D’Alembert does not so much deny that there may be other epistemological questions at stake, as deny that consideration of them could be of any value, suggesting that for fear of ‘obscuring a Truth acknowledg’d even by the Sceptics, when not heated in Dispute, we leave the capable Metaphysicians to discover the transcendental Cause in this Case’.71 Similarly with the question of God’s existence. He does not deny this, saying that it follows from reﬂection:72 it is just that it can play no fundamental role in our cognitive or moral thinking, for the ideas that underlie these derive exclusively from natural sources, notwithstanding that revelation may occasionally ‘serve as a Supplement to Natural Knowledge’.73 The grounding of knowledge in sensation leads to the question of the basic ways in which bodies affect us in sensation, and, as might expected, pleasure and pain are the pivotal sensations, with avoidance of pain turning out to be the basic determinant of behaviour. The move to pain is in effect a move from cognitive to affective states, a crucial ingredient in thinking through such questions in the Encyclope`die, for it allows a reconstruction of human capacities within an explicitly communal context. Starting from sensation means that we are free ‘from that pensive Solitude, in which we should otherwise remain’,74 allowing ‘such natural Reﬂections [which] infallibly arise in every Man left to himself, free from the prejudices of wrong Education or perverted Study’.75 These natural reﬂections reveal to us the path from our ﬁrst sense impressions, which induce our ﬁrst emotions, to the origins of language and society, for one of the ﬁrst things that we discover is that our needs and wants are shared by other human beings, and realizing that there are great advantages in communicating with these others so that we might discover what things in nature may beneﬁt or harm us, we increase our stock of ideas, not by new sensations, but by communication of ideas with others, which we ﬁnd to be a pleasurable activity. It is in this context that our ideas of justice and injustice, and good and evil, arise, so that far from being of religious origin, these are ‘the Voice of Nature, found in all men, and extending 71 72 73 74 75

Plan, 6; Encyclope´die, i. vii Plan, 10–11; Encyclope´die, i. ix. Plan, 23; Encyclope´die, i. xv. Plan, 5; Encyclope´die, i. vii. Plan, 7; Encyclope´die, i. viii.

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even to Savages’, which constitutes the original law of nature, on which all subsequent laws are based.76 Up to this point, we can think of d’Alembert’s task as a defence of ‘reason’ as the sole ultimate criterion of cognitive judgement. The next step, the association of reason with natural philosophy, is then straightforward. There are, he tells us, two ways by which we preserve our bodies from danger and provide them with what they need: by our own discoveries, or by those of others which are communicated to us.77 The ideas generated from these sources can then be combined and connected, providing we bear in mind that the ‘primitive Objects of our Sensations’ are individuals, which we group together under abstract names, and the classiﬁcations which result are necessarily arbitrary, for there are no genuinely natural divisions.78 Nevertheless, there are various kinds of connections that we can make between the phenomena, just as there are various degrees of understanding of these phenomena available, and d’Alembert makes it very clear that it is the deployment of algebraic procedures in the mathematical realm that constitutes the standard to which natural philosophy should aspire. D’Alembert’s commitment to a programme of rational mechanics has a strongly reductionist aspect, offering a model for understanding generally, even though as it stands—that is, before the details of the reductionist programme are spelled out—it is free of speculative hypotheses. There is in fact some degree of ambiguity in just what is being rejected as regards systems, not only in d’Alembert but among those associated with the project of the Encyclope´die, and indeed more generally among those philosophers and others in the early to mideighteenth century who espoused one or another version of Enlightenment. REASON AND THE UNITY OF KNOWLEDGE There was a wide spectrum of thought on the question of the rejection of systems, and at the extremes of the spectrum, at least, there was some degree of clarity. Buffon, for example, leaves his readers in no doubt about the lack of any system in nature and the futility of simply imposing a system on it.79 At the other end of the spectrum was Wolff, who, representing what is essentially a Leibnizian programme, saw systematic understanding as the key to Enlightenment.80 The 76

Plan, 8–9; Encyclope´die, i. viii. Plan, 11; Encyclope´die, i. ix. Plan, 49; Encyclope´die, i. xxvi. 79 As we saw in Ch. 6: we will be returning to these questions in Ch.11. 80 See e.g. Christian Wolff, Elementa matheseos universae . . . Editio Novissima (5 vols., Magderburg, 1733–42). In fact almost any work of Wolff ’s could be consulted, as the overlap between his books is very signiﬁcant. As one commentator has put it, ‘Wolff repeats himself lovingly from book to book. He is one the great self-plagiarizers of history’: Lewis White Beck, Early German Philosophy: Kant and his Predecessors (Bristol, 1996), 262. 77 78

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problem was that there was no single ﬁxed set of issues which Buffon and Wolff would have seen as the key to the problem. They were largely responding to different kinds of questions, and the difﬁculties are compounded as we move to the centre of the spectrum, where we ﬁnd d’Alembert (towards the Wolfﬁan end in certain respects), Diderot (towards the Buffon end, representing the development of the Lockean programme), and Condillac. The ambiguities of Condillac’s position give a good indication of the complexities here. Although he denies that the universe is governed by a single set of basic rules or principles, he makes it clear that knowledge consists in classiﬁcation of ideas into a hierarchy,81 and he uses explicit systematization of other philosophers’ work as a way of analysing and criticizing it, so his criticism of ‘systembuilding’ is not at all straightforward.82 His Essai sur l’origine des connaissances humaines (1746) opens with the statement of what looks like a revival of metaphysics: The science that makes the greatest contribution to illuminating, sharpening, and enlarging the mind, and so is best placed to prepare it for all other studies, is metaphysics. Today it is so neglected in France that this will seem paradoxical to many readers. I do not deny that there was a time when I too judged things in this way, so that, of all philosophers, metaphysicians seemed to me to be the least wise. Their works taught me nothing, for I found only phantoms in them, and I blamed metaphysics for the bewilderment of those who pursued it. I then decided to dispel this illusion and go to the source of so many errors, and those who strayed furthest from the truth came to be of the most use to me. No sooner did I learn the uncertain paths that they followed, than I thought I saw the direction that I should take. It seemed to me that one could reason in metaphysics and morals with as much precision as in geometry; that one could form ideas as exact as those of the geometers, and like them, give precise and constant meanings to expressions; in short, that one could work out, perhaps even better than they have done, a method that would be simple and practicable enough to achieve certainty.83

When one compares the discarded metaphysics with the new metaphysics with which Condillac aspires to replace it, however, it immediately becomes evident that what is being proposed is very different from the earlier attempts of Malebranche, Spinoza, Leibniz, or even Berkeley to offer a new metaphysics. The models for Condillac are Bacon, Newton, and particularly Locke. Condillac had distinguished three kinds of system: those based on abstract metaphysical principles, those based on hypotheses, and those based on observation and 81 See e.g. the discussion in his La Logique, ou les premiers de´veloppmens de l’art de penser: Condillac, Œuvres de Condillac, revues, corrige´es par l’auteur (23 vols., Paris, 1798), xxii. 96–140. Devising the requisite language is paramount here, for as he tells us in La Langue de Calculs, ‘All language is an analytic method, and all analytic method is a language’: ibid., xxiii. 1. 82 See Jeffrey Schwegman, ‘The “System” as a Reading Technology: Pedagogy and Philosophical Criticism in Condillac’s Traite des Systeˆmes’, Journal of the History of Ideas, 71 (2010), 387–409. 83 Essai sur l’origine des connaissances humaines: ouvrage ou` l’on re´duit a` un seul principe tout ce qui concerne l’entendement (2 vols., Amsterdam, 1746): Œuvres, i. 1–2.

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experiment. The crucial plank in his argument against metaphysical principles is the claim that they reverse the true order of discovery, proceeding from ideas (in particular innate ideas) to facts, whereas in reality all our knowledge begins from sensation. The Traite´ des syste`mes (1749), the ﬁrst third of which recapitulates the argument of the Essai, sets out Condillac’s general thesis, which is not that we should reject all systems, but that we should not construct our own systems. Rather, there were systems before system-builders, he tells us, and nature itself is a system. What we must do is not to construct systems but discover the system that is already there in nature. The procedure he recommends for this is what he calls analysis, and just as when we wish to understand the workings of an artefact such as a watch, what we must do is to take it to pieces in order to discover the fundamental working principles, so too in understanding the system of nature we need to break it down into parts and, through observation and experiment, uncover the basic principles underlying its workings, rather than trying to reconstruct nature from general, abstract principles as metaphysicians are wont to do.84 The distinctive feature of traditional metaphysics is the idea that one can explain everything, whereas Condillac advocates a rehabilitated metaphysics which starts from sense perception and is modest because it appreciates the limits of the human mind. Condillac’s two signiﬁcant deviations from Locke are his claim that all our knowledge begins from sensation (by contrast with Locke’s view that it starts from a combination of sensation and reﬂection), and his attempt to render the Lockean approach more systematic. The latter created signiﬁcant uncertainty, by contrast with Wolff ’s position, for example, which treated systematicity as an unqualiﬁed desideratum. The Lockean programme in natural philosophy differed in fundamental respects from the Leibnizian one, to such an extent that they can be seen as polar opposites. Yet d’Alembert’s own contribution to natural philosophy, which we shall be examining in the next chapter, is within a tradition of analytical mechanics which owes a great deal to Leibniz, and despite the attack on systems in the ‘Discours’, and the Lockean terms in which this attack was formulated, we can detect a measure of ambiguity on the question of systematic understanding in d’Alembert.85 Indeed, some level of ambiguity was intrinsic to the project itself. The general aim is described in the ‘Discours’ as having ‘two principal Views, that of an Encyclopædia, and that of a Philosophical Dictionary of Arts, 84 Traite´ des sisteˆmes, ou` l’on de´meˆle les inconve´niens et des avantages (The Hague, 1749), ch. 3: Œuvres, ii. 29–45. Condillac was particularly indebted to ’sGravesande and Chaˆtelet in his reﬂections on method: see Ellen McNiven Hine, A Critical Study of Condillac’s Traite´ des Syste`mes (The Hague, 1979), ch. 5. 85 Note in particular that in praising Condillac’s attack on systems in the ‘Discourse’, d’Alembert explicitly construes this as an attack on hypotheses and conjectures (Plan, 103–4), leaving open the possibility of a system (such as that which he provides in his rational mechanics) which is not hypothetical or conjectural but certain.

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Sciences, and Trades. As an Encyclopedia, it should exhibit, as much as possible, the Order, Succession, and Connection of all the Parts of human Knowledge: as a Philosophical Dictionary, it should contain the general Principles, or Fundamentals, of every Science, and every Art, whether liberal or mechanical.’86 A strong version of the encyclopedia model is advocated later in the ‘Discours’, when we are told, in terms that would not have been alien to Leibniz himself, that ‘the Universe itself, could we reduce it to a single Point of View, would be no more than a single pregnant Fact, or immense Verity.’ Moreover, the context is one in which the apparent diversity of physical phenomena, with their ‘apparently independent Properties’—triboelectricity and animal electricity are the examples given—is due to ‘the Weakness of human Understanding’, and ‘would be but one, if we could discover their primary Cause’.87 The implication is that merely phenomenal understanding can be replaced by an understanding in terms of underlying causes, one which uniﬁes otherwise disparate phenomena. It is just such an assumption that the Lockean programme questions, and one of the staunchest defenders of this aspect of the programme is Diderot. D’Alembert’s approach to questions in physical theory drives him in the opposite direction, but this does not mean that the anti-system statements of the ‘Discours’ are just rhetoric. For one thing, he sees mathematical certainty as being very restricted, and criticizes Johann Bernoulli’s attempt to apply mathematics to human physiology.88 More importantly, if the programme of analytical mechanics that he pursues tends towards the ideal of a unique and comprehensive systematic understanding, his commitment to the notion of the philosophe as someone who adheres to no system is at the same time wholly genuine and uncompromising. There are two relevant contrasting positions here. The ﬁrst is that of Diderot, who was committed both to the legitimacy of phenomenal explanation in its own right, and to a philosophical persona appropriate to such a commitment, namely the philosophe. The second is that of Wolff, who, as the main exponent of Leibnizianism in the eighteenth century, is committed to the view that true understanding derives uniquely from a grasp of fundamental principles, where the philosophical persona appropriate to such a commitment is not the philosophe, but someone who aspires to an independent but systematic grasp, and is better referred to by the German ‘equivalent’ term, Aufkla¨rer. There are many subtle and deep differences between the French and German Enlightenments. One need only think of Kant, Aufkla¨rer par excellence and the model of the Enlightenment philosopher in much historiography of Enlightenment thought which mistakenly sees it as having a single shared focus. As Catherine Wilson points out, Kant ‘created a new form of philosophical commentary that at once reﬂected his interest in and knowledge of political and social reality, and 86 87 88

Plan, 2; Encyclope´die, i. v. Plan, 27; Encyclope´die, i. xvii. D’Alembert, ‘Eloge de Bernoulli’, Œuvres, iii. 358.

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that was at the same time anchored in an aloof critical philosophy that excluded, on formal, philosophical grounds, social critique.’89 The contrast between Kant and philosophes such as Voltaire and Diderot could not be greater. We shall be turning to Diderot in Chapter 11, and we shall see that there is actually a gulf between Diderot and d’Alembert, which raises questions even more fundamental than those of the role of systematic understanding. By contrast, what is striking is the degree of convergence in the views of Wolff and d’Alembert, despite their very different starting points. Leibniz had been apologetic about his inability to provide a general overarching exposition of his philosophy, and this was the challenge that Wolff took up. The context in which it was taken up was one in which three competing notions of Aufkla¨rung were at stake.90 In the juristic civil philosophy of Thomasius, faced with the reality of competing religious confessions, the state and religion had to be kept wholly separate from one another, so that the political realm was not usurped by the religious fratricide of the Thirty Years War, and instead became a deconfessionalized tolerant civil sphere. Developing the Stoic theory of adiophora, whereby it is crucial to moral theory to ﬁrst identify and exclude those things that are indifferent to morality, Thomasius developed his account in terms of those things that are indifferent to salvation, and argued that these occupied the civil, not the religious realm. The Thomasian approach had more general implications, however, because the mixing of religion and civil matters was reﬂected at a theoretical level in Lutheran scholasticism, in its mixing of metaphysics and philosophy, and such mixing was likewise rejected by Thomasius. The second alternative was a form of pietism which centred around the idea of spiritual rebirth, especially as represented in the work of August Herman Francke. Although directed primarily against the same Wolfﬁan target as Thomasius, its aim was the spiritual enlightenment and reform of society, something that went directly against the thrust of Thomasius’ separation of the civil and religious spheres. Finally, there was the Wolfﬁan reform of the university curriculum, beginning with Wolff ’s appointment at the University of Halle in 1706, in which enlightenment was to be found through a purely intellectual exercise in which the ultimate foundations of understanding were sought in a single comprehensive metaphysical theory. 89 Catherine Wilson, ‘The Enlightenment Philosopher as Social Critic’, Intellectual History Review 18 (2008), 413–25: 413; cf. Peter Hanns Reill, The German Enlightenment and the Rise of Historicism (Berkeley, 1975), and John H. Zammito, Kant, Herder, and the Birth of Anthropology (Chicago, 2002). More generally on the German Enlightenment, see Detlef Do¨ring, Fru¨hAufkla¨rung und obrigkeitliche Zensur in Brandenburg: Friedrich Wilhelm Stosch und das Verfahren gegen sein Buch ‘Concordia rationis et ﬁdei’ (Berlin, 1995); Diethelm Klippel, ‘Von der Aufkla¨rung der Herrscher zur Herrschaft der Aufkla¨rung’, Zeitschrift fu¨r historische Forschung 17 (1990), 193–210; and Derek Beales, Enlightenment and Reform in Eighteenth-Century Europe (London, 2005). 90 See Hunter, ‘Multiple Enlightenments’; and Eric Watkins, ‘From Pre-established Harmony to Physical Inﬂux: Leibniz’s Reception in Eighteenth Century Germany’, Perspectives on Science 6 (1998), 136–203.

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All three movements offered reform through ‘enlightenment’, though it was a different form of enlightenment in each case. What Wolff was offering was an understanding of the world in terms of a deeper underlying structure which, by contrast with its Leibnizian precedents, was for all intents and purposes tantamount to a divine understanding. It is of importance to appreciate the context within which the Wolfﬁan project was devised, for the aim of this project was the reconciliation of faith and reason, a reconciliation that Thomasius and pietists denied, albeit on different grounds. To the extent to which Wolfﬁanism can be deﬁned in terms of what it opposed, and in terms of why it itself was opposed, the reconciliation of faith and reason was the key doctrine, and the distinctively Leibnizian way of realizing this aim, namely by means of a foundational metaphysics, was a sine qua non of the project.91 Critics of the Wolfﬁan project found its intellectualist religion at variance with Christianity, especially on such questions as divine freedom and providence, and indeed it was always a feature of the Leibnizian project of grounding Christianity rationally that what it might produce was something that bore little resemblance to traditional understandings of Christianity.92 By contrast, Voltairean rationalism, of the kind that d’Alembert takes up and develops,93 has no truck with foundational metaphysics, and the approach to religion varies between Lockean and Baylean pluralism. 91 The most notorious feature of this foundationalist metaphysics for Wolff ’s contemporaries was the doctrine of pre-established harmony, which laid itself open to mischievious misunderstandings. Euler attributes the dismissal of Wolff from the University of Halle, for example, to his advocacy of this doctrine: ‘There is another objection to be made to the system of pre-established harmony; namely, that it is utterly destructive of human liberty. . . . Of this we had a well-known example in the reign of his late Majesty, when Mr. Wolff taught at Halle the system of pre-established harmony. The King informed himself of this doctrine, which was then making a prodigious noise; and one of his Court having suggested to him that, according to Mr. Wolff ’ s doctrines, soldiers were mere machines, and that when one deserted, it was a necessary consequence of his particular structure, and therefore ought not to subject him to punishment, as would be the case, were a machine an object of punishment, for having performed such and such a motion; the King was so provoked at this representation, that he gave orders to banish Wolff from Halle, with certiﬁcation, that if he was found there at the end of twenty-four hours, he should be hanged up.’ Letters of Euler on Different Subjects in Physics, Addressed to a German Princess (2 vols., London, 1802), i. 321–2 (Letter LXXXIV). 92 In the Lutheran German and Scandanavian states, Wolfﬁanism, where it was taken any notice of at all, generally encountered hostility. The dispute over the Berlin Academy prize for 1747–8 for an essay on monadology (rigged by Euler to make sure that his anti-Wolfﬁan pupil, Johann Justi, won it) indicates a profound hostility to Wolff and his followers: see Clark, ‘The Death of Metaphysics in Enlightened Prussia’, 440–1. And in the case of Scandanavia, Lisbet Koerner notes that in 1732, for example, the president of Uppsala University ‘urged his professors to instruct their students “to thoughtfully read Wolff ’s and Leibnitz’s writings, and guard themselves against any news that may be found in them that could cause damage.” In their response, the professors congratulated themselves that they had no students “that loved such dangerous news”.’ Lisbet Koerner, Linnaeus: Nature and Nation (Cambridge, Mass., 1999), 35. In Catholic France, Wolff was elected an external member of the Acade´mie Franc¸aise in 1733 (the ﬁrst German member since Leibniz), but his doctrines seem to have had no inﬂuence at all. 93 On the importance of Voltaire for d’Alembert, see John N. Pappas, Voltaire and D’Alembert (Bloomington, 1962).

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The systematizing ‘rationalist’ stream in Enlightenment thought found its most distinctive natural-philosophical manifestation in the development of rational mechanics, which was envisaged by its proponents as being not only the most fundamental kind of natural-philosophical enquiry, to which all other forms will ultimately be reduced or assimilated, but also as the paradigm bearer of the clarity and distinctness to which every cognitive enterprise should aspire. The clarity and distinctness to which it aspired, however, were achieved only at the cost of removing it from the physical realm into one of mathematical abstraction, and, partly as a consequence of this, and partly as a consequence of successes in experimental disciplines such as chemistry, electricity, and physiology, canons of natural-philosophical explanation began to fragment.

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PART IV

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8 The Fortunes of a Mechanical Model for Natural Philosophy In Part III, we explored the complex processes whereby natural philosophy came to assume a broad cultural standing in France in the ﬁrst half of the eighteenth century. These processes by no means constituted the only way in which natural philosophy came to have this standing, and the situations in Britain and Germany were different, but the French model was to be an especially infuential one, and it had some general features that were not restricted to France. The process effectively began with the concerted attempt to present a particular model of natural philosophy, that pursued in the Acade´mie des Sciences, as something worthwhile, useful, and capable of acting as a paradigm of rational enquiry, in that it met rigorous standards of clarity and distinctness. In this way, the activities of the Acade´mie des Sciences, which might otherwise be considered esoteric and remote from anything outside their own narrowly circumscribed realm, could be vindicated. We have explored how these processes spun out of the control of the Acade´mie. But up to now we have only touched on a second question, of equal importance, namely the viability of the model of natural philosophy proposed. In this and the following two chapters, I want to explore this latter question by examining natural-philosophical models of explanation and reduction in mechanics, matter theory, and the life sciences. We shall see that the mechanical model was not at all viable, even as a model for enquiry in physics, and that with its demise came the demise of the idea that natural philosophy was a single uniﬁed enterprise. In other words, the inability of mechanics to act as a model for the whole of physical enquiry had profound ramiﬁcations for the ability of natural philosophy to act as a model for enquiry more generally. The questions go even deeper, however, for what examination of eighteenth-century matter theory and the life sciences brings to light is the perceived overwhelming need to rethink the nature of matter in such a way that forms of chemical, electrical, physiological, and developmental activity can be studied as autonomous phenomena. The shift from thinking of matter as inert to thinking of it as active was a fundamental development because it was accompanied by a questioning of the implicit model of understanding that complemented the explicit model of natural philosophy that Fontenelle and others had advocated. This questioning,

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which can be summed up under the idea of a move from reason to sensibility, will be our concern in Part V. EXPL ANAT OR Y M ODELS AND T HE UNITY OF NATURAL PHILOSOPHY With the move to increasing abstractness in mechanics, and the decline of interest in cosmological questions among its continental practitioners after 1700, the standing of mechanics as natural philosophy par excellence, a standing it had apparently consolidated with the publication of Newton’s Principia, became increasingly less secure. There was a shift in the centre of gravity of natural philosophy, or rather a loss of a centre of gravity, as mechanics in the form of rational mechanics, and matter theory in the form of chemistry and the theory of electricity, vied for a place at the centre of the natural-philosophical enterprise. Our primary concern in this and the next two chapters will be with the way in which the instability of the combination of matter theory and mechanics that had been established in mechanism was laid bare in a struggle between the claims of mechanics and matter theory to be the discipline that set the agenda for natural philosophy. This divergence in views on what is the fundamental project of natural philosophy is very signiﬁcant, and I shall use it to probe the question of what is at issue in the attempt to offer a comprehensive natural-philosophical view of the world. One question at issue here is that of reduction to, or assimilation to, some branch of natural philosophy considered to have a foundational standing. I have focused in earlier chapters on reduction exclusively in the context of microreduction, that is, vertical reduction to what, in the ﬁnal analysis, should be an ultimate ‘level’. Micro-reduction is a form of uniﬁcation through reduction, and it attempts to meet some general explanatory criteria—that the explanans should be clearer, more economical, and better understood than the explanandum—in a distinctive way which, in order to meet its uniﬁcatory aspirations, adds a metaphysical requirement from traditional matter theory, namely that the explanans reveal the unique ultimate constituents of the world. But the explanatory criteria can be separated from the project of providing a uniﬁed account of all physical phenomena, and can be met in different ways, not all of which are committed to the idea that ‘ultimate constituents’ necessarily have any explanatory role, or even any appropriate role. Indeed, for the proponents of these different explanatory projects, it may well be the very attempt to combine explanatory criteria with a notion of ultimate underlying structure—carried over from traditional speculative matter theory—that is considered to lie at the basis of the explanatory failure of mechanism. In particular, it may be that explanation and uniﬁcation pull in different, incompatible directions, and in

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such a situation it might be deemed better to retain explanatory power at the cost of a uniﬁed account. We have already seen such considerations at work in the competing claims of mechanism and experimental natural philosophy. As we move to the eighteenth-century disputes, matters become a little more complex, but in a way that enables us to see more clearly just what is at issue. In particular, we shall see that uniﬁcation does not have to be pursued through reduction, and that reduction does not have to be perceived in terms of its uniﬁcatory power, in that there may be different forms of reduction which are domain-speciﬁc and cannot be combined. Moreover, it may not be a straightforward question of a simple choice between uniﬁcation and explanation: rather, considerations of generality balanced against considerations of experimentally testable empirical content may mean that it is instead a matter of a carefully judged compromise between uniﬁcatory power and explanatory power. These questions come to the fore in the programmes at which we shall now be looking, and clariﬁcation of them will enable us to ﬁnd our way through the increased complexity of the competing claims of explanatory power and uniﬁcation. We can distinguish two different non-microreductive types of explanation in this respect: the assimilation of a broad class of phenomena to a narrower class which remains at the same level (in that it allows no stratiﬁcation), and hence is horizontal; and a form of vertical reduction, which is dictated by explanatory considerations rather than any sense of capturing a description in terms of the ultimate constituents of material entities, namely meso-reduction. The former is a form of explanation in terms of fundamental principles, where what makes them fundamental is that they are deemed to be a priori, so that the domain of explanation has to be assimilated to, or shown to follow directly from, these fundamental principles. This is the foundationalist project of rational mechanics, where the traditional mechanist attempts to ground matter theory in mechanics have been abandoned. Rather than a mechanically characterized micro-structure providing the explanans for a qualitatively characterized macro-structural explanandum, a mechanical model that makes no distinctions of kind corresponding to differences of scale is argued to have an a priori status, and is gradually expanded to greater and greater ranges of phenomena, so that all physical phenomena progressively fall under its purview. Meso-reduction, by contrast, is that form of reduction that we increasingly ﬁnd in chemistry in the eighteenth century, where a traditional form of mechanist micro-reduction to fundamental corpuscles is gradually replaced by a reduction to the level of fundamental chemical processes. What makes these latter processes fundamental is not that they are deemed to represent the activities of the smallest constituents in nature, for it was widely accepted that there may well be smaller micro-corpuscular processes: it was just that such smaller-level processes had no explanatory relevance to the chemical, electrical, physiological, and pharmaceutical qualities that were being discussed, and since it was qualities of this kind that were virtually constitutive of the domain of natural philosophy for many of its practitioners in

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the eighteenth century, there was a sense in which micro-reduction was relegated to a problematic metaphysical position of no practical explanatory relevance. Above all, what made the requisite meso-level processes fundamental depended on a variety of issues, paramount among which were the kind of instrumental questions that we looked at in examining Geoffroy in Chapter 5: they were describable in terms of the interactions of substances which could be yielded as the ultimate products of distillation or solvent procedures. More generally, in the course of the eighteenth century, we witness a fragmentation of natural philosophy, conceived as a single overarching enterprise in which various disciplines feed into a fundamental understanding of natural processes which takes its identity from what I shall characterize in terms of an explanatory model. Mechanics took over a role that had previously been occupied by Cartesian mechanism, in which an attempt had been made to combine mechanics and matter theory, and, in the form of rational mechanics, it attempted to establish an account of one part of the physical domain on a rigorous quantitative basis, offering in many respects something that was considered to have an a priori standing. Having achieved this, it then in effect issued promissory notes about what it considered to be cognate areas, such as electricity and magnetism, in the hope that these could be redeemed as the realm of mechanical investigation—which by mid-century had gone far beyond merely a theory of mass points and was dealing with rigid, ﬂexible, elastic, and ﬂuid bodies—was expanded outwards into new domains, in the process offering new and very exacting standards of rigour and demonstrative certainty. Just as rational mechanics, considered as a form of foundational natural philosophy, can be seen as emerging as a reaction to the inadequacy of Cartesian mechanism, so too matter theory, which had become temporarily mechanized through its integration into mechanism, now comes to be seen as a source of alternative resources to those offered by mechanism, not least in Newton. In the course of the eighteenth century, as attempts were made to understand electrical phenomena, chemical reactions, and physiological activity in fundamental terms, and as the inadequacy of picturing these on the model of mechanical interactions became evident, a newly devised chemical matter theory began to look much more promising as a basis for a foundational physical discipline than a rational mechanics which was becoming increasingly remote from the experimental realm. But there was no single model on offer in matter theory, on a par with that which had been advocated by mechanists in the seventeenth century for example. Moreover, those models that were on offer were somewhat different in nature from that of rational mechanics, which had diverged from the traditional notions of picturability that had shaped conceptions of what an acceptable explanation was in the seventeenth century, and which continued to inform natural-philosophical disciplines outside the domain of rational mechanics in the eighteenth.

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The upshot was that, by the middle of the eighteenth century, not only had consensus on models of explanation become much more difﬁcult to secure, but just what was required of an explanation had become contested. Since the fragmentation of natural philosophy that we shall be concerned with is above all a fragmentation of the explanatory ambitions of natural philosophy—rather than merely a division of different phenomena between distinct areas of expertise, for example—we need to begin by exploring in what way explanatory considerations can bring unity and coherence to the natural-philosophical enterprise. In considering what the unity or disunity of natural philosophy/science might consist in, our prime concern is not with a general philosophical model as such but rather with something speciﬁcally suited to helping us understand the issues at stake in natural philosophy in the ﬁrst half of the eighteenth century. This does not mean that there are no general philosophical issues at stake, just that we need to tailor these to our concerns. If we think of the unity of natural philosophy as being secured by a shared explanans, we need to distinguish between sharing an explanatory model and sharing explanatory resources. Explanatory resources are heterogeneous and potentially unlimited in scope. An explanatory model, by contrast, is a homogeneous and very speciﬁc explanatory archetype or explanatory ideal type. I shall characterize two areas as falling in the same domain if they share the same explanatory model, but if they merely access the same general kinds of explanatory resources, while having different explanatory models, then they fall in different domains. On one widespread conception of explanation, the aim of explanation is to assimilate the explanandum to the explanans in some way. However, to the extent to which explanation aspires to a signiﬁcant level of generality, the explanandum will typically be remote from the explanans. This means that the assimilation of the explanandum to the explanans proceeds via the other explanatory resources, appeal to which should be able to show how the explanans, as represented in the explanatory model, is ‘modiﬁed’ in such a way as to yield the phenomenon to be explained. To see how this works, consider seventeenth-century mechanism. Generically conceived, this is a general natural philosophy in that, in all its variants, all physical phenomena are considered to fall within its domain of explanation, including the ‘artiﬁcial’ or ‘accidental’ events that Aristotelian natural philosophy had excluded as falling outside the domain of natural-philosophical explanation.1 It is also a micro-corpuscularian natural philosophy, meaning that all macroscopic processes and events that fall within the domain of explanation have to be assimilated to a micro-corpuscularian explanans. In its Epicurean/Gassendist version, this explanans is shaped by the requirements of a theory of the basic properties of matter: the atoms it postulates inhabit and move in an otherwise 1

On the questions covered in this and the next paragraph, see the detailed discussion of the nature of mechanism in Gaukroger, Emergence, Part IV.

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empty space, and their behaviour is determined by their size, shape, surface features, and (in Gassendi’s version) their individual speed and direction of motion. These make up the explanatory model. To move from this explanatory model to the range of everyday macroscopic phenomena—which includes colours, tastes, and smells, as well as cohesion, liquidity and solidity, combustion, and chemical properties—a range of different kinds of account need to be invoked. For Gassendi, for example, these range from divine providence and the imposition of ﬁnal ends on some natural processes, to some basic mechanical and physico-chemical tenets which describe the macroscopic behaviour of certain kinds of body. By contrast, in the Cartesian version of mechanism, matter theory and mechanics are integrated to form a more powerful explanatory model. Micro-corpuscles are considered to be paradigmatically spherical and not only are size, speed, and direction of motion the sole properties invoked, at least in the limiting case, but they are fully quantiﬁed. In contrast with Gassendean atomism, here mechanics forms part of the explanatory model: in theory at least it must form part of any ultimate explanation. But the integration of matter theory and mechanics is far from complete. At the level of magnitude of the microcorpuscularian explanatory model itself, various basic features of micro-corpuscular processes which derive from matter theory required the postulation of shapeless forms of matter to ﬁll the interstices between corpuscles, and nonspherical shapes have to be introduced to account not merely for recalcitrant terrestrial phenomena such as magnetism, but also for a fuller understanding of what happens to spatially differentiable parts (slices) of bodies in collision. At the macroscopic level, contentious and wide-ranging reductive assumptions have to be introduced about vital processes, sensory qualities, and forms of apparently functional organization, and various assumptions have to be introduced in celestial mechanics, for example, to bridge the behaviour of micro-corpuscles in a void and the behaviour of bodies immersed in dense ﬂuids. The richness of the mechanist explanans comes in its highly developed explanatory resources, not in its very economical explanatory model. Gassendean and Cartesian mechanics had immense problems generating the right kind of explanatory resources with which to supplement their respective explanatory models. Natural philosophers with aspirations to a systematic understanding of the world that could successfully replace the systematic understanding offered by Aristotelian natural philosophy could focus either on the explanatory resources or on the explanatory model. Malebranche, for example, opts for the former, developing a highly elaborate account of primary and secondary qualities whereby secondary qualities are excluded from the domain of natural-philosophical explanation in their own right because they are not genuine phenomena, but more like interference effects created by the interaction of mechanically describable processes such as rotation of light corpuscles, and hard-wired sensory system/brain processes which respond to such rotating corpuscles by producing particular kinds of image that do not resemble anything in

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the world, as represented in the micro-corpuscularian explanatory model. The exercise here amounts to little more than saving the explanatory model, but the justiﬁcation offered for this is a potentially powerful one: namely, the mechanist explanatory model is the only one with any intrinsic credibility. The claim was that, by contrast with various Aristotelian and Neoplatonist alternatives, if one could assimilate the phenomena to a Cartesian mechanist explanatory model, for example, then one would genuinely have understood them. What drove such a claim was more than anything else the idea of picturability. Descartes owed a great deal in his model of mechanist explanation to Beeckman, who insisted from the beginning on appeal to a picturable or imaginable structure of parts whose motions are controlled within a theory of mechanics: to talk about effects you must be able to imagine how they are produced, and the exemplar of this resides in the mechanical arts, where one can command nature at a macroscopic level. Picturability is reinforced in Malebranche’s doctrine of primary and secondary qualities, where it is crucial to his promotion of the former and rejection of the latter as vehicles for explanation that our ideas of primary qualities resemble what they represent, by contrast with our ideas of secondary qualities, which fail to resemble anything external to us. The response that I have associated with Boyle, Locke, and Newton to this kind of approach is that of denying that we have any reason to believe that there is a single explanatory model adequate to the phenomena that the systematic mechanist attempts to capture. Colour phenomena are of particular signiﬁcance here because colour is in some respects a paradigm case of mechanist reduction, while in other respects it is a revealing example of mechanists ignoring phenomena that they are unable to account for. Boyle documented the phenomenology of colour, as I have indicated, showing that it is extremely complex, making it highly unlikely that a single explanatory model, of a mechanist or any other kind, could be adequate.2 It follows from this that manipulation of other explanatory 2 Boyle, Experiments and considerations touching colours. See Alan E. Shapiro, Fits, Passions, and Paroxysms: Physics, Method, and Chemistry and Newton’s Theories of Colored Bodies and Fits of Easy Reﬂection (Cambridge, 1993), ch. 3. Boyle here put his ﬁnger on one of the most problematic features of colour for any uniﬁed account of colour phenomena. Since the extreme complexity of colour phenomena is not always appreciated, it is perhaps worth noting here that several different kinds of ‘colour factory’ in nature are now recognized, producing very different kinds of chromatic phenomena. Consider just two of these: pigment colour and structural colour. When pigments are activated, the energy of the light is captured selectively, the captured energy allowing electrons to leave their original orbit and circulate along the single and double bonds of large pigment molecules, losing small amounts of energy as heat in transit so that only light of a certain wavelength— corresponding to the colour of the pigment—escapes. Pigments scatter light over 360 , which means that the colour is visible from every angle, and visible as the same colour, while, because of the dispersion, the intensity of the colour is not great. Structural colour factories, by contrast, comprise complex tiered layers of refractive material in which a small amount of monochrome light is reﬂected off each tier, the rest refracted, and where the cumulative behaviour of the reﬂected rays may be either strengthened or annulled, depending on whether it is in phase or out of phase. Colours produced by such structural means are not dispersed over 360 but over a very narrow band, and appear as very intense ﬂashes of iridescent colour (typically ten times more intense than

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resources, in an attempt to assimilate all colour phenomena to the mechanist corpuscular rotation model, is not only unlikely to be successful but, more importantly, may be counter-productive. As the mechanist response to Newton’s work on prisms showed, fruitful paths of enquiry were shunned because of their failure to offer an underlying picturable mechanist micro-structure for all colour phenomena. In place of a reductionist strategy, we might think of the alternative offered by Locke, as exempliﬁed in a practical natural-philosophical context in the work of Gray, for example, in terms of an openness to using one’s explanatory resources to generate possible explanatory models. Moreover, if we follow this path, then there is no reason to assume that the experimental investigation of the phenomena should converge on a single explanatory model. In other words, even in a case where identical explanatory resources are available, it may remain an open question not only what form one’s explanatory model should take, but whether a single explanatory model is adequate to account for the phenomena. Opponents of this approach wrongly assumed that the absence of a single explanatory model was tantamount to no explanatory model, and on this basis they were then understandably concerned that no explanation could be forthcoming, only an account of similarities and correlations which lacked any explanatory focus, and hence explanatory power. The rationale behind a commitment to a single explanatory model was, nevertheless, a powerful one, shaped in response to the widely perceived explanatory failure of Aristotelian natural philosophy. There was close to universal agreement by the middle of the seventeenth century that what was taken to be the Aristotelian method of enquiry was hopelessly misconceived, and that what were offered as explanations there were empty redescriptions.3 There was a widespread sense that a new start had to made, and if this was to have any chance of success, it had to be clear from the beginning just what the features were that successful explanations would need to possess. Finding the correct explanatory model was something on which the whole question of explanation hinged, and whose resolution was a prerequisite for proceeding further: in theory at least, until one had settled this question, natural philosophy could not even be attempted, because until one knew exactly what one was looking for in explanatory terms, pigment colours, and having a metallic sheen that distinguishes them immediately from pigment colours), depending on the viewer’s orientation: examples are some butterﬂy’s wings and peacock’s heads. These are only two of several very different types of colour factory in nature, with very different colour phenomenologies. Even conﬁning ourselves to these two, we should note that a new level of complexity may be introduced by camouﬂage. A beetle whose exoskeleton produces a green colour by structural means would stand out from the leaf on which it sits because of the different phenomenologies of structural and pigment colours, for example: to avoid this, some beetles have evolved scattering devices on the outer layer of their exoskeleton with the result that the structurally produced colours have a reduced intensity and wider viewing angle which mimics the leaf ’s pigment colour. On colour factories, see Andrew Parker, Seven Deadly Colours (London, 2005). Hooke and Newton independently discovered structural colours in examining thin ﬁlms. 3 See Gaukroger, Emergence, ch. 5.

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one could not proceed. Although the criterion of clarity and distinctness ﬁgured prominently in the new understanding of what explanation consisted in, what was at stake was not merely an abstract methodological criterion which could be supplied with content on a case-to-case basis. On the contrary, Descartes went to great lengths to establish mechanism as the sole manifestation of clarity and distinctness as far as understanding of the physical world was concerned, matching different single manifestations in the case of the other two substances, God and mind. The criterion of clarity and distinctness thus turned out to be not merely substantive but identiﬁed with a particular understanding of natural philosophy. Nevertheless, there was some degree of ﬂexibility here, and the model was certainly not closed to development and reﬁnement. In fact, what was offered had great intuitive, theoretical, and practical appeal. Giving it up, or refusing to engage such basic questions, were taken to indicate an inability to take seriously the contribution of natural philosophy to an understanding of the world. This is reﬂected in the sheer incomprehension that greeted Boylean pneumatics, Newton on the production of a spectrum, and Gray’s work on electrical conductivity. But the very fundamental nature of these results, and the fact that they could not be accommodated to any mechanist explanatory model, meant that the other kinds of explanatory model they suggested, despite their piecemeal nature, had to be taken seriously. For those committed to a single all-encompassing explanatory model, one could—rather than holding the explanatory model ﬁxed and hoping that massaging the explanatory resources would take one more plausibly from a very remote explanandum to one’s central explanans—instead choose to reﬁne the explanatory model. In particular, in the late seventeenth century, one way to overcome the increasingly obvious discrepancy between the mechanical and the matter-theoretical components of the Cartesian mechanist explanatory model was to jettison the matter-theoretical component. This was Huygens’ approach, for example. The hope was that by putting mechanics at the core of natural philosophy and establishing it on an absolutely secure basis, one might develop the discipline in terms of comprehension and sophistication, in the reasonable expectation that some questions that had fallen outside its purview, such as gravitation and magnetism, might yield to the newly developed resources. Galileo, in his treatment of falling bodies and projectile motion, had shown how to move from a simple, geometrical explanatory model—one in which bodies moved in a void, which he had established as the general explanatory model for kinematics—to the cases of bodies of various shapes and initial speeds moving in a resisting medium. This was the basis for Huygens’ approach to the more complex forms of motion that he investigated, and for Huygens, as for Newton, as we have seen, the geometrical picturability of the explanatory model was crucial, for this is what its clarity and distinctness consisted in: explanation involved the assimilation of something that was not well understood and which we wish to explain (the explanandum), to something that was well understood

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and indeed, if it conformed to the criteria of clarity and distinctness, could not be better understood (the explanans). However, as I have argued, the development of mathematics in the seventeenth century, with Descartes’ notion of analysis and then with Leibniz’s defence of the calculus, and its elaboration in the hands of the Bernoullis and others, suggested a different direction, one that broke with the intelligibility requirements associated with geometrical models in favour of algorithms whose functioning was not (or not always) open to a translation into geometrical terms.4 With the construal of mechanics in terms of a form of analysis in the work of Leibniz and his continental followers, considerations that one might initially have thought peculiar to mathematics become issues facing mechanics as well. And to the extent that mechanics is taken to lie at the core of natural philosophy, these issues become natural-philosophical ones. This raises a host of complex questions on the interplay between different kinds of things that might count as explanatory models. At the two poles are picturable representations of basic physical processes, e.g. the interactions of corpuscles at the microscopic level, and algorithmic compressions, which are typically not picturable. Algorithmic compressions are abbreviated representations of data,5 allowing us to present the information content of observational data, numerical data, or evidence generally in a more economical form, and this more economical presentation enables us to make predictions that can be compared with further data.6 When we explain something in terms of algorithmic compression, the aim is not to assimilate something poorly understood to something well understood, but to impose a particular kind of organizational device, supplied by the explanans, on the explanandum. The choice between picturable representations and algorithmic compressions forces a bifurcation of notions of what explanation consists in, a bifurcation that will henceforth be a permanent feature of enquiry, albeit manifested in different ways, and with different degrees of explicitness, in different contexts. The only general point 4 This was a problem that Descartes ﬁrst encountered in the late 1620s, when he tried to apply his method of rendering mathematics clear and distinct by means of translation of arithmetical operations into operations on line lengths, where the generation of the outcome of the operation (the sum, product, etc.) is paradigmatically transparent, to the new operations that his discovery and development of analysis had yielded. The application failed completely: the new operations either lacked any corresponding construction, or were matched by one so complex that clarity and distinctness were manifestly lost. I have argued elsewhere that this is what forced Descartes to abandon the Regulae : see Gaukroger, Descartes, An Intellectual Biography, 179–81. 5 Not all data has an algorithmic compression: a string of random numbers has none, for example, but the series 2, 4, 6, 8 . . . does, because it is just the sequence of positive even numbers. 6 On the formal theory of algorithmic compression, see G. Chaitin, Algorithmic Information Theory (Cambridge, 1987). Fontenelle had seen something akin to compression as distinctive of modern scientiﬁc thought. In his Digression sur les anciens et les modernes (1688), he writes: ‘mathematics and physics are sciences whose yoke became progressively heavier on the savants and it seemed that they would have to be abandoned, but at the same time method was developed: the same mind that perfects things by adding new ideas also perfects the method of learning them through abridgment, and provides new means for encompassing the expanded scope of science.’ Œuvres, iv. 194–5.

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to which I want to draw attention is it may not be possible for the choice to be a clean one: even where algorithmic compressions play an indispensable role in physical theorizing, for example, there seems to be an inevitable need to balance such wholly abstract representations with ones that enable us to picture what is happening in the explanans, and the way in which this ‘balancing’ occurs is of particular interest. A brief excursus may be helpful here if we are to appreciate the long-term importance of this question. Consider Peter Galison’s pioneering exploration of the complexities of ﬁnding a balance between picturability considerations and abstract statistical representations in post-war microphysics.7 The picturability/ algorithm divide here takes the form of two different technological traditions, ‘image’ and ‘logic’, developed independently and indeed in tension with one another. The former is the tradition of physical instruments that employ devices that can produce detailed, nearly complete pictures of individual events: detectors such as cloud chambers, photographic emulsions, and bubble chambers, which produce elaborate pictures of particle interactions, in which multiple tracks appear, allowing one to reconstruct in detail what has happened in a single event. The ‘logic’ tradition by contrast relies on electronic detectors such as Geiger-Mu¨ller tubes, scintillation counters, Cerenkov detectors, and spark chambers, so that whenever a particle having a certain property is detected, electronic blips or sparks are generated which are registered as counts. There is a gulf between the kinds of information produced by these types of devices, yet both are needed. Image devices typically produce copious information but in an indiscriminate way, because they usually involve simply opening a shutter letting in high-energy beams such as cosmic rays, something which is extremely difﬁcult to control. By contrast, logic devices are unable to display detail, but they allow ﬁne-grained control and a very large number of events can be recorded, which allows statistical conclusions to be drawn. Reduction of one to the other is not a possibility, nor more generally is any attempt at wholesale assimilation of one to the other. What Galison establishes is that the different instrumental traditions were gradually bridged, at a crucial juncture, which he devotes considerable attention to identifying, and which he describes in anthropological terms as a ‘trading zone’, with the formulation of a pidgin language—i.e. something that is not the native or natural language in either of the instrumental traditions—to communicate across the bridge. Note the parallels between the ways in which instrumental/experimental techniques shape one’s explanatory resources, and even one’s explanatory model, in this case,8 and the way in which instrumental/experimental techniques shaped explanatory resources in the seventeenth-century experimental 7

Peter Galison, Image and Logic: A Material Culture of Microphysics (Chicago, 1997). Cf. Nicolas Rasmussen and Alan Chalmers, ‘The Role of Theory in the Use of Instruments: Or, How Much Do We Need to Know About Electrons to do Science with an Electron 8

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philosophy tradition, which, rationalized by Locke, opened up the possibility of a plurality of explanatory models. In both cases, different kinds of explanation are dictated by what we do with given instruments. Note also that to advocate pluralism with respect to explanatory models is to deny uniﬁcation through reduction—whether wholesale assimilation of content or wholesale subordination of one content to another—but it is not by any means to deny linking of content in various ways, for example by means of the bridging procedures that Galison describes in the case of microphysics. Finally, we also need to be aware of the great potential value of establishing such links in cases where different explanatory models are at issue, but where these do not differ in kind, in that both may involve picturability and assimilation of the explanandum to the explanans. We would certainly expect such bridges to be established in the short term where possible, even if only as a prelude to a hoped-for uniﬁcation, and it remains an open empirical question whether there are cases—such as accounts of colour phenomena or combustion, two especially problematic areas in this respect in the eighteenth century—where they remain bridges without the possibility of uniﬁcation. M E C H A N I C S A S A N A P R I O R I D I S C I P L IN E One of the most prominent explanatory models of the eighteenth century was that of rational mechanics. As we saw in Part III, the physical credentials of Newtonianism had been established in France by the late 1730s, and from this time onwards rational mechanics was in effect a version of Newtonianism, but if what we are witnessing is the triumph of Newtonianism at the expense of vortex theory, at the same time it is the triumph of analytical mechanics over the Principia. In mid-century continental editions of the Principia, it was the rewritten version in the notes, not what was by then the geometrical fossil of the original text, that was the focus of attention for readers. The heavily annotated ‘Jesuit’ edition of the Principia (1739–42),9 was read for its hundreds of pages of notes, which drew on Varignon, L’Hoˆpital, Johann and Daniel Bernoulli, and Euler. The French translation by the Marquise du Chaˆtelet, Principes Mathe´matiques de la Philosophie Naturelle (Paris, 1759), was heavily annotated by her, drawing on Daniel Bernoulli and Clairaut, amongst others, and especially notable for the addition of an extensive commentary by Clairaut. But it was not merely a way of doing the mathematics that was at issue Microscope?’, in Jed Z. Buchwald and Andrew Warwick, eds., Histories of the Electron: The Birth of Microphysics (Cambridge, Mass., 2001), 467–502. 9 Philosophiae Naturalis Principia Mathematica auctore Isaaco Newtono, Eq. Aurato. Perpetuis Commentariis Illustrata par T. Le Seur and F. Jacquier (4 vols., Geneva, 1739–42). The editors were in fact Minim friars, not Jesuits.

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here. Rational mechanics was conceived by its practitioners to be unique in manifesting the qualities of clarity and distinctness, and thereby was taken to form the basis for any kind of enquiry into the natural world. This was in sharp contrast to Newton’s view, not only of what the clarity and distinctness of mathematical operations consisted in, but also to his view that what mechanics could achieve was limited, and that it had to be supplemented by matter theory, which offered a different form of enquiry. The translation of the project of the Principia into analytic form brought with it the idea that physics was ultimately just mechanics, and it was such an understanding that lay at the basis of the two mid-century attempts to provide a comprehensive foundation and rationale for rational mechanics, those of d’Alembert and Euler. The tradition of continental rational mechanics that began with Varignon and the Bernoullis and culminated mid-century in the work of Euler, devoted itself to the extension and uniﬁcation of mechanics, by focusing attention on a class of problems that had received only very elementary treatment in the mechanical tradition from Galileo to Newton and Leibniz: namely the dynamics of rigid, ﬂexible, and elastic bodies, and the dynamics of several bodies with mutual interactions. This concern with uniﬁcation was accompanied by a growing focus on foundational questions, which centred upon Newton’s conception of force. Dynamics had to come to terms with force one way or another, and there was general agreement that, while Newton’s notion of attractive force could not be replaced by restricting oneself to the kinds of approach that advocates of vortex theory had used, the Newtonian understanding of force was inadequate. Consequently, some new understanding of force had to be devised. There were two broad directions in which eighteenth-century natural philosophers went on this question. The ﬁrst was that followed by those who believed that matter theory provided at least part of the solution, and that some combination of the resources of matter theory and mechanics was necessary, albeit not a combination of the kind that had been envisaged by mechanists. The strategy of Boscovich and, later in the century, Kant, was to take force, a concept that seemed to resist mechanization, as a physically primitive notion, more primitive even than that of body.10 The project, reminiscent in some ways of De gravitatione, was to confer upon the idea of repulsive force exactly the same status that Newton had conferred upon attractive force, providing a uniﬁed conception of force, a conception which effectively made it a physically primitive notion, and which involved the idea that all forces act at a distance: what had traditionally been seen as the greatest ﬂaw in Newton’s account was thereby made its greatest virtue. The other direction was that followed by advocates of rational mechanics, and this is what we shall be concerned with here. Within this tradition, the 10

Roger Joseph Boscovich, Theoria philosophiae naturalis (Vienna, 1758); and Immanuel Kant, Metaphysische Anfangsgru¨nde der Naturwissenschaft (Riga, 1786).

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Newtonian concept of force was considered at best seriously incomplete and at worst an ‘obscure and metaphysical being capable of nothing but spreading darkness over a science clear by itself ’, as d’Alembert put it.11 D’Alembert attempted to reduce force to a kinematic concept, acceleration, thereby ridding dynamics of the notion altogether. Euler, by contrast, wanted neither to make force redundant nor to make it absolutely primitive, but instead offered an explanation of it in terms of something much more intuitive, the impenetrability of matter. On this account, as on d’Alembert’s, the ultimate foundations of mechanics had to be given in terms of something that could be grasped as being both necessary and self-evident, but for Euler the relevant necessary and selfevident truth was that bodies are impenetrable: it was conceptually impossible to conceive of a body (i.e. fully compact matter, free from interstitial vacua) being penetrated since this would require that two bodies be in the same place at the same time, which is impossible. In considering the foundational projects of d’Alembert and Euler, it is important to note at the outset that we tend to think of Newton’s laws as a synthesis of all that had gone before, but this was not at all how the situation was seen in the eighteenth century. The task was to reconcile a number of disparate and inconsistent laws, notably Descartes’ laws of motion, Galileo’s law of falling bodies, Huygens’ law of collision, laws of centrifugal force, laws of the pendulum, Leibniz’s law of the conservation of vis viva, and Newton’s general laws of motion.12 D’Alembert sets out his priorities in the Preface to his Traite´ de Dynamique of 1743, making it clear that ultimately the only way to establish a reconciliation is to treat these as conceptual truths: The certainty of mathematics is an advantage that the mathematical sciences owe principally to the simplicity of their object. It must also be pointed out that, since not all the parts of mathematics have an equally simple object, or a strict certainty, foundations due to principles that are necessarily true and evident in themselves do not belong equally or in the same way to all these parts. Several of them, resting on physical principles, that is to say on truths of observation, or on simple hypotheses, only have the certainty of observation, so to speak, or even that of pure supposition. Strictly speaking, it is only those that deal with the calculation of magnitudes, and of the general properties of extension—that is, algebra, geometry, and mechanics—that can be regarded as being marked with the seal of evidence. Moreover we can observe a type of gradation or, one might say, shading, in the enlightenment that these sciences produce in our mind. The more the object that they embrace is extended, and considered in a general and abstract way, the more their principles are free from obscurity and are clearer.13

11

D’Alembert, Traite´ de Dynamique, xvi. I take the list from the exemplary account in Thomas Hankins, Jean D’Alembert: Science and the Enlightenment (Oxford, 1970), 151–2. 13 D’Alembert, Traite´ de Dynamique, i–ii. 12

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The programme by which he effected this idea was resolutely Malebranchean. Dynamics for d’Alembert was a science of effects, not a science of causes, for this was a prerequisite of capturing physical phenomena in a clear and distinct way.14 The effects comprised the motions of idealized impenetrable geometrical ﬁgures moving at a uniform rate through empty space until they collided, the resultant behaviour being describable purely geometrically. D’Alembert did not deny the existence of causes however. Rather, he argues that there are only two types of cause that can produce or change a body’s motion. The ﬁrst kind, contact causes, manifest themselves in their effects and ‘have their source in the sensible and mutual action of bodies resulting from their impenetrability’. Any other causes, such as gravitation, ‘are known only by their effects and we are completely ignorant of their real nature’,15 and where he elaborates on gravity, as in the article on ‘attraction’ in the Encyclope´die, he makes it clear that it cannot be reduced to impact, but can only be considered an innate force. He is prepared to follow the ‘standard’ Newtonian interpretation, associated with Locke and Maclaurin, which is agnostic and wholly non-committal on the knowledge of causes, and which of course ﬁts in perfectly with his own Malebrancheaninspired approach, which offers a stronger but compatible view on causes. The treatment in the Traite´ is conﬁned to collision, and the aim is to show that the mechanics of collision can be seen to follow from necessary truths. The core issue is that of what actually happens in collision, something that has to be speciﬁed without reference to forces if the criteria of clarity and distinctness are to be met. The state of motion of bodies is changed in collision, and the ﬁrst question that needs to be resolved is whether this change is discrete or continuous. More speciﬁcally, does a new velocity simply replace the pre-impact velocity, or does there have to be a transition through all intervening degrees? Newton had prevaricated in the deployment of his second law of motion, as we saw in Chapter 2, between discontinuous and continuous changes. In the former, there is a total change of momentum, whereas in the latter there is a change in the rate of momentum. A change in the rate of momentum precludes discontinuous changes since a discontinuous change is an inﬁnite change as far as continuity is concerned, and so would require an inﬁnite force. One could of course instead assume elasticity, but elasticity means that the body would compress, that is, one part would move relative to another part: the problem is that when we get down to ultimate atoms, these have no parts (which is why we call them ultimate).16 Only inﬁnite divisibility is going to preserve continuity, and this is the route that Leibniz followed, securing continuity by insisting on the inﬁnite divisibility of matter, the ‘ultimate’ constituents of bodies being not something material but 14 Ibid., xxiii. See also Thomas L. Hankins, ‘The Inﬂuence of Malebranche on the Science of Mechanics During the Eighteenth Century’, Journal of the History of Ideas 18 (1967), 193–210. 15 Traite´ de Dynamique, x. 16 See the discussion in Hankins, Jean d’Alembert, 170–7.

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monads. This has the effect of making all matter equally and completely ﬂuid, which understandably appeared wholly counter-intuitive to his contemporaries. The alternative that d’Alembert takes up is to assume perfectly hard atoms, which he construes as inelastic. He describes the behaviour of these bodies in terms of three laws. The ﬁrst directly mirrors Newton’s ﬁrst law, although it makes it very clear that inertia is a property of bodies: this was in fact how it functioned in Newton, but Newton’s terminology was sometimes confusing, whereas d’Alembert is clear on this point. However, in keeping with his attempt to ground the basic principles of mechanics in necessary truths, d’Alembert attempts to justify the law of inertia in terms of a version of Leibniz’s principle of sufﬁcient reason: a body will not change its state without sufﬁcient reason, where the sufﬁcient reason is speciﬁed in terms of external forces. The idea that the law of inertia could be justiﬁed in these terms was quite common in the eighteenth century (Euler also argued in this way, as we shall see), but the proposed justiﬁcation was clearly question-begging. Aristotle, for example, had considered that every (terrestrial) motion must have an external cause, so that in the absence of this cause no body will maintain its motion, and such an account was not completely ruled out even in the eighteenth century: as we have already seen, the Jesuit contributors to the Journal de Tre´voux were still advocating it early to mid-century. This view of inertia could just as easily be based on the principle of sufﬁcient reason, but the law of inertia that would result would clearly be different from d’Alembert’s. Everything depends on how, and under what conditions, we assign forces. Only given a particular characterization of forces does the law of inertia follow from the principle of sufﬁcient reason. Because of the nature of the relation between a law of inertia and one’s characterization of force, any attempt to justify the one in terms of the other must be circular. D’Alembert’s second law describes what happens when the motions of the hard, impenetrable bodies bring them into contact with one another. The treatment here is distinctive. He begins by envisaging a situation in which we do not have to take mass into account: instead of dealing with the case of two identical spheres colliding, he investigates what happens when such a body strikes an impenetrable and immovable plane. Since we are dealing with inelastic bodies, if the ﬁrst body strikes the plane perpendicular to its surface it will stop, but if the plane is at an oblique angle, after impact the body will slide along the plane in the direction turned away from the perpendicular. This can be demonstrated simply on the basis of the analysis of motion into vertical and horizontal components, and the use of the parallelogram of motions. When the body strikes the plane at right angles there is no vertical component, only a horizontal one, which is destroyed on impact, so the body comes to a stop. In cases where the plane is at an angle to the trajectory of the body, the horizontal component is again destroyed; but there is a vertical component, so the body will slide along the plane with the other velocity component, namely the vertical one. There can be

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no doubting the ingenuity of this procedure, but there is also a sleight of hand, for the appearance that geometry alone is producing the result is misleading. The analysis works only if the velocity components are perpendicular and parallel to the plane, but geometry does not ﬁx the orientation of the parallelogram. The procedure simply takes the requisite orientation as given, which means that there is more than geometry at issue. Up to this point, we have been dealing with the change in the motion of a geometrically characterized body when it meets an obstacle: it comes to a stop or slides along the surface of the resisting plane. D’Alembert’s claim has been that nothing more than velocity and shape need be taken into account. But when the body offering the resistance is the same kind of body as that whose motion is resisted, something more is needed. In the Newtonian account, this extra ingredient is mass, but it is difﬁcult to separate the notion of mass from that of force, and appeal to a notion of force is precisely what d’Alembert is seeking to avoid. The case analysed in the third law is that of equal and opposite collinear collisions. He attempts to avoid mass by ﬂeshing out ‘equal’ here in terms of ‘same amount of matter’. As we noted earlier, mass was the last notion to be introduced when Newton was writing the Principia, and it appears only in the very last draft of De motu corporum. It is of course unavoidable once one introduces gravitation, but d’Alembert is explicitly not dealing with anything but collision, and he clearly thinks that he can do without it, although the term slips into the text. What he claims with respect to equal and opposite collisions is not that he has identiﬁed some new law but that he has provided a clear and distinct rationale for a traditional understanding of equal and opposite collinear collision. The two bodies have equal quantities of matter and equal and opposite velocities—the situation is wholly symmetrical—so that when they collide there is no reason why one should prevail over the other. D’Alembert proposed to model all other forms of collision on this case, but again the geometry that he appeals to is hardly sufﬁcient in itself to secure the outcome he speciﬁes. Descartes, for example, had argued that the outcome of such a collision (between non-elastic bodies) was that the two move off with the same speed but with their directions of motion reversed. No purely geometrical argument could establish d’Alembert’s account over that of Descartes. As well as the three laws designed to ground kinematics purely in geometry, there is one other crucial and fundamental ingredient in d’Alembert’s account, the principle that has come to be known as d’Alembert’s Principle. This is derived from the second and third laws, and is a way of construing collision so that what might appear to be a dynamic problem can be reduced to, and solved as, a problem in statics, which d’Alembert thinks can be handled without appeal to force.17 The basic idea is to think of collision in terms of a system of 17

As I argued in The Emergence of a Scientiﬁc Culture, 403–13, it was common in the late sixteenth century and the ﬁrst half of the seventeenth century to attempt to model dynamics on

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equilibrium. If we imagine all bodies in the system as being connected by perfectly rigid rods and non-elastic strings, and imagine the system itself as being in a state of equilibrium, then we can trace the effects of particular interactions in terms of the state of the system before and after collision. To conceive of the system purely in statical terms, d’Alembert manipulates his second and third laws and ingeniously introduces a ﬁctitious force equal in magnitude to the product of the mass (or quantity of matter) of the body and its acceleration, acting in the opposite direction. D’Alembert’s account is difﬁcult to follow in detail, in part because of inconsistencies in his vocabulary (the mass and forces which he wants to do without keep cropping up), but what lies behind his Principle can be expressed in more Newtonian terms as the idea that the forces of resistance to accelerations are just equal and opposite reactions to the actions by which the accelerations were produced.18 If we take any point in the system, its reaction against acceleration must be equal and opposite to the resultant of the forces which that point experiences. Consequently all the forces of the system, with the reactions against acceleration of the bodies composing it, form groups of systems in equilibrium for those bodies considered individually, and, by the superposition of forces in equilibrium, all the forces acting on bodies in the system form, with the reactions against equilibrium, an equilibrating set of forces on the whole system. D’Alembert’s Principle was of great use in the subsequent history of mechanics in that it allowed the treatment of complex and intractable dynamic problems in terms of statical ones which yielded to familiar techniques. But this does not in itself establish the foundational issue at stake, in that d’Alembert’s assumption that statics can be pursued without recourse to forces is as contentious as his assumption that dynamics can be pursued without recourse to forces. More generally, his idea that the clarity and distinctness of his mechanics can be established by making it rely purely on geometrical foundations is manifestly unsuccessful. A more promising attempt to establish the foundational standing of rational mechanics can be found in Euler, who in the course of his career provided three extended discussions of this foundational project, in 1736, 1750, and 1765, with no signiﬁcant variation in content.19 Euler’s foundational aim was to reformulate statics, but this was above all an attempt to model dynamical forces on statical ones. D’Alembert’s proposed reduction of dynamics to statics is quite different from this. 18 This is how it is routinely presented in textbooks. See e.g. the standard treatment in William Thomson and Peter G. Tait, Lectures on Natural Philosophy (Cambridge, 1879), }}229–41. 19 The ﬁrst is Chapters 2 and 3 of the Mechanica sive motus scientia analytice exposita (1736), in Leonhardi Euleri opera omnia, series 2, vols. i, ii (Leipzig & Berlin, 1912). The second is the short treatise ‘Recherches sur l’origine des forces’ (1750), in ibid., series 2, vol. v (Lausanne, 1957). The third is the Introductio to his Theoria motus corporum solidorum seu rigidorum (1765), in ibid., series 2, vols. iii, iv (Bern, 1948). I have followed the account in the Theoria motus in what follows, drawing on the fuller discussion in Stephen Gaukroger, ‘‘The Metaphysics of Impenetrability: Euler’s Conception of Force’, British Journal for the History of Science 15 (1982), 132–54. See also

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Newtonian dynamics in such a way that its apodeictic character was established. One of the main goals of the reformulation was the clariﬁcation of the idea of bodies acting upon one another and, in particular, the clariﬁcation of the notions of force and mass invoked to explain these actions. In setting out the conceptual foundations of mechanics, his focus is on the question of the source of forces, in an attempt to establish that forces derive from impenetrability and inertia. Having done this, Euler then goes on to compare the actions of forces. The treatment starts by providing the kinematics that Euler needs for his mechanics: all motions are characterizable vectorially and procedures for determining and resolving motions are provided. This clears the way for a discussion of the foundations of dynamics in terms of what action is due to internal factors and what to external ones. Euler insists that we begin with an isolated body, since here the separation of internal and external factors is clearest. The workings of the ‘internal’ principles are then investigated in terms of the conditions under which a body would have sufﬁcient reason to deviate from its state of rest or motion. He deﬁnes inertia in terms of the perseverance of a body in its state of rest or uniform rectilinear motion, and argues that when we detect no forces acting on a body then the absolute state of the body can be gauged. If a body is in absolute rest or motion, the axioms for relative rest and motion also apply; conversely, because of inertia, bodies will persist not only in the same absolute state but also in the same relative state on the condition that the body by which the motion is measured is absolutely at rest or has uniform velocity (i.e. providing the reference frame is inertial). The techniques required for a full analytic characterization of inertial motion are then provided and an inertial state is characterized in terms of the second-order differential of distance with respect to time, i.e. d 2s/(dt 2)¼0. ‘External’ principles, by contrast, take the form of forces, which are deﬁned as whatever changes the state of a body, and Euler invokes three foundational notions in accounting for the source and action of such forces: extension, impenetrability, and inertia. His account of impenetrability is the key innovation. Inasmuch as it is not quantiﬁable, impenetrability appears an unlikely prima facie contender for the role of a foundational concept in a quantitative dynamics, and the way in which it is invoked to account for forces is ingenious (Theoria, }131). Imagine two very small, perfectly hard (elastic) spherical bodies, both of which are initially in inertial states, colliding at a sufﬁciently large distance from any other bodies for these other bodies not to have any effect upon them. We know that bodies change state in impact, and Euler takes the generally accepted view that such changes of state must be instantaneous and hence discontinuous. It is also assumed that there are no forces acting on the bodies before or after impact, so that the motion of the bodies is inertial both immediately before and immediately after impact. Now since we also know, Clifford Truesdell, ‘The Rational Mechanics of Flexible or Elastic Bodies, 1638–1788’, Leonhardi Euleri opera omnia series 2, vol. xi section 2 (Zurich, 1960).

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from the law of inertia, that any change of state must be due to forces acting on the bodies, then, since there is a change of state, there must be such forces acting. The question therefore arises as to the source of these forces. Euler approaches this question by considering in the ﬁrst instance what would happen if there were no forces acting. In such a situation, the bodies would continue in their inertial motion, but to do so they would have to penetrate one another. Mutual penetration is impossible, however, and it is this very impossibility that results in forces being exercised. We might consider that each of the bodies changes its own inertial state in order to avoid penetration, but a force is required for this, and there is nothing to provide such a force. What must happen, Euler argues, is that each body changes the other’s state. A body A changes the state of a body B that would penetrate it if it continued in its motion, and vice versa. Consequently, the change of state that B undergoes is not due to some force which it produces itself, but to a force which acts from outside, from A. This force is ‘external’, in the sense that its source is external to the body on which it acts. A potential problem arises here, however, for if the source of the force acting to change B’s state is A, then it would seem that there is some sense in which the force is internal to A. In }121 of the Theoria, the internal principles of a body are said to be the source of the forces acting in impact: ‘it is the very faculty of individual bodies each to persist in its own state that furnishes the forces by which the state of other bodies is changed’. On the other hand, in }131 we are told just as clearly that it is impenetrability that is responsible: ‘as soon as bodies are unable to persist in their state without penetrating one another, impenetrability supplies forces by which their state is changed so that penetration is avoided’. These statements must somehow be reconciled with one another, and the only clue to this reconciliation is provided in }122: The cause of those forces by which the state of a body is changed may be agreed to lie not in inertia alone but in inertia coupled with impenetrability. Indeed, seeing that only bodies can be said to be impenetrable, and since bodies are necessarily endowed with inertia, impenetrability as such involves inertia, so that impenetrability alone is rightly considered the source of all forces by which the state of bodies is changed. It will therefore be proper to consider this property more exactly as being the origin of all forces.20 20 This suggests that when Euler subsequently talked about impenetrability being responsible for force—as in }131—what he meant was impenetrability and inertia. This interpretation of impact obviates the need for any internal forces and shows how impenetrability underpins the changes of state that result from impact. The interpretation depends, however, on the idea that contact and impenetrability provide the conditions under which inertia is dynamically effective, and this needs defending since, despite what he says in Theoria }122, Euler occasionally wrote in a way which suggests that it is impenetrability alone that is dynamically effective, or even perhaps that impenetrability and inertia may both be dynamically effective. }131 suggests this, as does }133: ‘the forces by which the state of bodies is changes [in impact] originate from their impenetrability and they produce so great an effect that penetration is prevented; and these forces are always so great that they sufﬁce for this’. }134 elaborates on the point: ‘the magnitude of these forces is not

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The ﬁrst problem is to determine the kinds of contribution made by inertia and impenetrability to the forces arising in impact. Impenetrability is absolute and a body’s inertia clearly cannot affect its impenetrability in any way. But the fact of a body’s impenetrability does have an effect on its inertial behaviour since if, as }121 indicates, inertia furnishes the forces to change other bodies’ states, then impenetrability would have to be presupposed here since these forces could not arise unless the body were impenetrable. Consequently, inertia with impenetrability is very different in its effects from inertia without impenetrability: impenetrability is a condition of inertia having any dynamic effect, but it is inertia, and not impenetrability, that actually has the dynamic effect. In asking what this dynamic effect is, we must remember that bodies are maintained in their states by their internal principles. Although Euler did not draw the conclusion explicitly, this implies that the state maintained is proportional to the internal principle maintaining that state. That internal principles are quantiﬁable is indicated by the way in which they were compared with external principles in }76: For whether a body be at rest or in motion, whether it remain at rest or acquire motion and continue in it in any way, it is necessary that these phenomena originate from particular causes. Certainly no matter what occurs in a body in respect of rest or motion, this must in no wise be set down as happening by chance and without a reasonable cause. Moreover, whatever this cause may be, it is necessary that it be sought either in the body itself which is being investigated, or outside it. Hence two classes of principles, by which the motion of bodies may be deﬁned, must be set up, the former of which I shall call internal and the latter external. I naturally classify among the internal principles whatever is present in the bodies themselves, containing the reasonable cause of their motion or rest.

Since bodies resist changes to their states, and since their states are due to their internal principles, they must resist changes to their internal principles, and this resistance must take the form of a force. Bearing this in mind, and bearing in mind that we do not have to take account of mass since we are, ex hypothesi, dealing with bodies of the same mass, we can construe impact as follows. When B comes into contact with A in impact, we can say that it experiences A’s internal principles as a force, a force which we would normally term A’s force of resistance to change of state. Note that the force is not in any sense in A: what is in A is its determined by impenetrability, which is not quantiﬁable, but by the change of state that it is obliged to bring about so that the bodies do not mutually penetrate one another’. If the only forces that acted were due to impenetrability, however, and if these acted solely to avoid penetration, then there would be no reason why the bodies should not simply stop, since this would be quite sufﬁcient to avoid penetration, as well as being very economical. Inertia must therefore be dynamically effective, and if it is, then recourse to extra forces deriving from impenetrability is otiose at best. Indeed, it is wholly obscure how impenetrability, which is unquantiﬁable, could give rise to a quantiﬁable force. It seems that we would have to imagine each body having a potentially inﬁnite reservoir of repulsive force, so that it would have sufﬁcient force to repulse any body in impact.

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internal principle, which is not a force because it only maintains A’s state. But this internal principle is experienced by B as a force. There is, therefore, an external force acting on B and this force is not internal to A. Nor does it act at a distance because it is a prior condition of there actually being a force that A and B be impenetrable and that they be in contact. Impenetrability and contact are therefore necessary conditions for this force, but they cannot be sufﬁcient conditions since there would be no force, for example, acting on two stationary impenetrable bodies in contact. For the sufﬁcient conditions to be realized there must be ‘fear of penetration’ and this only occurs when the bodies cannot continue in their present states, that is, when one of the bodies is moving with respect to the other such that the two bodies come into contact. Impenetrability and contact as such cannot, therefore, give rise to any forces, nor can inertia as such. All three are required if there is to be a force.21 Euler’s claim is that the action of all forces here has been explained on the one clear mechanical model: neither internal forces nor action at a distance have to be invoked. The relation of impenetrability to extension and inertia, which Euler also took as being primitive, was however not so straightforward. He made no attempt to deduce these from impenetrability and indeed it is difﬁcult to see how something like inertia could possibly be derived from impenetrability. This leaves us with the problem of showing why bodies must necessarily be extended and inertial, as Euler claimed. He provided no explicit arguments in the case of extension but we can gain some idea of the kind of defence he probably had in mind from looking at how he dealt with impenetrability. Impenetrability was defended on the grounds that it is both necessary and self-evident that bodies be impenetrable. The paradigm for arguments of this kind was Descartes’ demonstration that we cannot but conceive of bodies as extended. Euler accepted the conclusion here and there is every reason to think he accepted the argument. If we construe Euler’s reasoning in this way then the conclusion is that impenetrability and extension are necessary to body because we cannot conceive of a body being either penetrable or unextended; it is essential to what we mean by ‘body’ that bodies be impenetrable and extended. It might be objected that this was just an exercise in deﬁnition, and that a mere deﬁnition was not going to convince anyone, particularly those such as Kant who conceived of body in a very different way. But there was more at stake than mere deﬁnition. Euler’s argument can be seen as specifying the necessary and sufﬁcient conditions for something to be a body in the normal, generally accepted, sense of the term, and then proceeding to show that, given this intuitive and self-evident notion of body, we can build up a sophisticated quantitative mechanics without invoking any of the peculiar agencies that Newton had introduced.

21

This, incidentally, provides an interesting vindication of the inclusion of extension in the foundational concepts, for if bodies were not extended they could never be said to be in contact.

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Inertia was a problem in this respect, although Euler clearly thought it had the same primitive status as extension and impenetrability. The only justiﬁcation for the principle of inertia that we are given in the Theoria, and indeed the only justiﬁcation that we ever ﬁnd in Euler,22 is in terms of the principle of sufﬁcient reason: a body will not change its state without sufﬁcient reason, where the sufﬁcient reason is speciﬁed in terms of external forces. I indicated above, in discussing d’Alembert’s use of the same principle, that it is circular. Despite the fact that the law of inertia was universally accepted, inertia did not and could not have the same status as impenetrability and extension. We may not be able to conceive of a body being penetrable or unextended, but we can surely conceive of it not obeying Newton’s law of inertia; indeed, people had been doing so since at least the time of Aristotle up to the seventeenth century. This prompts the question what exactly the foundational standing of inertia was. Dynamics, whether it be Aristotelian, Cartesian, or Newtonian, deals with states, which are characterizable kinematically, and changes in these states, which are characterizable dynamically. The equation characterizing an inertial state in Euler’s mechanics is a second-order differential of distance with respect to time: d 2s/(dt 2)¼0, taken vectorially. On such a characterization rest and uniform rectilinear motion are clearly equivalent. When d 2s/(dt 2) has any value other than zero a change of state must be involved, and this requires the action of an external force. Euler’s dynamics was primarily concerned with such changes in state, to be explained in terms of force and change of motion. But the foundational concepts of extension and impenetrability were not sufﬁcient, in themselves, to allow an adequate characterization of the notions of force and change of motion. For this we also need inertia, which links kinematics and dynamics by linking the notions of motion and force. Indeed when Euler proceeds to the quantitative discussion, the value of the measure of inertia, inertial mass, is what directly links the value of the force to the value of the change of motion produced by that force. Clearly, then, no foundation for Eulerian dynamics could have been adequate without inertia. Insofar as his proposed justiﬁcation of inertia, at the foundational level, was circular, he failed to achieve his aim, namely to render the system of Newtonian dynamics, suitably reformulated, apodeictic. Its apodeictic appearance arises from the fact that two of its foundational concepts were based upon apparently unobjectionable metaphysical principles—the principle that two bodies cannot be in the same place at the same time, and the principle of sufﬁcient reason—and the third on something that had not only never been questioned but appeared unquestionable—that all bodies are extended. The fact remains, nevertheless, that although these foundations may appear apodeictic, they involved at least one crucial assumption—the assumption of inertia—which could not be justiﬁed at this level. Compare the justiﬁcation given here in }85 of the Theoria, with those provided in }56 of the Mechanica, and }3 of the ‘Recherches sur l’origine des forces’. 22

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Despite the failure of Euler’s aspirations to provide apodeictic foundations for mechanics, however, he did succeed in introducing fundamental clariﬁcations, and the elaboration of the notions of force and inertia in quantitative terms in Chapter 31 of the Theoria was a tour de force. Newtonian dynamics was provided with the basic algebraic form that has been standard since that time. Even more importantly, mass, which up to this point had been formulated rather vaguely and intuitively in terms of quantity of matter, density, volume, and in a host of other ways, came to be deﬁned operationally as a numerical coefﬁcient dependent upon the ratio between the force required to change a body’s state in a particular way and the acceleration of the body produced by that force. To determine exactly how forces change the state of a body, Euler takes inﬁnitesimal bodies and inﬁnitesimal periods, and then integrates to ﬁnd the change of motion in a ﬁnite period. The effect of a force is the distance through which it moves a body over and above that due to the body’s inertia. The procedures used for measuring forces on moving bodies derive from statics (which for Euler, as for d’Alembert, would seem to act as a model of clarity and distinctness), even though statics only concerns the measurement of forces acting upon stationary bodies, because the force acting on a moving body can be assimilated to that acting on a stationary one in as much as the magnitude of a force acting on a moving body is equal to the magnitude of that force which would have the same effect in the same time on that body at rest. The distinction between absolute forces (those forces such as gravitation which act in such a way that their dynamic effects are independent of whether the body affected is at rest or in motion) and relative forces (those forces the effect of which depends upon the velocity of the body, such as the hydrodynamic force of a liquid current on an object) is not relevant here because the calculation must always include that force which impels a moving body as if it were at rest. Consequently, if we calculate the effects of forces upon bodies at rest, we can calculate the effects on bodies in motion. The effects of forces–—distances covered in dt—are directly proportional to the forces themselves. The inertia of a body is proportional to the extent to which that body, when at rest, resists motion. To determine inertia we must consider unequal particles of matter: if equal forces act upon unequal particles of matter then the effects produced in the same inﬁnitesimal time will be reciprocally proportional to the quantities of inertia of the particles of matter. Since the mass of a body is its quantity of inertia, a body’s mass is not to be calculated from its volume but from the force required to move that body in a particular way. Distance moved is directly proportional to force and inversely proportional to mass, and if a body of mass M moves at a constant velocity then d 2s/(dt 2) will equal 0. If the body is accelerated by a force F in the direction of its motion, however, then d 2s/(dt 2) will be as F and reciprocally as M. Therefore, d 2s/(dt 2) will be as F/M, or F ¼ Ma, assuming units to be ﬁxed. On integration this gives us the extra distance traversed and hence a measure of the force, assuming this force to be constant.

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Moreover, by resolving the motion of a body along the three orthogonal axes x, y, and z, we can complete the treatment of inﬁnitesimal bodies by specifying their motions in terms of the forces acting in the three planes, so that we obtain three general equations:

I

d2 x f1 d 2 y f2 d 2 z f3 ¼ ¼ ¼ II III dt2 M dt2 M dt2 M

Having established units for these equations, Euler then uses them, together with the system of units established, to examine the motion of a point mass. On this basis, while continuously reﬁning the analytic techniques at his disposal, he was able to offer a treatment of an extended range of mechanical problems—the dynamics of points, ﬁnite rigid bodies, ﬂexible bodies, elastic bodies, several bodies with mutual interactions, and ﬁnally ﬂuids—on a secure and fruitful basis. Indeed, his treatment of the dynamics of points, rigid bodies, and ﬂuids went a large way towards providing the basis for all subsequent theoretical understanding of these phenomena. THE LIMITS OF MECHANICS We can distinguish two aspects of Euler’s foundational project. The ﬁrst is the attempt to provide apodeictic foundations for mechanics, and it is this that we have just examined. The second lay in the attempt to use such a foundationally secure mechanics as the basis for the whole of physics. More speciﬁcally, it lay in the idea that the processes and interactions described in rational mechanics were the basic form of all physical processes and interactions. For Euler, the development of a comprehensive rational mechanics was a prelude to a reduction of physics generally to mechanics, in effect a complete rejection of an autonomous matter theory. Some idea of the difﬁculties that such a programme encounters can be gleaned by considering two different kinds of question: how one builds up one’s resources so that one can move from simple mechanical phenomena to complex mechanical phenomena, and how one translates physical phenomena that seem to be intrinsically non-mechanical into the vocabulary of rational mechanics. An example of the ﬁrst is the move from his treatment of the mathematical behaviour of mass points to the actual behaviour of ﬂuids in observable physical situations. The second is the attempt to assimilate recalcitrant phenomena such as gravity, electricity, magnetism, and chemical reactions. On the ﬁrst set of questions, it is worth noting from the outset that the behaviour of ﬂuids played a central role in rational mechanics, for both theoretical and practical reasons. The origins of rational mechanics in the Malebranchean group in the Acade´mie des Sciences anchored its early fortunes in a rejection of

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action at a distance and a commitment to vortex theory, and this was no less the case in Basel, where the Bernoullis were among the staunchest and most able defenders of vortex theory. The understanding of the behaviour of ﬂuids was of immense theoretical importance in that it was on ﬂuid mechanics that the fortunes of vortex theory hung. At a practical level, the standing of, and support for, rational mechanics depended to a large extent on the ability of ﬂuid mechanics to inform ship design. Colbert was minister for the navy at the time that the Acade´mie was founded, and he made sure that the construction of faster, more agile ships was a high priority to which the Acade´mie was expected to contribute. Indeed, this was one area in which rational mechanics might have established its practical and technological relevance. Mechanics had replaced matter theory as the basis for understanding ﬂuids in a piecemeal way as early as Torricelli in 164423 and in a systematic way in Newton’s Principia, but it was transformed in rational mechanics. Two seminal treatises were Daniel Bernoulli’s Hydrodinamica sive de viribus et motibus ﬂuidorum commentarii (published in 1738 though composed around 1729) and Johann Bernoulli’s Hydraulica (1743).24 D’Alembert wrote two key texts on ﬂuid mechanics, Traite´ de l’equilibre et du mouvement des ﬂuides (Paris, 1744) and Essaie d’une nouvelle the´orie de la re´sistance des ﬂuides (Paris, 1752), as well as his Reﬂexions sur le cause general des vents (Paris, 1747). The tradition culminated in Euler’s numerous papers and treatises on ﬂuid mechanics from his 1745 commentary on Benjamin Robins’ New Principles of Gunnery25 to his writings on the construction and manoeuvrability of ships in the 1770s.26 At issue here are both theoretical questions, about the adequacy of the new forms of analysis of ﬂuids, and practical ones, about the technological implications of the work. From a theoretical point of view, the question is whether the mathematically sophisticated practitioners of rational mechanics were able to bridge the kind of divide we identiﬁed in Book II of Newton’s Principia, where there is a radical discontinuity between an idealized mass-point modelling and an experimentally driven account of the behaviour of ﬂuids. We saw in Chapter 2 that Book II of the Principia falls naturally into two parts. In the ﬁrst four sections, Newton invokes a ‘rare medium’ modelled on aggregations of mass points, and the focus 23 The work that is usually taken to initiate the mechanical treatment of ﬂuids is Torricelli’s ‘De motu gravium’, which appeared in his Opera geometrica of 1644. Fluid mechanics in the seventeenth and eighteenth centuries dealt with two main areas: the question of how ﬂuids are discharged through an opening in a tank, and the effects that a ﬂuid current exercises upon a body immersed in it. Torricelli’s contribution is to the ﬁrst question. Our concern will be with the second. 24 These two were translated as Daniel and Johann Bernoulli, Hydrodynamics and Hydraulics, trans. T. Carmody and H. Kobus (New York, 1968). 25 Euler wrote an extensive commentary for the German translation of Robins’ book, which had appeared in 1742. It was published as Neue Grundsa¨tze der Artillerie, aus dem Englischen des Herrn Benjamin Robins und mit vielen Anmerkungen versehen (Berlin, 1745). 26 The most complete account of these is Clifford Truesdell, ‘Rational Fluid Mechanics, 1687–1765’, and ‘Rational Fluid Mechanics, 1765–1788’.

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of the analysis is how such a medium affects the motion of bodies falling or orbiting through it. From the ﬁfth section onwards, however, the discussion proceeds in terms of ‘ﬂuids’, which are deﬁned in purely phenomenological terms, as something whose parts yield to forces applied to them. The challenge for rational mechanics was to provide the resources to bridge this gulf between a mechanically described medium and phenomenologically described elastic ﬂuids. We can trace a very signiﬁcant evolution in thinking about the behaviour of ﬂuids between Newton and Euler. For Newton, a ﬂuid such as air was an aggregate of particles that responded individually to the laws of mechanics, so that the force generated by the impact of a current against an object consisted of the sum of the effects of each individual impact. The application of the idea of impact to ﬂuids had been developed above all by Mariotte in the early 1680s,27 and it had resulted in the attempt to measure the force of jets of ﬂuid, whether water or air, by determining how much weight was needed to counterbalance them. This provided the hypothetical physical model—one based in hydrostatics—for research in ﬂuid mechanics over the next ﬁfty years, and it guided the work of the mathematicians and natural philosophers who worked on hydraulics, hydrostatics, hydrodynamics, and the stability of vessels.28 In the course of these investigations, which were supplemented with increasingly sophisticated experiments with towed models, there began a move away from the notion of impact towards the far more mathematically complex ideas of streamlines and pressure. This was in large part due to Daniel Bernoulli’s 1738 Hydrodinamica, which showed that hydraulic phenomena were quite different from those dealt with in statics. The basic problem with the Newtonian idea of ﬂuids as collections of hard particles imparting resistance through inelastic collisions, was that there was no way, on this basis, to treat a ﬂuid as a deformable mass. There were a number of steps in the transition to a more satisfactory account. First, Daniel Bernoulli linked ﬂuid pressure with its velocity, and Johann Bernoulli showed how to account for internal pressure by considering a ﬂuid as composed of inﬁnitesimal elements; at the same time Clairaut expressed equilibrium by means of partial differentials and, using this, d’Alembert (abandoning the impact model that he had advocated in the Traite´ of 1744) elaborated a conception of resistance due to pressure. Finally, Euler synthesized these accounts into a set of basic equations, treating a ﬂuid as a continuum, separated in the idealized case into elemental domains capable of supporting forces and internal pressures, whose spatio-

27 Edme´ Mariotte, Traite´ du mouvement des eaux et des autres corps ﬂuides (Paris, 1686). The work appeared posthumously, edited by La Hire, Mariotte having died in 1684. 28 It also had a central bearing on the application of inﬁnitesimal analysis to the discovery of the shape of the body of least resistance and the shape of hull of least resistance, the calculation of the shape of the stern of least resistance, and the investigation of the complex mathematics of the shape of inﬂated sails. On some of the mathematical challenges here see the papers collected in Craig Fraser, Calculus and Analytical Mechanics in the Age of Enlightenment (Aldershot, 1997).

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temporal evolution is regulated by the laws of dynamics, expressed by a set of differential equations.29 As we have seen, in Euler the continuum account of ﬂuids, like everything else in rational mechanics, can be traced back ultimately to his foundational account of the behaviour of mass points. In this sense, he would seem to have bridged the divide that Newton was unable to bridge in Book II. Certainly great progress had been made, but there was more—much more—than mathematics at issue.30 In particular, it was clear that the general theory of ﬂuids that Euler developed did not supply practical guidance, much less practical answers, and some fundamental factors such as ﬂuid friction were left completely open in this account. These questions had to be broached in an experimental way, as the coarse-grained practice of towing different shaped vessels through tanks replaced the ﬁnegrained procedures of analysis.31 It is in this context that the worry that rational mechanics deals at best with some useful abstractions becomes a pressing one. As far as practical questions were concerned, the precise mathematical treatment of the problem of the effects that a ﬂuid current exercises upon a body immersed in it would, on the face of it, seem to be clearly of practical signiﬁcance. Yet it is far from clear just how useful developments in rational mechanics were to shipbuilders, or more generally how much they needed it. As Ferreiro has pointed out, ‘sailing ships were the most complex engineering structures of the day. They combined the heavy wooden construction of the hull and masts with a dizzying array of standing rigging to support the masts, hundreds of lines and blocks to control the yardarms and sails, capstans for hauling up the anchors, tillers and wheels to turn the rudder, bilge pumps, and such, for which the constructors had overall responsibility to integrate into the ship.’32 These constructors were highly trained professionals who were familiar with arithmetic and geometry as far as it bore on their craft, but they were often otherwise illiterate. They picked up their skills in shipyards through apprenticeships, not at colleges and universities, and, since they were building ships for navies that were frequently at war, they often worked under conditions that called for quick practical judgements. Moreover, in military terms the ships they constructed were far more successful than infantry with respect to capacity, speed, and logistical costs. The theoretical work of the mathematicians held little attraction for those with 29

See the detailed treatment of these questions in Simo´n Calero, The Genesis of Fluid Mechanics. The main mathematical challenge was to integrate Euler’s equations, and Lagrange in particular reformulated them so as to allow more straightforward integration, initially in his ‘Me´moire sur la the´orie du mouvement des ﬂuides’, Histoire l’Acade´mie Royale des Sciences et des Belles-lettres de Berlin (1781), 151–98; and then in a more elaborate form in his Me´canique analytique (Paris, 1788). 31 The understanding of the motion of vessels through ﬂuids effectively came to a halt in the 1760s, to be resumed only with William Froude’s resolutely empirical towing-tank tests of the 1870s, which were devised speciﬁcally to investigate ﬂuid resistance and vessel stability. 32 Larrie D. Ferreiro, Ships and Science: The Birth of Naval Architecture in the Scientiﬁc Revolution, 1600–1800 (Cambridge, Mass., 2006), 24. 30

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responsibility for constructing such ships. Nor is this surprising, for this theoretical work was not developed in response to perceived problems with ship design, such as stability problems, which were in any case best solved by practical measures, since even if the theory could be applied, the calculations would be enormously complex and time consuming, and hence quite unproﬁtable. Ferreiro has argued plausibly that naval architecture was developed not in response to problems to do with the construction or functioning of ships at all, but rather ‘in response to a bureaucratic need by naval administrations for greater control over their constructors and for standardization of the ship design process’.33 This coheres well with what we saw of the rationale of the setting up of the Acade´mie in Chapter 6: namely, there was an explicit programme of rationalizing the various trades along the lines of a scientiﬁc method that realized the canons of objectivity, testing, and public scrutiny. The development of a successful navy did not require the imposition of such values, however; nor did it require bureaucratization and standardization, as the case of Britain, where such developments were rejected, indicates.34 What of the second set of issues, the assimilation of apparently non-mechanical phenomena to mechanics? Euler’s treatment of ﬂuids was of importance not just to his attempt to extend the analysis of mass points to elastic bodies, but also in the attempt to model physical phenomena more generally on a mechanical basis. The early attempts to develop an understanding of ﬂuids, in terms of hard particles imparting resistance through inelastic collisions, was a dead end for both enterprises. More generally, it was evident that the external forces invoked by Euler in accounting for impact were inadequate as a model for the action of all forces. Such forces are contact forces, and they are repulsive (in the passive sense of ‘resistive’ rather than in an active sense). But there are at least prima facie classes of forces which are not of this type. There are apparent contact forces which are attractive, such as the force of cohesion; apparent non-contact forces which are repulsive, such as the magnetic force existing between like poles; apparent non-contact forces which are attractive, such as gravitation and the magnetic force existing between unlike poles; and ﬁnally there are phenomena such as electricity where it is not immediately clear what kinds of force are acting. These were all phenomena of which Euler was aware, as were his contemporaries. Magnetic forces were generally taken to act mechanistically at this time, and several mechanistic models of gravitation were proposed, from Fatio de Duiller’s account of 1690 to that of LeSage in 1748.35 Gravitation was accounted for on this model by postulating a stream of ultraﬁne particles, themselves free 33

34 Ibid., 25. Ibid., 26. LeSage submitted his ‘Essai sur l’origine des forces mortes’ to the Acade´mie des Sciences in 1746, but it was not published on the grounds that he had been anticipated in the (by this stage largely forgotten) work of Fatio de Duiller and others, and the only exposition of it published in his lifetime was in his Essai de chimie me´canique (Rouen, 1758). 35

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from gravitational attraction. Because they impacted on bodies from all directions, their net effect cancelled out the individual impacts so that they did not move the body (although LeSage did allow for small temporary imbalances). Ordinary bodies could however cast what might be termed a ‘gravitational shadow’, in that some of the particles would be blocked along the lines connecting the parts of the bodies. This blockage would cause a disequilibrium which would give the effect of the bodies being attracted to one another, where the closer the bodies the greater was the blockage. Such a qualitative reconstruction of what happens was recognized as unsatisfactory, not least because it was unclear on this account why the impulsive force should vary with the mass of the bodies rather than their surface areas. But the model ﬁt well with the kinetic theory of gases, pioneered in Daniel Bernoulli’s Hidrodynamica, and held out some hope for those who saw the solution to gravitation in terms of its mechanical reduction. Like d’Alembert’s account in the Traite´ de Dynamique, Euler conﬁned himself to contact forces in the works we have looked at, but he does add an afterthought on gravitation, in which he opts for an aether-based account: For although no one has yet been in a position to demonstrate conclusively the cause of gravity and the forces by which celestial bodies are moved by means of collision or by centrifugal force, we must nevertheless admit that no one has demonstrated their impossibility. And it seems rather likely that all these bodies, which are indisputably surrounded by a subtle matter, are all put in motion by it, although we do not know the manner in which this is effected.36

Once Euler had moved away from the idea of hard particles imparting resistance through inelastic collisions, and had developed the notion of a continuum, the physically and mathematically richer notion of ﬂuids that it introduced made the idea of modelling a range of physical phenomena on ﬂuid mechanics more attractive, because continuum mechanics was more likely to be able to capture the complexities of such phenomena. That is, the vastly more powerful mathematical and physical resources that continuum mechanics provides potentially supplied an important ingredient in Euler’s programme of reduction to mechanics. In actuality, however, he was unable to deploy these resources. In the case of gravitation, the aether-based account that Euler hints at is manifestly unsatisfactory. It assumes a very dense aether without even raising the question of whether a dense ﬂuid would offer resistance to the motion of celestial bodies, where the very least resistance would be in conﬂict with the observed accuracy of Kepler’s laws. More generally, it skirts over the question of whether the aether in question is compressible (as in a gas) or incompressible (as in a liquid). The idea that the ﬂuid carries the bodies around suggests it is liquid, an incompressible ﬂuid, whereas the claim that it comprises ‘subtle’ matter suggests that it is more like a gas, that is, compressible and hence not the kind 36

‘Recherches sur l’origine des forces’, }59.

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of thing that could carry planets in its wake.37 Nevertheless, when we turn to developments in magnetism and electricity, we might expect to ﬁnd a different picture, for here resistance was not at issue.38 The traditional understanding of electricity, as we saw when considering Hauksbee in Chapter 5, was one that worked in terms of an emission of particles from the ‘electric’. The aether theory set out by Euler in the Lettres was closer to vortex accounts of gravitation, but as I have indicated, the understanding of ﬂuids was now much more sophisticated so that, as long as one did not have to face the physical problem of resistance, a ﬂuid theory was mathematically tractable. Yet by the 1750s, the range and complexity of electrical phenomena had increased so radically, in what was by this stage an extremely rich experimental movement, that Aepinus, a prote´ge´ of Euler’s, and the ﬁrst to offer a mathematical account of electrical phenomena, argued in the introduction to his pathbreaking Tentamen Theoria Electricitatis et Magnetismi of 1759 that the ﬁrst priority was to impose an order on electrical phenomena, rejecting the project of reduction to a mechanical model. Taking into account the enormous range of electrically induced phenomena, Aepinus dismissed the idea that electricity and magnetism could be derived from a single aether, as postulated by Euler, and Euler charged Aepinus with introducing arbitrary forces acting at a distance:39 as indeed he did, and explicitly so. He approached electrical theory as a self-contained domain, not as part of a more general mechanical project; this was much in the spirit of Gray, except that, crucial as experimental study was to Aepinus’ understanding, his aim was the imposition of order through quantiﬁcation.40 He invoked not only unexplained forces of attraction and repulsion in this exercise, but construed electrical activity in terms of action at a distance. The point is that, on the basis of these assumptions, he was able to develop electrical theory on a comprehensive mathematical basis, taking as his model Euler’s very successful attempt to place mechanics on this basis. But, far from assimilating electrical theory to mechanics, the exercise ended up reinforcing the idea of it as a separate physical domain. The development of powerful mathematical techniques in rational mechanics did not, then, in fact enhance the prospects of a reduction of physics to 37 Cf. Curtis Wilson, ‘Euler on Action-at-a-Distance and Fundamental Equations in Continuum Mechanics’, in P. M. Harman and Alan E. Shapiro, eds., The Investigation of Difﬁcult Things (Cambridge, 1992), 399–420. 38 There is an extended treatment of electricity in a 1754 essay by Euler’s son, to which Euler himself contributed (possibly to a signiﬁcant extent), in which an extremely subtle and extremely elastic aether is invoked: Johann Albrecht Euler, ‘Disquisitio de causa physica electricitatis’, in Dissertationes selectae Jo. Alberti Euleri, Paulli Frisii et Laurentii Beraud quae ad Imperialem Scientiarum Petropolitanam Academiam An. 1755 missae sunt (St Petersburg and Lucca, 1757), 1–40. See the discussion in Roderick W. Home, Aepinus’s Essay on the Theory of Electricity and Magnetism, introd. monograph and notes by R. W. Home, trans. P. J. O’Connor (Princeton, 1979), 68–71. 39 See Home, Aepinus’s Essay, for the relevant section of the Tentamen (243), a general discussion of the issues (68–9), and a statement of Euler’s reaction (15). 40 See the exemplary account ibid., 65–136.

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mechanics. This adds a new dimension of complexity to the question of the foundational status of rational mechanics. In looking at the foundational aspirations of d’Alembert and Euler, we have seen that the attempt to ground rational mechanics in a priori concepts was a failure. It is now also clear that the complexities of the behaviour of ﬂuids and bodies immersed in them goes well beyond the resources of the discipline of ﬂuid mechanics, which had to be replaced by experimentation when it came to an understanding of empirical, as opposed to idealized, behaviour. The problems were profound. It is worth remembering in this context that d’Alembert’s critics commented on his inability to deal with experiments, and his close friend Bossut noted that he had little respect for observation and practical mechanics, and was ignorant of basic physical facts.41 Although this could not be said of Euler, there is no doubt that d’Alembert’s attitude was a symptom of an underlying general problem with rational mechanics, and it was compounded not only by a sense that rational mechanics might be self-contained and isolated from other physical phenomena, but even that the analytic methods on which it rested had themselves reached their limits. Diderot for one is in no doubt as to the future of mathematics: We are on the verge of a great revolution in the sciences. Given the taste people seem to have for morals, belles-lettres, the history of nature and experimental physics, I dare say that before a hundred years have passed there will not be more than three great geometricians remaining in Europe. The science will stop short where the Bernoullis, the Eulers, the Maupertuis, the Clairaut, the Fontaines and the D’Alemberts will have left it.42

Diderot could be considered hostile to rational mechanics but his sentiments were mirrored in one of the greatest practitioners of the art, Lagrange, who wrote to d’Alembert in 1781 that he was not sure whether there would be anything more to achieve in analytic geometry in ten years’ time: It seems that the mine is almost too deep already, and that unless new seams are discovered, it will be necessary to abandon it sooner or later. Physics [i.e. areas such as electricity] and chemistry now offer riches that are more brilliant and easier to exploit; also the taste of the age appears to be turned entirely in that direction, and it is not impossible that the places of Geometry in the Academies will some day go the same way as the chairs in Arabic at the Universities today.43

The problems that rational mechanics was encountering by the second half of the eighteenth century were profound. The attempt to deal with physical problems in a mathematical form was unprecedented in the rigour, depth, and 41 Charles Bossut, Histoire ge´ne´rale des mathe´matiques depuis leur origine jusqu’a` l’anne´e 1808 (2 vols., Paris, 1810), ii. 431. 42 Diderot, Pense´es sur l’interpre´tation de la nature (Paris, 1753), } 4. 43 Joseph Louis Lagrange, Œuvres (14 vols., Paris, 1867–92), xiii. 368. Quoted in Hankins, Jean D’Alembert, 99–100.

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sophistication of the techniques that it brought to bear, but this was at the cost of transporting the discipline into a realm of almost Platonic abstraction, losing contact with empirical, experimental programmes and, in spite of the initial hopes of its proponents, looking increasingly less plausible as a model for physical enquiry generally. Although its fortunes had improved somewhat by the turn of the century, due to the systematic breakthroughs in celestial and general mechanics by Laplace and Lagrange, mechanics was by this stage largely isolated from the mainstream of physical enquiry. This was, at least in part, a potential step backwards to a pre-Galilean standing for mechanics, for it was Galileo who had ﬁrst shown in detail, in his treatment of falling bodies, how to pursue mechanics so that it was no longer a practical-mathematical discipline, but a genuine form of physical enquiry. It now turned out that the ability of mechanics to engage physical questions fully was very limited, and this role was increasingly returned to matter theory. A case of particular interest in this respect is that of optical refraction, for what was at stake here is a fundamental assumption of mechanism, and one which, in this context, had gone unchallenged even by Newton. This is the assumption of the ultimate homogeneity of matter.44 Newton’s prism experiments had shown that different colours are refracted differently, and it was evident that this is what is responsible for chromatic aberration. He explored whether it might be possible to avoid chromatic aberration by using composite lenses—thin lenses glued together—where the divergence of different coloured rays induced by the ﬁrst lens was corrected in the second lens. What one would need to do to construct such an achromatic lens would be to coordinate the refractive indices of the two joined lenses in such a way as to cause the rays to re-converge. Newton calculated that a combination could never be made to work better than a single lens, however, which meant that the problem of chromatic aberration could not be overcome in refracting telescopes. In response, he developed a reﬂecting telescope. Yet right from the start there was reluctance to embrace the reﬂecting telescope: the reﬂection by the mirror produced an image much weaker than that of refracting telescopes, and the mirror itself tended to tarnish very quickly. These difﬁculties were signiﬁcant, and meant that the refracting telescope was that used throughout the rest of the century,45 with Hooke in particular arguing that the difﬁculties with the refracting telescope could be overcome.46 The formula for refraction on which Newton’s calculations rested was not questioned until 1748, however, when Euler replaced it with one which had the consequence

44 See Keith Hutchison, ‘Idiosyncrasy, Achromatic Lenses, and Early Romanticism’, Centaurus 34 (1991), 125–71, to which I am particularly indebted here. 45 See Albert van Helden, ‘The Telescope in the Seventeenth Century’, Isis 65 (1974), 38–58. 46 See Hideto Nakajima, ‘Robert Hooke as an Astronomer’, in Michael Cooper and Michael Hunter, eds., Robert Hooke: Tercentennial Studies (Aldershot, 2006), 49–62.

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that achromatic lenses were in fact possible in principle.47 Much controversy surrounded this move, but in 1757 a compound achromatic lens was patented, and an account of it published, by a lens-maker, John Dolland.48 On the face of it, Euler had been vindicated. The problem was that Dolland did not work from formulas expressing ratios between refractive indices, as Newton and Euler did, but instead ignored such considerations and designed the lenses on the basis of measured values of the refractive indices. These measurements did not ﬁt either Newton’s or Euler’s formula: in fact they did not ﬁt any formula. Euler characterizes Dolland’s calculations as ‘bizarre and revolting’, and attempts, unsuccessfully, to develop a new theory of achromatic lenses in which the regularity of refractive indices is retained.49 Hutchinson has pointed out that the success of Dolland’s lenses undermined a fundamental tenet of mechanistic optics, namely the uniformity of refraction. By the principle of the uniformity of refraction, each interface and medium were held to have characteristic refractive powers, so that if two interfaces had the same power they would produce identical refractions; moreover, the equality of refracting powers could be tested by passing rays of any particular colour through them. Above all, refracting powers were held to be related to the density of the material, construed as homogeneous. But Dolland’s experience with lenses showed that individual media exerted idiosyncratic inﬂuences on the rays that passed through them. The rays in some cases simply seemed to react with the medium through which they passed, and their behaviour was capturable, if at all, in terms of chemical afﬁnities, rather than in terms of some homogeneous material.50 A range of questions which had seemed absolutely secure—aetherial explanation, optical density, median rays, and Newton’s harmonic division of the spectrum—thereby came into question. It now looked as if the wrong kind of resources had been deployed, at least beyond a certain level of approximation, and even d’Alembert came to accept that it could not simply be a question of equations for refraction, writing that ‘there is no theoretical way either to establish or refute Newton’s equation or that of Euler . . . experience is the only completely reliable means of determining, not only the [values of the various refractive indices] but also [the fourth] when one knows [the other three].’51 47 Simplifying somewhat, take the case where a homogeneous light ray travelling through a medium (say air) meets one of two different optically denser media (medium 1 and medium 2). In both cases, blue rays and red rays will diverge on entering the denser medium. Let B and R be the refractive indices for the blue and red rays in medium 1, and b and r be the refractive indices for the red and blue rays in medium 2. Newton’s formula is: (R–1)/(B–1) ¼ (r–1)/(b–1). Euler shows, on theoretical grounds, that this cannot be correct, and substitutes a different formula: logR/logB ¼ logr/logb. 48 John Dolland, ‘An Account of Some Experiments Concerning the Different Refrangibility of Light’, Philosophical Transactions 50 (1757–8), 733–43. 49 See Hutchison’s masterly account in his ‘Idiosyncrasy, Achromatic Lenses, and Early Romanticism’, 145–50. 50 Ibid., 150–1.

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By the 1780s, the a priorist aspirations of mid-century rational mechanics had been abandoned by French natural philosophers. Some of the most important developments in areas such as celestial mechanics, one of the core concerns of rational mechanics, were no longer a result of deriving theorems from ﬁrst principles, but rather arose from the development of a probability theory of errors, enabling one to derive the most probable value from a series of different observations. It was on these probabilistic grounds, for example, that Laplace was able to establish the stability of planetary orbits. At the same time, d’Alembert’s prote´ge´ Condorcet had explicitly abandoned the attempts to present some truths of the physical sciences as rationally necessary, and was arguing that these truths, like those of the moral sciences, were all contingent, to be explored using the calculus of probability that had been developed in the moral sciences.52 52

See Baker, Condorcet, 171–89.

9 Material Activity For seventeenth-century mechanists, uniﬁcation of natural philosophy had been the single greatest aspiration. This aspiration had not been abandoned in rational mechanics, which can be seen as an extensively revised version of the mechanist project. However, whereas for most mechanists the bulk of their activity had been devoted to accounting for those areas that seemed to fall outside the resources of micro-corpuscularianism by showing—typically either through the distinction between primary and secondary qualities, or through the reductionist programme in biomechanics—how they might be accommodated to these resources, practitioners of rational mechanics by contrast devoted themselves to the development of what they took to be the core of the discipline. If rational mechanics was genuinely the core, then everything else—the periphery—could be expected to fall into place around it, in the sense that one should be able to work outwards by employing the increasingly sophisticated resources of the core. This project failed, for reasons that we explored in the last chapter. The ‘core’ was so self-contained that contact with other physical phenomena could hardly be established, with the result that rational mechanics lost its putative role as the core of natural philosophy, as it became merely one of a number of naturalphilosophical disciplines. Rational mechanics had assumed the role of a mathematically precise substitute for matter theory, something that would replace the diffuse uncoordinated ensemble of disciplines that had come to the fore with the demise of Aristotelian matter theory and the rise of experimental disciplines and traditions. But it was increasingly unable to satisfy this role, and its failure in this respect meant that matter theory gradually took on a degree of autonomy, not least from mechanics, that it had not experienced since before the rise of mechanism. The difference was that matter theory was no longer in competition with a dominant account, Aristotelianism, with which it had to engage and which it had to displace: a project that had been at the core of Bacon’s approach, for example. Rather, it was now free from the demands of integration into a system and, as in the cases of Gray and Geoffroy, could bypass considerations of micro-corpuscularian activity and offer an account in terms of phenomenal relations. This latter kind of account could be highly systematic: as in Geoffroy’s case, which involved ordering phenomena on the basis of experimentally induced afﬁnities. What it is not is an instance of a programme of uniﬁcation through reduction, something which characterized mechanism and some earlier forms of

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matter theory. Neither is it an instance of a programme of uniﬁcation through assimilation, as rational mechanics is: there is no attempt, for example, to argue that chemical afﬁnities stand at the basis of, or are the model for, all other physical phenomena. As we move into the eighteenth century, matter theory—under which we can group any discipline outside mechanics that looks at physical features of material objects and their interactions, such as the study of electricity, pneumatics, chemistry, and physiology—appears as a network of different kinds of practice having no intrinsic substantial connections with one another, and having no intrinsic relation with the mechanics that aspires to reduce and unify them. In the early decades of the century, there were attempts—in England just as much as in France—to establish some kind of micro-corpuscularian basis for these areas of matter theory. But with the appearance of the later editions of Newton’s Opticks, where the introduction of an aether seriously challenged the reductionist aspirations of Newtonians, a more cautious attitude towards reductive explanation emerged. The absence of intrinsic relations between the disciplines, and the absence of any plausible reductive strategy, suggest that there may well be nothing (other than merely semantic considerations) that holds natural philosophy together as a distinctive enterprise. Natural philosophy could function perfectly well as a loose grouping of disciplines, related by various dependencies and overlaps, but not forming a single enterprise. But there were various extrinsic constraints acting as well, and these played a crucial role. We cannot ask what it is that holds natural philosophy together, without ﬁrst asking why we should assume that anything holds it together, and, if we ﬁnd that it is extrinsic rather than intrinsic constraints that are at issue, we need to ask what demands were being made on natural philosophy such that it needed to be uniﬁed. By midcentury, natural philosophy had taken on the role of paradigm bearer of cognitive values in French Enlightenment projects that we discussed in Part III. To act in this role, many considered that some degree of unity in the make-up of the bearer was necessary. If it was to function as a model of rationality, a signiﬁcant degree of coherence was needed, although, as I have indicated, the understanding of what was at issue in France was different from that which we ﬁnd, for example, in the system-building of Wolff in Germany: and, in turn, this was different from the kind of coherence required by physico-theological projects that abounded in England at the turn of the century. We shall see in Chapter 11 how the image of natural philosophy was transformed so that what it told us about, above all, was sensibility. In this way, a new basis for the integrity and relevance of natural philosophy came into existence. This conception was in some respects at odds with the idea that natural philosophy embodied canons of rationality. It uses lessons learned from matter theory to transform natural philosophy so that it can conform to its role as model for knowledge. It is therefore appropriate to ask in what ways matter theory, as a set of—at best—loosely coordinated disciplines, could embody forms of

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understanding of the natural world that had been absent in the project of uniﬁcation by reduction or assimilation. THE RESURGENCE OF AN AUTONOMOUS M AT T E R T H E O R Y Before the seventeenth century, matter theory had been constitutive of physical enquiry. This changed in the course of the century, as mechanists offered an integration of mechanics into matter theory yielding something that aspired to provide a wholly new vision of what natural philosophy might be like. This integration was spectacularly successful at a programmatic level, but at that of ﬁne detail, the problems remained recalcitrant. From an early stage in his career, Newton, initially a proponent of the new mechanism, had found the predominant form of integration, Cartesianism, to be in many respects problematic and counter-productive, and, failing to offer anything that might replace it, he had in effect prised the two disciplines apart and pursued matter theory and mechanics separately. Newton had always hoped that the two could be united into a comprehensive account but, unlike many of his contemporaries, he never allowed this aspiration to determine the direction of either his mechanics or his matter theory. The mechanist project of integrating mechanics into matter theory had transformed the latter in a number of respects, however, and it was not simply a question of abandoning inappropriate connections that mechanists had attempted to establish between them. At the most general level, matter theory had been provided with new tasks, ones that differed signiﬁcantly from those of its pre-mechanist version. But in the early decades of the eighteenth century, as matter theory came to be largely dissociated from developments in mechanics and even to some extent from micro-corpuscularianism, just how these tasks were to be assessed became deeply problematic. Some basic forms of enquiry were taken over from the mechanist project, for the new matter theories could not just abandon what was in many respects a very successful micro-corpuscularian programme. But it could never have been simply a question of realizing goals that had been set by mechanism. There was a broad conception of the explanatory domain of matter theory that pre-dated mechanism, which had effectively been abandoned as long as the reductive aspirations of mechanism had seemed to be successful, but which, in the wake of the demise of mechanism, were revived and became central in a reassessment of just what kinds of phenomena it could be invoked to explain. We have looked at one attempt to reconcile these two sets of constraints, in Leibniz, but Leibniz’s solution was idiosyncratic in a number of respects. What marked out his proposed solution from other attempts, especially in areas such as chemistry, was his advocacy of a systematic metaphysics as an underpinning for natural

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philosophy, and, as we have seen, his matter theory—turning as it does on his account of force—occupies an uneasy space between his metaphysics and the natural philosophy it is designed to ground. By contrast, the chemists, physiologists, and others who pursued matter theory as an autonomous enterprise in the ﬁrst half of the eighteenth century eschewed metaphysical systems. At stake here were issues deriving from the divergence between systematic natural philosophy and experimental natural philosophy, which had direct consequences for matter theory in that it prompted a division between systematic matter theory and matter theory as a form of experimental natural philosophy. Among the questions that I include in those deriving from the mechanization of matter theory, and which continued to be pursued after that mechanization had been called into question, are those that were prompted by Newton’s Queries to the Opticks, which turn on whether matter is fundamentally particulate or ﬂuid. In some respects, this is a dispute that goes back to the Epicureans and Stoics, but it is transformed by matter theory having been subjected to the rigours of mechanization. It was gravitation above all that resisted such mechanization, and hence it was on the question of gravity that the issues were now focused, which made them signiﬁcantly different from those that occupied the Hellenistic disputes. In the speciﬁc context of gravitation, a good deal of the discussion turned on a choice between particulate and aether theories. But there was a broader issue at stake, closely tied in with this dichotomy, namely whether the ultimate substance of which things were composed was ﬂuid, associated with living things, or dry, associated with non-living ones.1 Here the revival of the pre-mechanist concerns of matter theory becomes important. The microcorpuscularian reduction programme that was part of the mechanization of matter for mechanists had required two seemingly unrelated things. First, it had required the reduction of macroscopic phenomena to micro-corpuscles, which were discontinuous bits of hard matter. Macroscopic bodies, including liquids such as water, the pneumatic phenomenon of air, and phenomena such as ﬁre, were reduced, as a precondition of explanation, to the level of the action of hard microscopic corpuscles. Second, it had required the assimilation of living things to non-living ones, through the programme of biomechanics. Traditional matter theory—that of Aristotle for example—had not only not offered a reductive account of living things, but had in fact taken living things very much as its model case, developing its explanatory principles on questions such as the nature of change around those different forms of change to which living things are subject, which included generation and corruption, and change of 1 The association between ﬂuids and life had been one that was dominant in many ancient cultures. An example is the ancient Greek view that life is a process whereby liquid gradually diminishes until the ﬁnal desiccation, which is death: see Richard Broxton Onians, The Origins of European Thought about the Body, the Mind, the Soul, the World, Time, and Fate (2nd edn., Cambridge, 1954), ch. 6.

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qualities such as colouring, as well as local motion. In other words, the treatment of living things was an integral part of matter theory. With the gradual demise of mechanism, its adherence to hard microscopic corpuscles seemed to many to be connected with the increasingly profound problems it faced in dealing with living things. In particular, a contrast was drawn between living and dead matter, the former characterized by ﬂuidity and the latter by dryness. On this conception, what the mechanists had in effect concerned themselves with was dead matter, but, it was now argued, dead matter, far from being the paradigm form of matter, was simply matter that had lost the interesting dynamic properties of living matter, and—it was argued by some—it was this latter that was the proper subject of matter theory and natural philosophy more generally. Coupled with these differences are differences in explanatory models. As we saw when we looked at Geoffroy in Chapter 5, his chemical theory rejected notions of underlying micro-corpuscularian structure in favour of afﬁnities manifested through an ability to react with a solvent and displace other substances. Chemical investigation had originally been developed in metallurgy and pharmaceutical botany, and it is perhaps not surprising that in Geoffroy it takes on the form of a system of classiﬁcation reminiscent in many respects of the new approach to botanical classiﬁcation evident in the later work of Ray. Moreover, it is worth remembering in this context that chemistry had been associated explicitly with experimental natural philosophy as early as Boyle, and experimental natural philosophy had drawn on a range of observational disciplines, most notably natural history.2 With this kind of approach to chemistry, it is no longer a question of mechanist matter theory and post-mechanist matter theory doing broadly the same things but in different ways. Rather, they are signiﬁcantly different kinds of enquiry. Post-mechanist matter theory depends crucially on developments in areas such as the physiology of the nervous system, and debates over systems of botanical and zoological classiﬁcation, in a way that would have been wholly alien to mechanist matter theory. The separation between mathematical approaches to physical enquiry and the experimental approach of matter theory is frequently stressed, with Nollet, the key ﬁgure in electricity in the 1740s, warning for example that it is dangerous for a physicist to develop too great a taste for geometry.3 We can take the problems bequeathed by Newton as our starting point. As we saw in Chapter 2, Newton struggled with the question of continuity versus discontinuity in his matter theory in two areas. The ﬁrst was in the discussion of ﬂuids in Book II of the Principia, where his technique of building up ﬂuids from mass points proved unequal to the task of accounting for those of their properties relevant to the understanding of the motion of bodies through ﬂuids, 2

See Gaukroger, Emergence, chs. 7 and 11. Cited in Roderick W. Home, ‘Mechanics and Experimental Physics’, in Roy Porter, ed., The Cambridge History of Science, iv: Eighteenth-Century Science (Cambridge, 2003), 354–75: 371. 3

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with the result that, in the second half of Book II, he shifted from an analytical into a phenomenological mode. The second was in his attempt to devise a satisfactory account of the mechanism whereby gravitational attraction could act between separated bodies. The ﬁrst question, as we have seen, prompted attempts within rational mechanics to extend its techniques so as to provide a more satisfactory analysis of the behaviour of ﬂuids. The problem of gravitation, by contrast, was in effect put to one side in the rational mechanics tradition, and the difﬁculty was not one that improvements in analytical techniques could have helped resolve. It was, more than any other question, the outstanding naturalphilosophical problem bequeathed to the eighteenth century by Newton, and because it was conceived as a problem in matter theory, it helped push matter theory to the fore of eighteenth-century natural philosophy. What made gravitation such a problem in the ﬁrst place was not a difﬁculty in matter theory as such but rather one in mechanics. It was a fundamental feature of Newton’s approach to mechanics that he opted for the Galilean kinematic model for dynamics, by contrast with the Cartesian hydrostatic model. The difference was that the hydrostatic model investigated the behaviour of bodies in terms of their interaction with the surrounding medium, whereas the kinematic model started from the behaviour of a body free of any constraints—which Galileo established, in the context of kinematics, is the case of an isolated body. On the Galilean model, having established constraint-free behaviour, one then proceeds by showing how this behaviour is modiﬁed as the body is subjected to forces. Where the only form of interaction is collision, the kinematic model is completely successful, whereas the hydrostatic model is hampered by conﬂation of static and dynamic forces, inappropriately applying the resources of statics, particularly the notion of equilibrium, to the dynamic characterization of bodies in inertial states. The procedure of ﬂeshing out kinematically identiﬁed states in dynamic terms was so successful in the case which seventeenth-century physical theory, under the inﬂuence of mechanism, had focused on, namely that of collision, that its credentials as a general model were a crucial part of the success of Newtonianism. But while the dynamics of colliding bodies could be ﬂeshed out in a satisfactory way on this model, it was useless for understanding the nature of gravitation. The nature of gravitational action—the cause or source of the gravitational phenomena that the Principia accounts for—simply fell outside the mechanical exemplar that Newton deployed so successfully in the case of contact action, and in effect what this meant was that it fell outside mechanics per se. In other words, it became a problem in matter theory by default. Matter theory became the discipline in which one investigated the nature of gravitational action, not because it was especially well equipped to deal with this question, but because mechanics, which had generated the problem in the ﬁrst place, worked with an explanatory model that offered no resources to deal with it. Nor indeed did it have the resources to deal with the short-range attractive forces introduced in the ﬁrst edition of the Opticks to account for chemical phenomena, or the non-

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material aether introduced in the 1718 edition. These problems were assumed to be the business of matter theory. The writings of Newtonians on matter theory in the 1690s and the early decades of the eighteenth century reveal signiﬁcant hesitation and confusion on basic questions. Richard Bentley, in his Boyle lectures of 1692, spiritualizes attractive forces, reﬂecting a view that Newton himself had held but on which he was becoming more cautious, so that in the famous letter of January 1693, he chastises Bentley for suggesting that he might have offered an account of the nature of gravity.4 There were general attempts to set out some kind of Newtonian grounding for a matter theory, but they did not take one very far.5 John Keill’s published version of his Oxford natural philosophy lectures given in 1700 was a standard textbook,6 and went through a number of editions up to midcentury, appearing in English and French versions, but its early sections on general natural-philosophical issues did not engage matter theory in a serious way, and the primary focus of the work was mechanics. In 1702, George Cheyne, who represents what is very much a triumphalist stream of Newtonianism, was in effect construing the Principia as the realization of a mechanist project when he wrote: ‘All is nonsense, unless they ﬁrst shew their systems and chymical effects to be necessary corollaries from the known laws of motion, i.e. unless their philosophy, and chymistry too, be ﬁrst mechanically explain’d.’7 No one, least of all Newton, had any idea how such a project might be realized. In particular, this mechanist approach to chemistry failed on the central questions of the persistent identity of certain substances and the regularity of varying combinations. John Freind’s 1709 Oxford lectures certainly threw no new light on the matter, failing to make any connection between his Newtonianized corpuscularian axioms, set out with a view to providing a foundation for chemical reactions, and the chemical processes themselves.8 William Derham, in his 1711/12 Boyle lectures,9 takes a far more cautious anti-hypothetical view of the Newtonian enterprise, but he is unable to further matter theory on this basis. The later editions of Clarke’s annotated version of the Latin translation of Rohault’s Cartesian natural philosophy textbook, still widely used in English universities 4

Newton, Correspondence, iii. 240. See Robert E. Schoﬁeld, Mechanism and Materialism: British Natural Philosophy in An Age of Reason (Princeton, 1970), ch. 2. 6 John Keill, Introductio ad veram physicam, accedunt Christiani Hugenii theoremata de vi centrifuga et motu circu (Oxford, 1701). 7 George Cheyne, An Essay Concerning the Improvements of the Theory of Medicine, preﬁxed to the 2nd edn. of A New Theory of Acute and Slow Continu’d Fevers Mechanically Explain’d (London, 1702), 11. Cheyne later adopted the ‘subtle spirit’ of the 1718 edition of the Opticks to introduce a ‘spiritual’ dimension into physiology: see Anita Guerrini, ‘James Keil, George Cheyne, and Newtonian Physiology, 1690–1740’, Journal of the History of Biology 18 (1985), 247–66: 260–5. 8 John Freind, Praelectiones Chymicae (London, 1709). 9 William Derham, Physico-Theology: or, A Demonstration of the Being and Attributes of God, from his Works of Creation (London, 1713). 5

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in the ﬁrst half of the eighteenth century, provided a vehicle for contrasting the Cartesian view, in the text, with the Newtonian one, in the very extensive notes, and because Cartesianism was mechanized matter theory, there was, in theory, ample opportunity to engage issues in matter theory.10 The difﬁculty was that the text provided the structure within which the discussion was pursued in the notes, and the constraints that this brought with it meant that there was no scope for a systematic account of a non-Cartesian matter theory. Finally, we might note that Newtonianism, of a Lockean variety, received its canonical statement midcentury in the work of Maclaurin. Maclaurin’s interest, however, was in mechanics rather than matter theory as such, and there was not, and could not have been, a canonical statement of Newtonian matter theory because there was no such thing. Although many eighteenth-century writers on matter theory naturally looked to Newton for guidance, help on substantive issues was not forthcoming. Indeed it was not even forthcoming on methodological questions, for his account of the aether in the Queries to the Opticks was manifestly at variance with the kind of anti-hypothesis strategy that was employed so successfully in the case of his mechanics. Here we come back to the more basic question: what would a systematic matter theory that replaced mechanism look like? Indeed, one might even ask what it would include. In the long Query 31 of (the second edition of ) the Opticks, the impression one gets is that it would provide an account of attraction and repulsion.11 But the phenomena that this includes are impossibly broad. Under the heading of attraction, Newton includes refraction and inﬂection of light, gravity, magnetism and electricity, deliquescence, chemical composition and decomposition, ebullition, dissolution, concretion, crystallization, cohesion, congelation, and capillarity. Under repulsion fall reﬂection and emission of light, volatility and evaporation, fermentation and putrefaction, elasticity and disjunction. One is reminded of Bacon’s list, in Novum Organum, of phenomena we need to take account of in studying heat: everything from the rays of the sun, meteors, thunderbolts, natural warm-baths, and air conﬁned underground, to wool and down, conﬁned vegetable matter, the insides of animals, horse dung, and aromatic herbs.12 Simply identifying the phenomena and asking what unites them is as hopeless in the case of attraction and repulsion as it is in Bacon’s enquiries into heat. The general principles of organization of the ﬁeld of matter theory that emerged in the ﬁrst half of the eighteenth century were increasingly unconstrained by considerations of whether they were compatible with micro-corpuscularian 10 Jacob [¼Jacques] Rohault, Rohault’s System of Natural Philosophy, Illustrated with Dr. Samuel Clarke’s Notes taken mostly out of Sir Isaac Newton’s Philosophy, trans. John Clarke (2nd edn., 2 vols., London, 1723). 11 See especially Newton, Opera, iv. 256. 12 Bacon, Works, i. 236–8.

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reduction, and were largely guided by attempts to make sense of an expanding mass of experimental phenomena. Experiments in chemistry and electricity, the two main forms of matter theory, often included living things along with nonliving ones, and there were no a priori constraints on what was examined with what, particularly in an area such as electricity, where the phenomena provoked such constant surprise that setting the parameters in experiments was a question of experience and expertise (not to mention the search for novelties), rather than one of what the theoretical expectations were. The contrast with rational mechanics could not be greater. In rational mechanics, the goals—such as ﬁnding the shape of a stern that offered least resistance—were routinely given in advance, and the point of the exercise was to devise sufﬁciently powerful mathematical and conceptual resources to solve given problems. But, as I have indicated, matter theory, as well as having its own independent and long-standing programmes, especially in areas such as chemistry, was also in effect the dumping ground for all the problems that mechanics, whose degree of success stood in a direct relation to its ability to narrow its purview, had dismissed from its immediate concerns. In the light of this, it would clearly have been fruitless to expect some ‘natural’ coherence in the domain of investigation of matter theory (along the lines of the natural coherence that we ﬁnd in Aristotelian matter theory for example), but it would have been just as fruitless to attempt to impose some overarching order on the ﬁeld, especially if this were motivated by a priori considerations, for example of the kind we have found in rational mechanics. It is important here that we keep focused on the general question, raised in the last chapter, and to which we will return in the next chapter, of the standing of natural philosophy as a model for other forms of cognitive enterprise. Our overriding concern here is to assess whether available forms of natural philosophy were able to play this part. While rational mechanics, with its unassailable standards of rigour and precision, might have aspired to this standing, matter theory was an unlikely candidate for this role. Yet if natural philosophy was to have a future as a form of understanding of the natural world that both engaged fundamental issues and was practically relevant, that future seemed to lie with matter theory rather than mechanics. This prompts the question of how matter theory could proceed without overarching fundamental principles of the kind that mechanism had offered. ELECTRIFIED MATTER A manifestly problematic case for the mechanist understanding of the nature of matter was electricity. We saw in looking at Hauksbee’s reports of his experiments in 1706 that he had expected electricity to behave like a ﬂuid, and indeed in the main this is what results indicated, but in some respects the electrical efﬂuvia behaved like a solid, pushing outwards, and in others like neither: it

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penetrated glass without difﬁculty, for example, yet was unable to penetrate a material as ﬂimsy and porous as muslin. The question for matter theory was what kind of substance these electrical efﬂuvia were. Electricity seemed to defy all conventional notions of material substances, yet its physical effects suggested that it was most likely a material substance of some kind. Even more perplexing was its relation to other phenomena such as light and gravity. If the problematic nature of these phenomena could somehow be shown to be shared, then this was a signiﬁcant advance. Newton had hoped to draw analogies between electricity and optics, and electricity and gravitation, but the problems that electricity presented were novel. The tube in Hauksbee’s apparatus grew more luminous as it was evacuated, for example, but its electrical activity decreased with evacuation, undermining the idea that there might be any direct connection between light and electricity. Similarly with gravity: Hauksbee’s electrical threads were attracted to the centre of the electric, suggesting an analogy with gravitation, but, as the experimenter stretched out his ﬁnger, the electrical threads—far from being attracted to another piece of matter—shrank back. Nevertheless, there was one phenomenon that the nature of electricity was particularly closely tied in with, namely heat and ﬁre. There were many reports of inﬂammable substances being ignited electrically, for example, and there was a widely held view that electricity and ﬁre were basically the same thing. From the point of view of matter theory, this was a potentially revealing point of entry into understanding electricity. The importance of accounting for the nature of ﬁre in the eighteenth century illustrates some of the continuities between pre-mechanist and post-mechanist theories of matter. Chemists had never really wholly stopped thinking in traditional terms of a small number of basic elements, from which everything else was constructed, and which were themselves indestructible. As far as Aristotle’s four elements were concerned, mechanism had treated earth, water, and air in straightforward micro-corpuscularian terms, although the account worked better for solids than it worked for ﬂuids. As far as mechanics was concerned, we can think of ﬂuids as being either compressible or incompressible. Compressible ﬂuids, what we now think of as gases, but which were generally conceived at the time as varieties of air, exhibited problematic behaviour from a mechanist point of view and, as Boyle’s work had demonstrated, micro-corpuscularian reduction was an unproductive path to follow in pneumatics. But the mechanical characterization faced a more immediate problem with the reports of various experiments published in 1728 by Stephen Hales, on the release of ‘ﬁxed’ air, for what the experiments effectively showed was that ‘air’ could exist in a compressed form.13 Hales reported that ‘air’ could exist hidden, in a ﬁxed or inelastic form in solids and 13 Stephen Hales, Vegetable Staticks: Or, An Account of some Statical Experiments on the Sap in Vegetables: being an essay towards a Natural History of Vegetation. Also, a Specimen of An Attempt to Analyse the Air, by a great Variety of Chymio-Statical Experiments (London, 1728).

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liquids, and this ﬁxed air could be released by destructive distillation. Moreover, the phenomenon was widespread, and Hales had managed to release ﬁxed air not just from a wide variety of plants, but also from hog’s blood, amber, oyster shells, beeswax, wheat, tobacco, gallstones, and urinary calculi. Hales’ various experiments opened up a ﬁeld that could receive no guidance whatsoever from microcorpuscular reduction. Nor did the literature on the mechanics of ﬂuids have much to offer. After all, the ‘ﬁxed’ air, despite being incompressible and inelastic, was not a liquid: no one was advocating the notion that ‘air’ existed in a liquid form, or for that matter in a solid form, when it was ﬁxed in substances. The basic characterization of the states of matter had to be rethought, and the vehicle for such rethinking had to be experimental chemistry. Like ‘ﬁxed air’, heat was hidden or concealed in bodies. It presented especially profound problems, however, because by contrast with the other ‘elements’, it was not treated as a material substance, but considered a particular state of microcorpuscles, one which involved a high degree of agitation of a particularly small variety of such corpuscles. The idea of heat as corpuscular agitation, shared by Galileo and Newton as well as mechanists, had worked so well that it was effectively treated as an emblem of the demystiﬁcation of basic physical processes that corpuscularianism had brought into play.14 But there was an ambiguity in that it was not merely a motion, but more often than not the motion of a particular kind of corpuscle, namely an especially ﬁne one. Heat or ﬁre was supposed to be merely a condition of a substance, not a substance itself, but its restriction to a particular kind of matter carried the risk that it would be associated with that particular kind of matter, rather than with a condition of the matter. For chemists, heat was, along with solvents, their primary means of regulating chemical processes, and a working understanding of heat, something that went beyond the crude qualitative idea of heat producing its chemical effects just by shaking substances up, was clearly needed. The work of the Dutch physician, botanist, and chemist Herman Boerhaave in the 1730s was crucial here.15 Boerhaave had originally attempted to reduce heat to a range of mechanically describable properties of micro-corpuscles, but he was struck by the inability of such an account to explain phenomena such as heat transfer, change of state, or heat retention. In response, he moved from the idea that heat was a property of matter to the idea that it was associated with a particular kind of matter, that it was a distinctive quality of a particular kind of matter. What was involved was a particularly subtle substance which could move through the spaces between corpuscles, causing friction, and thereby heat; in the absence of this 14

See e.g. Descartes’ account in chapter 2 of Le Monde: Œuvres, xi. 7–11. Hermann Boerhaave, Elementa chemiae (2 vols., Leiden, 1732). An earlier version appeared as Institutiones et Experimenta Chemiæ (2 vols., ‘Paris’ [Leiden?], 1724), which was actually published from lecture notes by his students. See Tenney L. Davis, ‘The Vicissitudes of Boerhaave’s Textbook of Chemistry’, Isis 10 (1928), 33–46. 15

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subtle matter, there would be less friction and the body would cool. The subtle substance itself was uncontainable, but the idea was that its activity could be gauged through its effects, notably heat transfer, heat retention, and change of state, which were quantitatively determinable in that the friction produced a measurable quantity of heat, which was a function of the ‘heat capacity’ and density of the particular material. Boerhaave’s account of ﬁre as a substance was popular among those looking for guidance on the nature of electricity, and it was ﬁrst introduced in a serious way by Nollet. To understand Nollet’s project, however, the context within which he was working needs clarifying. Nollet was a prote´ge´ of Dufay, who was the ﬁrst to bring a semblance of order to electrical phenomena in the 1730s.16 Dufay’s own interests initially lay in the chemical phenomenon of phosphorescence, and more generally in luminescence, which had puzzled his contemporaries in that there seemed to be nothing common to the various circumstances in which it was produced. Dufay distinguished the production of luminescence by friction, by heat, and by light, and showed how many of the erratic failures to produce luminescence were caused by traces of air or water vapour in evacuated tubes, as well as showing how to remedy this defect. In 1733, he learned of Gray’s experimental discoveries, and took on the task of discovering an order in electrical phenomena. He presented a survey of the area, and then set out a number of questions that needed to be answered if electrical phenomena were to be organized: can all bodies be made electric through rubbing? Can all bodies be electriﬁed by contact or proximity to an electric? What bodies stop and which facilitate the transmission of electric virtue? What bodies are most strongly attracted by an excited electric? How are attractive and repulsive virtues related? What is the relation between the strength of electricity and air pressure and temperature? What is the connection between electricity and luminescence?17 Dufay’s approach was highly experimental, and although he was unable to electrify metals by friction, everything else that could be rubbed he managed to electrify. He was able to establish that not only was triboelectricity a near universal quality of matter, contrary to what had previously been thought, but also, more importantly, his experiments with the communication of electricity demonstrated that (when properly insulated) metals as well as non-metals could be electriﬁed, and that actual contact was not needed, since in the right conditions the materials could be separated by a distance of up to about a foot. The trouble was that the establishment of points of uniﬁcation often raised new problems. The universality of the communication of electricity was an important result, for example, but in the course of establishing it Dufay noted that wetting conducting lines promotes the ﬂow of electricity, a completely inexplicable phenomenon. 16

See Heilbron, Electricity in the Seventeenth and Eighteenth Centuries, ch. 9. Charles Franc¸ois de Cisternay Dufay, ‘Memoires sur l’e´lectricite´. 1er. L’Histoire de l’e´lectricite´’, Me´moires de l’Acade´mie des sciences (1733), 23–35; ‘Memoires sur l’e´lectricite´. 2e. Quels sont les corps qui sont susceptibles d’e´lectricite´’, ibid., 73–4. 17

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Having established the near universal ability of matter to acquire electrical virtue, Dufay’s experiments led him to accept that there was attractive and repulsive electricity. He detected a sequence in electriﬁcation: an unelectriﬁed body was ﬁrst attracted to an electric, which communicated its electricity to the former, and, seemingly as a result of this, the newly electriﬁed body was then immediately repulsed. However, in the course of the experiments, he discovered that a particular kind of gum when electriﬁed was attracted to the charged body, and it subsequently turned out that resin and wax acted similarly. This seemed a fundamental difference, and he distinguished two kinds of electricity18—vitreous, which results in repulsion (like glass), and resinous, which results in attraction—where the body electriﬁed by communication (by contrast with rubbing) receives the type of electricity that is in the body that communicates it.19 The most signiﬁcant developments of Dufay’s work in electricity were those of Nollet, who, with Franklin, was to become a focus for disputes over the nature of electricity in mid-century. In a key essay of 1745,20 which set the trend for all his subsequent writings on electricity, Nollet set out the premiss of his enquiry, namely that electricity was an effect of rubbing and not a causal agent as such, and that the task was to account for electrical attraction and repulsion. Yet whereas rubbing had, in earlier writers, been very much a sign of a microcorpuscularian programme in which—from among the very limited range of interactions between micro-corpuscles that were conceivable—friction was in effect the only form of action between micro-corpuscles that could produce the effects, Nollet did not propose a micro-corpuscularian model as such. Nor did he follow the idea of a universal aether which the later editions of Newton’s Opticks had put very much at the centre of discussion as a medium for electrical activity. Rather, he adapted Boerhaave’s account of ﬁre as a material substance to the case of electricity. Heat, light, and electricity had all been centrally involved in the effects produced by Hauksbee’s machine and its descendants, and it is not surprising that mutual guidance was sought, especially when something was offered that accounted for hitherto inexplicable phenomena in a quantitative way. Nollet— whose treatment of ﬁre, optics, and electricity occupy the bulk of the last three of the six volumes of his Lec¸ons de physique expe´rimentale21—took over Boerhaave’s account of a substance of ﬁre and heat, arguing that when a body is rubbed, this substance (surrounded by an oily ﬁlm) is squeezed from its surface, only to be replenished in the body by subtle matter (in a purer form) rushing in from other 18 These are not two distinct electrical ﬂuids so much as two different forms of electriﬁcation: see Home, The Efﬂuvial Theory, 56–9. 19 Dufay, ‘Memoires sur l’e´lectricite´. 4e. L’attraction et la re´pulsion des corps e´lectriques’, Me´moires de l’Acade´mie des sciences (1733), 457–76. 20 Jean Antoine Nollet, ‘Conjectures sur les causes de l’e´lectricite´ des corps’, Me´moires de l’Acade´mie des sciences (1745), 107–51. 21 Idem, Lec¸ons de Physique Expe´rimentale (9th edn., 6 vols., Paris, 1779–83).

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Fig 9.1

bodies outside it.22 This sets up two streams, one leaving the body via a small number of pores, and one entering it from outside over its whole surface (see Fig. 9.1). Bodies near the electriﬁed object will be affected by both streams, and because the outward moving streams are isotropic, whereas the inward moving ones are focused, the body will be drawn inwards, becoming electriﬁed in the process, which causes it to develop its own atmosphere of efﬂuent matter, which in turn increases its effective surface area in such a way that it now becomes more subject to the impact of the outward streams, and moves away from the electriﬁed object. Various experimental tests are proposed for this account: the streams are visible in a darkened room when the electricity is luminous, and, in 22

See Home, Aepinus’s Essay, 73–7.

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cases where it is not luminous, ﬁne powder can be sprinkled on the conductor’s surface, causing it to be projected in jets.23 In short, the two postulated streams differ in direction of ﬂow and in strength, and what Dufay had identiﬁed as two kinds of electricity are put down simply to differences in permeability. His elaborate 1749 defence of his theory brings out well the way in which Nollet sifts through a mass of experimental data, trying to impose some structure, and showing how the two-stream theory emerges as a coherent principle of structuring.24 Among the experiments he invokes are those showing that rates of evaporation and outﬂow in ﬂuids descending in capillary tubes are not only greater when they are electriﬁed, but also when they are situated near electriﬁed bodies, which can only be explained by inﬂowing matter. The real test for theories of electricity came with the discovery of the condenser or capacitor in 1745. Known as the Leyden jar because its co-inventor, Musschenbroek, constructed the device in Leiden, it comprised a generator such as Hauksbee’s tube, a glass jar of water, and a wire connecting the two.25 These were part of the equipment of any electrical experimenter, and the particular arrangement that produced the powerful electric shock that was distinctive of the Leyden jar was discovered by accident. Musschenbroek had placed the jar on a thick stand (i.e. he insulated it), and placed a wire in it from the generator, with a view to ﬁlling the jar with electricity, and when this was done, he drew a spark with his ﬁnger. A friend, Andreas Cuneaus, who witnessed the experiment, tried it at home, but knowing little of electricity, neglected to insulate the jar, simply holding it in his hand, and as a result received a wholly unexpected severe shock. Musschenbroek repeated the experiment with a large globe instead of a small jar, receiving an even more severe shock but managing to escape with his life, and circulated a detailed description of the apparatus to Re´aumur at the Paris Acade´mie. It was soon discovered that the effect could be increased by connecting a series of Leyden jars, and Nollet was subsequently able to electrify a line of 180 soldiers and then 200 monks. Accounting for the behaviour of the Leyden jar immediately became the most pressing topic among electrical experimenters, and the dominant issue was that between Nollet’s two-stream account and Franklin’s two-charge account. Nollet accounted for the severity of the shock from the Leyden jar on the model of the lesser shock caused by an ordinary electric spark. His theory was that the latter was due to a stream of electrical matter that issued from one’s ﬁnger encountering a stream from the electriﬁed globe, the impact of this interaction being transferred to the mass of electrical ﬂuid contained within one’s body. But 23 At the same time, but quite independently, Franklin was performing the same experiment with smoke. 24 Jean Antoine Nollet, Recherches sur les causes particulie`res des phe´nome`nes ´electriques, et sur les effets nuisables ou avantageux qu’on peut en attendre (Paris, 1749). 25 There is a comprehensive account of the discovery of the Leyden jar in Heilbron, Electricity in the Seventeenth and Eighteenth Centuries, ch. 13.

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his claim that the shock from the Leyden jar operated in the same way, but with greater intensity, could not be reconciled with his general account of electriﬁcation. One central claim of this theory was that conductors, such as human bodies, provided a readier passage for the electrical stream than did air, so that when an electriﬁed body was touched by a conductor, the efﬂuvia emitted found it easier to pass through the conductor than through the air. But in the case of the Leyden jar, he had to ascribe to the glass an ability to prevent the emission of efﬂuvia—to retain its electricity—yet not only was the introduction of the properties of glass completely ad hoc, but from the point of view of his general theory, the properties of glass could have nothing to do with electriﬁcation.26 Franklin had a far more satisfactory account of why glass did not conduct electricity but did transmit electrical inﬂuence, showing that the impermeability of the glass was the crucial factor. The electricity emitted from the outside conductor and that taken in by the inside conductor were the same, so the only way in which the phenomena could be explained satisfactorily was if there were different positively and negatively charged states of this electrical ﬂuid: the inside of the glass was positively charged, the outside negatively charged.27 The glass itself was impermeable, and equilibrium could be regained only if there was contact between the external and internal surfaces. It contained a ﬁxed amount of ‘electrical ﬁre’,28 so that if extra electricity were added to one side of the glass, the same amount of electricity would be emitted from the other side, unless of course the glass was insulated, in which case it would not become charged. When uninsulated, the restoration of equilibrium would be achieved via the discharge of ‘electrical ﬁre’ through the man’s body, and this is what would cause the shock.29 Franklin’s approach to electricity exempliﬁes some central aspects of mideighteenth-century Newtonianism. Although he always put a hypothetical gloss on any underlying models that he proposed, he postulated the existence of ‘electrical atmospheres’ surrounding the electriﬁed body which mediated attractions and repulsions, and required that there be direct contact between the electrical atmosphere and the object that was attracted before the attraction could occur. Nevertheless, the primary point of the exercise for Franklin was to bring some order to electrical phenomena, not to provide an account of underlying mechanisms. His account of a positively or negatively charged single electrical ﬂuid provided a new understanding of the nature of electricity, not by uncovering an underlying micro-structure but by offering a new picture of what was happening at a macroscopic level: namely, by showing why the notion 26

See the account in Home, The Efﬂuvial Theory, 146–57. Benjamin Franklin’s Experiments. A New Edition of Franklin’s Experiments and Observations on Electricity, ed. I. B. Cohen (Cambridge, Mass., 1941), 191. 28 Note that the term ‘electrical ﬁre’ does not mean that Franklin identiﬁed electricity and ﬁre; in contrast with many of his contemporaries, he did not identify the two: see Cohen, Franklin and Newton, 323–6. 29 Benjamin Franklin’s Experiments, 181. 27

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that electriﬁcation consisted in the activation of a ﬂuid already present in bodies had to be replaced by the idea of accumulation (or loss) of something.30 Moreover, to an even greater extent than Nollet, he showed—particularly in his 1749 demonstration that lightning was an electrical discharge—that electricity was a fundamental natural phenomenon, not a special effect that needed to be artiﬁcially induced, and that it lies at the core of physical enquiry.31 The 1752 French translation of Franklin’s letters on electricity caused a fundamental rift in the Acade´mie.32 It was sponsored by Buffon, a ﬁerce critic not just of mechanism, but of the kind of systematic programmes in natural philosophy to which rational mechanics aspired. In particular, Franklin’s openended and very consciously anti-dogmatic approach, reminiscent of Boyle in many ways, was that associated with the Newtonianism established by Maupertuis and Voltaire, and pitted, by Buffon and others, against what was conceived as the discredited corpuscularianism of Re´aumur and his prote´ge´, Nollet. It might seem odd that Nollet, a committed and indeed fervent experimentalist, should be associated with what was in effect a Malebranchean position, against the true road of Newtonian experimental philosophy, but the debates were ﬁnetuned by mid-century, and turned on whether one was prepared to accept attraction at face value, or whether one sought an underlying mechanical explanation for attraction and repulsion. Nollet criticized Franklin on the grounds that he had not provided ‘truly physical causes’, that is, he had not traced electrical effects to the motion of a ﬂuid.33 When Buffon was attacked in a work sponsored by Re´aumur, namely Lelarge de Lignac’s Lettres a` un Ame´riquain sur l’Histoire naturelle, the ﬁrst volume of which appeared in 1751, a core criticism was that, when he ran out of arguments, Buffon simple-mindedly invoked the word ‘attraction’.34 Attraction was the dividing line, and it separated Nollet and Franklin, who had demolished Nollet’s more reductionist account of electricity, just as Maupertuis had demolished Fontenelle’s commitment to vortex theory in favour of Newtonian attraction. Moreover there was a persistent theme in disputes over natural philosophy from the 1720s onwards, brought to a head by Voltaire and then again with the publication of the Encyclope´die, namely that advocates of a systematic natural philosophy—under which experimentalists such as Re´aumur and Nollet could be included because, although they renounced wholesale geometricization, they still had micro-corpuscularian 30

Cf. Home, The Efﬂuvial Theory, 254–6. On the rapid move of electricity from the periphery to the core of physical enquiry in the mid-eighteenth century, see Cohen, Franklin and Newton, ch. 9. See also, for a contemporary estimation, Joseph Priestley, The History and Present State of Electricity, with Original Experiments (London, 1767). 32 See Heilbron, Electricity in the Seventeenth and Eighteenth Centuries, ch. 15. 33 Jean Antoine Nollet, Lettres sur l’e´lectricite´ (3 vols., Paris, 1753–67), ii. 13–14. 34 See Joseph Adrien Lelarge de Lignac, Lettres a` un Ame´riquain sur l’Histoire Naturelle, ge´ne´rale et particulie`re, de M. de Buffon (5 vols., ‘Hamburg’ [Paris], 1751–6), i. 96–9. 31

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aspirations—sought, and claimed to have achieved, what was in fact an impossible completeness in their accounts; whereas the experimental natural philosophy tradition, now quite narrowly circumscribed, did not seek to reduce everything to mechanical causes, and was therefore open-minded as to what form explanations might take. ‘Attraction’ begins to take on positive connotations in this context. I have noted that attraction was invoked both in mechanical contexts, as in Newton’s Principia, where what were involved were mutually gravitating bodies at immense distances from one another, and in chemical contexts, where the existence of attractive and repulsive forces acting over microscopic distances was not only far more intuitive, but very much a staple of chemical theory, even if such forces were as problematic in their nature and activity as the long-distance ones. Moreover, attraction and repulsion seemed far more suited to accounting for a range of matter-theoretical tasks, from explaining chemical afﬁnities to characterizing electrical behaviour, than did the language of corpuscular motions. Instead of constantly coming up against different forms of attraction and repulsion simply as insuperable problems for an understanding of the fundamentals of matter theory, one alternative approach was to think in terms of a general theory of attraction and repulsion, of which the various forces operative in nature, contact forces as well as gravitational, chemical, and electrical forces, were individual manifestations. There were a number of attempts from the early decades of the eighteenth century onwards that offered a uniﬁed conception of force by thinking of matter in terms of repulsive and attractive forces. Benjamin Worster and John Rowning both proposed such accounts in the 1720s and 1730s,35 but it was only with the appearance of Boscovich’s Theoria philosophiae naturalis in 1758 that we ﬁnd a developed proposal of this kind. Boscovich, in a Newtonian vein, did not offer an account of the ultimate nature of force, which he considered unknowable; rather, force is simply a matter of the propensity of masses to approach and recede. The idea is that there must be repulsive forces associated with matter if resistance and impenetrability were to be explained, and he assumes that there are repulsive forces acting in the proximity of particles that are strong enough to repel other particles. But if this is the case, we do not need to assume material extension at all; we only need an unextended point which has a force associated with it. This is an understanding of matter that we have found Newton speculating on, in the unpublished and unknown De gravitatione, and in Leibniz, who was a source of inspiration to Boscovich. But he develops this conception much more extensively, in such a way that we can detect the beginnings of a radical rethinking of 35 Benjamin Worster, A Compendious and Methodical Account of the Principles of Natural Philosophy, as They are Explained and Illustrated in the Course of Experiments perform’d at the Academy in Little-Tower Street (London, 1722); Rowning, A Compendious System of Natural Philosophy. See the account in Schoﬁeld, Mechanism and Materialism, 34–9.

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346 B D´

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matter which goes beyond Newton and Leibniz. The corpuscularian view had been that matter cannot act beyond its boundaries, which rules out action at a distance. Alternatively, if we take gravitational attraction, for example, as given, then we can accommodate our understanding of matter to this by redeﬁning the boundary as wherever the action of the body ceases. This has the consequence in the case of gravitational attraction, which extends to inﬁnity, that the boundaries extend to inﬁnity. On the face of it this is quite counter-intuitive, but we might think of it as substituting a physical for a material understanding of boundaries, and this was not something alien to mechanics, although it was of course wholly alien to matter theory. On Boscovich’s account, the single force that the point mass exercises is attractive or repulsive depending on the distance from the point centre of the force (see Fig. 9.2). There is nothing more mysterious and inexplicable about long-range forces such as gravitation on this account than there is about contact forces. Moreover, there is no need to invoke an aether: what Boscovich is offering is in fact still a form of corpuscularianism, even if the corpuscles are themselves unextended and as a consequence have lost a good deal of their materiality. At a great distance from the point centre only attractive force acts, which explains gravity. Close to the point centre only repulsive forces act, which explains resistance. Finally, very close to the point centre these forces increase exponentially, approaching inﬁnity, which explains impenetrability.36 There is one single force, then, that changes sign from attractive to repulsive in a series of cycles as one body approaches another, and which is deemed to account for the complex pattern of chemical reactions and physical, including electrical,

36

See Roger Joseph Boscovich, A Theory of Natural Philosophy (Cambridge, Mass., 1966), 53–4.

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properties. Every point centre becomes related to every other dynamically, and the magnitude and direction of the force involved is a function of distance. While Boscovich’s Theoria offered the ﬁrst detailed treatment of a dynamic theory of matter, it was profoundly unsatisfactory as a general physical theory in a number of respects. In much of the discussion, it is unclear whether the points on Boscovich’s curve are supposed to represent physical, metaphysical, or mathematical properties, for example, and as Schoﬁeld has pointed out, Boscovich simply adapted his theory to the nature of any generally accepted explanation of the day, and ‘in almost every critical problem of eighteenth-century natural philosophy, where substances had replaced force as an explanatory device, Boscovich’s explanations accept substance and assert only that these substances can, in some undisclosed way, be reduced to the combinations of geometrical points and their summed force-curves.’37 What Boscovich is offering is essentially a reductive account in line with approaches in rational mechanics, where material properties are built up out of operations on mass points, although the way in which he seeks to achieve this differs signiﬁcantly from that of d’Alembert and Euler for example. It turns out that it does even less work than their foundational systems however, because they put these systems directly to work, in such a way that the limits to their applicability were evident, whereas Boscovich merely tells us that results across the whole range of natural philosophy can simply be mapped on to his system. Compare this reductive account with Franklin’s approach. One striking feature of Franklin’s account of electricity was that electrical charge obeyed a conservation law. By contrast with the concerted concern with conservation laws in the nineteenth century,38 they were rare in seventeenth- and eighteenthcentury physics. Descartes had tried to establish that the (scalar) quantity of motion was conserved, but this attempt had failed and in its place emerged the vis viva controversy, over whether momentum or energy was conserved. This was effectively the sum total of concern with conservation. Other physical phenomena were not discussed in terms of conservation—the conservation of matter and the conservation of heat were not postulated until later in the century—and there was no reason to think that they were regulated by conservation laws. Indeed, as Bernard Cohen has pointed out,39 heat is not conserved as such: it may be augmented by rubbing—the same process that produces electriﬁcation—but it is not as if one body cools down to balance the increase in heat in the other, for they both heat up. Given the parallels between heat and electricity, and the identity in their mode of generation, conservation of electrical charge would have been a 37

Schoﬁeld, Mechanism and Materialism, 241. On just how important the case of the conservation of energy was to nineteenth-century physics, for example, see Yehuda Elkana, The Discovery of the Conservation of Energy (London, 1974); and Kenneth L. Caneva, Robert Mayer and the Conservation of Energy (Princeton, 1993). 39 See Cohen, Franklin and Newton, 301. 38

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highly counter-intuitive principle. This is particularly the case if one were working on corpuscularian assumptions, for conservation of charge is inherently macroscopic. Like the law of the pendulum, or the gas laws, it is insensitive to microscopic behaviour. Consequently, the language of microscopic constituents is inappropriate. The language that Franklin employs is one borrowed from a variety of sources, notably, democratic politics and accounting, where maintaining a balance or equilibrium is seen as paramount. On Franklin’s account of electriﬁcation, bodies are in one of three states: either the body has an ‘over quantity’ of electricity in which case it is described as being in credit, or, as his terminology changes, the amount of electricity is described as positive (þ); or it has an ‘under quantity’, in which case the amount of electricity is described as negative (–); or it is neutral, in which case it is in equilibrium, where the þ and the – cancel out, and this is designated the natural state. The description mirrors that of his ‘Dissertation on liberty and necessity’ (1725), in which the avoidance of pain is the prime aim of life, and where, as a general principle, uneasiness always produces a desire to be freed from it which is in exact proportion to the uneasiness. The exact proportion is described in accounting terms: if a man has ten degrees of pleasure then ten degrees of pain are debited to his account.40 The doctrine itself was later abandoned, but the imagery of a neutral equilibrium state which can go into credit (þ) or debit (–) is retained, and indeed provides Franklin with a way of thinking through electrical ‘charge’, itself a term deriving from the economic context of charging, and of discharging, a debt.41 The language is that of positively charged bodies actively desiring to give electricity, and negatively charged bodies actively desiring to be given electricity, something evident for Franklin in the crooked path of lightening which unfailingly sought out and turned in the direction of conductors.42 It is precisely such imagery that Nollet and his followers rejected.43 In response to the suggestion of the Italian Franklinist Giambattista Beccaria44 that electrical attraction had to be explained in terms of full bodies needing to give, and empty bodies needing to receive, 40

See the discussion in J. L. Heilbron, ‘Franklin as an Enlightened Natural Philosopher’, in J. A. Leo Lemay, ed., Reappraising Benjamin Franklin: A Bicentennial Perspective (Newark, 1993), 196–220: 207–8. 41 See Heinz Otto Sibum, ‘The Bookkeeper of Nature: Benjamin Franklin’s Electrical Research and the Development of Experimental Natural Philosophy in the Eighteenth Century’, in J. A. Leo Lemay, ed., Reappraising Benjamin Franklin: A Bicentennial Perspective (Newark, 1993), 221–42: 228. There is a case to be made that Hume used the reverse analogy, thinking of ﬂuids and the ﬂow of electricity in his economic thinking, which focused on the nature of money: see Margaret Schabas, The Natural Origins of Economics (Chicago, 2005), 70–4. 42 See Franklin to Jan Ingenhousz, 21 June 1782: in The Writings of Benjamin Franklin, ed. Albert Henry Smyth (10 vols., New York, 1907), vii. 88–97. 43 See Jessica Riskin, Science in the Age of Sensibility: The Sentimental Empiricists of the French Enlightenment (Chicago, 2002), 78. 44 Beccaria was the author of the standard Franklinist treatise on electricity in Italian: Dell’elettricismo artiﬁciale e naturale libri due (Turin, 1753).

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electrical matter, Nollet wrote that, if he saw an inanimate object move towards another, for the sole reason that it lacked what the other could supply it with, he would believe he had seen a miracle.45 The pressing question here is whether Nollet has characterized what is at issue in the most helpful and productive way. He is in effect insisting that a microreductive account of electrical discharge of the kind he is offering is the only satisfactory type of explanation, yet this kind of explanation is quite inappropriate. Rather, deviation from and restoration of equilibrium are the notions that now seem to be doing the explanatory work. At one point Franklin asks us to imagine the Leyden jar as a bent spring which, in order to restore itself to its natural conﬁguration, must symmetrically contract on the extended side, and extend on the contracted side, the two motions occurring simultaneously if either is to occur at all.46 He points out that no one would suggest either that the operation was effected through collision, or that the spring gained elasticity in bending and lost it in restoration. The Leyden jar can be conceived as acting in the same way: it acts to restore equilibrium. In the Franklinist scheme of things the idea of restoration of equilibrium is a very general notion, the scope of which ranges from sensory excitation to economic transactions. There are two questions of fundamental importance that arise here. The ﬁrst concerns the nature of matter: if electrical phenomena cannot be accommodated to the prevailing notion of matter, inherited from mechanism, is it a viable, or fruitful, response to revise one’s conception of matter so as to accommodate it to electrical phenomena? The second concerns uniﬁcation. Nollet’s approach can be seen as an extension of mechanism, to the extent to which its micro-reductive strategy is motivated in large part by the idea that there is a fundamental level of physical or material activity at which all material bodies have identical constituents whose behaviour is regulated by identical simple basic laws, in this way unifying the whole physical domain. If uniﬁcation though shared micro-structure is now in question, is there not some form of uniﬁcation through forms of activity shared across a far broader spectrum than that occupied solely by natural philosophy, as the language of Franklin and his followers suggests? These questions had become particularly urgent ones by the late 1740s, as a major dispute broke out between Buffon and Re´aumur over the viability of biomechanics. Life is not simply a form of organization superimposed on lifeless matter on Buffon’s account. Each part of a living thing is homologous to the whole, and not reducible to inorganic constituents. Together with his collaborator, the abbe´ Needham, Buffon performed a series of microscopic observations involving almond seeds, crushed wheat, and meat juices, claiming to have observed spontaneous generation, and defending the view that matter, far from 45 46

Nollet, Lettres sur l’e´lectricite´, ii. 161–2. Benjamin Franklin’s Experiments, 190–1.

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being inert, was permeated with soul and reproductive tendencies.47 We shall be looking at Buffon below. For the moment, I just want to signal that the problem for those with any lingering sympathy for mechanism was that the organic and the inorganic were becoming increasingly difﬁcult to separate in the disputes within matter theory, and that organic activity could no longer simply be reduced to, or even counted as an emergent property of, lifeless micro-constituents. The question of the ways in which matter itself is active, and what this activity amounts to—ranging from dynamic properties to vital ones—is now raised about the micro-constituents themselves, considered as irreducible. T H E C H E M IS T R Y O F F L UI D S A N D S Y M P A T H I E S To what, then, should we look in order to understand the nature of matter more fully? By the 1740s, the question of what the activity of matter consists in was no longer a question for mechanics, but one for chemistry. To secure this role for itself, chemistry needed to mark out a domain of enquiry fully autonomous from that of mechanics. But the battle for autonomy inevitably brought with it the question of which of the disciplines had priority with respect to the other. Up to this point, there had been a general assumption that it was mechanics that was prior because it was more fundamental than chemistry, in that it was mechanics that characterized the constituents of the bodies that chemistry studies, and it was taken as given that it was the behaviour of these mechanically characterized microscopic constituents that ultimately determined the chemical behaviour of the larger bodies that chemistry investigated. In the course of the 1740s and 1750s, we witness a reversal of fortunes, as chemistry comes to play the role of the dominant partner. Attempts to mechanize chemistry, as I have indicated, never provided any remotely satisfactory account of the two outstanding problems facing explanations of chemical behaviour: the persistent identity of certain substances and the regularity of varying combinations. The failure of a mechanical approach to these questions had been diagnosed as early as 1706 by Stahl as lying in its inability to penetrate beyond the surface of bodies.48 Mechanists had effectively assumed that, because they were dealing with ultimate constituents, it was a question of the behaviour of smaller bodies explaining the behaviour of larger ones, but the new turn in chemistry completely marginalized such considerations, making the issues hinge instead on internal and external properties, where questions of size are irrelevant to the contrast between interior and surface. Moreover, it was a premiss of the kind of micro-corpuscularianism that mechanism worked with that matter was ultimately homogeneous, but Stahl insisted that at a sensory level 47 48

See Roger, Buffon, 139–47. See Georg Ernst Stahl, Disquisitio de mechanismi et organismi diversitate (Halle, 1706).

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every indication was that matter was heterogeneous, and, accepting that matter may indeed be composed of micro-corpuscles, he advocated a basic number of larger-scale elements—made up from aggregates of micro-corpuscles in some way which could not be explained—to account for chemical properties, since the micro-corpuscles themselves had no explanatory value as far as chemistry was concerned.49 The effect of Stahl began to be felt in French chemistry in the 1720s and in England in the 1730s, and was in both cases presented as a Newtonian form of chemistry,50 although it was not until the 1740s in Paris that Stahl became incorporated into the mainstream of chemistry.51 The crucial move came with Macquer, who combined Stahlian chemistry with the afﬁnity chemistry of Geoffroy,52 and explicitly associated afﬁnity with Newtonian attraction.53 Stahl’s chemistry brought a principle of organization to the subject matter that ﬁt well with the doctrine of chemical afﬁnities. French chemists worked with a basic number of principles, as we saw in Chapter 5. Homberg had attempted to restrict the principles to ﬁve, whereas Geoffroy accepted three, namely ﬁre, water, and earth. Stahl offered a system of hierarchical ordering that reined in the complexity of experimental results in a more satisfactory way.54 He classiﬁed natural bodies into simple and complex. Simple bodies were principles, and he uses both chemical principles—salt, sulphur, and mercury—and physical principles—air, water, and earth. Compound bodies were classiﬁed into ‘mixts’ (the account of which is complicated but which, for our purposes, can be identiﬁed as substances separated out in chemical analysis), aggregates (simple collections of particles), and compounds (which are not simple collections in that their production must have involved a qualitative change in the substance). In his account of physical principles, Stahl considered that air did not enter into chemical combination, so that earth and water formed the physical or material basis for all bodies. Earth is treated as coming in three kinds, however, and

49

See He´le`ne Metzger, Newton, Stahl, Boerhaave et la doctrine chimique (Paris, 1930), 102–6. In France, the ﬁrst Stahlian chemistry textbook was Jean-Baptiste Senac, Nouveau cours de chimie, suivant les principes de Newton & de Sthall (Paris, 1723). In England, Stahl’s Fundamenta Chymia Dogmaticae et Experimentalis (Nuremberg, 1723) was translated into English by Peter Shaw as The Principles of Universal Chemistry (London, 1730), the ‘universal’ mirroring Newton’s universal gravitation. Shaw followed up the translation in 1731 with his own Three Essays in Artiﬁcial, or Universal Chemistry (London, 1731). 51 See Martin Fichman, ‘French Stahlism and Chemical Studies of Air’, Ambix 18 (1971), 94–122. 52 Pierre-Joseph Macquer, Ele´mens de chimie-the´orique (Paris, 1749); idem, Ele´mens de chimiepratique, contenant la description des ope´rations fondamentales de la chymie, avec des explications & des remarques sur chaque ope´ration (2 vols., Paris, 1751). Macquer’s most lasting contribution to chemistry was his concerted attempt to clear up the highly confused and confusing nomenclature of chemical substances in his Dictionnaire de Chymie, the ﬁrst edition of which appeared in 1766. On the question of nomenclature, see M. P. Crossland, Historical Studies in the Language of Chemistry (New York, 1978), 114–30. 53 See Kim, Afﬁnity, 220. 54 See ibid., 171–4. 50

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(although Stahl himself denied any direct connection) these seem to have an association with the three chemical principles: there is the earth that renders bodies solid and vitriﬁable (salt); there is the earth that provides colour, odour, and combustibility (sulphur); and there is the earth that provides weight, ductility, and volatility (mercury). The second kind of earth, which Stahl identiﬁed as having a moist oily character, was different from the other two in that it did not form any stable compound and could be separated from the bodies in which it existed. He called this second kind of earth ‘phlogiston’ (from the Greek word meaning ‘burning up’), and it was the principle of combustibility. The essential feature of combustion, Stahl argued, was the liberation of the principle behind combustion, which in escaping gives rise to the motion that constitutes ﬂame. In the slow combustion—which he refers to as calcination—of ignoble metals, phlogiston is liberated, but the process can be reversed, he argued, so that the metallic ash can be converted back into the metal by taking up phlogiston. Phlogiston also seemed to be responsible for the solidity of bodies (since when they had burned the remaining ash had lost its solidity), and their colour (which they also typically lost on burning). The signiﬁcance of the idea of phlogiston for Geoffroy arose from Stahl’s observation that if one mixed vitriolic acid with salt of tartar, there was a way of treating the product such that the acid could be separated out again. Geoffroy was puzzled by this, for vitriolic acid was the strongest acid and salt of tartar the strongest alkali, so no other acid or alkali could break their union.55 Experimenting on this process, he melted salt of tartar saturated by vitriolic acid on a crucible with some salt of tartar and some inﬂammable material. The contents violently burst into ﬂames and produced copious fumes. Taking the residue, a saline sulphurous material, he dissolved it water, ﬁltered it, poured it over a distilled weak acid spirit such as vinegar, and obtained sulphur. Geoffroy identiﬁed the active agent as phlogiston, the ‘principle of inﬂammability’ which he placed just below vitriolic acid in a revised version of his table. His interpretation of what had happened in the process he witnessed was that the oily principle, phlogiston, contained in the inﬂammable material, had been rareﬁed and set in motion by the element of ﬁre, and having more afﬁnity with vitriolic acid than with the ﬁxed alkali salt, it united with the former, which became detached from the alkali salt. On this reading there are three ingredients in the combustion process: the ‘principle’ of combustion, namely phlogiston, the combustible substance, and the substance with which it combines. Phlogiston is thought of as forming the food or nourishment for combustion. It leaves the combustible substance and enters the other until the other is full, and the rate and violence with which this is effected is a function of the degree of afﬁnity between the two substances. The imagery is reminiscent in some ways of that used in describing electricity, and the 55

See ibid., 146–51, for a full account of the experiments.

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phenomenon of effervescence that accompanies the reaction of acids and alkalis was seen, as Reill puts it, ‘as the result of similar parts, propelled by their inherent principles, rushing to embrace each other, breaking down earlier combinations and forming new ones’.56 As I noted when examining Geoffroy’s table of afﬁnities, the criteria by which different types of substance and chemical property were identiﬁed were motivated instrumentally. Their connection was not with any supposed microcorpuscularian constitution, but rather with how one operated on substances to get them to behave in chemically deﬁned ways. This operational approach identiﬁed what might be termed a paradigm form of material substances. Rational mechanics had in effect done this also, for although both inﬂexible solids and ﬂuids had to be constructed out of mass points, the direction of construction—from mass points, to inﬂexible solids, to ﬂexible solids, to elastic solids, to ﬂuids—meant that solids were primitive with respect to ﬂuids, in that one had to understand solids in order to understand the more complex case of ﬂuids. Note also that, although mass points cannot strictly speaking be identiﬁed with the material micro-corpuscles of mechanism, it was inevitable that the two would be identiﬁed by anyone seeking to ﬂesh out mechanics in material terms, and the basic form of matter theory was one in which hard corpuscles ﬁgured. In chemistry, by contrast, the operational path whereby the properties of matter were identiﬁed meant that the paradigm form of material substances was thought of in terms of the action of ﬂuids. The language of chemical analysis was that of solvents and distillation. To discover the constituents of something, one did not physically break it down into its homogeneous micro-corpuscles, but one began by liquefying it, dissolving it in an acid or alkali: its properties could be revealed only once it was in a liquid form. One could heat the substance to be analysed, breaking it down in this way, but for this to be instructive from the point of view of analysis, the nature of heating had to be understood. The models that were developed to understand the action of heating in chemistry, by contrast with the primitive mechanist understanding in terms of increased motion, worked in terms of ﬂuids. There were various possibilities: heat was conceived along the lines of a ﬂuid; or heating was thought of in terms of matter being energized by an active subtle ﬂuid; or it was thought of as ﬂowing between bodies due to the pull of attractive forces; and so on. All the options substantialized heat in one way or another, and the substantialization was in every case reduction to a ﬂuid. Underlying these theories was the idea that ﬂuidity is in some way the basic form or state of matter. The clearest statement of this view can be found in Maupertuis, whose understanding of the fundamental nature of matter does not draw on mechanics, or even on chemistry in this respect, but on natural history, where what is crucial about natural history is that it is a developmental theory. ‘In 56

Peter Hans Reill, Vitalizing Nature in the Enlightenment (Berkeley, 2005), 77.

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order to turn natural history into a true science’, he argues, ‘one would need to devote oneself, not to investigations telling us about the shape of such and such an animal, but to those telling us about those general processes in nature concerning the production and preservation of animals.’57 Everything begins in a ﬂuid condition, Maupertuis insists, in which the more active particles form animals, and the less active ones minerals.58 If the replacement of solidity by ﬂuidity is the path from a micro-corpuscularian understanding of matter to a chemical one, it is the replacement of contact action by attraction or sympathy that cements the transition. In particular, as questions of sympathetic interaction between parts of the natural realm came to the fore, attention comes to be focused on functional questions: considerations of harmony or equilibrium among the active relations between the constituents of natural processes became paramount, and analogical reasoning takes on a new importance. The life sciences begin to supplant mechanics as a model for understanding the physical realm, the notion that nature is animated opening up the idea that matter might be in some way subject to developmental stages. In place of reductive notions of explanation, we begin to ﬁnd the idea that explanation consists in the ordering of natural events in an appropriate sequence. 57

Maupertuis, ‘Lettre sur le progre`s des sciences’: Œuvres, ii. 386. This is in direct contrast to the view of Linnaeus, for whom the world is full and completely static, mirroring a divine economy in which each species reproduces in just the right numbers, and with the right lifespan, to provide nourishment for others while being able to persist itself. See Wolf Lepenies, ‘Linnaeus’s Nemesis divina and the Conception of Divine Retaliation’, Isis 73 (1982), 11–27. 58 Maupertuis, Syste`me de la nature }49: Œuvres, ii. 153.

10 Living and Dead Matter In his 1696 De praxi medica, Giorgio Baglivi set out the aspirations for—and vindication of—iatromechanics in terms which graphically summed up the reductive programme of Cartesian biomechanics: As soon as physicians began using geometrical and mechanical principles, as well as physical, mechanical, and chemical experiments, to study the structure and action of the animate body, they discovered not only innumerable phenomena unknown to preceding centuries, but also became aware that, as far as its natural actions are concerned, the human body is nothing more than a complex system of chemico-mechanical movements that obey purely mathematical laws. Whoever examines the bodily organism attentively cannot fail to discern pincers in the jaws and teeth, a container in the stomach, hydraulic machines in the veins, the arteries and the other ducts, a piston in the heart, sieves or ﬁlters in the bowels, bellows in the lungs, the power of the lever in the muscles, a pulley in the corner of the eye, and so on. However much the chemists continue to explain natural phenomena in complex terms such as fusion, sublimation, precipitation, and so on, in this way pursuing a different philosophy, it remains beyond question that all these phenomena must be seen in terms of the forces of the wedge, of equilibrium, of the lever, of the spring, and of all the other principles of mechanics. In short, there is no clearer and easier way to explain the natural functions of the living body than by means of the experimental and mathematical principles with which nature herself speaks.1

In the light of the developments in matter theory that we looked at in the last chapter, it is not surprising that mechanical reduction of this kind quickly lost any plausibility in the course of the eighteenth century. A mechanics that was unable to account for physical phenomena such as electricity and chemistry was hardly going to be able to provide a basis for understanding animate bodies. More signiﬁcantly, it could no longer plausibly claim to be offering a general model for natural philosophy. Electricity and chemistry had encouraged an understanding of matter as something active, an understanding wholly antithetical to the whole mechanist programme, but they were unable to offer

1 Giorgio Baglivi, De praxi medica cap. XI, }VII: Opera omnia medico-practica, et anatomica, Editio Quarta Veneta (Venice, 1738), 78. Construals of the body as a machine had become very common by the early eighteenth century: see Roy Porter, Flesh in the Age of Reason (London, 2003).

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any account of what this activity was in general terms, and to what extent it characterized matter beyond the local phenomena that these disciplines studied. A general account of the activity of matter was needed if there was to be a hope of replacing what many considered the now defunct mechanist model. Such a general account emerged in natural history in the 1740s, as it became transformed, especially in the work of Buffon, into a powerful, large-scale form of natural philosophy in which matter as conceived by mechanists became merely a sub-species when matter was construed in its most general terms. MATTER AND ACTIVITY The question of the activity of matter was closely tied to the understanding of electricity, as electricity became the central concern of natural philosophy.2 The pivotal role of electricity was advanced in 1740, when Stephen Hales proposed the thesis of a nervous electric ﬂuid.3 The general idea was that bodily functions might be effected through electricity, and it is around this time that the idea of electricity as an adjunct to physiology begins to emerge in a serious way. In the ﬁfth Discours of his 1749 Recherches sur les causes particulie`res des phe´nome`nes ´electriques, Nollet devotes his attention to ‘the effects of the electric virtue on organized bodies’, that is, on organic bodies. He begins by reporting various experiments on the beneﬁcial effects of electriﬁcation on the growth of seeds, before turning to animals. Then, noting that it is evident from his study of capillary action that electriﬁcation causes increased ﬂow through pipes and increased evaporation, he asks what effect it has on an animal body, which is crossed with various tube-like structures. To this end, he reports a number of experiments which deal in large part with the increased rate of perspiration induced by electriﬁcation, and he draws up a number of developmental charts. His attention was not conﬁned to animals, and he used experiments on patients

2 In a 1750 letter, for example, Horace Walpole noted the widespread use of electrical models, writing that ‘everything is resolved into electrical appearances, as fomerly everything was accounted for by Descartes’ vortices and Sir Isaac’s gravitation’: quoted in Anne Janowitz, ‘“What a rich fund of Images is treasured up here”: Poetic Commonplaces of the Sublime Universe’, Studies in Romanticism 44 (2005), 469–92: 492. 3 Stephen Hales, Statical Essays: Containing Haemestatics; or An Account of Some Hydraulic and Hydrostatical Experiments Made on the Blood and Blood-vessels of Animals (2 vols., London, 1740), i. 87–94. Although the electrical account of nervous action was attractive to many writers in the late 1740s and 1750s, it was subject to numerous problems. Above all, the tissue surrounding the nerve was electrically conductive, so it was a mystery how the electrical discharge could be conﬁned to the nerve; and it was a mystery how an electrical disturbance in the brain could be conﬁned to a single nerve. See Roderick W. Home, ‘Electricity and the Nervous Fluid’, Journal of the History of Biology 3 (1970), 235–51.

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at the Hoˆtel Royal des Invalides to explore the use of electriﬁcation as a cure for paralysis, noting average positive responses.4 There was some dispute over his results, with a surgeon at the Hoˆpital Ge´ne´ral de Paris claiming that there had been no detectable improvement, but his criticism is of Nollet’s understanding of electricity and of medicine, not of the attempt to establish practical connections between the two. We have seen that matter theory was unable to rely on mechanism for help, and received little guidance from micro-corpuscularianism more generally, in attempting to impose some order on the domain of enquiry that it had inherited in the wake of the demise of mechanism. We have also seen how, in the case of electricity in particular, a broadly experimental approach, which was in many respects sui generis, predominated. There was no longer any single discipline to which the various emerging forms of natural philosophy, broadly conceived, could look as a model. Rather, there were various different approaches which either acted as partial models, such as natural history, or which provided a focus for the disciplines. One development, above any other, provoked a fundamental rethinking of the issues, and acted as a centre around which various questions not apparently connected to one another in any intrinsic way came to be crystallized. This was the reproductive behaviour of the freshwater polyps, which ﬁrst came to public attention in an announcement by Re´aumur, a leading ﬁgure in the study of animal reproduction. Re´aumur was the pre-eminent natural historian of the 1730s, a pre-eminence displayed in his seven-volume Me´moires pour servir a` l’histoire naturelle des insects, published between 1734 and 1742. This was a deﬁnitive work on insects, demonstrating beyond question, for example, that the insect pupa is not an egg but a stage of development of the life cycle of a single individual, and thereby solving what had previously been the intractable problem of metamorphosis, by showing that insects conformed to the normal pattern of reproduction. The work was consciously opposed to the kind of systematizing trend represented and defended in the Acade´mie by Fontenelle. Re´aumur was a devout Catholic, and mirroring—and perhaps inﬂuenced by—the Catholic antisystem rhetoric of the Journal de Tre´voux, he relied more on revealing divine providence in nature than on imposing any system of classiﬁcation on, or even analysis of, the overwhelming amount of information piled up in the treatise. In the sixth volume, published in 1742, he announced the results of a series of experiments that he had performed with two Swiss researchers, Charles Bonnet 4 See the discussion in Enrico Belloni, A World on Paper: Studies on the Second Scientiﬁc Revolution (Cambridge, Mass., 1980), 147–50. Nollet also had a long-running dispute with William Watson, the leading electrical experimenter in the Royal Society, on this question: see Simon Schaffer, ‘Natural Philosophy and Public Spectacle in the Eighteenth Century’, History of Science 21 (1983), 1–43: 12–14. Franklin too experimented with the use of electric shocks for the cure of paralysis: see I. Bernard Cohen, Benjamin’s Franklin’s Science (Cambridge, Mass., 1990), 55. By the 1760s reports of medical uses of electricity were becoming common.

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and Abraham Trembley, in which various polyps, water worms, and earthworms had been dissected and carefully observed using microscopes and magnifying glasses. Trembley, who had discovered the peculiarities of the freshwater polyp (hydra), which was attached to aquatic plants, as early as 1740, set out his own account of the experiments in 1744.5 What was reported was astonishing. Reproduction in the polyp did not involve sexual contact. Rather, it regenerated by budding, like a plant. Moreover it rapidly regenerated, as a matter of course, arms and legs which had been removed by dissection. Most remarkable of all, if the polyp were cut into multiple parts, each part would regenerate, with all the features of the whole polyp—mouth, arms, legs, stomachs—appearing quickly, no matter from what segments of the original the cut part came from. Among the many questions thrown open by the discovery of the reproductive behaviour of the polyp, there were three fundamental ones. First, there was the theory of preformation,6 according to which the rudiments of the organism, and all its subsequent progeny, existed in the female egg (oval preformation), or in the semen (animalculist preformation), before conception.7 Preformation was considered vital to biomechanics, but Trembley’s freshwater polyp reproduced in a way that could not be reconciled with preformation. As a result, the whole programme of biomechanics was in deep trouble. Second, it was far from clear to those who examined the reproductive behaviour of the polyp, not least Trembley himself, whether it should be characterized as an animal or a plant, and Diderot and others argued that, rather than there being sharp lines between the vegetable and animal realms, there was in fact a continuous transition, perhaps even extending to that between the vegetable and the mineral. Third, the ability of the sliced pieces of the polyp to regenerate into individual complete polyps indicated that nature was able to generate living beings. But if this was the case—and especially if the distinctions between mineral, plant, and animal realms were ones of degree rather than ones of kind—then the question had to be raised whether matter was intrinsically active.

5

Abraham Trembley, Me´moires pour servir a` l’histoire d’un genre de polypes d’eau douce (Leiden, 1744). Re´aumur had read out a report of Trembley’s discovery to the Acade´mie in March 1741. On the discovery and its reporting, see Virginia P. Dawson, Nature’s Enigma: The Problem of the Polyp in the Letters of Bonnet, Trembley, and Re´aumur (Philadelphia, 1987). 6 For my limited purposes here, I have included preformation and pre-existence under the rubric of the former. Strict preformation required that the seed was produced whole by the (male) progenitor, whereas pre-existence required that God had created all future generations, in seed, at the beginning of creation. 7 In theory at least, there was a straightforward ‘crucial experiment’ by which one might decide between oval and animalculist preformation. Since it was assumed that it was possible for species, no matter how distant, to cross, it was simply a question of mating across species. An Aristotelian animalculist such as Fortunio Liceti, for example, maintained that a cow impregnated by a man would give birth to a complete cow, whereas a Galenist ovist such as Mundinus Mundinius would expect human offspring: see Jacques Roger, The Life Sciences in Eighteenth-Century French Thought (Stanford, Calif., 1997), 63–4; 97–104, and more generally ch. 5.

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Preformation theories had triumphed over epigenetic accounts from the 1670s onwards. Descartes had been a particularly staunch proponent of epigenesis, rejecting the traditional view that foetal development was due to the realization of an intrinsic goal, because at the basis of his biomechanical understanding of the process was the belief that foetal matter is initially undifferentiated, and is, like all matter, completely inert. He proposed an account in which this initially undifferentiated matter is formed, by means of mechanically characterizable processes such as fermentation, pressure, and expansion, into something that has the organized complexity of the mature foetus. It is the internal conﬁguration of the womb, and the physical processes at work in the womb, that effect foetal development, and there is no need for teleological explanations.8 On this kind of account, since what we are dealing with is a mechanical set of operations shaping or forming matter in a particular way, we might expect primitive living organisms to be formed spontaneously on occasion, since such processes could occur randomly, and indeed it was widely believed that there was no shortage of evidence of spontaneous generation. But microscopic observations from 1668 suggested otherwise: Redi and Leeuwenhoek showed that, contrary to what had been thought, maggots in decaying meat do not arise spontaneously,9 and Swammerdam and others showed that insects in plant galls actually developed from eggs laid by ﬂies.10 At the same time, Malebranche, one of the greatest defenders of biomechanics, realized that the epigenetic account that Descartes had proposed faced insuperable obstacles in explaining how an undifferentiated piece of matter could result in the organized complexity of the mature foetus. Preformation—in this case in the form of pre-existence—was by contrast a perfect complement to mechanism, since it avoided the impossible task of explaining how undifferentiated matter could be formed into an infant of a particular species simply by mechanical means. Along with Malebranche, the other great defender of oval pre-existence was Leibniz, not of course for reasons of compatibility with mechanism, but rather because of the idea that each and every member of the progeny was contained in the mother, and existed there wholly self-contained and impervious to any external events. It is hard to imagine that this rather exotic aspect of preformation would have held any attractions for a mechanist like Malebranche, and must rather have seemed the price one had to pay for the overwhelming advantages that preformation offered in other respects. But for Leibniz it exactly mirrored, at the material level, what he offered in his account of monads at the spiritual level. Indeed, he seems to have considered this as something like an empirical manifestation of his theory of 18

See Gaukroger, Emergence, 337–46. Francesco Redi, Esperienze Intorno all Generazione degl’Insetti (Florence, 1668); Anton von Leeuwenhoek, letter to the Royal Society May 1694: Letter 83 of Opera Omnia seu Arcana Naturae (Leiden, 1722), 456–82. 10 Jan Swammerdam, Historia insectorum generalis (Leiden, 1685). 19

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pre-established harmony. No wonder that he maintains, in his objections to Stahl’s Theoria medica vera, that ‘the success of [my] whole system is due to divine preformation.’11 A particularly striking piece of potential evidence for preformation was parthenogenesis. In 1740, Bonnet isolated a newly born female aphid, reared her in seclusion and noted that she eventually produced ﬁfty-nine young; and he was later able to rear ten generations of lice under similar conditions.12 Of course, this was compatible with epigenesis, just not the kind of thing one would expect to happen on the epigenesis account: if it did occur it would be more akin to spontaneous generation, which was considered a discredited theory. The problems with epigenesis had derived, more than from any other source, from its assumption of an inert matter worked on by purely mechanical processes. This conception had come under attack, for reasons that had nothing to do with questions of embryonic development, in the disputes over Newtonianism, and it is Maupertuis, the great defender of Newtonian attraction in the 1730s, who revives epigenesis. Maupertuis had always been a keen zoologist, keeping a menagerie at his home and publishing two early papers on salamanders and scorpions,13 and in 1744 he published a two-part essay, Ve´nus physique,14 on generation. The ostensible topic of the essay was a report on an albino negro child who was being exhibited as a curiosity in Paris at the time, and the second part of the essay looks at inherited racial differences, particularly those associated with skin colouring and climatic differences. The problem, as Maupertuis conceives it, is to account for white offspring of black parents, given that the child develops from an embryo whose characteristics derive from the paternal and/or maternal bodies, which are black. His response is to argue that the seminal ﬂuid contained elements from distant ancestors as well as from parents, and since we ﬁnd white children with black parents, but never black children with white parents, we may conclude that our ﬁrst ancestors were white, and that albinism is the result of an accident that activates such atavistic elements. In the ﬁrst part of the essay, Maupertuis looked more generally at the question of inheritable characteristics, thereby potentially transforming biological investigation by showing how the investigation of generation can be (and subsequently was) opened up to include a mass of phenomena which now had evidential relevance. He notes that offspring generally share characteristics with each 11 Lelland J. Rather and John B. Frerichs, ‘The Leibniz-Stahl Controversy (I). Leibniz’ Opening Objections to the Theoria medica vera’, Clio Medica 3 (1968), 21–40: 28. Cf. Leibniz to Bourguet 11 July 1714: phil. Schriften, vii. 579. On the controversy with Stahl, see Franc¸ois Duchesneau, Les mode`les du vivant de Descartes a` Leibniz (Paris, 1998), 335–44. 12 Charles Bonnet, ‘Observations sur les pucerons’ [1745]: Œuvres d’Histoire Naturelle et de Philosophie (10 vols., Neuchatel, 1779), i. 1–115. 13 Pierre-Louis Moreau de Maupertuis, ‘Observations et expe´riences sur une espe`ce de salamandre’, Me´moires de l’Acade´mie royale des sciences (1729), 38–45; ‘Expe´riences sur les scorpions’, Me´moires de l’Acade´mie royale des sciences (1733), 223–9. 14 Pierre-Louis Moreau de Maupertuis, Ve´nus physique (Paris, 1745).

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parent, and that the regularity of such characteristics over several generations indicates that they are inherited from both parents. But preformation only allows characteristics of the offspring to derive from a single parent, the mother in the case of oval preformation, and the father in the case of animalculist preformation. Moreover, he argues, the fact that women occasionally give birth to monstrosities is difﬁcult to account for on the preformationist account, whereas the contingencies of foetal formation on the epigenetic account make it a straightforward matter. Combined with Trembley’s discovery, these effectively rule out preformation in Maupertuis’ view. It was important for the success of Maupertuis’ advocacy of epigenesis that, while he supplied a number of complimentary references to Descartes, he had rejected the account of inert matter that largely motivated Descartes’ formulation of epigenesis in the ﬁrst place. As we saw in Chapter 6, it was central to Maupertuis’ introduction of Newtonian physical theory that attraction be taken as given. We also saw that, for French chemists, microscopic forms of attraction had not posed the kinds of conceptual problems that macroscopic forms had done for those working in physics. In reformulating the Cartesian account of epigenesis, on which a mixing of secretions from both parents is necessary for the formation of the foetus, Maupertuis makes it clear from the outset that the model should be chemistry, not micro-corpuscularian matter theory. In a procedure known to alchemists, and more recently described in detail by his fellow academicians Lemery and Homberg, Maupertuis notes how, when one adds silver and spirits of nitre with mercury and water, after some time the ‘particles of these substances come together themselves to form a growth so similar to a tree that it is impossible to refuse it the name’. Moreover, he notes, since the discovery of this kind of growth, various others have been found.15 He identiﬁes the basic operation at work in these processes as attraction. Astronomers—by which he means Newtonian ‘astronomers’ like himself— were the ﬁrst to recognize the need for the principle of attraction, he tells us, to be followed by chemists, ‘whose understanding of it extends further than that of astronomers’.16 This, he argues, is the kind of process that occurs in the womb. In the ﬁrst (1744) version of Ve´nus physique, he is explicit about the role of attraction, telling us that: ‘If we allow such properties or afﬁnities in nature, we shall not abandon all hope of explaining the most difﬁcult phenomena. Let there be in each seed the parts that are destined to form the heart, the head, the bowels, the arms, the legs; and let each of these parts possess the greatest afﬁnity of union with the one that, in the formation of the animal, must be its neighbour; the foetus will be formed: and even if it were a thousand times more complex in

15 Ve´nus physique, ch. 17: Œuvres de Mr de Maupertuis, nouvelle edition (4 vols., Lyon, 1756), ii. 85–6. 16 Ibid., Œuvres, ii. 89.

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organization, it would still be formed.’17 Nevertheless, allowing attraction is one thing; providing an understanding of matter that allows one to make sense of epigenesis, in a way that the inert matter of mechanism failed to do, was a far more difﬁcult question. The problem of what properties the matter constituting the foetus had to have in order for foetal development to occur raised the more general issue of whether this was an exceptional or marginal question for matter theory, or whether it went to the core of our understanding of what matter was. By the mid to late 1740s, it had become a central question in matter theory. In Maupertuis’ Ve´nus physique, it is the chemical doctrine of afﬁnities that is supposed to carry the explanatory weight, but in work published in 1751 under the pseudonym of Dr Baumann, Dissertatio inauguralis metaphysica de universali naturae systemate, subsequently known under the title of its French version, Syste`me de la nature, Maupertuis argues that even with the addition of gravity18 and chemical afﬁnities to the basic mechanical properties of impenetrability, extension, and inertia, ‘we are far from being able to explain the formation of a plant or an animal’.19 Rather, what is needed is set out in these terms: A uniform and blind attraction extended across all the parts of matter does not explain how these parts are arranged in such as way as to form a body with the simplest organization. If all of them have the same tendency, the same force for coming together with each other, why do some go to form the eye, others the ear?; why do they form this wonderful arrangement? And why do they not come together in random ways? If we want to come to terms with this, even if only by analogy, we need to have recourse to some principle of intelligence, to something similar to what we call desire, aversion, memory.20

Such questions fell within the ambit of matter theory on the Aristotelian account, but had been removed from it by the mechanist de-teleologization of matter theory, most notably by Descartes. Maupertuis puts them back into matter theory, seemingly advocating a form of hylozoism.21 How, we might ask, has this happened? Assuming that the nature of matter, at the most fundamental level, did not change depending on whether it constituted something that was mineral, vegetable, or animal, we can ask what consequences this assumption had for the characterization of matter. This brings us to the second of the questions that I asked. While by generally accepted criteria the polyp was an animal, its 17 Maupertuis, Dissertation physique a` l’occasion du ne`gre blanc (Leiden, 1745), 89. The text was subsequently altered slightly, and talk of ‘afﬁnities’ dropped, as Maupertuis abandons the idea that a Newtonian-style attraction held the key. 18 The mutual attraction of seminal particles, for Maupertuis as for Buffon, follows an inverse square law, but Maupertuis thinks something more must be involved: see Maupertuis, Œuvres, ii. 139. 19 Maupertuis, Syste`me de la nature, }4: Œuvres, ii. 141. 20 Ibid., }14: Œuvres, ii. 147. 21 ‘Seemingly’ because, as Terrall points out, the terms function more metaphorically than literally: The Man Who Flattened the Earth, 328–9.

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reproductive behaviour resembled that of a plant. Trembley himself had profound doubts about how to classify the polyp, referring to it at one point as an ‘animal-plant’.22 In the long article on ‘animal’ in the Encyclope´die, written by Diderot and Daubenton, the consequences of this are drawn in a radical fashion. They begin by discussing Buffon’s Lockean deﬁnition of the concept of an animal, as a general idea formed from particular ideas, where these particular ideas are taken from our ideas of dogs, horses, etc., animals with which we are familiar and which are regarded as paradigm exemplars of the concept. But the further we get from such everyday cases, they point out, the less the things we identify as animals seem to manifest these paradigm qualities, and the more conventional the concept appears. Trembley’s apparently insuperable problems with whether to classify the polyps as an animal or a plant are then taken as a reductio of the notion that ‘animal’ can be taken as a category ﬁxed in nature, and Trembley’s work, we are told bluntly, has shown that the most basic distinction of natural history—that between minerals, plants, and animals—is misguided and false.23 There is no sharp line between animals and plants, which are on a continuum. On the division between these and the mineral realm, the authors show a little more ambiguity: the division is described as ‘sharp’, although the possibility is raised that some minerals are ‘more dead than others’.24 Buffon— on whose account in the early volumes of his Histoire naturelle, which appeared in 1749, the entry relies—had advocated the idea of a continuum between the animal and the vegetable realms,25 and had urged a sharp separation between these and the mineral realm. In the mineral realm, we ﬁnd two quite distinct kinds of matter, living and dead, each dispersed throughout, and circulating throughout, nature. It is the living matter that nourishes plants, and these plants then nourish animals, and it returns to the natural cycle as animals decompose and decay. Moreover, it is worth noting that Buffon accepted that a basic Newtonian force of attraction pervaded all matter, and consequently he did not conceive of dead matter as being wholly inert in the mechanist sense. This brings us to the third question: the ‘activity of matter’. The ability of the sliced pieces of the polyp to regenerate into whole polyps indicated that nature was able to generate living beings. The polyp was not a living thing in virtue of some immaterial organizing principle, like a human soul. Rather, because the whole organism seemed to be able to regenerate from every bit of its matter, no matter how it had been sliced, it was as if the vital properties of the polyp, what it was that made it a living being, something with highly organized complexity, 22

Trembley, Me´moires, 77. Encyclope´die, ii. 673. 24 Ibid., ii. 674. In his Pense´es sur l’interpretation de nature ([Paris?], 1753) LVIII qu. 6, Diderot asks: ‘Could so-called living matter not simply be matter which moves by itself? And could so-called dead matter not be one type of matter moved by another?’ Œuvres, ii. 59. 25 The relation between the animal and the vegetable realms is discussed in ch. 1 of ‘Histoire des animaux’: Buffon, Œuvres completes, x. 275–92. 23

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were suffused throughout the matter. But if this was the case—and especially if the distinctions between mineral, plant, and animal realms were ones of degree rather than ones of kind—then the question had to be raised whether matter was intrinsically active. Indeed, Buffon’s microscopist collaborator, Turberville Needham, had reinvestigated the origin of objects seen in infusions of plant and animal matter, and concluded, from experiments with these infusions contained in what he described as tightly corked glass jars, and sterilized by heat, for periods of a week or more, that they could not possibly have derived either from any fermentation of the liquid, nor from ‘seeds’ present in the air, given that they were so numerous, and given that their motion was not like that of independent animals. He concluded that the observed animalcules must have been born of dead matter, and there must be a ‘vegetative force’ in every particle of matter.26 Spontaneous generation, which microscopic observation had ruled out at the end of the seventeenth century, was now ruled back in by microscopic observation, and it clearly had a bearing on the question of whether matter was active, and what this activity amounted to. Ordinary sexual reproduction also raised questions about the activity of matter. Buffon accepted the Cartesian idea that the mixing of two seminal ﬂuids, one male and one female, was necessary for the foetus to form.27 But his account of the constituents of these ﬂuids is framed in chemical, as opposed to mechanical, terms, and the chemistry is very much that of afﬁnities. On Buffon’s account, the ‘organic living parts’ in the material making up the seminal ﬂuids are prevented from combining under normal circumstances, because this material is constantly circulated and recycled. But when opposite living parts from the two parents come into contact during intercourse, their opposing ‘penetrating forces’, conceived along the lines of gravitation and magnetism, but also along those of elective afﬁnities, draw them into contact, and they form an ‘interior mould’ which imposes a structure on them. The conception of matter that Buffon invokes in his characterization of the process of generation makes it clear that it is not simply a question of living organic matter as opposed to dead inorganic matter, for he explicitly invokes the latter to bring out the general idea that we need to penetrate beyond its surface to understand the properties of matter: In the same way that we can make moulds with which we give whatever shape we please to the exterior of a body, suppose that nature can make moulds with which it can not only provide external shape, but also internal form: would we not have here a means by which

26 J. Turberville Needham, ‘Observations upon the Generation, Composition, and Decomposition of Animal and Vegetable Substances’, Philosophical Transactions 45 (1748), 615–66. See the account of Needham’s work in Roger, The Life Sciences in Eighteenth-Century French Thought, 399–420. 27 See Buffon’s ‘Histoire des animaux’, the bulk of which is devoted to reproduction and foetal development: Œuvres completes de Buffon, x. 273–456, xi. 3–341.

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reproduction could be effected? Consider ﬁrst what this supposition is based on, and let us examine whether it is free from contradiction, and then we shall see what consequences we can draw from it. As our senses only judge the exteriors of bodies, we clearly understand the external appearances (affectations) and the different shapes of the surfaces, and we can imitate nature and render the external shapes by different means of representation, such as painting, sculpture, and moulds. But although our senses only judge external qualities, we do not fail to recognise that there are internal qualities in bodies, some of which are general, such as weight; and this quality or force does not act relative to surfaces, but is proportional to mass, that is, to the quantity of matter. There are, therefore, qualities in nature, even very active ones, which penetrate into the body as far as its innermost parts. We do not have a clear idea of these qualities because, as I have said, they are not external, and consequently they cannot fall under our senses; but we can compare their effects, and we may draw analogies to explain the effects of qualities of the same kind.28

In fact, he asks, what is our conﬁdence in external qualities—extension, impenetrability, motion, external shape, divisibility, communication of motion in collision and through the action of springs—based on? Mechanists had taken these to be the fundamental principles of matter, but, he suggests, perhaps they are just a function of our ways of seeing: ‘Is it not the case that, if our senses were different than what they are, we would recognise qualities in matter different from these?’29 In other words, mechanics has built up the fundamental qualities of matter on the basis of an extrapolation from a set of sensory qualities that are simply what we can identify in virtue of the sense organs we happen to be endowed with. Note that Buffon is careful not to deny that these are fundamental qualities (after all, as we have seen in Euler, the primacy of extension or impenetrability can be defended as being conceptual truths about the nature of matter, not simply on sensory grounds), only that there is no reason why they should be identiﬁed as the only fundamental qualities. The claim is that qualities identiﬁed as fundamental by mechanics in no way exhaust the class of those that are genuinely fundamental, and mechanics conﬁnes itself to external qualities, giving the misleading impression that matter itself is as inert as these qualities would suggest. A D EVELOPMENTAL HISTORY OF THE WORLD Jacques Roger has remarked of Maupertuis’ work that ‘it would be impossible to overemphasize the crucial inﬂuence of the reintroduction of duration, an essential dimension, into the science of life. In the area of nature in its totality, Maupertuis found himself led to an examination of the data of heredity, to the idea of the history of life, and to the afﬁrmation of a generally operant 28

Ibid., x. 310.

29

Ibid., x. 328.

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transformationism.’30 If it is with Maupertuis that the life sciences begin to develop their own distinctive developmental model, it is with Buffon that this developmental model comes to dominate the whole ﬁeld of natural philosophy. Natural history had played a role in attempts to reform natural philosophy, particularly as regards questions of use of, and assessment of, evidence as early as the sixteenth century, and Bacon’s attempted reforms of natural philosophy had employed natural history as an important resource.31 Yet the seventeenth-century success of mechanism and of mechanics meant that natural history remained as marginal to natural philosophy as it had been in those earlier eras dominated by Aristotelian notions, whereby natural history was deemed unable to offer genuine explanations of the phenomena. Attempts to transform it into something with genuine explanatory power, from Cesalpino onwards, had worked within the framework of Aristotelianism, however, something that was wholly antithetical to mechanist notions. Indeed, one of the unintended effects of the narrowness of the purview of mechanics had been to allow neo-Aristotelian and quasi-Aristotelian conceptions to thrive in those areas of natural history in which a mechanist model was either manifestly deﬁcient or simply irrelevant. But in the course of the eighteenth century, especially with the rise of Lockeanism, this became an increasingly unattractive option. Buffon’s project—as set out in his immensely inﬂuential Histoire naturelle32—was inspired in crucial respects by the Lockean programme, but rather than moving in a phenomenalist direction, it sought instead to understand structure through genesis, not through essence, with a view to putting developmental concepts at the centre of naturalphilosophical thinking more generally. It should be noted from the outset that neither a commitment to Lockeanism nor an interest in geology was sufﬁcient to motivate a developmental notion. Voltaire is a case in point. His Essai sur les mœurs has a preliminary paragraph devoted to geology, and he argues that any scientiﬁc work concerning the origins of the world should start with geology, because we can have no knowledge at all of the earlier process of creation. But the geology he advocates is radically at odds with developments in the discipline from Hooke and Steno onwards, rejecting any notion of developmental stages. One central motivation here on Voltaire’s part is his determination to combat the orthodox Christian view, and in particular to demonstrate the absurdity of the story of the Flood.33 The rationale for his 30

The Life Sciences in Eighteenth-Century French Thought, 393. See Gaukroger, Emergence, 129–53, 356–61. By 1780, the 36-volume set was the third most commonly owned book in France: see Mornet, ‘Les enseignements des bibliothe`ques prive´es, 1750–1780’. The popularity of the text was by no means conﬁned to France, and Francis Galton’s great-aunt recalled being read passages from Buffon’s Natural History on her mother’s knee in the 1780s: see Jenny Uglow, The Lunar Men (London, 2002), 313. 33 See Brumﬁtt, Voltaire Historian, 87. On the question of orthodoxy, it should be noted that there were also devotees of a universal Flood who were heterodox. In his posthumously published L’Antiquite´ de´voile´e par ses usages (3 vols., Amsterdam, 1766), Nicolas-Antoine Boulanger had 31 32

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argument, however, is one that Voltaire derives from what he takes to be a proNewtonian, anti-Cartesian stance. He begins his Dissertation sur les changements arrive´s dans notre globe, submitted to the Academy of Bologna in 1749, as follows: There are errors that are unique to the people: others are unique to philosophers. Perhaps one error of the latter kind is the idea of so many natural philosophers, who ﬁnd evidence all over the earth of a general upheaval. In the mountains of Hesse a stone is found that seems to bear the impression of a turbot, and on the Alps a petriﬁed pike; and it is concluded from these that the sea and the rivers have run, by turns, in these mountains. It would be more natural to surmise that these ﬁsh, carried by some traveller, went bad and were thrown away, and became petriﬁed in the course of time; but this idea is too simple and insufﬁciently systematic.34

Voltaire identiﬁes what he considers two sources of misunderstanding here. In the ﬁrst place, people seek spectacles in nature just as they do at the theatre, so rather than settling for the obvious explanation, they overextend their imagination and devise a ridiculous one.35 Second, natural terrestrial processes can produce all kinds of shapes, not to mention grains and fruits, so there is no reason to suppose that they cannot produce the various shapes identiﬁed as fossilized animals.36 He identiﬁes Palissy, Descartes, Burnet, Woodward, Buffon, and Maillet as all mistaken, and their mistakes are driven by an urge to offer wild general hypotheses instead of sticking to the facts. What the facts actually show, according to Voltaire, is that ‘there is no system that can provide the least support

argued that the Flood had left several mountain peaks as refuges, so that it was not just Noah and his family that survived. He reasoned that study of the commemorative cults of mountain peoples was consequently of special anthropological importance. 34 Œuvres comple`tes de Voltaire (72 vols., Gotha, 1784–90), xxxi. 375–6. 35 Ibid., 381. 36 A problem with this reasoning is that, as well as fossilized animals, there was also fossilized wood, and buried teeth and bones. Because, unlike the case of fossilized ﬁsh and shells on mountaintops and far inland, there was usually no problem of transport—i.e. no question had to be raised as to how they got where they were (sharks’ teeth being an obvious exception)—there was widespread agreement in recognizing these as fossils: see Rappaport, When Geologists Were Historians, ch. 4. One alternative for Voltaire would have been to deny that these were genuine fossils, but were simply the result of terrestrial processes producing misleadingly organic looking shapes, thereby going against what was an otherwise universal consensus on their being genuine fossils. Alternatively, he would have to show that there was some relevant signiﬁcant difference between these and genuine fossils. Everything hinged on the question of transport and deposition, a problem considered solved by many if there had indeed been a universal Flood, although it should be noted that there were those who, accepting the existence of a universal Flood, doubted whether water could transport heavy shells, and accounted for apparently fossilized shells in other terms, such as spontaneous generation: see e.g. the Ricreatione dell’ochio e della mente (Rome, 1681) of the Jesuit Filippo Buonanni. Note also that Ray (who in any case had doubts about the universality of the Flood) questioned whether the Flood could affect the earth’s crust to any signiﬁcant depth. There was also the outstanding problem, one that had ﬁrst been raised by Woodward, that the ordering of fossils in sediments did not reﬂect their speciﬁc weights, which opened up the possibility that they had not been deposited all at the same time.

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for the prevalent idea that the face of the earth has changed its appearance, that the ocean covered the earth over a long period, and that men formerly lived where today there are whales and porpoises.’ The reason for this is that ‘nothing that vegetates and is animated changes; all species have remained invariably the same; it would be very strange indeed if a grain of millet had eternally conserved its nature whereas the whole earth had varied its nature’.37 It is Newton who is invoked in justiﬁcation of this stand. ‘Nature is content with uniformity and constancy’, he tells us, ‘whereas our imaginations love great changes: and, as Newton says, natura est sibi consona.’38 What is at issue for Voltaire here seems a good deal broader than just a problem in geology, and indeed goes beyond the question of hypotheses to a core issue of what we require from explanations in natural philosophy. While mechanics remained the model for natural philosophy, the idea of developmental stages could play no role in natural-philosophical explanation. But with the mid-century eclipse of mechanics in favour of the collection of disciplines I have treated under the generic heading of matter theory, and even more so with the developments in natural history that were associated with Buffon, the notion of explanation through identiﬁcation of developmental stages assumes an important role. Buffon’s Histoire naturelle is described on its title page as ‘general and particular’, yet, despite the fact that it offered an extensive coverage of ornithology, it is unlike the ‘particular’ natural histories that appeared in France in the 1730s and 1740s. Re´aumur’s seven-volume Me´moires pour servir a` l’histoire naturelle des insects was comprehensive in its coverage of insects and remained the deﬁnitive work on them.39 ‘Particular’ is a word that also appropriately describes the major work on water spiders of Re´aumur’s student and follower Lelarge de Lignac, Me´moires pour servir a` commencer l’histoire des araigne´es aquatiques. Both works, despite their comprehensive treatment of their subject matter, style themselves ‘Memoire to Introduce . . . ’, a kind of modesty associated with the genre of natural history. It would have been far from clear to Re´aumur and Lelarge de Lignac just what qualiﬁed Buffon to describe what he was doing as a ‘particular’ history, and indeed what qualiﬁed him to carry out such a project. Correspondingly, Buffon was contemptuous of what he considered to be the mere imposition of conventions and an arbitrary language, without teaching us anything about the nature of things.40

37 Œuvres comple`tes de Voltaire, xxxi. 385–6. One work of which Voltaire may have been aware is the very popular Histoire physique de la mer (1725), by Luigi Ferdinando Marsili, in which it was argued in detail that the earth’s basic structure had not changed since creation. 38 Œuvres comple`tes, xxxi. 387. 39 It should nevertheless be remembered that, as well as insects proper, it also covered what we would now class as crustaceans and reptiles (the crocodile is described as a ‘furious insect’). Unaccountably, a few birds also sneak in. 40 Buffon, Œuvres, i. 71–6.

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Buffon was elected to the Acade´mie des Sciences in 1733 as adjointme´canicien, making a name for himself as a mathematician, botanist, and as an experimenter in physics. Although in 1739 he was appointed steward of the Jardin du Roi—which, as well as being a botanical garden, housed the king’s natural history collection and an amphitheatre for public lectures on natural history41—he never followed the traditional career of the naturalist, relying more on an unparalleled knowledge of secondary sources than on extensive detailed observations of his own, something that would in any case have been impossible given the scope of his enterprise. His interests were motivated above all by the problem of generation, which he had worked on from the early 1730s, and it is the application of the general question of generation to natural history that allows him to conceive of the latter in such a way that he can place it at the centre of natural philosophy. Although foetal development had been a core problem in Descartes’ account of living things, and generation generally had been the greatest obstacle to biomechanics (at least until the general move towards preformation/preexistence theories at the end of the seventeenth century), natural history had not engaged issues of development at all. Indeed, it had lacked a temporal dimension: the term ‘history’ in ‘natural history’ had a Greek root—historia (inquiry)—which simply meant an account of something. It was preoccupied with description and classiﬁcation, and to the extent to which its aim went beyond the phenomenal level, it was to uncover a natural structure which had been imposed by God on his creation. Buffon denied that this was an aim that could guide natural-historical enquiry, and in its place he sought a naturalistic account of the structure of living systems in their developmental history. In the Histoire’s prefatory ‘Discours de la manie`re d’e´tudier et de traiter l’histoire naturelle’, he asks whether a natural inclination to see uniformity and order in everything leads us to attempt to capture the divine order in nature in terms of abstractions produced by our necessarily limited intelligence.42 In fact, he argues, there is as much disharmony and disorder in nature as there is harmony and order, and there are no clear-cut species because various qualities that one might use to mark out one species from another come in imperceptible gradations, even to the extent of there being ‘zoophytes’ such as sponges that fall between animal and plant.43 The alternative is not, and cannot be, a mere description of natural phenomena. As Buffon sees it, the distinctive feature of natural history is that it is not susceptible to the kind of quantiﬁcation that characterizes mechanics, for example, and requires a wholly different method, one that employs probabilities and analogies: When the subject matter is too complicated for calculations and measurement to be of use—as is almost all that in natural history and in observational/experimental physics 41

See Spary, Utopia’s Garden, ch. 1.

42

Buffon, Œuvres, i. 61.

43

Ibid., i. 63–4.

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[physique particulie`re]—it seems to me that the true method of conducting the mind in its research is to have recourse to observations, to combine them, and to make something new of them, and to gather enough of them to assure ourselves of the truth of the principal facts, and only to employ the mathematical method to estimate the probabilities of the consequences that one can draw from these facts; above all, it is necessary to try to generalize them and to distinguish properly between those that are essential and those that are just a feature of the subject that we are considering; it is necessary then to tie them together through analogies, to conﬁrm or rule out certain doubtful points by means of experiments, to structure explanation on the basis of the combination of all these relations, and to present them in the most natural order. This order can be taken in two ways: the ﬁrst is to ascend from particular effects to the most general effects, and the other is to descend from the general to the particular: both are legitimate, and the choice of the one or the other depends on the ingenuity of the author rather than on the nature of things.44

At the most fundamental level, the task Buffon sets himself is that of establishing an approach to natural-philosophical explanation and understanding which takes a suitably reformulated natural history as its model, where the reformulation—in taking developmental issues as providing the explanatory core of the discipline, and by engaging the methodological questions of truth and evidence that this raises—secures a distinctive standing for natural history as a paradigmatic form of enquiry. Natural history for Buffon comprises ‘exact description and faithful history’. The description should cover internal and external functions, and the history of an animal must not be a history of the individual, but that of the whole species of these animals; it must include their generation, the duration of pregnancy, birth, the number of young, the care of fathers and mothers, their type of rearing, their instinct, place of habitation, diet, the way that they obtain their food, their habits, tricks, way of hunting, and then the services that they can render us, and all the uses or commodities that we can obtain from them.45

If there is an order underlying nature, it is not one of ﬁxed and static structures, but rather one of the activities or operations of nature.46 Putting natural history—a natural history whose goals have been reformulated in this way—at the fore of natural-philosophical enquiry required that Buffon’s coverage be radically different from that of naturalists such as Re´aumur and Lelarge de Lignac. The scope of the project is on a par with natural philosophy, not the ‘particular’ enquiries of naturalists, and the ﬁrst three volumes of the Histoire, which appeared in 1749, dealt with the history and theory of the earth, the formation of the planets, general problems in the life sciences (with special 44

Ibid., i. 116–17. Ibid., i. 82. As Roger puts it, it is ‘an order of the processes that give rise to life and its perpetual renewal, an order of the forces that animate the living world and the laws that govern them’: Buffon, 90. 45 46

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emphasis on questions in reproduction), and a ‘natural history of man’. The history and theory of the earth takes up a second Discours, ‘Histoire et the´orie de la terre’, which is followed by nineteen extensive articles on particular issues in geology.47 It mirrors Part IV of Descartes’ Principia philosophiae—although it begins with a discussion of the formation of the planets, which is covered in Part III of the Principia—and it can be read as a radically revisionary updating of Descartes’ account. In part, the revisions are due to the replacement of Cartesian mechanics by Newtonian mechanics, but the whole Cartesian project is transformed in Buffon’s hands. Descartes had attempted to incorporate an account of developmental processes into an essentially atemporal mechanist natural philosophy. Buffon effectively reverses the direction of explanation here, using the developmental processes as the skeleton on which to ﬂesh out—and dynamize as it were—natural philosophy. The initial problem raised is indicative of Buffon’s new approach. It is that of how, using only what we can observe at present (both in terms of the conﬁgurations of the planets and what causes act), we can reconstruct the past of the solar system, and of the earth in particular.48 He considers that the motions of comets are too irregular, both as regards the directions of their motions and the plane of their orbits, to be susceptible to this kind of analysis, whereas planetary orbits are very regular, which he takes to indicate some common source of their ‘impulsion’.49 The hypothesis he proposes is, in brief, one which accounts for the orbital plane of the planets as well as the fact that they all revolve in the same direction. He calculates the probability of the former occurring by chance to be 1:64, the probability of the latter occurring by chance being 1:7,692,624. Such a degree of unlikelihood indicates that these are not coincidences, and the comet theory, while quite hypothetical, is nevertheless supported by the fact that it provides a single cause for a phenomenon that does not seem to be otherwise explicable in natural terms.50 Assuming that the sun was a sphere of matter 47 Natural history traditionally covered the mineral ‘kingdom’ as well as the animal and plant ‘kingdoms’, and minerals and rocks were classiﬁed into orders, families, genera, and species, just as animals and plants were. See Martin J. S. Rudwick, Bursting the Limits of Time: The Reconstruction of Geohistory in the Age of Revolution (Chicago, 2005), 59–71. 48 The move to a natural-historical modality raised questions that were associated with a Cartesian mechanist approach, rather than the Newtonian mechanical one that had displaced it. This is particularly true of the question of the origins of the solar system, although a naturalhistorical approach has quite different motivation from a mechanist one. Turgot was particularly concerned, asking Buffon why he undertook to explain such phenomena as the origins of the solar system: ‘Why do you want to deprive Newtonian science of its characteristic simplicity and wise restraint? By plunging us back into the obscurity of hypotheses, aren’t you vindicating Cartesianism, with its three elements and its account of the formation of the world?’ Anne Robert Jacques Turgot, Œuvres de Turgot, ed. Euge`ne Daire (2 vols., Paris, 1844), ii. 96. Turgot misses the novelty of Buffon’s approach. 49 Buffon, Œuvres, i. 197–9. 50 The precedent for this kind of approach is to be found in Daniel Bernoulli’s answer to the prize-essay competition proposed by the Acade´mie des Sciences for 1732, which asks for the cause of the mutual inclinations of the orbital planes of the planets. Prior to investigating the cause,

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liqueﬁed by intense heat, and assuming, as his contemporaries did, that comets are very large dense bodies (so dense that, as observation showed, they emerged intact from very close encounters with the sun), he considers what would happen if a comet had struck the sun at an oblique angle, tearing away some of its mass (he calculates that 1/650 of its mass would be needed51). The expelled molten matter would condense into spheres which, he argues, would orbit the sun with a speed, and in a direction, determined by the speed of the comet and its angle of impact. The oblique collision would cause a rotation in the original expelled mass, which would be maintained by the spheres of condensed matter. These spheres are, of course, the planets, and the centrifugal force arising in the case of those that revolve at the greatest speeds causes smaller pieces of matter to be expelled from them, these being the planetary satellites. Subsequent cooling and solidiﬁcation gives the planets and their satellites their familiar properties. Buffon goes on to argue that the planets that rotate at the greatest speeds are those that have the most ﬂattened poles (this being what we would expect of a rotating sphere of molten matter) and the greatest number of satellites, and that the outermost planets are the lightest, in contrast to the account of Descartes, for whom they must be the heaviest (Descartes does not distinguish speciﬁc and absolute weight in this context) because centrifugal force pushes the heaviest matter to the periphery. When he turns to the formation of the earth, Buffon begins by offering lengthy criticisms of Burnet, Whiston, and Woodward,52 and the core of his criticism is physico-theology. He pours scorn on the idea that one could explain theological truths in physical terms, showing in particular how Whiston’s physico-theological account of the earth’s formation contradicted scripture on a number of counts.53 He proposes leaving religious considerations out entirely, and dealing with the formation of the earth purely in physical terms. This might seem to be a safer option than that proposed by physico-theological writers, in some ways more in keeping with the Catholic stress on the role of miracles, but physico-theological accounts of the earth’s development were traditionally believed to offer something that purely physical accounts lacked: a chronology. The bible had offered a way of ﬂeshing out the kind of abstract rational reconstruction Bernoulli sets out to calculate the probability of there being such a cause, and demonstrates that the chances against the phenomenon occurring are so high that they could not be attributed to chance. Daniel Bernoulli, ‘Recherches physiques et astronomiques, sur le proble`me propose´ . . . “Quelle est la cause physique de l’inclinaison des plan des orbites des plane`tes par rapport au plan de l’e´quateur de la re´volution du soleil autour de son axes; et d’ou` vient que les inclinaisons de ces orbites sont diffe´rentes entre elles?”’ Receuil des pie`ces qui sont remporte´ les prix de l’Acade´mie royale des sciences (9 vols., Paris, 1721–77), iii. [1752], 93–122. 51 Buffon, Œuvres, i. 204. 52 Ibid., i. 239–60. 53 The review of Buffon in the Journal de Tre´voux applauded Buffon’s separation of natural history and religious precepts, and suggested that his criticism of Whiston was ‘worthy of being inscribed in letters of gold’: Journal de Tre´voux (October 1749), 2244–5.

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offered by Descartes in terms of datable events. Biblical dating had not been straightforward, however. The Greek Septuagint dated the creation to 5199 BCE, but it also dated the Apocalypse to 6,000 years after creation, and since that date had passed without event, its chronology was generally rejected. The shorter chronologies, those of the Hebrew bible, and the Samaritan Pentateuch discovered in 1624, had their own problems, however. One such problem was whether the shorter chronologies allowed sufﬁcient time for datable events to have occurred. In 1637, for example, Jesuit missionaries to China were given permission by the Vatican to use the longer Septuagint chronology in their teaching because the Hebrew chronology placed the Flood around 2300 BCE, which the Chinese pointed out could not be correct as they had records that went back to 2925 BCE (the beginning of the reign of the ﬁrst emperor), and these records contained no mention of a ﬂood.54 But there can be little doubt that this was regarded as a stop-gap measure, and the Septuagint chronology could not be accepted as a correct chronology. A very speciﬁc dating, using the Samaritan Pentateuch, was offered in 1650. After years of painstaking work, Bishop Ussher published his complex calculations showing that the world was created at 6.00 pm on 22 October 4004 BCE.55 This was the date that subsequently provided a framework within which to place geological events. In rejecting physico-theology, Buffon was in effect rejecting any connection between the bible and the study of natural philosophy.56 This included the use of astronomy to clarify biblical chronology, as much as it did the use of biblical chronology to set a time frame for geology. A good example of the former is Newton’s elaborate attempt, in his Chronology of Ancient Kingdoms,57 to show that the date of 1184 BCE given by Ussher for the Greek capture of Troy, a date which conventionally marked the beginnings of Greek civilization, could not be correct, as that would mean that it pre-dated by two centuries the construction of the ﬁrst temple by the Israelites, and Newton was not prepared to accept that Greek civilization could pre-date that of God’s chosen people. Since the voyage of Jason and the Argonauts was made just a few years before the fall of Troy, he attempted to recalculate this date on the basis of the precession of equinoxes (caused by the very gradual change in the tilt of the earth’s axis) which should be evident from star maps. Using various historical sources to determine the 54 The question of the Chinese chronology was to worry generations of scholars. In 1684–5, the Acade´mie des Sciences drew up a list of questions for French Jesuits about to depart for China, and the ﬁrst question was about chronology and the ‘annals’ listing the reigns of the emperors. See Pinot, La Chine et la formation de l’esprit philosophique, ii. 7–9. More generally on the role of the Jesuits in disputes over chronology, see David E. Mungello, Curious Land: Jesuit Accommodation and the Origins of Sinology (Stuttgart, 1985). 55 James Ussher, Annales veteris et Novi Testamenti (London, 1650). 56 Buffon’s powerful position in the French establishment effectively protected him from criticism from Catholic theologians at the Sorbonne on these questions. See Jean Stengers, ‘Buffon et la Sorbonne’, E´tudes sur le XVIIIe Sie`cle 1 (1974), 97–127. 57 Newton, Opera, v. 1–263.

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description of the celestial sphere that the Argonauts carried for navigational purposes, he concluded that they travelled in 937 BCE. This use of natural philosophy to clarify biblical chronology was rare, however, and Newton’s astronomical ingenuity wasted, since his use of historical sources was so selective as to be entirely implausible, to the extent that when the Abbe´ Conti made his copy of Newton’s manuscript available to scholars at the Acade´mie des Inscriptions in 1724, they were appalled by his calculations.58 Far more common was the converse procedure, typical of physico-theology, namely the use of the biblical account to provide a framework for geological chronology or the geological sequence of events. For Buffon, these questions were to be decided, not on biblical grounds, but on purely physical ones, that is, by working backwards from what was known of present geological formations and the action of physical causes. Paramount amongst these latter were the movement of water in the oceans and sea currents, regular winds, and erosion. Starting from the observation that marine fossils are of the same material as the rocks in which they are found, he infers that they must have been deposited there at the same time that the rocks were formed; and since such fossils are evident everywhere, including mountain tops, all continents must have been submerged at some time in their history. The problem is therefore twofold: how were submarine depositions effected, and how were submarine landforms sculpted? The answer lies, he argues, in the well-attested general east to west motion of the oceans which, following the path of the moon, removed material from European coasts, which show erosion, and carried it towards the American continent, the shores of which show evidence of being progressively built up. It is this movement of water that is invoked to explain the submarine shaping of the sea ﬂoor, currents behaving at a submarine level in the way that rivers do at a terrestrial level. Emerging above sea level (by means of some process on which he does not elaborate), the land becomes stratiﬁed with granite forming the oldest layers, followed by calcareous layers formed by the remains of organic matter, although erosion means that what actually emerges is something more mixed than simple consecutive layering. Because he does not have to explain biblical events such as the Flood, Buffon eschews reference to one-off events and accidental occurrences such as earthquakes. The kinds of causes that we must seek in geology, he argues, must be on a par with those that have been invoked in his account of the formation of the planets, and those which Newton offers to account for the motions of celestial 58 See Nicolas Fre´ret, De´fence de la chronologie fonde´e sur les monuments de l’histoire ancienne, contre le syste`me chronologique de M. Newton (Paris, 1758). See also Conti’s defence of his making public Newton’s manuscript: Abate Antonio Conti, Re´ponse aux Observations sur la chronologie de M. Newton, avec une lettre de M. l’Abbe´ Conti au sujet de la dite re´ponse (Paris, 1726). On the whole episode, see Manuel, The Eighteenth Century Confronts the Gods, 85–102. See also Garry W. Trompf, ‘On Newtonian History’, in S. Gaukroger, ed., The Uses of Antiquity: The Scientiﬁc Revolution and the Classical Tradition (Dordrecht, 1991), 213–49.

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bodies generally: all we are entitled to call upon are regular and purely natural causes. Buffon points out that mountain chains are not placed haphazardly but in a regular way, and he notes Bourget’s observation that the salient and re-entry angles always correspond on the two sides of a valley: something that is mirrored in submarine valleys, as in the English Channel, where the strata on either side correspond in the sequence of sedimentary deposits. Moreover, contrary to the account given in Woodward, he notes that the layers are not superposed in such a way that the heaviest are always at the bottom. Often heavier rocks were found on lighter ones, which would be impossible if they were deposited there at the same time. The exclusive recourse to present causal processes posed a problem of geological chronology for Buffon. While naturalists such as Steno, Thomas Molyneux, and Dezallier had considered the biblical time-scale if anything too long, asking how buried organisms could be preserved in rocks and soil for as long as 4,000 years,59 the kinds of causal processes Buffon evokes are very slow-acting, and could not possibly be accommodated within the biblical time frame. This question is left unposed in the Histoire naturelle,60 but there had in fact been in circulation since 1722 an anonymous manuscript, Telliamed—actually the name of the author, Benoit de Maillet, with the order of the letters reversed— which was published in 1748 and which we have no reason to believe a proliﬁc reader like Buffon would not have known when writing the ﬁrst volume of the Histoire. Here a terrestrial chronology of two billion years was advocated, based purely on natural-philosophical arguments. The manuscript offers a number of radical theses, not least the view that Genesis talks only of God giving form to matter, not creating it, for the Hebrew word Barach means ‘made’ or ‘formed’ and the word ‘create’ is much more recent.61 As regards questions of chronology, Maillet’s argument, which takes the form of a ﬁctionalized conversation with a wise Indian philosopher, was based on the rate of fall in the level of the world’s oceans, as revealed in observations in changes of sea level around islands, and the 59

See Rappaport, When Geologists were Historians, 191. It must be remembered in this context that seventeenth- and eighteenth-century thought tended to work in terms of clear-cut dichotomies which pitted Christian teaching against pagan thought, preferably something associated with Epicureanism. For example, the Christian doctrine of the cosmos as the work of a benevolent creator was contrasted with the Epicurean doctrine that it came about purely through chance: not until Darwinism was there a serious third alternative offered. In the present case the dichotomy was between biblical time and the ancient philosophies of eternalism, and the latter could not offer any time frame for geological events. It was not simply a question of replacing biblical chronology with one which accommodated geological ﬁndings, for this begged the question of why that should be the direction of the accommodation: many natural historians had devised ‘catastrophic’ explanations which accommodated geological ﬁndings to biblical chronology. The underlying problem was to establish the legitimacy of an alternative to eternalism and biblical chronology, something for which there was no classical or religious precedent. 61 Benoit de Maillet, Telliamed; ou Entretiens d’un philosophe indien avec un missionaire franc¸ois sur la diminution de la Mer, la formation de la Terre . . . (2 vols., Amsterdam, 1748), ii. 61–2. 60

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presence of sea-shells embedded in rocks.62 The lowering of the sea level was put down to evaporation, and his interlocutors report (ﬁctionalized) experiments in which the sea level drops by three inches per century.63 Seeking conﬁrmation of his account for periods that pre-date reliable written records, he turns to archaeological evidence, notably the situation of the ruins of cities along the north– south axis from Alexandria to Nubia, now surrounded by desert, but which, at one time, must have had access to waterborne trade. Moreover, taking sightings of mermaids and mermen seriously, he also presents an account of the evolution of modern humans from these aquatic human forms. Although, like Maillet, Buffon believed these questions could only be decided in natural-philosophical terms, he did not accept either the ﬁgure that Maillet came up with, or the method by which it was supposedly reached. The problem was that he himself had no means for working back from the processes such as erosion, which he had postulated as the active causes in geological change, to a feasible time scale. There was another way of proceeding, however. In the Principia, Newton had noted that the comet of 1680 had come so close to the sun that it must have been heated to a very high degree, and must have retained this heat over a long time. He notes that a red-hot iron sphere of a diameter of one inch, when left to cool in the air, takes over an hour to get down to the ambient temperature. Extrapolating to a red-hot iron sphere of the size of our earth, which is forty million feet in diameter, it would take in the order of 50,000 years to cool.64 Since Newton accepted Ussher’s date for the creation, the calculation was purely hypothetical and had no natural-philosophical implications for him. Buffon, however, conﬁnes himself to natural-philosophical considerations, so this calculation potentially has great signiﬁcance, one that became evident on his reading a memoir on the general cause of heat in summer and cold in winter presented to the Acade´mie des Sciences in 1765 by Mairan.65 Mairan showed that temperature differences in summer and winter did not correspond to differences in sunshine. If sunshine were the only factor, winters would be much colder, which suggests 62 The idea of falling sea levels was not Maillet’s invention, and Swedish observers had reported a falling in the level of the Baltic in only a few generations, although the residents of Venice were aware of the opposite phenomenon, the rise of the Adriatic. ‘Rise’ and ‘fall’ here are relative of course, and the observations were compatible with a rise of the land in the Baltic and a fall in the land level in the Adriatic. Note, however, that both rise of the one and fall of the other may play a role. In the case of Venice, for example, there is a gradual sinking of the land mass, but there is also the cyclical acqua alta occuring when wind, tide, and current combine to form a rise in sea level, and the problem is compounded by a sieche, an oscillation or standing wave in the shallow waters of the Adriatic. 63 This kind of approach was not without precedent, and, in 1715, Halley had suggested that the rate of increase of the ocean’s salt content, caused by constant evaporation, could act as a means of determining the earth’s age: Edmond Halley, ‘A Short Account of the Cause of the Saltiness of the Ocean’, Philosophical Transcations 29 (1715), 296–300. 64 Newton, Principia, Book III, prop. 41: Cohen and Whitman edn., 919. 65 See Roger, Buffon, 387. Roger notes that the theory proposed had in fact appeared in the fourth edition of his Dissertation sur la glace (Paris, 1749).

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that the earth itself has a fund of heat. Buffon adds a number of other factors: the increase in temperature as one descends into mines, and the constant temperature of the depth of oceans where sunlight does not penetrate. This suggested to him a completely new development. In the early volumes of the Histoire, he made no connection between his account of the formation of the planets from molten debris from the sun and his account of the formation of the earth. But in the period between 1765 and 1767, he connects the two directly. If the earth’s core was hot, then perhaps this heat was that remaining from the original heat of the solar matter. This opens up the question of the age of the earth, for if the earth were still cooling, and we had some idea of at least the order of magnitude of its initial temperature, then, if we could determine the rate of cooling, we could calculate its age. Buffon sets out the details in a number of places, most notably in his E´poches de la Nature of 1778. Using an industrial forge set up on his estate, he had been experimenting on the rates of cooling of iron spheres for some time, and, reviewing Newton’s experiments and calculations, he had concluded that an iron ball the size of the earth would take just over 96,670 years to cool to its present temperature. However, the earth had not cooled in air but in a vacuum, and it was not an iron ball; rather ‘in reality, the principal materials of which the earth is made, such as clays, sandstone, stones etc., must cool in less time than iron.’ After 150 pages of calculations the published ﬁgure that he comes up with is 74,832 years, although he continued to recalculate and in manuscript drafts he makes it clear that the timescale involved is probably of the order of three million years.66 Because of the close association between heat and life in Buffon, the idea of a central heat radiating outwards takes on biological signiﬁcance. In particular, the idea that the earth may have been steadily cooling threw light on a number of previously inexplicable phenomena, not least the numerous tusks and bones of warm-climate animals such as elephants, hippopotamuses, and rhinoceroses found in northern Europe and Siberia:67 the greater heat of the earth’s interior meant, he argues, that at an earlier time these regions had been as warm as present-day tropical climates. More importantly, his calculations as to the rate of cooling of the earth provided a biological time frame. Newton’s original calculations gave three stages of the iron sphere: red hot, just hot enough to touch, and the reaching of ambient temperature. Buffon’s calculations do likewise, and the middle stage is important because this gives us an indication of the time at which life might have emerged: life began when the temperature dropped sufﬁciently to support it, assuming, as Buffon does, that life emerges spontaneously as soon as 66

See the discussion in Roger, Buffon, 409–13. There were a signiﬁcant number of reports of such remains, and an especially important source was Johann Philip Breynius, ‘Observations, and a Description of Some Mammoth’s Bones Dug Up in Siberia, Proving Them to Have Belonged to Elephants’, Philosophical Transactions 40 (1741), 124–39. 67

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conditions are right. His account of the origins of life is too sketchy to be reconstructed with any conﬁdence,68 but the key event is the action of heat on matter to form organic ‘molecules’, i.e. those smallest units capable of sentience.69 The theory of the formation of the earth leads naturally to the theory of its inhabitants in the Histoire, and however hesitant Buffon may have been on the origins of life, he was forthcoming on the deﬁning feature of living things: it was ‘the capacity to reproduce’,70 a capacity which, he considers, makes animals and plants ‘practically of the same order’. On the face of it, this might seem innocuous. After all, botanists who considered themselves Aristotelians had concentrated on the reproductive parts of plants in classifying them, even though it was the morphological features of these reproductive parts that provided the concrete classiﬁcatory criteria, and animal species had been identiﬁed in terms of ability to interbreed. Buffon rejects morphological criteria entirely and deﬁnes an animal species in these reproductive terms: ‘One must consider as the same species, that which by means of copulation perpetuates itself and conserves the similarities of that species, and as different species, those that through the same means can produce nothing together.’71 But the crucial thing to remember here is that, for Buffon, ability to interbreed is a functional criterion, not one that mirrors essential similarities and differences.72 Indeed, there seem to be no essential 68 See ibid., 414–17. Buffon’s is not an evolutionary conception, and the ﬁrst animals to be formed, for example, are complex ones, such as the hippopotamus. 69 The notion of organic ‘molecules’ was widespread in the life sciences in the mid-eighteenth century, and was the subject of much dispute: see e.g. Charles T. Wolfe, ‘Endowed Molecules and Emergent Organization: The Maupertuis-Diderot Debate’, Early Science and Medicine 15 (2010), 38–65. 70 Buffon, ‘Histoire des animaux’, ch. 1: Œuvres, x. 276–7. 71 Ibid., x. 285. 72 Actually, the criterion is ambiguous: it is necessary to distinguish between pre-mating behaviour—animals not attempting to mate because they do not identify the other animal as a mating partner—and post-mating behaviour—animals that mate with one another unsuccessfully, in the sense of not producing offspring. We also need to take account of mating behaviour in conditions where normal pre-mating abstinence is overidden and where the mating is successful. Lions and leopards will not mate in the wild for example, because they will not identify one another as suitable mating partners, but they can mate successfully when brought together in the same area in a zoo. In this case, although the male offspring are infertile, the females are fertile. The idea of interbreeding as a criterion for species identity would seem to break down here, but I take this not as a criticism of Buffon’s choice of interbreeding, but as a reinforcement of his argument that it is a merely functional criterion. On such a conception, anomalies are clearly less serious than they are on a species essentialist account. Note that the idea of animals of different species mating in artiﬁcial or conﬁned circumstances was common in the seventeenth century, and was indeed considered a source of increasing diversity in species. See e.g. George Abbot, A Briefe Description of the Whole World (London, 1599): ‘this may be said of Africke in generall, that it bringeth forth store of all sorts of wild Beasts, as Elephants, Lyons, Panthers, Tygers, and the like; . . . Often times new and strange shapes of Beasts are brought foorth there: the reason whereof is, that the Countrie being hott and full of Wildernesses, which haue in them little water, the Beastes of all sortes are enforced to meete at those few watering places that be, where often times contrary kinds haue conjunction the one with the other: so that there ariseth new kinds of species, which taketh part of both.’ Quoted in Adam Nicolson, God’s Secretaries: The Making of the King James Bible (London, 2003), 160.

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similarities and differences of any kind. God has not put any ﬁxed differences between animals and plants, we are told, and ‘the living and the animate, far from being a metaphysical quality of beings, are physical properties of matter.’73 In studying living things, one is not studying some essential quality of plants and animals, and in this respect Buffon’s project is in line with that of biomechanics. But whereas the core problem for biomechanics is that of organized complexity, Buffon makes it clear that ‘the production of organized beings costs God nothing’, and such complexity is not the deﬁning feature of living organisms for him. Moreover, generation is reproduction for Buffon, and the pre-existence theories that had dominated biomechanist thought in the wake of Malebranche are effectively excluded from consideration. Treatment of reproduction must begin from the simplest cases, and, among these, plants and simple animals hold the key. A fragment of an elm and a polyp can regenerate the complete organism, and such regeneration can only be explained, he believes, on the basis of ‘organic molecules’ making up any living thing, which after regeneration are used up in the process of growth. Having analysed the simplest and most fundamental cases in this way, a wholly new account of sexual reproduction can be provided, one in which the organic ‘molecules’ that are no longer needed for nutrition assemble in the reproductive organs (conﬁrmed by the fact that animals reproduce only when they have ﬁnished growing), forming seminal ﬂuids which need to be mixed for generation to occur (conﬁrmed by the resemblance of offspring to both parents).74 Although his Histoire is primarily devoted to zoology, Buffon’s understanding of what falls under zoology is comprehensive and includes a detailed account of what he terms ‘the history of man’, revised and augmented as the project continued. It begins with human developmental history—childhood, puberty, adulthood, old age, death, and embalming—followed by an examination of a number of questions to do with sensation: the sensory faculties, especially those of sight, hearing, and touch; the human voice; and the temperature range in which human beings can survive. There follows a section of the ‘varieties of human species’, which examines the characteristics of different races, and concludes with a section on monstrous births. Finally, there is an ‘essay on moral arithmetic’ (inserted in later editions but incorporating some very early material), followed by over 100 pages of statistical tables on births, deaths, and marriages, and analysis of the ﬁgures. Buffon’s strategy involves two very signiﬁcant moves. He explicitly incorporates anthropology into natural history; and he introduces quantiﬁcation, in the form of statistical tables, into the discipline. In these respects, his natural history of man marks a crucial early move in a transition from religious and humanistic 73

Buffon, Œuvres, x. 292. The quasi-instantaneous formation of the embryo and its early development are discussed in detail in the last chapters of the ‘Histoire des animaux’. 74

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understandings of human behaviour to a very different form of understanding, one much more closely allied to a natural-philosophical model.75 Conversely, his account illustrates one way in which Lockean sensationalism can be used to exploit, and reshape, a natural-philosophical model so that it becomes one of much greater applicability, if at the cost—if indeed it is a cost—of failing to offer precise guidance. It should be noted from the outset that the study of human beings qua animals was not novel in itself. There was a philosophical tradition deriving from Aristotle which allowed for such treatment, and it had always been commonplace in anatomy and physiology. Moreover, although Buffon criticized Linnaeus’ creation of an ‘anthropomorphic order’ among quadrupeds in which human beings were grouped with monkeys, lizards, and sloths, what was at issue here was not the idea of classifying human beings along with other animals, but what he considered some manifestly absurd consequences of trying to capture a ‘natural’ classiﬁcation. What was contentious in Buffon’s approach was not, then, the fact of classifying humans among animals. Nor did such an approach carry with it any connotations of materialism: Buffon begins his account with a steadfast statement of Cartesian dualism.76 Rather, it is his advocacy of a radical form of Lockean sensationalism that gives a naturalistic edge to his attempt to apply the same procedures of enquiry to human development as those he has applied to animal development. An understanding of human affairs was traditionally thought to fall within, or at least be informed by, a religious understanding, especially as far as its moral dimensions were concerned. But it also fell within the scope of belles-lettres, or humane learning, which had classical precedents, and which had in fact been the main vehicle for dealing with such questions, at least at an explicitly philosophical level, since the Renaissance. Humane learning and theologically driven accounts of the human condition had come into conﬂict as early as Machiavelli, 75

The use of statistics (birth and death rates) was pioneered in a social context as early as the 1660s by Graunt and Petty in the context of ‘political arithmetic’, a procedure originally designed to estimate each individual’s contribution to the public good by measuring what he or she contributed to, or withdrew from, the national stock. See, in particular, John Graunt, Natural and Political Observations mentioned in a following Index, and made upon the Bills of Mortality (London, 1662), where Graunt applies what he terms his ‘Shop-Arithmetique’ (ibid., 7) to London bills of mortality, construing these as Baconian-style tables of discovery which might be made to yield a natural history of man, and initiating the investigation of death as a function of age: see Daston, Classical Probability in the Enlightenment, 127–9. See also William Petty, An Essay Concerning the Multiplication of Mankind together with another Essay in Political Arithmetic (London, 1683). These works, especially the latter, bear directly on the development of political economy, treatment of which I shall defer to the next volume, but see the general account in Andrea A. Rusnock, ‘Biopolitics: Political Arithmetic in the Enlightenment’, in W. Clarke, J. Golinski, and S. Schaffer, eds., The Sciences in Enlightened Europe (Chicago, 1999), 49–68. The most important mathematical attempt to deal with the ‘moral sciences’ was Part IV of Jakob Bernoulli, Ars conjectandi (Basel, 1713), published eight years after his death. Despite its date, I shall defer consideration of this too to the next volume, where I shall be dealing with the development of probability theory. 76 Buffon, ‘De l’Homme’, De la nature de l’homme: Œuvres, xi. 343–4.

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but by the middle of the eighteenth century there had emerged a form of naturalization of human behaviour which offered an alternative to both these. What was distinctive about this new mode of enquiry was that it did not seek to provide a uniﬁed theory of human behaviour in competition with those of theological and humanistic accounts. This is particularly evident in Montesquieu’s De l’esprit des lois, published in 1748, in which human behaviour is extensively contextualized and made relative to particular laws, customs, institutions, and the particular vagaries of morality and religion operative at particular times and places. De l’esprit des lois is travel literature transformed into a philosophico-political textbook. Human nature appears not as something ﬁxed but rather, in crucial respects, as a kind of interference effect of a wide and potentially open-ended range of factors ranging from climate and diet to contextualized moral scruples. The ﬁxed point around which everything turns is sensibility, for laws must always suit ‘the degree of sensibility’ of those governed by those laws.77 In very broad terms, there is an analogy between this way of construing the political realm and Locke’s advocacy of a conception of natural philosophy as a non-uniﬁed, experimental domain. Locke made no attempt to introduce an analogy with the political realm, and as we have seen he himself believed that there was a universal moral and (minimally construed) Christian basis for the understanding of the state. But his questioning of the unique legitimacy of systematic explanation, which became a general ideology in the generation of the Encyclope´die, can be seen as supporting a general framework of understanding with implications for the social and political realm as well as that of natural philosophy. Lockean considerations play an explicit role in Buffon’s thinking about species, as we have seen, and his nominalism on species is less hesitant than that of Locke. In pursuing his account of natural history into the human realm, his focus on particularity generates a radical contextualization of human nature on a par with that of Montesquieu. His ‘natural history of man’ includes an account of the development of moral, social, and intellectual life, and the extended resources outlined at the beginning of the Histoire naturelle—which include not merely physiology but the care and attention of the parents in nurturing their young, their education, and the instincts, habits, and wiles that the children develop—become even more central in the case of human beings than in the animals dealt with up to this point. The developmental role of sensation plays a pivotal role in Buffon’s account, and indeed there was something of a priority dispute with Condillac over the use of the thought experiment of the statue receiving various sensory faculties, although it is an image that originates much earlier, in Descartes’ Le Monde. Buffon and Condillac use the thought experiment (which we shall be exploring 77

Montesquieu, De l’esprit des lois (Geneva, 1748), Bk. XIV, ch. 2.

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more fully in the next chapter) in the same way, and reach much the same conclusions. In particular, Buffon argues that the statue at ﬁrst believes all its sensations to refer to internal experiences, and it only when a tactile faculty is provided that it realizes, ‘in horror’, that there is something outside it. Only touch can provide a sense of an external world, and with this sense effectively comes a precondition for morality, in that with it comes a recognition of the existence of others, and a love for them replaces the earlier narcissism. Sensibility and a recognition of an external world come simultaneously, and this is important for the Lockean tradition in France. Its importance lies in the fact that it is intended as a replacement for an inadequate innate ideas tradition, in which the qualitative difference between mere sensation and perceptual experience comes with innate ideas. Buffon, Condillac, and Diderot each want to register the qualitative difference between merely sensing and having an experience of an external world, and for them this qualitative difference comes with sensibility, which thereby does much of the work that innate ideas did in the pre-Lockean account.78 Moreover, in Buffon, this emergence of sensibility can be naturalized through an account of sensation, and particularly touch, by contrast with the wholly speculative postulation of innate ideas. The naturalization comes in the context of a large-scale account of natural history, in which human capacities can be seen to emerge seamlessly from an analysis that follows an account leading from the emergence of life on the planet, through animals, to distinctively human behaviour and faculties. Such questions as the ambient temperature necessary for life to emerge on the planet, for example, are carried over into an ethnographic discussion of the climates in which different races live and the distinctive human characteristics that are observable as a result of climatic differences. Such characteristics include height, hair type, skin colour, and shapes of lips, nose, face, and eyes, but also dress, sexual habits, and morality. Although climate does not explain ethical mores to the extent that it explains skin colour, it is nevertheless now part of what needs to be taken into account in explaining the former. Buffon’s discussion draws on a very diverse mass of travel literature in this respect, and travel literature here provides the raw material, just as does dissection and experiment in the case of animal generation. It is no longer merely a source of counter-examples: it is the basic material which any theory of human behaviour has to account for. In this respect Buffon’s project may seem very similar to that of Montesquieu, for example, but the very fact of its integration into a detailed naturalistic account of living things means that it is part of a comprehensive vision on a par with that of the mechanist picture that reigned in the second half of the seventeenth century and which had been relegated very much to the margins of naturalphilosophical thought by the middle of the eighteenth century. It is really the ﬁrst 78

Cf. Riskin, Science in the Age of Sensibility, ch. 2.

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such comprehensive vision to replace that of mechanism, offering not merely an account of the nature of the world, but an account of our relation to this world, in the form of an account of how we emerge from the world as the subjects of cognitive and affective states, which reveal to us the ‘otherness’ of the world. We have in Buffon’s work a clear example of questions of human behaviour being formulated in line with an anthropological conception based on a newly reformed natural-philosophical model of understanding. The natural-philosophical model at issue has some features that mark it out strongly from a microreductive model. In the ﬁrst place, it takes collective behaviour to be distinct from the distributive behaviour of the participants. Just as natural philosophers had treated the law of the pendulum, for example, as something to be accounted for in its own (macroscopic) right, not as the sum of the motions of its constituent (microscopic) corpuscles, so Buffon not only insists that it is species not individuals that are our proper objects of study, but averages out human behaviour no less than his tables of statistics average out births and deaths, for that is the way to understand characteristically human phenomena. Second, it is a premiss of Buffon’s approach that this collective behaviour, which Voltaire, Montesquieu, and others had attempted to capture in qualitative terms, can also be captured in quantitative ones. Traditional natural-philosophical models had been highly geometrical in orientation, and geometricization and quantiﬁcation had effectively been treated as the same thing. But, as far as quantiﬁcation was concerned, in the new moral sciences it was numbers that were at issue. The move from what might be termed a timeless or atemporal conception of natural philosophy (of the kind we ﬁnd in mid-century rational mechanics) to a developmental conception, is mirrored in the move from geometrical to arithmetical models of quantiﬁcation.79 79 Although the application of probabilities to statistics still lay far in the future—see Theodore M. Porter, The Rise of Statistical Thinking 1820–1900 (Princeton, 1986)—we ﬁnd in Buffon the ﬁrst awareness of how quantiﬁcation might be appropriate in a model of natural philosophy which is completely different from that offered by mechanism. We shall be pursuing these questions in subsequent volumes, as the most important developments fall outside our present time frame.

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PART V

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11 The Realm of Sensibility In Part III, we traced the origins of a complex process by which knowledge in general, and rationality in particular, came to be associated with natural philosophy. But as we have just seen in Part IV, natural philosophy was at the same time moving in two quite different directions. There was an increasingly rareﬁed and abstract form of rational mechanics, whose mathematical sophistication was not mirrored in—and in some cases was inversely proportional to—its ability to explain empirical phenomena. There was also a sprawling matter theory, upon which had been foisted the many problems that fell outside the narrow range of the rational mechanics that had replaced mechanism. This matter theory, by contrast with rational mechanics, lacked the kind of overarching systematic structure one might assume to be needed if it were to act as a paradigmatic form of knowledge. Lack of systematic structure does not necessarily mean lack of focus, however. Micro-corpuscularianism had provided intrinsic principles of uniﬁcation for mechanism in virtue of the fact that the micro-corpuscularian level was deemed one of ‘common causation’: it was the fundamental level in the sense that it was that at which the kind of causal processes involved are identical for any physical phenomenon. The forms of matter theory that we have considered in Chapters 9 and 10 can provide nothing of this kind. As we have seen, many of the disparate disciplines that made up matter theory were, individually, highly systematic and structured, but this did not provide it with an intrinsic focus. There were extrinsic sources of focus, however. In particular, some of the key disciplines that explored the nature of matter had a close connection with medicine. We have seen that chemistry was in large part motivated by questions in pharmaceutical botany in the seventeenth and eighteenth centuries, and, along with mineral extraction, this provided it with its rationale at the level of support in the universities as well as in the Acade´mie des Sciences in France, and the Royal Society and the College of Physicians in Britain. Electricity, at least from the 1740s onwards, was likewise seen as having medicinal beneﬁts, and this was the paramount practical role for electricity up until the late nineteenth century, by which time electriﬁcation had become the paradigm form of treatment of nervous disorders.1 At the same time, the emancipation of the life sciences 1

See Schaffer, ‘Natural Philosophy and Public Spectacle in the Eighteenth Century’; and Linda Simon, Dark Light: Electricity and Anxiety from the Telegraph to the X-Ray (Orlando, Fla., 2004).

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from biomechanics meant that basic biological processes could be investigated from a matter-theoretical point of view without this necessitating a reductive strategy. What matter-theoretical considerations there were could now be treated in the context of what is needed to realize certain functions, and what properties matter must have if it is to behave in the appropriate—biologically characterized— way: in particular, whether one should be thinking in terms of extrinsic principles acting on an inert matter, or whether there was a place for a conception of living matter. The questions of the development of the notion of an organism, and the treatment of organs as autonomously functioning entities which, when combined in a coordinated way, form the organism—questions that we shall be investigating below—inevitably bring with them considerations of health. Nevertheless, if we are to describe what happens here in terms of a medical model replacing a micro-corpuscularian one, or a mechanical one, we need to be careful to register the fact that such models work in very different terms, and replacement could not be a question of one model doing the same work that the earlier one did but in a different way. The micro-corpuscularian and mechanical models were both reductive, in their different ways, whereas a medical model is not reductive. Moreover, what it captures, in its capacity as a model, is something quite different from the other two and, most importantly, it provides a more explicit connection between our understanding of the natural world and an understanding of our place in the natural world. Such a connection had been largely absent from mechanist conceptions.2 On a medical model, however, it is a natural way of thinking about things, because we are very much part of the world we are examining, and the line between subject and object becomes blurred and problematic. Indeed, this examination will often be tied in with a project of selfunderstanding: both corporeal and psychological self-understanding. Here we have at least the elements of an answer to the question of how natural philosophy was transformed in the mid-eighteenth century so that it was able to conform to its proposed role as a model for knowledge. What we shall discover in this chapter is that the transformation that occurred was one in which the central role accorded to rationality in the ﬁrst half of the century, now comes to be translated into terms of sensibility. If natural philosophy was to meet the 2 The principal exception was Spinoza, who tried to reconcile mechanism as the single legitimate way of understanding the world with a general understanding of our place in the world which had the depth and richness to underpin questions of morality, culture, and civil and political values. The attempt was unsuccessful, partly because of the mechanism that Spinoza advocated was not viable— see Gaukroger, Emergence, 471–92—and partly because of the rejection of such systematic forms of understanding in the wake of the uptake of Locke’s work, whether in its original form or in the more radical Baylean variety. Jonathan Israel’s assimilation of Spinozean and Baylean currents into his notion of ‘radical Enlightenment’—see especially his Radical Enlightenment—misses this contrast between the (systematic) Spinozean and (anti-systematic) Baylean approaches, a contrast which is absolutely fundamental in the eighteenth century and one which explains how Bayle’s radicalism— which well may have been inﬂuenced by Spinoza—comes to be associated with the very different Lockean programme.

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demands that its post-Voltairean standing placed on it, its task was not just one of understanding the natural world, but also that of understanding our place in that natural world, and the move to sensibility brings with it a signiﬁcantly greater degree of success in this enterprise than anything on offer in the 1730s or early 1740s. This is especially the case on the question of just how comprehensive a vision a natural-philosophical model can support, for sensibility allows connections to be made between natural-philosophical and moral, political, and psychological theories in a new way, shaping a new ﬁeld of the ‘moral sciences’. F R O M S E N S IB I L I T Y T O S EN S I BI L I S M The idea that natural philosophy could serve as the bearer of cognitive standards must be examined both with respect to the implications of this for natural philosophy, and with respect to its implications for cognitive standards. In Part III, we considered how natural philosophy might provide general cognitive standards, but of at least equal importance are the consequences for natural philosophy of its taking on the role of the bearer of a set of standards that extend well beyond its own speciﬁc practices, and indeed beyond those areas—and this is especially so in the case of mechanics—that it takes to be models for natural philosophy generally. By mid-century, the move to construe natural philosophy— represented by the mechanical model that had prevailed from the middle of the seventeenth century—as manifesting the canons of reason was increasingly deemed to be premissed on a misunderstanding of what natural processes consisted in, and what our relation to nature consisted in. In particular, if natural philosophy was to be the bearer of cognitive standards, attention had to be paid to what the basis of cognition was. Up to now we have taken natural philosophy as ﬁxed and asked how cognitive standards generally might be modelled on it. Our task in this chapter is to explore the converse question: whether and in what way natural philosophy was adapted if it was to aspire to the provision of general cognitive standards. The initial move in this project was to consider cognition in terms of sensibility, something construed on a Lockean model by Condillac, Buffon, Diderot, and others. The principal target of this way of proceeding was the idea that cognitive grasp exclusively inhabited the realm of reason. It was not just our cognitive relation to nature that was at issue, however, but nature itself. Reason might be thought to reﬂect nature, but how could sensibility reﬂect nature? In the Encyclope´die, there are two main entries for ‘sensibilite´ ’, one coming under the rubric of ‘morals’, the other under the rubric of ‘medicine’. The former deﬁnes sensibility as the ‘delicate and tender disposition of the soul that makes it easily moved and affected’, and is spelled out in these terms: The sensibility of the soul, as the author of Les moeurs [Voltaire] accurately puts it, imparts a kind of wisdom about propriety, and it goes further than the penetration of the

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mind alone. Sensitive souls may be caused by their intensity to make mistakes that men who lack this would never commit; but they make up for this through the abundance of goodness they generate. Sensible souls get more out of life than others; both the good and the ill are increased for them. Reﬂection can make a man of probity; but sensibility makes a man virtuous. Sensibility is the mother of humanity and of noble-mindedness [generosite´ ]; it increases worth, it helps the spirit, and it carries persuasion.3

The other entry, that falling under the rubric of ‘medicine’, describes ‘sensibilite´, sentiment’ as ‘the faculty of sensing, the sensitive principle’, deﬁning it as ‘the basis and conserving agent of life, animality par excellence, the most beautiful and most singular phenomenon of nature’. Sensibility, we are told, ‘is in the living body, [and is] a property by which certain parts perceive the impressions of external objects, and in consequence of this produce motions in proportion to the degree of intensity of this perception’.4 This is a long and detailed entry, covering the history of the notion of the ‘sensitive soul’ in both the philosophical and the medical literature from antiquity onwards, and highlighting the role of the nerves. Subsections are devoted to sensitivity/sensibility in the foetus; the nature of sense organs; sensitivity/sensibility in physiologically normal and in pathological states; nervous disorders, convulsions, and spasms; the effects of air, external objects, the stars, and climate on sensibility; and the phenomenon of muscle irritability. Although the two entries are separate, there is no doubt that the connection between the phenomena described is not merely accidental. By the mid-century, in the work of writers such as Diderot, sensibility/sensitivity/sensation is a uniﬁed phenomenon having physiological, moral, and aesthetic dimensions, and it lies at the basis of our relation to the physical world: it is what natural understanding has to be premissed on. Not only that, but it has come to encompass those dimensions of natural processes that mechanism had written out of the picture, dimensions captured for example in chemistry—in the afﬁnities that seemed to guide the relations between chemical substances, and the mixing of different bodies so intimately as to be fused and inseparable by mechanical means—and in physiology, as in the phenomenon of irritability whereby, when touched, muscles contract with a force much greater than the original cause. Nature seemed to harbour a power and responsiveness that was capturable in terms of some broad notion of sensibility/sensitivity. If natural philosophy was to provide a general cognitive model, it had to adapt its explanatory resources to these phenomena, and to become part of the programme of sensibility. In examining these questions, let us ﬁrst remind ourselves of the conditions under which natural philosophy was able to emerge as a general cognitive model. We have seen that, in the second half of the seventeenth century, there developed in Paris a distinctive literary culture, which seeded the transformation of the 3

Diderot, Encyclope´die, xiii. 810.

4

Ibid., 780.

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Republic of Letters in France and propelled it to centre stage. There were two distinct characteristics of the literary culture that emerged at this time: there was a change in what literature did and how it did it, and there was a change in who literature was written for and who was to assess its value. It is in the second set of questions that we see the consequences of Fontenelle’s largely successful attempts at incorporating natural philosophy into the Republic of Letters, and for this reason I focused on these in Chapter 6. The ﬁrst set of issues also had signiﬁcant ramiﬁcations outside literature, however, and these helped seed deep questions about the nature of ‘enlightenment’, and especially about the comparative standing of reason and sensibility. As I have indicated, the traditional prose and poetic forms that had dominated literary culture up to the middle of the seventeenth century, as those best suited to conveying the moral and other qualities that literature fostered and displayed, were replaced by a new literary form. This new literary form is what would subsequently develop into the novel, which displayed very different kinds of values, and displayed them in a very different way. From the mid-seventeenth century onwards, literary prose works began to appear which were ill-adapted to capturing the kinds of values that drove the classical models, but were nevertheless able to engage much the same range of issues, albeit from a completely different source, as it were. The classical ideas of passion and ´emotion which Descartes had explored in his Passions de l’aˆme of 1649, for example, were replaced by those of tendresse and sentiment.5 These latter were not grounded in medical concepts, as Descartes’ were, and they had a value not in relation to a natural order but in relation to an inner mental and emotional life: what we might term a personal psychology. Affective states generated in this way give us an entry into the psychology of the character rather than offering a way of placing the behaviour of the character in a natural order. Consequently, even if, in the case of something like love, they are identiﬁable in broad terms as the same affective state as that described in classical genres, they are embedded in a wholly different phenomenology, and it is this latter that the literary genre makes it own and uses as a vehicle for its exploration of such affective states. In the case of the emerging prose literature, such exploration construes the emotions in terms of shared experiences, by contrast with the account in the Passions de l’aˆme, whereby an emotion—following what is in effect a medical model—is a solitary experience that disturbs or unsettles the soul. We can see the transition from the passion/e´motion conception to that of tendresse and sentiment in the novels of Madeleine de Scude´ry. These comprise two ten-volume novels—Artame`ne, ou le grand Cyrus (1649–53) and Cle´lie, histoire romaine (1654–60)—whose sheer length and scope indicate that they take the epic as their model although, as DeJean has pointed out, in its transition from poetry to prose the genre becomes 5

DeJean, Ancients against Moderns, 81–2.

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Fig 11.1

transformed, as shared emotional experience becomes the key to understanding and appreciation.6 In Cle´lie, Scude´ry literally maps the emotions, by providing a map of the imaginary land of ‘Tenderness’ in which the narrative is set, replete with such topographical features as ‘Lake Indifference’ (Fig. 11.1). By the time of Marie-Madeleine de La Fayette’s La princesse de Cle`ves (1678), it is internal psychological exploration, in the form of reﬁned sensibility, rather than external events that have become the focus of the novel. In some ways this development is in accord with Malebranche’s assessment, in De la recherche de la ve´rite´, where he tells us that it is the delicacy of the brain ﬁbres typically found in women that gives them: their so exact acquaintance with all things that strike upon their Senses. ’Tis the Woman’s Province to determine concerning the Fashions, to judge of Language, to distinguish the genteel Mein, and the ﬁne and courtly Behaviour: They far out-do men in the Science, Skill, and Dexterity about these things. All that depends upon the Tast falls under their jurisdiction; but generally they are incapable of Penetrating into Truths that Have any Difﬁculty in the Discovery. All Things of an abstracted Nature are Incomprehensible to Them.7

6 De Jean, Ancients against Moderns, 83–7. As DeJean points out, Scude´ry transforms the meaning of sentiment, which in earlier usage had meant ‘opinion’. 7 La Recherche, Book II, Part 2, ch. 1. Translation from Father Malebranche his treatise concerning the search after truth, i. 64.

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The further we move into the eighteenth century, however, the more we ﬁnd the values that Malebranche characterizes as those of women taking a central place at the expense of the abstraction of thought that he characterizes as the domain of men. What is at issue here is not Malebranche’s misogyny, for this is not what his successors are criticizing or distancing themselves from, but rather the fact that, for mid-century Enlightenment thinkers, Malebranche has radically mis-assessed the role of sensibility, and his contrast between sensibility and reason is profoundly mistaken. Sensibility is not an added extra: it is what underlies our cognitive life. A crucial factor in this transformation is the role played by the Republic of Letters. As we saw in Chapter 6, the works in the new literary form of the novel were directed at a very broad audience, who were invited to offer judgements on them. In France, it was in the salons, reading groups, and periodicals such as Mercure galant, where readers, men and women alike, were invited to comment on the latest literary works, that the value of new works, and engagement with the moral and social issues they raise, were discussed. Of particular interest here is the way in which the questions of sensibility and judgement become associated, raising the more general issue of whether reason is the sole arbiter in judgement generally, or whether something like sentiment must also play a role. When Lockean sensationalism comes to be introduced into French thinking about cognition, this is the public culture into which it is introduced, and what results is a transformation of Lockeanism into a radical form of sensibilism that has profound consequences for our understanding of what our cognitive engagement with the world consists in. In what follows, I want to examine what this sensibilism was, with a view to understanding how it reshaped traditional disciplines into something that could aspire to a general theory of the world and our place in it, in a more satisfactory way than anything else on offer, superior not only to a mechanical model, but to any model of cognition that placed it wholly within the domain of reason. The prime importance of sensibility lies in the fact that it was the point of contact between the natural and the emerging ‘moral’ sciences. Speciﬁcally, the former come to be moralized on the basis of the latter, just as the latter come to be naturalized on the model of the former.8 Both of these developments are quite distinctive, and I shall look at the growth of notions of sensibility in two very different areas, physiology and moral theory, before exploring the convergence of such concerns in the moralization of cognition through sensibility in Diderot and others, and the exploration of the relation between reason and sensibility in Hume. 8 Cf. Riskin, Science in the Age of Sensibility: ‘A central effect of sentimental empiricism was the corresponding intimacy between the natural sciences and the emerging moral sciences. . . . A scientiﬁc, naturalizing approach to such moral subjects arose during the Age of Sensibility in unison with newly moralized natural sciences’ (4–5).

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Matter-theoretical disciplines in the eighteenth century routinely posed problems for a mechanical understanding of fundamental processes. It was afﬁnities that seemed to guide the relations between chemical substances, for example, where bodies mixed so intimately as to be fused and inseparable by mechanical means. Likewise, in electricity, the guiding principles of electrical behaviour appeared to be macroscopic, and indifferent to the behaviour of the individual material constituents of bodies. But it was in physiology that the most unmechanical behaviour was exhibited. The basic law of equality of action and reaction seemed to be violated in the phenomenon of irritability, where muscles contracted with a force much greater than the original cause. A formative ﬁgure in freeing physiology from biomechanics was Stahl. It is in Stahl’s work that we ﬁrst ﬁnd the notion of an organism, a crucial ingredient in eighteenth-century physiology.9 As Stahl conceives it, the organism is a heterogeneous collection of bodies. The matter that makes it up is mucous, fatty, and moist, and because of this it is subject to quick dissolution and corruption, yet despite this it is conserved and persists. For Stahl, to understand living things is to understand what causes this conservation and persistence, and his view is that it must be an intrinsic cause, something absent in non-living bodies. His concern is with the origins and manifestations of life, and this concern is inevitably anchored within matter theory, because it was considerations of matter theory that motivated the biomechanics that he opposed. The anima that he postulates as the intrinsic cause of life in organisms achieves its ends via circulation, secretion, and excretion of humours. Circulation has a conserving effect on those parts of the organism which it services, and Stahl traces the principal source of illness to stasis of the blood. For proper circulation to occur, the blood must always conserve its ﬂuidity, and here secretion (of lymph, milk, sperm, etc.) and excretion play a crucial role in maintaining ﬂuidity. Filtration is particularly important in this context, and Stahl rejects the biomechanical account whereby it is simply a matter of correspondence between the size and shape of speciﬁc humoral particles and the size and shape of the pores that allow passage to each type of humour. The argument proceeds in large part on an appreciation of the ﬂuid nature of the circulating humours.10 On the biomechanical account, it is assumed that the humoral particles cross into the channels one by one, but the reduction of ﬂuids into solid constituents here is 9 Georg Ernst Stahl, Theoria medica vera (2 vols., Halle, 1708). See Franc¸ois Duchesneau, La physiologie des lumie`res: Empirisme, mode`les et the´ories (The Hague, 1982), ch. 1, to which I am particularly indebted; and more generally Georges Canguilhem, E´tudes d’histoire et de philosophie des sciences (Paris, 1975), 226–73. 10 Stahl, Theoria medica vera, 95–6.

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unjustiﬁed, for the structure of ﬂuids is such that they act as an aggregate (a problem that rational mechanics had to come to terms with, as we saw in Chapter 8). It also assumes perfect congruity between the particles and the pores, whereas the motion is in fact random, which means that there has to be some extra ingredient in the ushering of the particles through the pores. Moreover, smaller particles would always be able to get through the pores on the biomechanical account, in which case the pores would lose their speciﬁcity, not to mention the fact that, once one goes beyond highly symmetrical ﬁgures such as perfect spheres, lining up three-dimensional shapes is actually quite a complex business. Finally, it is manifest from examination of secreted humours that they are not in fact homogeneous, as the biomechanical account requires, but highly heterogeneous. None of this means that matching of size and conﬁguration of particles and pores plays no role at all in secretion and excretion: it is just that these mechanical considerations are not sufﬁcient. The choice, as Stahl sees it, is between Democritean or Epicurean chance, and teleology, and since the former is manifestly unsatisfactory in explaining the success of processes like secretion and excretion, we must consider these processes to be goal directed.11 Refusing to deduce function in terms of visible structure, he holds that certain structures (whether visible or not) work well because they satisfy a certain function adequately, and explanation must start from function and move to structure: The property that an organism needs to have . . . is that of possessing a mechanical disposition: and this not only in the way that any corporeal subject must have a mechanical disposition, but also in a speciﬁc sense, namely as a disposition that tends towards and corresponds to what it is that is that thing’s goal, and solely by mechanical proportion. This determination in the organ is just its generic and material constitution; but its speciﬁc and formal constitution is of a wholly different kind, and in the main is absolutely foreign to mechanism. For it consists not only in its goal, but also in its actual role in producing a very special effect; and it is in fact so exceptional that outside the very special determination by which it aims at a fully determined end, there is no other reason for its existence.12

Stahl’s core criticism of mechanist models was that they do not allow one to conceive of vital phenomena as speciﬁc autonomous phenomena, and he distinguished ‘mechanical’ bodies from living systems, which had their own laws, goals, uses, and effects. This became an increasingly widely held view in the early to middle decades of the eighteenth century. The autonomy of physiology could be secured, it was believed, only if it was considered as part of medicine, rather than as part of physical theory. Yet it is striking how much still depended on questions in matter theory, since a good deal hinged on whether matter was ‘active’ or not, and how quickly developments in physiology impacted upon matter theory. Stahl had invoked a conscious will to account for vital 11

Ibid., 7.

12

Ibid., 16.

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phenomena, but mid-century physiologists were as unsympathetic to such ‘animist’ accounts as they were to mechanist ones. The problem lay in ﬁnding some third alternative, which was conceived to lie in the middle ground between animism and mechanism. Both these construed matter as inert: the disagreement lay on whether this inert matter needed to be supplemented to account for physiological activity. Seeking an alternative to animism and mechanism automatically meant that the question of the active nature of matter had to be raised, because these two exhausted the possibilities of inert matter. There were a number of attempts to explore the middle ground, and a good idea of the issues can be gained from a comparison of four mid-century accounts: those of Haller, Whytt, La Mettrie, and Bordeu.13 Haller, who was professor of anatomy, surgery, and medicine at the University of Go¨ttingen, had been dealing with questions of involuntary and semivoluntary animal motions, such as the beating of the heart and circulation of the blood, from as early as 1729, working on the structure of the human diaphragm and the role of the intercostal muscles in respiration, and he showed that the cerebellum was not (as Willis had maintained) the primary regulatory mechanism for heart activity and respiration. The decentralization of regulatory mechanisms was a serious difﬁculty for animism, but the problems were not conﬁned to animism: regulation, whether local or central, was something that mechanism could not accommodate with ease. Haller’s concern was with speciﬁc functions of muscle and nerve ﬁbres, correlating deﬁned functions with particular structures. The core of his account of local regulation was a distinction between irritability and sensibility. In his comprehensive notes on Boerhaave’s lectures,14 he sought the cause of cardiac activity—one of the major problems of physiology bequeathed by Harvey—in the structure of the heart, and he gradually developed an account which located this cause in muscle irritability, or contractibility of muscle ﬁbres. Glisson and Baglivi had already explored irritability to some extent, but it was Haller who established it in its full generality, showing that every animal muscle ﬁbre contracts upon stimulation, and that there is a scale of degrees of irritability, depending on how strong the stimulus has to be to provoke a response. Irritability is a completely different phenomenon from sensibility on Haller’s account: sensibility is a property of tissues imbued with nerves, whereas the nerves play no role in irritability. Refusing to account for irritability in terms of elasticity, he modelled it on gravitation, arguing that it belongs to the glutinous component of muscle ﬁbres—ﬁbres being the basic elements of physiology for Haller—in the same way that gravity belongs to matter.15 13 There is a good account of these questions in Reill, Vitalizing Nature, ch. 3; and a comprehensive treatment in Duchesneau, La physiologie des lumie`res, chs. 4–8. 14 Albrecht von Haller, Hermanni Boerhaave Praelectiones academicae in proprias institutiones rei medicae edidit . . . (7 vols., Go¨ttingen, 1739–44). 15 Albrecht von Haller, A Dissertation on the Sensible and Irritable Parts of Animals (London, 1755), 59–60. The most comprehensive statement of Haller’s position is to be found in his Elementa physiologia corporis humani (8 vols., Lausanne, 1757–66).

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It was on the issue of irritability that a dispute broke out between Haller and Whytt. Whytt was professor of medicine at Edinburgh, and, like Haller, he had a wide range of interests in physiology, medicine, and the life sciences generally.16 In his 1751 Essay on the Vital and other Involuntary Motions of Animals, Whytt offered a general theory of sensibility, arguing that the capacity of the muscles to contract depended on the nerves, and that sensibility was widespread throughout the body. Whytt’s rejection of irritability results from his refusal to accept that there can be genuinely local powers in organs: SOME may, perhaps, be of opinion, that the all-wise AUTHOR of nature hath endued the muscular ﬁbres of animals with certain active powers, far superior to those of common matter, and that the motions of irritated muscles are owing to these. And indeed we cannot but readily acknowledge, that he has animated all the muscles and ﬁbres of animals, with an active sentient PRINCIPLE united to their bodies, and that, to the energy of this PRINCIPLE, are owing, the contractions of stimulated muscles. But if it be imagined that he has given to animal ﬁbres a power of sensation, and of generating motion, without superadding or uniting to them an active PRINCIPLE, as the subject and cause of these, we presume to say, that a supposition of this kind ought by no means to be admitted; since, to afﬁrm that matter can, of itself, by any modiﬁcation of its parts, be rendered capable of sensation, or of generating motion, is equally absurd, as to ascribe to it the power of thinking. Matter, so far as we can judge of it by all its known properties, appears to be incapable either of sensation or thought: the whole phenomena of the mere material world evidently shew, that it acts invariably according to certain laws prescribed to it, and without any feeling, inclination or choice of its own; nor is there any thing more resembling will, self-determination, or real active power in the most reﬁned and subtile parts of matter, than in the grossest and most sluggish.17

The question of the ability of organs to act locally is clearly made a question of matter theory here, for the issue turns on that of whether there are intrinsic active powers in matter. Haller responded in 1752, arguing that many organs were quite insensible and that nervous activity was irrelevant to their functioning.18 As regards the question of sensibility, Haller presented experimental ﬁndings to show that a number of parts of the body were insensitive in that animals showed no pain when these parts were stimulated, and there was no evidence of nerves. The parts included

16 The Edinburgh medical school was ﬁrmly modelled on Leiden in the mid-eighteenth century: up to 1762, it was the works of Boerhaave that formed the core of the teaching, and after that the works of his pupil Glaub. It was to become a centre for vitalist thought later in the century, taking the vitalist baton, as it were, from Montpellier, which had traditionally been at the centre of vitalism. 17 Robert Whytt, An Essay on the Vital and other Involuntary Motions of Animals (Edinburgh, 1751), 241–2. 18 Albrecht von Haller, De partibus corporis humani sensibilibus et irritabilibus (Go¨ttingen, 1752). There was a series of replies and counter-replies continuing up to 1764: see R. K. French, Robert Whytt, The Soul, and Medicine (London, 1969), ch. 6, to which I am indebted here.

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tendons, marrow, aponeuroses, dura and pia mater, ligaments, pleura, capsulae of the articulations, periosteum, peritoneum, bones, pericardium, mediastinum, and cornea. Whytt responded in two ways. First, he noted the inhibitory mechanism of shock in experiments on the nervous system: direct stimulation may result in the pain being overridden, rather than being absent. Second, he disputed the lack of sensitivity in some of the parts listed by Haller. There had been an experiment on the marrow of live animals performed by the physician Du Verney in which it was reported that the marrow was indeed sensitive. Haller noted, however, that this was a single experiment, and its standing open to dispute. Moreover, the experiment did not reveal any nerves, and Whytt had simply assumed that, because sensitivity was reported, there must have been nerves. Other cases were similarly inconclusive. Whytt reported sensitivity in the cornea for example, which Haller had denied on the grounds that all membranes were insensitive. Here Haller allowed sensitivity, but argued that it was the conjunctiva that was actually touched, and what was stimulated was a nerve running through the membranes. On Whytt’s account the power of contraction could only be awakened by the sentient activity of the soul in the nerves, whereas for Haller the nerves are not involved. What marks out sensitivity and irritability on Haller’s view is that, for the case to be one of sensibility, the stimulation results in a conscious sensation in the mind, whereas irritability results in no conscious sensation. Whytt, by contrast, invoked unconscious sensations as well as conscious ones, the former playing an important role in his rejection of Stahl’s view that the sentient cause of life must be a consciously reasoning soul.19 But there are cases of responses to stimulation which cannot be characterized as unconscious sensations. As Haller points out, one can detect irritability in amputated arms and surgically removed intestines, where, although nerves are present, there can be no question of their being attached to a centralized agency such as the soul.20 Whereas Haller opted for sensibility and irritability, and Whytt for sensibility alone, there was another option, irritability alone, which was taken up by La Mettrie. La Mettrie was an avid defender of a materialist theory of mind, arguing that various psychological states could be traced to physical factors: illness, fatigue, hunger, diet, pregnancy, sexual stimulation, age, climate, and so on. He was also as close as one gets to a biomechanist in the mid-eighteenth century. Realizing that inert matter is not going to provide the kind of reductive substratum that earlier biomechanists had sought, however, he supplements what would otherwise have been inert matter with the quality of irritability. In his L’Homme-machine (1747), dedicated to Haller, La Mettrie dispenses with the notions of soul and substantial forms: all that is needed to

19 20

Whytt, An Essay, 268. Albrecht von Haller, Ad Roberti Whyttii nuperum scriptum Apologia (Go¨ttingen, 1764), 20.

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account for the internal principle by which living matter is regulated is muscular irritability: Here then are a number of facts, even more than are requisite, to give us the most undeniable proofs that every ﬁbre, that the minutest parts of organized bodies, are put into motion by a principle inherent in themselves; nor does their action depend upon the nerves, as if they were voluntary motions, because these motions, the subject of our present enquiry, are performed whilst the parts in which they happen, have no communication with the general circulation.21

The combination of muscular irritability and reﬂex is, La Mettrie believes, all one needs for a self-moving organism. In his L’Homme plante (1748), he draws attention to a number of analogies between plants and humans, from matters of anatomical detail to reactions to climate. There is what he refers to as an ‘imperceptibly graduated ladder’ between the two,22 and a progression in the faculties of feeling and movement as we ascend from the one to the other, these being provided by nature to the extent required in each species.23 La Mettrie was an overt materialist, determinist, and atheist. Haller was not, although he was accused of both materialism and impiety, and his principal response to these charges was to argue that the powers that organs have which are manifested in irritability derive directly from God, and require no intermediary soul. They manifest something that can be characterized as a life force, by contrast both with a view of matter as inert, and that of being acted upon from outside. The local, intrinsic regulation of the operations of organs brings with it a rethinking of the nature of matter. But it also brings with it a rethinking of the idea of an organism. Centralized, extrinsic regulation of organs, of the kind advocated by Whytt,24 provided a source of uniﬁcation for the organism whose organs these are. Local, intrinsic regulation of the kind advocated by Haller prompts the question of what the unity of the organism consists in. If all there were to the organism were localized centres of irritability, then there could be no unity. But it is not as if a centralized sensibility could simply be added to a localized irritability to provide a unifying principle for the organism, for Haller’s point was that organs exhibiting irritability do so independently of whether or not nerves are present, and if they are not present, then such organs can hardly be connected through sensibility, which requires nerves. The solution to this problem was set out by The´ophile de Bordeu, who developed an account whereby each organ leads a life of its own,25 and where 21

Julien Offray de La Mettrie, Man a Machine (2nd edn., London, 1750), 58. La Mettrie, Œuvres philosophiques (3 vols., Berlin, 1796), ii. 69. 23 Ibid., 66–8. 24 Note, however, that Whytt does not locate the regulating sentient principle exclusively in the brain: this is just its chief seat. See An Essay, 282–5, 390–2. 25 The´ophile de Bordeu, Recherches sur les maladies chroniques (Paris, 1775); in Bordeu, Œuvres comple`tes, ed. A. Richerand (2 vols., Paris, 1818), ii. 829. 22

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the lives of organs contribute to, indeed constitute, the collective life of the organism. In general terms, one might say that it is because the parts are living that the whole is living, and it is because the living parts are connected in the way they are that the whole is the way it is. Buffon held an even stronger view, arguing that all matter is active in itself,26 and that ‘the life of the whole seems to be just the result of the life of all the actions, of all the separate little lives, if I may be permitted to express myself in these terms, of each of those active molecules whose life is primitive and apparently indestructible.’27 For Bordeu, ‘life is only feeling and movement’,28 that is—in the context of physiology—irritability and sensation. The structure of ﬁbres making up the organs of the body is the core issue for Bordeu. These he regards as extensions of the nerves, embedded in a spongy, mucous, cellular substance,29 which serves both to provide nourishment for the ﬁbres that it encases, and, as it stretches from organ to organ, to connect these different organs.30 This mucous cellular substance orders the agitations of the ﬁbres, making them act harmoniously and producing the visible functions of the body. Although, like Whytt, Bordeu attributes sensibility to all organs, this sensibility has now become localized, and an image that he uses is that of bees forming a colony: In order that we might grasp the particular action of each of its parts better, we compare the living body to a swarm of bees, which gather together in a cluster and hang from a tree like a bunch of grapes. We do not ﬁnd it amiss that one ancient author has said of one of the viscera of the abdomen that it was an ‘animal in animali’: each part is, so to say, not an animal, certainly, but a kind of separate machine, which contributes, each in its own way, to the general life of the body. To continue with the comparison with the swarm of bees, it is a whole glued to the branch of a tree by the action of a good many of the bees which need to act in unison in order to hold on; there are those that attach themselves ﬁrst, and those that attach themselves to these; they combine to form a very solid body yet each has its own separate action; were one to give way or act too vigourously the whole mass would be disturbed; when they conspire to huddle together and to clasp one another in the required order and proportions, they compose a whole which persists until it is disturbed. Applying [this metaphor] is straightforward: the bodily organs are joined together; they each have their own area and action. The relation between these actions, and the harmony that results, is what constitutes well-being. If this harmony is disturbed, whether it be by some part relaxing or because it dislodges an antagonist, if the actions are upset, if they no longer follow the natural order, these changes will constitute more or less serious disorders.31

26

Buffon, ‘Introduction a` l’histoire des mine´raux’, Œuvres, iii. 78. Idem, ‘Histoire des animaux’, Œuvres, xi. 220. ‘Molecules’ are the smallest units capable of sentience. 28 Bordeu, Œuvres, ii. 831. 29 Ibid., 829. 30 Idem, Recherches sur le tissu muqueux (Paris, 1767); Œuvres, ii. 738–9. 31 Idem, Œuvres, i. 187. 27

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This is an image that will be taken up and elaborated upon by a number of writers, not least by Diderot in La Reˆve de d’Alembert.32 But it is in the entry on ‘observation’ in the Encyclope´die, by the Montpellier-trained physician Jean Jacques Me´nuret, that the nature of the connections is spelled out most clearly: Following these authors, one could compare man to a ﬂock of cranes, which ﬂy together in a particular order, without any mutual assistance or dependence on one another. The physicians or philosophers who have studied and carefully observed man have noticed this sympathy in all animal motions: this constant and necessary agreement in the interaction of the various parts, however disparate or distant from one another. They have also noticed the disturbance that results in the whole from the sensible disagreement of a single part. A famous physician (Bordeu) and an illustrious physicist (Maupertuis) likewise compared man, from an illuminating and philosophical point of view, to a swarm of bees that strive together to hang to a branch of a tree. One can see them pressing together and holding one another in place, forming a kind of whole in which each living part contributes in its way, by the correspondence between and direction of its movements, to sustain this kind of life of the whole body, if we may refer in this way to a mere combination of actions.33

The explorations of the relations between organisms and organs to which Haller, Whytt, and Bordeu were party raise fundamental questions. Above all, the task of capturing those relations between autonomous organs that allow them to form organized bodies were not conﬁned to the life sciences. In his Reˆve de d’Alembert, written in 1769, and in the E´le´ments de physiologie, published in 1778, Diderot used the model of the unity of the organism to show how there can be a unity of the subject of thought without postulating an immaterial soul.34 And Rousseau moved effortlessly from the biological version of the question to a political one,35 asking in Du Contrat Social how an aggregate of individual wills can be transformed into a collective will, and identifying the discovery of a form of government that achieves this as the fundamental problem to which the social contract is a solution.36 The use of biological models was not simply a blind 32

Diderot, Œuvres comple`tes, ed. J. Asse´zat and M. Tourneux (20 vols., Paris, 1875–9), ii. 126–30. Encyclope´die, xxiii. 301–2. See Charles T. Wolfe and Motoichi Terada, ‘The Animal Economy as Object and Program in Montpellier Vitalism’, Science in Context 21 (2008), 537–80. 34 See Timo Kaitaro, Diderot’s Holism (Frankfurt am Main, 1997), ch. 3; and Franc¸ois Duchesneau, ‘Diderot et la physiologie de la sensibilite´’, Dix-Huitie`me Sie`cle 31 (1999), 195–216. 35 In fact, the behaviour of bees had traditionally been given political connotations, but these had been very different from those that Rousseau invokes. They had traditionally been considered a model monarchical community. See, for example, from among the more inﬂuential works: Charles Butler, The Feminine Monarchy, or, A Treatise concerning bees, and the due ordering of them (Oxford, 1609); Samuel Purchas, A Theatre of Politicall Flying-Insects wherein especially the nature, the vvorth, the vvork, the wonder, and the manner of right-ordering of the bee, is discovered and described (London, 1657); Joseph Warder, The True Amazons: Or, The True Monarchy of Bees (3rd edn. London, 1716); John Thorley, ¯¸ˇ¸ˇˆ` or, the Female Monarchy. Being an Enquiry into the Nature, Order, and Government of Bees (London, 1744). 36 Jean-Jacques Rousseau, Du Contrat Social, ou Principes du Droit Politique (‘Amsterdam’ [i.e. Germany], 1762), Book I, chs. 6 and 7; idem, Œuvres Comple`tes (4 vols., Paris, 1883), i. 644–6. 33

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extrapolation, however, and a crucial link was provided by the way in which the notion of sensibility had come to ﬁgure as a key notion in the literature on moral and political philosophy. MORAL SENSIBILITY A distinctive feature of mid-eighteenth century thought is the way in which questions of cognition, morality, and civic responsibilities come to be grounded in sensibility. At the same time there is an emerging use of empirical methods, sometimes mirroring those of natural philosophy, to open up questions that had traditionally occupied the realms of humane learning and religious doctrine. What lies behind these developments is a concern to come to terms with cultural difference and moral diversity. From the end of the sixteenth century, with the appearance of travel books describing nonEuropean lands and peoples, as well as the reports on China and elsewhere by Jesuits, the possibility began to be raised—slowly at ﬁrst, but coming to a head by the last decades of the seventeenth century—that a number of fundamental beliefs that had been taken to be universal were in fact culturally variable. There were deep and difﬁcult issues here, not least that of the language in which one should speak of such cultural variability, either to keep it in check or to explore it more fully. Locke is an important source of the disputes on these questions, which emerged in a sophisticated philosophical form in the wake of the Essay. Book I of the Essay, on innate ideas, contained hardly any references to philosophical works, but copious reference was made to travel literature.37 It combed through empirical evidence bearing on the question of the universality of moral and religious ideas, and the methods of natural history were used to subject purported innate ideas to examination, in order to build up an empirical case against them. It is important to note just how distinctive this procedure was. In Hellenistic antiquity, the Pyrrhonists had used various cultural and moral differences to undermine Stoic claims to universal moral principles, but their role had been as one-off counter-examples. Pyrrhonists were committed to the idea that peace of mind—the end point of philosophical wisdom for all the Hellenistic schools—was to be achieved not through knowledge of truth and falsity, as the Stoics and Epicureans believed, but through the realization that grasping the truth was impossible, because there was simply no truth to grasp: there was nothing underlying the appearances, and this was the realization from which

37 Locke had 195 travel titles in his library, and Laslett has noted that all but one of the sixteen works quoted in Book I of the ﬁfth edition of the Essay (1705) were from his own collection of travel literature: J. Harrison and P. Laslett, The Library of John Locke (2nd edn., Oxford, 1971), 27–8.

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philosophical understanding, and peace of mind, sprang.38 This general philosophical position was effectively a priori, however, and was not the kind of thing that could be dislodged by empirical evidence, any more than could Stoic or Epicurean commitment to uncovering the truth underlying the phenomena. Locke is engaged in a completely different kind of exercise. He is suggesting the testimonies of travellers as an empirical basis on which to construct a theory of human behaviour. Of course, these testimonies were open to interpretation, and Locke’s own interpretation was contested, in some cases bitterly.39 Moreover, there were those who simply refused to accept such testimonies as having evidential value when they were clearly in contradiction with what were considered basic and unquestionable features of human morality and religious belief. Yet Locke initiates a tradition which will shape moral thinking over the next sixty years, culminating, in its most radical form, in Montesquieu’s claim that different moral principles are appropriate for different kinds of society. Locke’s treatment of such questions as empirical ones might have been expected in polemical literature, such as the writings of Bayle, but the Essay did not fall into this genre. It was a work of reﬂection which set out the conditions for philosophical engagement, and such an empirical treatment was in line with the conception of enquiry that Locke advocated there: indeed, it was one of the most striking manifestations of his approach. What it represented was an empirical mode of enquiry into questions that had traditionally fallen under humane learning, or under religious teaching. Both of these had sought to set out the underlying uniformity in human beliefs and behaviour. The cases of various practices of ‘primitive’ peoples that Locke culled from the travel literature—child murder, parricide, cannibalism, and incest40—threw doubt on whether there was indeed any underlying moral uniformity;41 and the cases of atheist societies in China, Brazil, and the Caribbean undermined conﬁdence in the existence of any 38

See Stephen Gaukroger, ‘The Ten Modes of Aenesidemus and the Myth of Ancient Scepticism’, British Journal for the History of Philosophy 3 (1995), 371–87. 39 See Daniel Carey, Locke, Shaftesbury, and Hutcheson: Contesting Diversity in the Enlightenment and Beyond (Cambridge 2006), ch. 3. 40 Locke, Essay, I. iii. 9. 41 Although Locke himself appears by default to exempt his own society from this kind of variation, there is a case to be made that fundamentally different kinds of morality were appropriate to the different ‘ofﬁces’ within late seventeenth- and early eighteenth-century England. Keith Thomas, in his The Ends of Life: Roads to Fulﬁlment in Early Modern England (Oxford, 2009), in looking at notions of fulﬁlment associated with various occupations in seventeenth- and eighteenthcentury England, offers a revealing account of fundamentally different conceptions of life which must surely harbour quite different moral conceptions. See for example his account (ch. 2) of the gloriﬁcation of violence among the military in England in the seventeenth century (declining in the course of the eighteenth century), in which not only inﬂicting a gory and violent end on others, but also suffering a gory and violent end oneself, are considered among the highest values in terms of personal fulﬁlment. The sense of moral behaviour that accompanies such an understanding of the aims of living differed radically from that of merchants or scholars for example. It is hard to imagine how this might be construed as a superﬁcial difference in which the underlying morality was the same, without the supposed underlying morality becoming purely notional.

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universal religious precepts.42 In accounting for these questions, Locke distinguishes divine law, civil law, and what he calls ‘the law of opinion or reputation’, telling us in connection with the last that these Names Vertue and Vice, in the particular Instance of their Application, thro’ the several Nations and Societies of Men in the World, are constantly attributed only to such Actions, as in each Country and Society are in Reputation or Discredit. Nor is it to be thought strange, that men every where should give the name of Vertue to those Actions, which amongst them are judg’d praise-worthy; and call that Vice, which they account blameable: since otherwise they would condemn themselves, if they should think any thing right, to which they allow’d Commendation; any thing wrong, which they let pass without Blame. Thus the Measure of what is every where call’d and esteem’d Vertue and Vice is this Approbation or Dislike, Praise or Blame, which by a secret and tacit Consent establishes it self in the several Societies, Tribes, and Clubs of Man in the World; whereby several Actions come to ﬁnd Credit or Disgrace amongst them, according to the Judgement, Maxims, or Fashions of that Place.43

It is helpful to distinguish two kinds of response to dealing with this question of variability in basic human values, both of them raised by Locke, although Locke himself is more concerned with exploring the problems than trying to ﬁx on one solution. The ﬁrst, the synchronic approach, turned on whether the variation in human values between particular societies was in fact superﬁcial, whether there was a uniformity underlying these superﬁcial variations. The basis of any such uniformity, in turn, was disputed in terms of whether it rested on fundamental moral principles which were innate, or on fundamental moral principles which, far from being innate, were a necessary condition for civilized society and formed through political and pedagogic means. This will be our concern in this chapter. The second set of issues, the diachronic ones, turned on the question whether the variation in human values followed a historical path, roughly from primitive to civilized. This will be our concern in the next chapter. The immediate response to Locke was to reassert the principle of universal consent as something far more fundamental than the variations that Locke had pointed to. This, for example, was the response of Stillingﬂeet, who refused to take what he considered to be the manifestly inhuman behaviour of savages as any kind of standard or evidence, writing that they are ‘not ﬁt to be a standard for the Sense of Mankind, being a People so strangely bereft of common Sense, that they can hardly be reckoned among Mankind’.44 There were considered to be various reasons why such behaviour might occur, and it was generally taken to demonstrate a decline into corruption incident upon the Fall.45 This kind 42

43 Locke, Essay, I. iv. 8. Ibid., II. xxviii. 10. Edward Stillingﬂeet, The Bishop of Worcester’s Answer to Mr. Locke’s Letter (London, 1697), 89–90. 45 Cf. John Edwards, A Free Discourse Concerning Truth and Error, Especially in Matters of Religion (London, 1701), 48–52. 44

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of response, although typically defended in terms of Stoic arguments for ‘common principles’ of morality, simply takes Christianity as a norm, so that deviations from it are what require explanation: they themselves cannot be treated as evidence that might undermine the norm. By contrast, there were two inﬂuential attempts to deal with the questions raised in Locke in a less summary way: those of Shaftesbury and Hutcheson.46 Shaftesbury has a very direct connection with both Locke and Diderot: Locke was his tutor, and one of the keystone essays of Shaftesbury’s major work, the Characteristicks, was translated into French by Diderot. The Characteristicks are very much a reaction to a number of central ingredients in Locke’s account, at the core of which lies the issue of the relationship between morality and religion. Locke, as we have seen, espoused a very minimal form of Christianity, and since he argued that reason alone can teach about morality, the question arises what his minimal Christianity can add to this: why is not reason alone sufﬁcient for morality? The answer given in his Reasonableness of Christianity is that the task of discovering the basic laws of nature regulating morality is too difﬁcult for reason.47 Moreover, even if such laws could have been discovered, what they would provide would be a guide to a good life, not something morally binding, in the sense in which Christianity is morally binding because God has laid down moral laws, and has instituted a system of punishment and rewards in relation to them. For Locke, it is precisely this sense of obligation that makes them speciﬁcally moral goods.48 It is this doctrine that is Shaftesbury’s prime target. Religious obligation cannot underlie morality for Shaftesbury. Rather than morality having a religious basis, he argues, it is the other way around: it is religion that requires a moral basis. Indeed, it is by morality that true and false religion are to be distinguished. The study of ‘human affection’, he writes, has not its Name, as other Philosophys, from mere Subtlety and Nicety of the Speculation; but by way of Excellence, from its being superior to all other Speculations; from its presiding over all other Sciences and Occupations; teaching the measure of each, and assigning the just Value of everything in Life. By this Science Religion itself is judged, Spirits are search’d, Prophecys prov’d, Miracles distinguish’d: the sole Measure and Standard being taken from moral Rectitude, and from the Discernment of what is sound and just in the Affections.49 46

See Carey, Locke, Shaftesbury, and Hutcheson, chs. 4 and 5. See Locke, Works, ii. 536–8. 48 See the discussion in J. B. Schneewind, The Invention of Autonomy (Cambridge, 1998), 141– 59. More generally on the idea of the connection betweeen morality and divine commands, see the thought-provoking discussion in Re´mi Brague, The Law of God: The Philosophical History of an Idea (Chicago, 2007). 49 Anthony Ashley Cooper, Earl of Shaftesbury, Characteristics of Man, Manners, Opinions, Times, ed. John M. Roberston (2 vols. in 1, Indianapolis, 1964), i. 297–8. The original text appeared in three volumes in 1711. The essays published in the collection were ‘An Inquiry concerning Virtue or Merit’ (1699), ‘A Letter concerning Enthusiasm’ (1708), ‘Sensus Communis, An Essay on the Freedom of Wit and Humour’ (1709), ‘The Moralists, A 47

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The question then arises what it is that provides this moral basis. Since ‘by means of corrupt religion or superstition, many things the most horridly unnatural and inhuman come to be received as excellent, good, and laudable in themselves’,50 we must ask how we recognize genuine morality, by contrast with whatever it is merely that is valued in the society in which we live. The answer is that we have recourse to a form of sensibility, a ‘natural moral sense’,51 evidently not unlike the ﬁve senses, and distinct from conscience, for conscience is a form of reasoning rather than sensibility.52 Shaftesbury has no doubts about the importance of Locke’s rejection of innate ideas, however, so it is crucial to the case that he wants to make that the postulated moral sense is not taken to be something innate. The object of our moral sense is passions and desires, those of ourselves and those of others, and this moral sense is able to distinguish between these states on the basis of ‘harmony’, an objective property of particular passions and desires, which is experienced not as a rational judgement but as a subjective feeling.53 Moral and aesthetic judgements are very much on a par for Shaftesbury. Both are designed to capture a harmony that is there in nature, and he rejects the idea that something could be good or beautiful simply because God willed it to be so. That would simply be to misunderstand the nature of goodness and beauty.54 Indeed, it is our natural ability to recognize goodness that enables us to judge in the ﬁrst place, and the fact that immorality attracts punishment is not relevant to its standing as something immoral: And thus religious conscience supposes moral or natural conscience. And though the former be understood to carry with it the fear of divine punishment, it has its force however from the apprehended moral deformity and odiousness of any act with respect purely to the Divine Presence, and the natural veneration due to such a supposed being. For in such a presence the shame of villainy or vice must have its force, independently on that further apprehension of the magisterial capacity of such a being, and his dispensation of particular rewards or punishments in a future state.55

Shaftesbury’s idea of moral sense has the advantage that it is an internal criterion, so not something subject to variations in social circumstances or religious doctrines; on the other hand, it is not a form of reasoning but a form of

Philosophical Rhapsody’ (1709), ‘Soliloquy, or Advice to an Author’ (1710), together with an introductory essay, ‘Miscellaneous Reﬂections on the Preceding Treatises’. References will be to the modern edition. 50 51 Cooper, Characteristics, 262. Ibid. 52 Thomas Burnet, Remarks upon an Essay Concerning Humane Understanding (London [1699]), 4–5, had earlier made the same point, stressing that the process by which we distinguish good and evil was not reasoning but sensibility, like the sense of smell. See Schneewind, The Invention of Autonomy, 301–2, n. 28. 53 Shafterbury, Charactaristics, i. 181. 54 55 Ibid. i. 264. Ibid., i. 305–6.

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sensibility, and is thereby distinguished from innate ideas which provide us with the ability to make cognitive judgements which we would not otherwise be able to make. Moral sense is not concerned with cognitive judgements, but is a capacity for recognizing harmony, and it is manifested in a distinctive form of sensibility. In 1745, Diderot published a French paraphrase of Shaftesbury’s 1699 An Inquiry concerning Virtue and Merit, a book which later formed part of the Characteristicks. Accompanying the text is a set of ‘reﬂections’ in a prologue, and lengthy footnotes setting out further reﬂections on Shaftesbury’s account.56 Diderot plays up the radical elements, supplying footnotes at the points in the text where Shaftesbury is heterodox, as well as quotations from sceptical authors such as Montaigne.57 The work appeared anonymously—neither Diderot’s name nor that of Shaftesbury was mentioned—and with a false imprint, but it was well received, the reviewer in the Journal de Tre´voux asking the reader to think of it as Locke writing a treatise on morality.58 Diderot’s ‘reﬂections’ and notes make it clear that Shaftesbury shaped Diderot’s thinking, just before he was about to begin work on the Encyclope´die. The article on sensibilite´ begins, however, with a long quotation not from Shaftesbury, but from Hutcheson. Hutcheson represents a similar Lockean vein, and, following Shaftesbury, he adopts a quasi-aesthetic account of virtue whereby one is drawn to virtue and repulsed by vice in much the same way that someone of developed aesthetic sensibilities is drawn to beauty and repulsed by ugliness. Hutcheson’s ﬁrst work, An Inquiry into the Original of our Ideas of Beauty and Virtue of 1726, was written as a defence of Shaftesbury, but he varied from Shaftesbury on the core question of how to counter moral diversity in different societies without relying on something that could be construed as innate.59 He developed a dispositional model for a natural moral sense more explicitly than Shaftesbury, arguing that this moral sense was prior to the exercise of the will, rational reﬂection, or social circumstances. Such a sense did not have to result in either actual common consent and universal acceptance of virtue, because he was aware that neither of these were supported by the evidence, and his explicitly Lockean commitments meant that evidence was crucial to moral argument as much as it was to natural-philosophical argument.60 56 Denis Diderot. Principes de la philosophie morale; ou Essai de M. S*** sur le me´rite et la vertue. Avec re´ﬂexions (‘Amsterdam’ [i.e. Paris], 1745). 57 See Arthur M. Wilson, Diderot (New York, 1972), 50–2. 58 Journal de Tre´voux, February 1746, 200. 59 Francis Hutcheson, An Inquiry into the Original of our Ideas of Beauty and Virtue (London, 1726); idem, An Essay on the Nature and Conduct of the Passions and Affections, with Illustrations upon the Moral Sense (London, 1728). 60 Diderot’s attitude to Hutcheson is complex however. In his article ‘Beau’ in the Encyclope´die, he replaces Hutcheson’s internal sense of beauty with an account in which an appreciation of beauty is a slowly acquired capacity, and in a letter of 4 October 1767, he writes: ‘this sixth sense, which a few metaphysicians have brought into fashion from England, is a ﬁgment of the imagination: all our

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If one sees the aim of the exercise in terms of how successfully one establishes a notion of moral sensibility while avoiding innate ideas of one kind or another, then it cannot be said that Hutcheson is more successful than Shaftesbury. It was unclear that there was any solution to this problem as it stood, and later developments go in other directions: either, with Montesquieu, in the direction of retaining a fundamental role for morality while accepting a degree of socially and culturally shaped moral relativity between societies which went beyond anything that Locke, Shaftesbury, and Hutcheson were prepared to accept; or in the direction of those who—like Hume, Smith, and Ferguson—secured a solution in terms of social development towards a universal moral sensibility. For the present, I want to focus on the way in which questions of evidence and questions of sensibility came to the fore in the work of Locke, Shaftesbury, and Hutcheson. In the preface to Hutcheson’s posthumous A System of Moral Philosophy (1755), by William Leechman, Professor of Divinity at the University of Glasgow, we are told that, when appointed to his chair at Glasgow, Hutcheson concentrated on the study of ‘human nature’ and he had high thoughts of its original dignity, and was persuaded, that even in this corrupt state, it was capable of great improvements by proper instruction and assiduous culture. The progression of Moral Philosophy was the province assigned him in the College. In cultivating this science he pursued the same method in which he began, setting aside all researches into the abstract relations and eternal ﬁtness and unﬁtness of things, and directing his enquiries into what is more obvious and immediately known from observation and experience, viz. What is in fact the present constitution of human nature; what is that state of heart, and course of life which is most correspondent to the whole frame. He had observed, that it was the happiness and glory of the present age, that they had thrown off the method of forming hypotheses and suppositions in natural philosophy, and had set themselves to make observations and experiments on the constitution of the material world itself, and to mark the powers and principles which are discerned operating in it: he saw plainly that it was by adhering strictly to this method that natural philosophy had been carried to a greater degree of perfection than ever it was before, and that it is only by pursuing the same method that we can hope to reach higher improvements in that science.61

The empirical nature of Hutcheson’s enquiry and the move to thinking of morality in terms of sensibility are not two unconnected features of his programme. Sensibility was exactly the kind of thing that could be explored empirically, in a way that rationality could not be. Reason was considered fundamental in the sense that doubts about the rationality of particular peoples could not throw reason per se into doubt, in the way that doubts about the moral sensibilities of particular peoples could, now, throw the basic principles of moral ideas come from experience’: Diderot, Correspondance, ed. George Roth and Jean Varloot (16 vols., Paris 1955–70), vii. 163. 61 Francis Hutcheson, A System of Moral Philosophy (3 vols., Glasgow, 1755), i. pp. vii–xiv.

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sensibility into doubt. Sensibility was perfect for the kind of empirical enquiry that aspired to a Newtonian archetype, for it promised the application of objective criteria to dealing with questions that had been the subject of ingrained and unexamined assumptions. At the same time, the kind of empirical enquiry that aspired to a Newtonian model could at last extend its scope, in a way that was not possible while mechanics provided the model for natural-philosophical enquiry. Nor was reductionism part of the package with sensibility, as it had been with a mechanical model, in the case of biomechanics for example. Sanction for the use of empirical forms of enquiry may have been sought in Newtonian natural philosophy, but there was no question of reduction to, or assimilation to, Newtonian natural philosophy. Empirical methods of enquiry had existed in legal, philological, and natural-historical disciplines since the ﬁfteenth century, and the move from natural history reports, to travel books, to the use of the reports of non-European customs in travel books in investigating the universality of particular moral principles and socials mores, for example, was not something especially indirect. THE UNITY OF SENSIBILITY The introduction of a comprehensive Lockean philosophy in France came in the wake of Voltaire’s Lettres philosophiques, in Condillac’s writings. In his Essai sur l’origine des connaissances humaines (1746), as in his subsequent Traite´ des sensations of 1754, Condillac went beyond straightforward epistemological questions and developed a more general notion of sensibility which had consequences for a far broader range of issues, building on themes that had been developed by Diderot in his Lettre sur les aveugles (1749) and Lettre sur les sourds et muets (1751), where exploration of sensory handicaps is used to reveal that what we take as given in perception is the result of a complex learning process, involving construction, abstraction, and language use. In these works, of Diderot and Condillac alike, questions of cognition are removed from the conﬁnes of a narrowly conceived, sceptically driven epistemology, so that affective states and moral questions are caught up in the enquiry. What happens, in effect, is that affective states come to underpin cognitive ones. The best way to understand how this happens is to focus on the contrast in how the knowing subject is conceived in Cartesian and Lockean accounts of perceptual cognition.62 Descartes and Cartesians such as Malebranche and Arnauld argued that our perceptual images of the world need not resemble what there is in the world, only represent it. The function of such cognitive representation was not to provide us with access to the real natures of things— 62

I draw here on my ‘“Home Alone”: Cognitive Solipsism in the Early-Modern Era’, Proceedings and Addresses of the American Philosophical Association 80/2 (2006), 63–78.

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that was the aim of natural philosophy alone—but to help us preserve our bodies from harm. Colour perception, for example, was construed as a form of visual enhancement that improves acuity, thereby enabling us to distinguish things visually in a more effective way. This kind of perceptual process involves a good deal of ‘hard-wired’ sophistication,63 ‘hard wiring’ that makes sure you get the right kind of representations: that you see light, that is, have a visual image which displays colours and shapes, when stimulated in the requisite way. As Descartes’ detailed discussion of the physiology of automata in L’Homme makes clear, this hard-wiring is shared by animals and humans,64 and the wholly mechanistic psycho-physiology set out there accounts for perceptual processes fully at the material level. The difference between humans and animals, on Descartes’ view, is that humans, unlike animals, are able to reﬂect upon their psycho-physiological states, and make judgements about them. They can make judgements about their veridicality for example: they can argue that even though the world appears to be coloured, to us and to animals, we have a mechanistic theory of the nature of light and a mechanistic theory of psycho-physiology which account for the phenomena much better than alternative theories, and so we may conclude that colour does not reside in things at all, but is rather a function of the surface properties of the object, illumination, and hard-wired features of sensory perception systems. On this construal, an animal may have the same functional neuroanatomy as we do, but its understanding of the world nevertheless remains fundamentally different from ours. The visual ﬁeld of animals has everything in it that ours does, but their perception lacks the kind of discrimination that ours has. Animals are sentient but not conscious on the Cartesian account, and this is reﬂected in their perceptual states. Their perceptions, he tells us, are ‘not like ours’,65 for ‘animals do not see as we do when we are aware that we see, but only as we do when our mind is elsewhere.’66 Animals see the same world as we do, with the same things in it, standing in the same relations, but the animal does not see the world as an independent reality, whereas we do. And we are able to see the world as an independent reality to the extent that we can stand back from our perceptual states and make conscious judgements about the content of those states. But now consider the Lockean doctrine that perception is not sensation plus something else, but simply successful sensation. For Locke, the perceptual unity of the thinking thing that engages in the perceptual judgement of the world is 63 Descartes’ term is of course not ‘hard wired’ but ‘ordained by nature’: La dioptrique, Discours 6 (Œuvres, vi. 130). 64 The phenomenon of colour blindness in humans was unknown until the mid-eighteenth century at the earliest: the ﬁrst published description was Joseph Huddart, ‘An Account of Persons Who Could Not Distinguish Colours’, Philosophical Transactions of the Royal Society of London, 67 (1777), 260–5. Later, there developed the view that animals had varying degrees of colour blindness, but, at least before the nineteenth century, as far as I can tell everyone would have assumed that animals, to the extent to which they saw things, saw them in colour (and indeed saw them in the same colours that we do). 65 66 Œuvres, iii. 121. Cf. v. 276–7. Œuvres, i. 413. Cf. i. 576.

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just the phenomenal unity of perceptual experience, and we cannot infer anything from this alone about the ultimate unity or simplicity of any further underlying self.67 Considered from a Cartesian point of view, on this Lockean account of perception we would be denied the ability to see the world as independent: for the Cartesian, a separate act of conscious judgement is required for us to grasp that our perceptions reﬂect a physical reality independent of us. In order to probe more deeply into what is at issue here, it will be helpful to consider the responses to the Molyneux problem. William Molyneux was a driving force behind the Dublin Philosophical Society, and author of the ﬁrst substantial treatise on optics in English: Dioptrica Nova (1692). His wife had lost her sight as a result of a stroke in the ﬁrst year of their marriage, and he developed a deep interest in blindness. In 1688, on reading a French extract of Locke’s Essay in which Locke distinguishes ideas acquired by one sense alone, such as our idea of colours, and ideas acquired by means of more than one sense, such as space, rest, motion, and shape, Molyneux poses a problem about the last, perception of shape. In a letter to Locke of the same year, he imagines a man blind from birth who is able to distinguish various shapes by touch, who subsequently gains his sight. He asks whether such a person would be able, using his newly restored vision alone, to identify a shape with which he had been familiar through touch. Locke and Molyneux believed that the man would not be able to identify the shape distinguished visually as the same shape he had identiﬁed by touch, by contrast with Leibniz, for example, who argued that he would know immediately that the shape was the same as the one identiﬁed by touch. The issue of interest to us here is not so much what answers were given, but the basis on which they were given. Locke and Molyneux saw the question in terms of innate ideas, arguing that advocates of innate ideas mistakenly maintain that we have an innate idea of shape and so are able to identify shapes no matter what the organ used to detect them. But in fact the arguments did not hinge on innate ideas as such. Rather, there was a three-way dispute, which turned on the sensus communis, the faculty taken as given from medieval faculty psychology through the Renaissance and early-modern period, in which the sense impressions from the various sense organs were uniﬁed into a coherent whole, into a uniﬁed image of the world. First, there were those, such as Leibniz, who held that the sensus communis consisted of ideas of things, as opposed to purely visual or tactile representations of things, from which the previously blind person can reconstruct the visual image of a cube or a sphere: after all, cubes and spheres are geometrical ﬁgures which are abstract ideas, not concrete images. Second, Locke and Molyneux likewise held that visual and tactile experiences of shape held a basic essential relationship to one another: but whereas Leibniz argued that the correlation between visual and tactile ﬁgures followed automatically from the possession of 67

Locke, Essay Concerning Human Understanding, II. xxvii. 9.

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general non-sense-speciﬁc geometrical ideas, Molyneux and Locke held that these correlations had to be learned through ‘exercise’68 or ‘experience’.69 Third, there was the view that the very idea of a sensus communis containing ideas which are not those speciﬁc to particular senses is mistaken; in particular, that there is no geometrical ‘abstract extension’ common to sight and touch. This was Berkeley’s radical view.70 Moreover, not only did Berkeley argue that the visual and the tactile worlds are wholly different and heterogeneous worlds, but, in the Essay towards a New Theory of Vision, that the visual world is not a ‘real’ world because, despite Descartes’ arguments on distance vision, our visual perception is only two-dimensional (a position that Molyneux had defended): our only three-dimensional perception of the world, which Berkeley takes to mean our only perception of a three-dimensional world, is through touch. Touch alone reveals the genuine three-dimensional world to us.71 By the argument of the New Theory of Vision, the visual world is a world of our own making, not one independent of us. Everything depends on the ability of touch to take us out from our own thoughts into a three-dimensional physical world. Berkeley’s theory of the heterogeneity of sense perception raises the key question of modularity in a stark form. For Descartes, the animal has no uniﬁed cognitive life, and to this extent such cognitive life as it has is modularized. Human beings, by contrast, because they possess a rational soul, are able to stand back from their cognitive representations of the world, recognize them as their representations, make judgements about them, and exercise free will in respect to them: these are requirements of moral agency, language use, and various other distinctive features of human beings in Descartes’ view. Human beings are able to transcend modularity because they are able to unify their mental life, and it is this uniﬁed mental life, this uniﬁed locus of subjectivity, the self, that enables them to stand in a relation to something that is not them, namely an independent world. An independent world comes with a sense of self.72 The transcendence of modularity is also crucial for Locke, but he has a more difﬁcult problem because the uniﬁcation now takes place at the level of sensation itself: perception is simply successful sensation, there is no question of a separate process of judgement. The idea of a unity of sensibility plays much the role that unity of subjectivity plays in Descartes, and in particular, the homogeneous nature of the content of sensations means that they represent something that 68

William Molyneux, Dioptrica Nova: A Treatise of Dioptrics (London, 1692), 113. Locke, Essay Concerning Human Understanding, II. ix. 8. George Berkeley, An Essay towards a New Theory of Vision (Dublin, 1709), }127. 71 There was a tradition of thinking that touch was especially highly developed in humans. Aristotle, for example, remarks that the sense of touch reaches it highest form in man (De anima, 421a22). By the late eighteenth century, the development of touch had become associated with socialization: the reports of Pinel and Bonnaterre on the 12-year-old ‘wild boy’ of Aveyron, found outside a wood near the village of Lacaune in 1797, stress the fact that his sense of touch was underdeveloped. See Harlan L. Lane, The Wild Boy of Aveyron (Cambridge, Mass., 1976), 37. 72 See Gaukroger, Descartes’ System, chs. 7 and 8. 69 70

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goes beyond our sensations. They provide us with access to something that goes beyond the capacities of our particular sense organs, even if this access were only to establish the existence of something independent of us, not its nature. To modularize sensation in the way that Berkeley does would seriously jeopardize our ability to see our mental states as reﬂecting an independent physical reality, for even if the touch option were viable, the independent world would not be the world we see but a completely different one, no closer to the visual world than the divine one that Berkeley ultimately opts for.73 This is not an option in the Cartesian and Lockean traditions, although their routes to avoiding modularity differ: establishing unity of subjectivity in the former, and unity of sensibility in the latter. Yet there is a shared ground that has almost always been overlooked in comparisons of the two. Once we ask what unity of subjectivity amounts to in Descartes, it soon becomes clear that we are dealing with questions of the unity of the person, and the issues are not restricted to cognitive states but essentially include affective states and questions of morality. The unity of subjectivity comes into its own in Descartes’ criticisms of the habit of scholastic psychology of breaking up the mind into higher and lower faculties.74 What he fears is fragmentation of the soul: how can we hold ourselves responsible if there is not something that lies behind our cognitive and affective states? Unity of subjectivity is, however, not in fact something that comes naturally, and it is rarely achieved fully. Indeed, a good deal of Cartesian moral philosophy consists in advice on how to shape oneself into a uniﬁed self, so that one can take control of one’s passions, use them fruitfully, and thereby form oneself as a fully morally responsible agent. The transcendence of modularity, the forging of a mental unity, is above all the shaping of a moral persona. The question of a uniﬁed subjectivity is intimately and essentially bound up with questions of affective states as well as cognitive ones, and it is intimately and essentially bound up with moral questions. Similarly with Locke’s unity of sensibility. But in neither case are the more general implications explored. When they come to be explored fully, in Diderot, it is in the context of a form of Lockeanism that goes beyond anything Locke himself had envisaged, and which is pitted against a view of Descartes and Cartesianism as a form of ‘rationalism’ wholly lacking in any appreciation of the role of affective states. In his Traite´ des sensations, Condillac goes beyond Locke’s enquiry into how ideas come into our mind, asking also about the origins of our mental faculties 73 In his later (1710) A Treatise concerning the Principles of Human Knowledge, XLIV, Berkeley writes that he had said that objects exist in a physical realm only as a sop to ‘vulgar error’, whereas his real view was that these exist in a non-physical divine realm. Since in his notebooks, the ‘Philosophical Commentaries’, he holds a similar view, and since these pre-date the Essay, it seems certain that his considered view at the time of the Essay was that touch does not in fact connect our sensations to a physical world, despite what he says there. 74 See e.g. Descartes, Œuvres, vi. 56–7.

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themselves. Starting from a Lockean account of the nature and origin of our ideas of the world, the problem is to discover how we could know anything outside our own mental states. He asks us to imagine a statue which we bring alive, as it were, by attributing, one by one, various sensory faculties to it, asking what its experience of the world would be like.75 Let us say, for example, that we give the statue the power to smell. We place a ﬂower in front of its nose, and the statue experiences the odour of a rose, or a carnation, or whatever, depending on what object stimulates it. The olfactory sensation is not experienced as being that of an external object, however, but simply as an experiential state. Suppose that we give it the power to hear, so that it can experience the full range of auditory variation in pitch, tone, and intensity. Again, there is nothing in this experience that would lead the statue to imagine that that experience had an external source. Vision likewise: the statue would experience light and colour, but there is nothing in this experience that would even suggest an external source of the experience. To gain a general idea of ‘sensation’, the statue must reﬂect on the qualities it senses without reference to the ﬁve ways in which the bodies are affecting its organs: that is, it must run together all the individual sensations it receives to form a single class. Nevertheless, even a statue with all ﬁve of the senses which was able to compare, reﬂect, remember, and accomplish the other intellectual operations, would not be led, on these grounds alone, to imagine that its states were anything but internal and self-contained. Despite having a grasp of spatial relations, for example, the statue would be solipsistic: its sensory experiences would not project it into, or connect it with, the world. On the contrary, it would remain isolated and self-contained. How, then, could we develop a conception of the world as independent of us on the sensationalist view? Condillac’s answer is that a sense of reﬂection emerges from the sensations, allowing us to distinguish our own body from the sensations themselves, by combining the sensations and making something new out of them, in which the various objects of sensation can be compared under different descriptions.76 How this sense of reﬂection arises is left unexplained however. Diderot takes a different tack, expanding Lockean sensationalism into a fullyﬂedged sensibilism. Diderot’s interest in Molyneux’s problem was different from that of his predecessors and contemporaries. Locke, Berkeley, and others had used Molyneux’s problem as a means of reﬂecting on our original perceptions: putting ourselves in the position of someone born blind so that we might 75 Etienne Bonnet de Condillac, Traite´ des sensations (Paris, 1754), Part I. In 1749, Buffon, in De l’homme, in the section ‘Des senses en ge´ne´ral’ (Œuvres completes, xii. 165–86), which looks at the early development and coordination of the sense organs, had argued that ‘it is by touch alone that we are able to acquire complete and real knowledge’ (177) setting out a reconstruction of how this happens. Charles Bonnet subsequently asked what physiology we would have to add to enable it to have the sensations speciﬁcally required on Condillac’s account: Essai de psychologie; ou considerations sur les operations de l’ame, sur l’habitude et sur l’education (London, 1755). 76 Condillac, Traite´ des sensations, ch. 8 }14: Œuvres de Condillac, iii. 216.

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reconstruct what it would be like to see without prior judgements and habits. As we have seen, the ﬁrst generation of responses, as it were, had construed the question in terms of whether the man with the newly restored sight would be able to recognize objects previously identiﬁed by touch. Molyneux had assumed, and made it a condition of the problem, that a congenitally blind person, on recovering his sight (typically through the removal of cataracts), would have normal, properly functioning vision. In fact, it had been recognized as early as the 1670s that patients recovering from cataract operations would always need strong spectacles if they were to see with any distinctness,77 and the entry on cataracts in the Encyclope´die also makes this very clear. Condillac argued that the parts of the eye require exercise if they are to work in the coordinated fashion required for vision: lack of adaption to luminosity, lack of accommodation in the lens so that the image is blurred, inability of the ﬁbres to transmit sensations to the brain properly, are all features that have to be corrected through learning.78 Diderot goes even further. Whereas Condillac had drawn attention to the need for exercise if the organs used in vision were to function properly, Diderot considers that vision itself must be learned: the eye must learn to see, and for this reason the previously blind man will be able to see nothing at ﬁrst. Diderot sees limited value in providing an answer to Molyneux’s question, however, doubting whether investigation of a blind person having his sight restored was in fact an appropriate way of discovering the relation between sight and touch, arguing that ‘primitive’ people, metaphysicians, and mathematicians might in fact react very differently on having their sight restored.79 The question that really interests Diderot is how the ‘mentality’ of a blind person, not just his perceptual states, differs from that of a sighted person, and what this tells us about sensibility in general. His interest focused on two cases, the Cheseldon report and Nicholas Saunderson. The Cheseldon report appeared in 1728 in the Philosophical Transactions of the Royal Society. It was a report by an English surgeon, William Cheselden, ‘An Account of some Observations Made by a Young Gentleman, who was Born Blind, or Lost his Sight so Early, that he had No Remembrance of Ever Having Seen’. Cheselden had, over a twelve-month period, removed cataracts from each eye of the patient, and his report contained a reasonably detailed account of the recovery. He was not interested in, and it seems had no knowledge of, Molyneux’s problem, which in any case he would have been unable to give a deﬁnitive

77 See e.g. Rohault, Traite´ de physique, 488. In fact, everything depends on the age at which the cataract develops, and on the extent of the blindness. If there is lack of visual stimulation during the crucial developmental period, the person will never learn to distinguish one object from another visually. Generally, see Marjolein Degenaar, Molyneux’s Problem (Dordrecht, 1996). 78 Essai sur l’origine des connoisances humanies, ch. 2 }21; Œuvres, i. 58–60. 79 [Denis Diderot], Lettre sur les aveugles, a´ l’usage de ceux qui voient (London, 1749); Diderot, Œuvres, i. 312–27.

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empirical answer to, because what happens depends to such a great degree on pre-operative and post-operative variables. Nevertheless, the report fuelled debate among those who were concerned with Molyneux’s problem, with Berkeley for example regarding the case as deﬁnitive support for his position, and Condillac arguing that Cheselden’s report was ﬂawed.80 But some saw Cheselden’s report in a more general light, and the key contribution here was Diderot’s Lettre sur les aveugles. The Lettre combined consideration of the Cheseldon case, which explores what happens when sight is restored, with another, that of Nicholas Saunderson, in which the implications of lack of sight are explored. Saunderson was Lucasian Professor of Mathematics at Cambridge and author of a large posthumously published two-volume Elements of Algebra. The striking thing about Saunderson is that he was blind, and Diderot, drawing on the memoir by his friends that prefaces the Elements,81 makes him the primary subject of the Lettre sur les aveugles. In effect, what Diderot does is to use the case of Saunderson to pit unity of sensibility against a Cartesian unity of subjectivity, arguing that the unity of sensibility, properly construed, is essentially something socially responsible that encourages a well-formed persona, whereas the Cartesian is insensible to the world and works merely in abstractions. It is Saunderson’s very blindness that in effect denies him a fully developed unity of sensibility. A deﬁcient sensibility is primarily a question of an emotional, aesthetic, and moral challenge for Diderot. Because of their impoverished sensibilities, the blind turn their minds inwards and are drawn to thinking in terms of abstractions. Jessica Riskin puts the point well, noting that ‘this made them natural mathematicians and rationalists: in a word, Cartesians. Conversely, Cartesians’ abstract, inward focus made them insensible to the world outside their minds: philosophically blind.’ This leads Diderot to suggest that both the blind and Cartesians, because of their solipsistic cast of mind, were inhumane.82 The blind offer a crucial case study for Diderot because he believes that their abstract manner of experiencing pain in others weakens their sense of sympathy for the suffering of others.83 The situation is in effect the analogue of what in the Cartesian case would be someone—lacking the ability to unify their mental life (perhaps because of melancholia or what we would now think of as various forms of neuroses), and thereby failing to shape oneself satisfactorily into a moral persona—whose moral agency, and humanity, would be deﬁcient in comparison with someone (an honneˆte homme) who had achieved this.

80

See Degenaar, Molyneux’s Problem, ch. 4. Nicholas Saunderson, The Elements of Algebra (2 vols., Cambridge, 1740), i. i–xxvi. Riskin, Science in the Age of Sensibility, 21. 83 See e.g. Diderot, Œuvres, i. 288–9, where he suggests that the reaction to a man urinating and spurting blood is effectively on a par in the blind. 81 82

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What is ultimately at stake for Diderot is the sensory basis of civic life, where the contrast is between sensibility and solipsistic rationalism.84 The general question underlying this is where the ideas that regulate our lives—our moral, emotional, social, political and intellectual lives—come from. The consequences for language, culture, and history of the Lockean claim that all knowledge derives from sense perception had been drawn in detail by Condillac in his Essai sur l’origine des connaissances humaines of 1746. Eight years later, in his Traite´ des sensations, his uncompromisingly sensationalist epistemology was employed in the service of the reform of social and political ideas, fundamentally recasting the origins of human abilities and capacities in an effort to reject all outdated sources of authority. This approach is strengthened in a radical way in Diderot, who goes far beyond anything advocated by Condillac, in his distinctive effort to separate morality completely from religion and to rebuild it on a sensationalist basis. It is axiomatic to the sensationalist project that one begins life with a tabula rasa, and the question is not just how one develops a cognitive, affective, and moral life on this basis, but whether, having grasped that this is the context in which development occurs—that is to say, having grasped that traditional sources of authority, most notably religious authority, can no longer play this role—there are any guidelines that we can follow in cultivating responsible citizens.85 In dealing with this question, there are two extreme alternatives that he rejected.86 The ﬁrst was associated with mechanism, more speciﬁcally biomechanics. I have noted that the classical ideas of passion and ´emotion which Descartes had explored in his Passions de l’aˆme were grounded medically, and indeed his general theory of the passions is built very much around a medical understanding of the passions. This approach was subsequently developed in detail by Antoine Le Camus, in his Me´dicine de l’esprit of 1753, in which all defects of the understanding are treated as being ultimately a matter of the ﬂow of animal spirits, and hence their cure falls within the compass of biomechanics. It is not surprising that Diderot would have rejected this approach, but the second alternative, which is the polar opposite of this, is a different matter. This is the theory we ﬁnd in Helve´tius, whereby the human mind is wholly determined by the sensations it receives, so that it is simply a question of controlling the environment in which the child is reared and educated to the greatest possible 84 At a personal level, the case was undoubtedly helped by Descartes’ reclusive behaviour, especially during his twenty years in the Netherlands. 85 An important text speciﬁcally devoted to this question is Charles Pinot Duclos, Conside´rations sur les mœurs de ce sie`cle (Paris, 1751). Duclos articulated his concerns about education, as opposed to mere instruction, in terms of a sense of patriotism, and this was a crucial theme in educational reformers: see e.g. Gabriel-Franc¸ois Coyer, Disserations pour ˆetres lues: la premie`re sur le vieux mot de patrie, la seconde sur la nature du people (La Haye, 1755); idem, Plan de l’e´ducation publique (Paris, 1770); and Louis-Rene´ Caradeuc de La Chalotais, Essai d’e´ducation nationale, ou plan d’e´tudes pour la jeunesse ([Paris], 1763). For a very different approach, compare the most famous pedagogic work of the Enlightenment: Jean-Jacques Rousseau, E´mile, ou De l’e´ducation (Paris, 1762). 86 See the discussion in Kaitaro, Diderot’s Holism, 133–7.

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degree.87 Diderot certainly agrees with Helve´tius that education is the basis on which to form morally and socially responsible citizens,88 but he does not agree that the mind is determined simply by the sensations it receives.89 More generally, he is critical of the ‘analytical method’ whereby one isolates individuals and then adds them together in a kind of social arithmetic, and he draws lessons for the psychological realm from this as well.90 One’s psychological life is determined by an equilibrium between, or internal organization of, the constituent parts, and this equilibrium will vary from person to person, affecting their responses to their environment. The human being is a collection of separate animals each conserving its particular function, but at the same time sympathizing naturally, or through habit, with others.91 In his early Essai sur la me´rit et la vertue, Diderot borrows an architectural metaphor from Shaftesbury, noting that just as a building requires a careful balance between its constituent parts, the passions of a person form a system in which it is the balance, rather than the individual passions, that matters.92 Helve´tius had maintained that one’s sensibilities are wholly determined by one’s environment, but Diderot, arguing from the organic complexity of bodies and the need for an internal organization, had no difﬁculty showing that the environment is just one element that shapes one’s sensibilities. Nevertheless, this does not alter the fact that, for Diderot, our relation to the world depends very much upon how we arrive at that relation, and one assimilates cognitive information in a process which is always and necessarily social, cultural, and has moral implications, so that what is shaped is not merely a cognitive sensibility but a sensibility in which cognitive, affective, and moral questions are inextricably tied together. We can see this development as the outcome of two currents of thought, one distinctive of the Enlightenment, the other something which has pervaded philosophical discourse from its origins. The ﬁrst is the project of establishing how we come by our social and moral ideas once the mind has been naturalized in the sensibilist fashion, that is, once non-sensory sources of authority have been eliminated as inauthentic. The contrast drawn is a sharp one. On the one hand there is the development of a persona which reﬂects on its own ideas, asking whether there is anything physical that corresponds to these ideas, a paradigmatically Cartesian procedure: it is a mind complete in its own right, enquiring into the world only as it needs. On the other, there is the sensibilist position whereby 87 Claude Adrien Helve´tius, De l’esprit (2 vols., Amsterdam, 1758); see also his posthumously published De l’homme, de ses facultie´s intellectuelles, et de son ´education (London, 1773). 88 For Helve´tius, education forms a trope in his Voltairean contrast between Britain and France: ‘In London it is a merit to be instructed; in Paris it is ridiculous’: De l’esprit, Book II, ch. 20. 89 Many criticisms of Helve´tius’ De l’homme are to be found in Diderot’s huge compendium of medicine and physiology, Ele´ments de physiologie, which was left incomplete at his death. There is a modern critical edition of the work: Ele´ments de physiologie, ed. Jean Mayer (Paris, 1964). 90 Diderot, Re´futation de l’Homme: Œuvres, ii. 351–2. 91 Ele´ments de physiologie, 287. 92 Œuvres, i. 98 and 120.

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the development of a uniﬁed persona starts with experiences in which there is often no neat separation of cognitive, affective, and moral factors. The second current of thought is that of the shaping of the persona of the philosopher. Here we have a tradition that goes back to the origins of philosophy, in Plato’s deﬁnition of the philosopher in the early Socratic dialogues, where, as well as those reasoning skills and commitment to argument that are associated with the sophist, Plato insists on a commitment to a form of intellectual morality. The theme pervades the history of philosophy, reappearing in various forms in the Hellenistic, medieval, Renaissance, and early modern periods.93 In the Encyclope´die, considerations of a philosophically appropriate persona are drawn out in a number of entries, notably those on eclecticism and the philosophe, which we have looked at. While there are some very traditional tropes here—self-knowledge and self-control remain core issues for example—there are two distinctive features that are comparatively new. The ﬁrst is the move away from the idea that the ideal persona is restricted to an elite group. Rather, the qualities manifested in such a persona are available to all, at least in theory.94 In particular, they are not connected with esoteric philosophical training, as was the case with the ancient philosophical schools, or with membership of a particular social group, as Descartes’ honneˆt homme had been for example.95 The second feature is directly connected with the ﬁrst. It lies in an explicit commitment to a life of social engagement and political reform, by contrast with a life of withdrawal from the world and contemplation. The second feature, by itself, had been an explicit part of a number of conceptions of the philosophical life, from Plato to Bacon, but its combination with the ﬁrst feature results in something distinctive. The package of the two together brings both a rejection of cognitive authority vested in a particular group and a rejection of political authority vested in a particular group. The radical democratic politics that issues from this package is a distinctive feature of French Enlightenment thought, but it is certainly not the only direction in which a concern with sensibility drives Enlightenment thought. A different kind of approach, one which explicitly eschews any form of political radicalism, is that of Hume, whose philosophical 93

See Gaukroger, Emergence, ch. 7. In fact, the philosophes generally did not ignore social ranking. In his Reﬂe´xions sur l’histoire, for example, d’Alembert urges historians to learn from the past the duties attaching to each social rank so that children could be educated accordingly: see d’Alembert, Œuvres, ii. 9. 95 In the entry on the philosophe (by Du Marsais) in the Encyclope´die, the philosophe is treated as an honneˆte homme, in that he requires more than bare necessities, but this is less an association of the philosophe with a particular social class so much as a rejection of an ascetic ideal of the philosopher. As Mark Hulliung points out, the philosophe ‘is as much a denunciation of the old model of the Stoic sage as an idealized depiction of the new man of letters. No philosophical ﬁgure fares worse in the writings of the philosophes than the Stoic, no philosophy comes under attack more often than Stoicism. It was the strategy of the encyclopedists to expose the Stoic ideal as impossible, inhuman, and as less the vision of a wise man than the fool.’ The Autocritique of Enlightenment: Rousseau and the Philosophes (Cambridge, Mass., 1994), 88. 94

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work was celebrated more in France than in Britain in his own time,96 but who thrived in a political culture—which can be traced to the 1688 Revolution—of toleration quite different from that of France, and he was a staunch and conservative defender of this political system, which he did not doubt was the best that had ever come into existence. At the same time, Hume probes more deeply into the questions of reason and sensibility than anyone else, although, like Locke, he has no qualms about raising profound issues even if he cannot provide an answer to them. Different as the approaches of d’Alembert and Hume are, both of them employ the resources of history to explore and open up the question of the human condition. Up to now we have focused on the disciplines of natural philosophy, metaphysics, and Christian theology, but there is a fourth strand, which went into decline to some extent in the seventeenth century, namely the tradition of civic humanism or belles-lettres. Philosophically informed history falls under this rubric, and its ﬂowering in the second quarter of the eighteenth century allows the emergence of historically informed philosophy. It is to these questions that we now turn. 96 For details, see Michel Malherbe, ‘Hume’s Reception in France’, in Peter Jones, ed., The Reception of David Hume in Europe (London, 2005), 43–97.

12 Historical Understanding and the Human Condition It was Hobbes’ achievement to have shown that all human beings were sufﬁciently equal in their faculties of mind and body as to preclude considerations of rank being relevant to their standing as equal partners in the development of a political compact. This provided the basis for a general political theory, in Hobbes himself, but also in the republican tradition that included thinkers as various as Spinoza and Locke. It presupposed—or postulated—a level of basic political uniformity, however, a shared level of universal moral/political/social discourse. In the course of the eighteenth century, this uniformity was put in question, both wittingly and unwittingly. Wittingly, by Montesquieu who, in his De l’esprit des lois (1748), denied that there was a basic morality that underlay every society, that there was something that existed in various degrees of realization and anchored the other achievements of that society. For Montesquieu, different moral principles are suited to different types of society, where the ‘type’ of society may be a function of geographical as much as historical factors. Moreover, although he thought that religion was always necessary for morality, he was prepared, in Book X of De l’esprit, to subject religions to a factual assessment of their moral effects, comparing Judaism, Christianity, and Islam in this regard. By contrast, writers such as Shaftesbury and Hutcheson, who were concerned to establish a basic form of morality that might show moral diversity to be superﬁcial, and might ground religious precepts, found themselves, by their failure to establish this without recourse to innate ideas, with a resolutely intractable problem of moral diversity. In the Essay, Locke presented moral diversity as a fact of life, as it were. The case is established not so much through traditional philosophical argument as on the basis of a body of travel reports, and other material resembling the natural history reports that were ﬁlling the pages of the published records of the Royal Society. It remains at the phenomenal level, without the question of whether it might be appropriate to attempt to provide reasons for this diversity even being raised. In the second of his Two Treatises of Government, by contrast, he offered a conception of moral and social diversity somewhat at odds with that which he proposes in the Essay. In the second Treatise, in discussing the rights of settlers to occupy Amerindian lands, Locke puts forward an account of the difference that

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goes beyond the phenomenal, purely evidential level, and comes closer to an explanation. His discussion in ‘Of the Beginning of Political Societies’ has been described as treating America as a kind of political embryo, allowing us to understand how Western and Asian societies might have developed.1 It is in some respects reminiscent of the way in which the case of Molyneux’s blind man regaining his sight was used by Locke and early eighteenth-century British philosophers, namely as a means of reﬂecting on our original perceptions by putting ourselves in the position of someone born blind so that we might reconstruct what it would be like to see without prior judgements and habits. The point of investigation of Amerindian social and economic organization is not to bring to light the profound differences between their practices and European ones, but rather to show how practices of the former kind can be transformed into the latter.2 There is no doubt about the superiority of European practices for Locke—hence the legitimacy of displacing the Indians—so there is no sense in which the diversity of beliefs and practices is problematic, in the way that it is in the Essay account. Rather, the question is, if Locke’s own society did not arise from nothing, how, and with what rationale, might it have developed or evolved from an original form of social grouping (which Locke associates with the patriarchal family) into its present form? It is clear from the discussion that such a development or evolution is a natural one for Locke, and the transition from primitive to modern society is sketched in ‘Of the Beginning of Political Societies’ in terms of what are in effect developmental stages. This was certainly not the ﬁrst attempt to employ developmental stages in understanding modern institutions, but in a context in which traditional religious and humanistic assumptions about universal moral, social, and other values have come loose, it takes on a new standing. With the eighteenth-century radicalization of Locke that came with the reading of him in Baylean terms, the idea of the present being a culmination of, and in many respects an inevitable outcome of, all that went before takes on a signiﬁcance that it could not have had in Locke himself. In a development that owes more to Bacon than Locke, universal values now include cognitive as well as moral and social values, and they take on a prescriptive dimension. We have seen how Voltaire relativized cognitive values, including those that led to success in natural philosophy, to a contrast between English and French political and religious cultures. By mid-century this 1 Second Treatise, ch. 8: Works, ii. 185–93. See James Tully, An Approach to Political Philosophy: Locke in Contexts (Cambridge, 1980), ch. 5. 2 See Carey, Locke, Shaftesbury, and Hutcheson, 92–7. It is possible that Montesquieu may have held a developmental view something along these lines, in that he seems to allow that the growth of civilization gradually liberates human beings from physical factors such as climate, so that the determining factor in their behaviour increasingly becomes their moral nature, and there is a case to be made that he considers this at least less culturally relative than the societies he investigates: the case is set out in Gustave Lanson, ‘Le de´terminisme historique et l’ide´alisme social dans l’Esprit des Lois ’, Revue de me´taphysique et de morale 23 (1916), 177–202.

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process has been taken one step further, and in d’Alembert’s preliminary ‘Discours’ to the Encyclope´die, the notion that it is natural philosophy that provides all cognitive standards is combined with the view that all cognitive paths lead to the Encyclope´die. The division in Locke between a strictly factual record that rejects any speculation and hypotheses, and what might be called a conjectural history, is one that will permeate eighteenth-century thought on history. What was for many purposes a new kind of history, a form of social, cultural, and intellectual history which can be pursued by comparatively traditional means, or alternatively through an explicitly hypothetical or conjectural rational reconstruction, comes to a head mid-century. Among those who pursued it strictly along traditional lines, Voltaire is a key ﬁgure, above all his Le sie`cle de Louis XIV, the ﬁrst parts of which appeared in 1739, and Essai sur les Mœurs et l’esprit des nations (1756–62). By contrast, there were those who believed that the time for such traditional history was past, and who pursued exclusively conjectural history. ‘The science of history,’ writes d’Alembert in his Me´moires et re´ﬂexions sur Christine, reine de Sue`de, ‘unless it is written [e´claire´e] by a philosopher, is the lowest form of human knowledge’,3 and Diderot’s entry on ‘Art’ in the Encyclope´die explicitly recommends philosophical history over ‘a true history’. The great value of ‘philosophical’ or ‘conjectural’ history, on d’Alembert’s understanding of it, was moral: shunning claims to certainty, it teaches us our limitations and encourages moderation in our claims.4 The gulf between the two ways of pursuing history took on political and personal overtones in Paris, and Madame Geoffrin arranged for the ´erudites and the philosophes to attend her salons on different evenings.5 Yet the division was not always clear cut, and many writers employed one or the other form of history for different purposes. THE HISTORY OF MANNERS To say that Voltaire worked in a genre of traditional history needs immediate qualiﬁcation, for the model he employed was largely a late seventeenth-century one. This model was a reaction to the predominant form of historical writing in the seventeenth century, one that continued the Renaissance humanist tradition, based on the precepts of Cicero, and taking Livy and Sallust as its exemplars. This tradition had aimed at moral instruction and artistic excellence.6 To achieve the ﬁrst it had concentrated on the individuals who had made the moral decisions; to 3

D’Alembert, Œuvres, ii. 119. Idem, ‘Portrait de l’auteur fait par lui-meˆme’: Œuvres, i. 9. See Hulliung, The Autocritique of Enlightenment, 41. 6 See Brumﬁtt, Voltaire Historian, 2–3; also Arnoldo D. Momigliano, Studies in Historiography (New York, 1966), 42–4. 4 5

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achieve the second, highly embellished accounts had been provided of noble deeds on the battleﬁeld and at court. At the same time as such accounts were degenerating into mere attempts to achieve aesthetic effects, there was a newly emerging growth of historical scholarship in which palaeography, archaeology, numismatics, and diplomatics were used as evidential tools.7 But these tools often undermined the grounds on which history had been pursued. Developments in chronology, for example, rendered impossible a literal reading of the Old Testament, the one document that had been deemed certain and the only one that offered a chronology that went back to the beginning. Bayle’s Dictionnaire defended a ‘Pyrrhonisme de l’histoire’ in which various unconnected but relatively secure historical facts could be safeguarded, but in which no overriding narrative emerged. The need for such an overriding narrative, one that would, for example, indicate something as basic as what types of facts it was important to establish, became increasingly pressing in the early decades of the eighteenth century. The required focus was located by writers like Fontenelle and Bayle in ‘l’histoire de l’esprit humain’, and this was as much a project of the ´erudites, by contrast with the humanist historians, as it was of the more conjectural ‘philosophical’ histories, although, at the level of detail, the interests that guided it differed. Both were concerned with what might be termed the history of civilization, conceived as a means to understanding the present, but they differed on just what it was that one needed to know in order to have such an understanding. Fontenelle’s L’Histoire des oracles, for example, explores the origins of thought about the world and the ﬁrst attempts at reasoning generally, whereas Voltaire is not interested in the mind itself but rather in writing an account of its products. But Voltaire is, nevertheless, something of a hybrid. He rejects the kinds of conjectural enquiry so characteristic of philosophe history, yet his ‘history of manners’ is a formative inﬂuence on the historical thinking of the mid-century philosophes. 7 Palaeography was especially important here. The key works are Jean Mabillon, De re diplomatica libri VI. in quibus quidquid ad veterum instrumentorum antiquitatem, materiam, scripturam, & stilum; quidquid ad sigilla, monogrammata, subscriptiones, ac notas chronologicas (Paris, 1681); and Bernard de Montfaucon, Palaeographia graeca, sive De ortu et progressu literatum græcarium, et de variis omnium sæculorum scriptionis græcæ generibus (1708). Montfaucon, for example, notes that the older the book the less likely it is to contain errors and doubtful readings, so it is important to be able to distinguish different types of parchment, different inks, different scribal hands, and variations in punctuation. Works of literature are thereby treated in such a way that they yield physical, non-literary evidence. Numismatics also became important with the pioneering work of Charles Patin, who proceeded on the basis that whereas inscriptions might exaggerate the virtues of a ruler, images inadvertently conveyed information about the customs of the ruler’s time. See Charles Patin, Introduction a l’histoire, par la connoissance des medailles (Paris, 1665) and Histoire des medailles ou introduction a la conoissance de cette science (Paris, 1695). This approach is followed up in a number of archaeological texts: for example, Robert Sibbald, Historical Inquiries, concerning the Roman monuments and antiquities in the north part of Britain called Scotland (Edinburgh, 1707), where it is argued that the only sure form of history comes from the study of arches, temples, pyramids, etc., by contrast with the mere opinions of ancient authors. Generally, see Barret-Kriegel, Les historiens et la monarchie, vol. i.

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Voltaire’s ﬁrst distinctive history was his Sie`cle de Louis XIV, published in 1751. As the title indicates, this is not an account of an individual but an attempt to reconstruct an age. What is noteworthy about the treatment is not the incorporation of new factual material, which is very minimal, but the playing down of genealogies, battles, and the like, and the inclusion of material on social, economic, and cultural questions. It is structured around issues rather than events, and the nature and quality of artistic production is one of the central issues. In one respect, the work complements the Lettres, for there Voltaire had compared Britain favourably with contemporary France, that of Louis XV. In the Sie`cle, he is concerned to stress the political, artistic, and cultural achievements of Louis XIV, the contrast being with the decline in these areas during the reign of his successor. This requires quite focused notions of achievements and decline, since these deﬁne the issues on which the narrative hinges. The Essai sur les mœurs, begun in the 1740s and completed between 1756 and 1762, develops these themes in the context of a ‘universal history’ of ‘manners’. This last term is an important one, and does not designate something conventional or superﬁcial, but rather an end point of the development of civilization.8 Although nominally beginning with the start of what eighteenth-century historians designated the ‘modern’ era, that is, with Charlemagne,9 the Essai also deals with China, the decline of the Roman empire, and the rise of the papacy. The treatment of the Middle Ages is distinctive in that Voltaire’s aim is to understand feudalism: how the nobility came into existence and how it evolved, the military and economic organization of feudal society, the inadequacy of medieval legal processes, and the economic (as opposed to religious) motivation for the Crusades. The opening chapter, which deals with the history and cultural achievements of China, serves above all to distance the reader from Western developments, praising Chinese scientiﬁc and legal practice, distinguishing a religion of the learned (Confucianism) from popular superstition, and above all reminding us that there are civilizations older than those of the West and the Middle East. The early sections also deal with India and Islamic countries, and his treatment is again sympathetic, forcing the reader to take seriously the issue of non-western civilizations, and thereby abandoning the Christocentric, Eurocentric accounts of writers like Bossuet. China and India are wholly alien to Christian culture, and beginning with them rules out the kind of Christocentric history that Bossuet engaged in. As Pocock points out, the 8

As Pocock has noted, ‘the reduction of philosophy and theology from perception of reality to sociable discourse (subject to the disciplines of politeness) formed part of what may very well have been the greatest change wrought by Enlightenment in the ﬁeld of social and historical thought: the perception of society as the movement towards “manners” or moeurs ’: Barbarism and Religion, ii. 19. 9 By contrast with the ‘ancient’ era, which centred on Greece and Rome, the ‘modern’ era for eighteenth-century historians effectively began when Christianity became dominant, and this was traditionally dated to Charlemagne. What for eighteenth-century historians was deemed modern roughly corresponds to what we would term ‘medieval’. See J. G. A. Pocock, ‘Perceptions of Modernity in Early Modern Historical Thinking’, Intellectual History Review 17 (2007), 55–63.

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consideration of China acts to provide a counter-history capable of displacing the Judaeo-Christian scheme, for here we have a body of rationally organised historical literature fully as reliable as that in the Hebrew Scriptures, but impossible to conﬂate with it as Assyrian and Egyptian scriptures had been conﬂated in the Christian science of chronology. Behind this there is a body of myths and traditions giving an account of the world and its origins incompatible with that in Genesis; and not only is this account as plausible as any other, but it is absurd to suppose that God was not as concerned with a civilization so ancient, and so capable of presenting its antiquity, as he was with the small and unprepossessing nation of the Jews.10

The skeleton for European history is provided not by a Christocentric narrative, then, any more than it is by the reigns of rulers, but rather by what Voltaire identiﬁes as four ‘ages’ in which the arts were brought to perfection, only to be followed by a decline.11 These were, ﬁrst, the age of Philip and Alexander, although the leading ﬁgures include Plato and Phidias, from an earlier period, as well as Aristotle and Praxiteles; the second is the age of Caesar and Augustus, where the key ﬁgures are Cicero, Lucretius, Livy, Virgil, Horace, and Ovid; the third is the age of the Medici; and the fourth that of Louis XIV. It is important to appreciate here that Voltaire sees no evidence for, or reason to assume, fundamental changes in historical development, no evolution, at least beyond very primitive stages, but rather a continuity in which there are (rare) peaks and (far more prolonged) troughs, which are manifestations of an underlying human condition. It is a view of history in many respects more cyclical than linear, and quite at odds with prevailing views among his Francophone contemporaries.12 There are two questions raised by Voltaire’s account, around which I propose to structure our investigation of the role of the construction of historical narratives. The ﬁrst is that of developmental stages. The second is that of a history whose narrative is shaped by the identiﬁcation of cultural achievements, which can then be used as a basis for judgements about particular societies. It is obviously possible to have the ﬁrst without the second, but it is also, less obviously, possible to have second without the ﬁrst: Vico, for example, denied the ﬁrst but accepted the second, treating the three successive chronological periods that he identiﬁed in his Scienza Nuova—divine, heroic, and human—as autonomous with respect to one another.13 Here I want to focus on how the combination of developmental

10

Pocock, Barbarism and Religion, ii. 106. The idea of four ages ﬁrst appeared in Jean-Baptiste Dubos, Re´ﬂexions critiques sur la poesie et sur la peinture, ﬁrst published anonymously in 1719, but it had no general currency until Voltaire. 12 The ﬁgure who has most in common with Voltaire here is Turgot, who, while acknowledging that knowledge and science progress, argues that this progress does not necessarily improve the human condition, and he draws attention to the short ascents and long declines in human history, asking: ‘Do men rise only in order to fall?’ Œuvres de Turgot, ii. 606. 13 The work ﬁrst appeared in 1725, and then in radically revised editions in 1730 and 1744. The third and deﬁnitive edition of the text appeared as Giambattista Vico, Principj di una Scienza Nuova 11

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and cultural concerns allows a history of understanding of the world in which the present—the ‘enlightened’ present—can be construed as a culmination of the processes of understanding, one which provides a secure vantage point to survey claims to knowledge. FROM MYTH TO REASO N Developmental notions come to pervade a number of areas around the middle of the eighteenth century. None of these is more striking than one of the core ideas of the Encyclope´die, set out in d’Alembert’s preliminary Discours, that knowledge itself can be subjected to a developmental understanding. At roughly the midpoint of the discussion of the nature of knowledge in the Discours, d’Alembert’s account shifts gear. Up to this point, the discussion has been pursued via epistemology, speciﬁcally via a rewriting of Cartesian epistemology in sensationalist terms, and concluding that the sole ultimate criterion of cognitive judgement is natural philosophy. With a complete change of trajectory, he now suddenly shifts from epistemology to conjectural history, introducing the shift in these terms: We now proceed to consider our Encyclopædia as a systematical Dictionary of Arts and Sciences. This Part is of greater Importance, as it concerns the greater Number of Readers; and therefore requires more Conduct and Industry in its Execution. To prepare the Way for this Purpose, we should enquire into the present State of the Arts and Sciences; and shew by what Steps they arrived at this State. The metaphysical History of the Origin, and Connection, of the Sciences has been of great Use to us in forming our systematical Table: and an historical Explanation of the Order, wherein the several Parts of our Knowledge succeed each another, will prove as serviceable in directing us how to lay them properly before the reader.14

What he goes on to provide is nothing less than a genealogy of reason whereby understanding in its historical forms converges on the project embodied in the Encyclope´die, which thereby represents the culmination of human cognitive endeavour and constitutes the starting point for further enquiry.15 intorno alla natura delle nazioni, per la quale si ritruovano i principj di altro sistema del Diritto Naturale delle genti (2 vols., Naples, 1744). 14 Plan, 62–3; Encyclope´die, i. xxxii. 15 D’Alembert’s is the most ambitious version of a project to construct a genealogy of knowledge, but not the only one, and the exercise was not conﬁned to France. Maclaurin provided an extensive history of science in his An Account of Sir Isaac Newton’s Philosophical Discoveries (1748), in which science is traced through the unintelligible mysticism of the Platonists (38), the ‘Gothic barbarity’ of the Middle Ages (40), and the ‘extravagent undertakings’ in Descartes and the metaphysical system-builders who followed in his wake (67). The true path is identiﬁed as that of Pythagoras, Socrates, Copernicus, Kepler, Galileo, Bacon, Boyle, and of course the terminus ad quem, Newton. Cf. Adam Smith’s ‘History of Astronomy’,

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Before turning to the details of d’Alembert’s very inﬂuential account, it will be helpful to see this development against the backdrop of the elaboration of the notion of primitive mentality, which can be traced back to the late seventeenth century. A genealogical theory of the triumph of reason of the kind that d’Alembert offered required a theory of the primitive to mark itself out clearly, in order to provide something against which it could display its wares. The primitive existed in both synchronic and diachronic forms, however, and the one was used to elucidate the other. This is particularly the case with the use of classical antiquity to provide a framework for understanding American Indians.16 In the key early seventeenth-century introduction to the culture of the New World, for example, Marc Lescarbot’s Histoire de la nouvelle France (1609), the whole of the sixth Book is devoted to setting out disparities and conformities with the ancients, offering clariﬁcation by means of Greco-Roman analogues. This remained a standard mode of treatment, followed up a number of basic works, including Richard Blome’s The Present State of his Majestie’s Isles and Territories in America (1687). Brahmanism was assimilated to a form of Greco-Roman thought in this way in mid-century in Abraham Roger’s De opendeure tot het verbogen heydendom (1651); Zoroastrianism was construed in terms of a Greco-Roman model at the end of the century in Thomas Hyde’s Historia religionis veterum Persarum (1700); and Buddhism follows this model closely in Noe¨l Alexandre’s Conformite´ des ce´remonies chinoises avec l’idolatrie grecque et romaine (1700). In the course of the eighteenth century, however, we ﬁnd a move in the opposite direction, namely the use of studies of primitive peoples as described in travel books to elucidate the classical pre-history of the Enlightenment. The 1704 book by a gentleman traveller, M. de La Cre´quinie`re, Conformite´ des coutumes des Indiens orientaux, avec celles des Juifs & des autres peuples de l’antiquite´, sets out to provide a ‘knowledge of antiquity’: knowledge of Indian customs is of no value in its own right, he assures us, but is invaluable for the light it throws on ancient Greek and Jewish customs and religions. Assimilation of ancient and modern forms of the primitive was driven partly by purely pragmatic concerns, in that the audience for literature on the New World, for example, which would have included directors of trading companies and those religious organizations engaged in missionary work as well as a general readership, had been raised on classical literature, and this was its route to understanding anything outside its own culture. But it was also partly driven by the fact that, while there was some degree of recognition of variations in the primitive state, for example between New World Indians and the early Greeks, it was important that there was a fundamental conformity among the varieties of the primitive, for the composed in large part around the same time, when Smith was still a student at Oxford: Essays on Philosophical Subjects, ed. W. D. P Wightman (Oxford, 1980), 31–105, esp. 48–53 (‘On the Origin of Philosophy’). 16 See Manuel, The Eighteenth Century Confronts the Gods, 15–19, on which I draw here.

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move from the primitive to the present was driven by various internal forces, generally considered as being due to fundamental features of human nature, towards a shared goal, typically identiﬁed with rationality. The most distinctive feature of primitive mentality in this regard was superstition, something which eighteenth-century thinkers believed had characterized pagan mentality. There were two features of primitive mentality that stood out. First, although superstition had, it was believed, been of epidemic proportions in pre-Christian times, it had not wholly disappeared with the advent of the Christian era, despite condemnation from the Church.17 The persistence of superstition required explanation. Second, there was a strongly held view that the pagan religion of antiquity was not sui generis but had in fact borrowed from and distorted the true religion, that of the Bible. But the problem here was a possible blurring of the line between pagan superstition and Christian religion. On the ﬁrst question, among the explanations for the continued persistence of superstition on offer, the most common was that superstition emerged when one faced something one was unable to explain but which impinged on one’s life directly. John Trenchard, for example, argued that superstition was due to an attempt to avoid pain, and above all that greatest of pains, death: because its cause was hidden, people had subjected themselves to the word of authority or devised imaginary causes.18 The problem here is that Trenchard’s complaint is reminiscent of Protestant attacks on Catholicism—highlighting the combination of personal intrinsic weakness and extrinsic fraud, the latter possibly backed up by the authority of an organized religion—so that seemingly uncontentious attacks on pagan superstition could be, and were, read as attacks on contemporary Christian forms of superstition.19 Above all, they harboured the possibility 17 In the case of England, it seems actually to have increased in the sixteenth and seventeenth centuries: see Keith Thomas, Religion and the Decline of Magic (London, 1971). 18 Detailing forms of superstition bewildering in their diversity and obscurity, he writes:

To these Weaknesses and our own, and Frauds of others, we owe the Heathen Gods and Godesses, Oracles and Prophets, Nimphs and Satyrs, Fawns and Tritons, Furies and Demons, most of the Stories of Conjurers and Witches, Spirits and Apparitions, Fairies and Hobgoblins, the Doctrine of Prognosticks, the numerous ways of Divination, viz. Oniromancy, Sideromancy, Tephranomancy, Botonomancy, Crommyomancy, Cleromancy, Aeromancy, Onomatomancy, Arithmomancy, Geomancy, Alectryomancy, Cephalomancy, Axinomancy, Coscinomancy, Hydromancy, Onychomancy, Dactylomancy, Christallomancy, Cataptromancy, Gastromancy, Lecanonmancy, Alphitomancy, Chiromancy, Orneomancy, and Necromancy, Horoscopy, Astrology and Augury, Metoposcopy and Palmistry, the fear of Eclipses, Comets, Meteors, Earthquakes, Inundations, and any uncommon Appearances, though never so much depending upon Natural and Necessary Causes, nor are there wanting People otherwise of good understanding, who are affected with the falling of a Salt-Seller, crossing of a Hare, croaking of a Raven, howling of Dogs, screaching of Owls, the motion of Worms in a Bedsteed, mistaken for Death-Watches, and other senseless and triﬂing accidents.

John Trenchard, The Natural History of Superstition (London, 1709), 10–11. 19 See e.g. Conyers Middleton, A Letter from Rome, Shewing an Exact Conformity between Popery and Paganism: or, The Religion of the Present Romans to be Derived Entirely from that of their Heathen Ancestors (London, 1729).

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that these could be used to discredit Christianity per se, by construing it, whether Catholic or Protestant, as a form of superstition. Bayle, for one, had made no bones about the parallels between the ridiculousness of pagans taking their gods literally and Catholics taking literally the Assumption and the liquefaction of the blood of St Januarius. As Manuel notes, ‘for learned anti-clericals the nature of paganism was most favourable battle terrain. The erudite researchers into the beliefs, rites, and theologies of the ancients always had one eye cocked on orthodox Christianity.’20 On the second question, that of a possible blurring of the line between pagan superstition and Christian religion, there had been a well-established view among orthodox Christians that pagan myths were simply corruptions of sacred history, each god being traced back to a Hebrew patriarch or to the chance misreading of an obscure biblical name.21 The tradition goes back to Clement of Alexandria, who had argued that the learning of the Greeks derived from the Jews. In the 1670s, Theophilus Gale’s The Court of the Gentiles had set out to demonstrate ‘that the wisest of the Hethans stole their choicest Notions and Contemplations both Philologic, and Philosophic; as wel Natural and Moral, as Divine, from the sacred Oracles’,22 and he traces the dissemination of Jewish wisdom through the Egyptians to the Greeks.23 Samuel Shuckford’s Sacred and Profane History of the World (1728) goes even further in assimilating all non-biblical traditions to scripture. In Shuckford’s hands, Hesiod’s theogony becomes political history, with Cronus’ devouring of his children meaning simply that he sent them to school in foreign parts, and Zeus made into a contemporary of Moses who ruled Crete wisely, administered justice through subordinates, and was later divinized.24 20

Manuel, The Eighteenth Century Confronts the Gods, 22. One of the most extreme examples of this kind of approach is Daniel Huet, Demonstratio evangelica ad serenissimum delphinum (Paris, 1679), in which all Greek myths are interpreted as fragmentary and distorted records of events recorded in Genesis, and numerous ancient ﬁgures are identiﬁed as pagan memories of Moses. Huet’s approach is not quite as Christocentric as it might appear, however, for in his Alnetanae quaestiones he set out a detailed account of the common traits of sacred and profane theologies, causing some critics to accuse him of trying to derive all religions from a natural revelation: see Rappaport, When Geologists were Historians, 147–8. 22 Theophilus Gale, The Court of the Gentiles (2 vols., London, 1672–82), p.[i]. Cf., in a similar vein, Etienne Fourmont, Re´ﬂexions critiques sur les histoires des anciens peuples (Paris, 1735). 23 Gale’s reasoning was called into question by John Spencer, who—in his Dissertatio De Urim and Thummin (Cambridge, 1669) and De Legibus Hebraeorum Earum Rationibus (Cambridge, 1685)—argued that the Jews owed their divinatory practices to the Egyptians. Spencer’s denial that the Jews were the fountainhead of civilization was attacked vigorously by a number of writers, notably Hermann Witsius, Aegyptiaca et DE˚`FLˇN (2nd edn., Amsterdam, 1696), and John Edwards, —Eˇ¸—ˇ˚¸ˇ ˇ`: A Compleat History or Survey of All the Dispensations and Methods of Religion, From the Beginning of the World to the Consummation of All Things (London, 1699). See John Gascoigne, ‘“The Wisdom of the Egyptians” and the Secularisation of History in the Age of Newton’, in S. Gaukroger, ed., The Uses of Antiquity: The Scientiﬁc Revolution and the Classical Tradition (Dordrecht, 1991), 171–212: 173–84. 24 I take the example from Manuel, The Eighteenth Century Confronts the Gods, 119. 21

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The attempt to naturalize ancient and non-Christian myths and religions, while it had a long history in the Christian Church, going back at least as far as Augustine, was on dangerous ground by the second half of the seventeenth century, a danger much compounded by the eighteenth. The danger is evident once one thinks of the enterprise of mythological and religious interpretation in its broadest terms. It is basically an anthropological enquiry into non-rational forms of belief, their persistence, their legitimacy, and their origins. ‘Nonrational’ here does not mean irrational, but rather any forms of belief whose rationale does not depend on reason and evidence which can be objectively assessed, of the kind for which natural philosophy replaced ‘reason’ as the model and standard (because it became the archetypical form of reason) by the 1740s. Clearly Christian beliefs as well as ancient forms of superstition come under this rubric, and whatever attempts were made subsequently to differentiate Christian beliefs from mere superstition (attempts complicated by the Protestant attack on papal idolatry), the damage had been done. This is evident from the fact that attacks on pagan superstitions, such as Fontenelle’s Histoires des oracles (1686), did not have to mention Christianity at all for readers to make the connection immediately, and draw the appropriate lesson. Fontenelle’s Histoires drew extensively on the treatise De Oraculis Ethnicorum, by the Dutch physician Antoine van Dale, ﬁrst published in 1683.25 This dealt speciﬁcally with the role of superstition in pre-Christian religions, in particular the prophecies of oracles, but drew more general conclusions on the question of popular superstitions.26 Ever since the publication of Vossius’ De Theologia gentili (1641), there had been signiﬁcant interest in ancient pagan religions, especially among English deists. Lord Herbert of Cherbury, in his posthumously published De religione gentilium (1663), had used Vossius’ work to mount a general criticism of popular superstition, ancient and modern, and Charles Blount, in his pamphlet Great is Diana of the Ephesians (1680), had argued that, before the appearance of religions, worship of God had been pursued in a wholly rational way by philosophers who manifested piety in their exemplary 25

See also the subsequent work of van Dale, Dissertationes de origine ac progressu idolatriae et superstitionum (Amsterdam, 1696). It is likely that Fontenelle would have known of van Dale’s book from Bayle’s enthusiastic review, which appeared as the opening article of the ﬁrst issue of Nouvelles de la Republique des Lettres in 1686. Fontenelle made no secret of his indebtedness to van Dale, stating in the Preface that he was primarily an adapter and translator of van Dale’s work, and the most detailed response to the Histoire des oracles, by Jean Franc¸ois Baltus, is entitled Re´ponse a` l’Histoire des oracles . . . dans laquelle on re´fute le syste`me de M. Van D. (Paris, 1707). In the article on ‘oracles’ in his Dictionnaire philosophique, Voltaire does not mention Fontenelle’s well-known text, but refers instead to van Dale’s De oraculis. Brumﬁtt, Voltaire Historian, 35, puts this down, however, to Voltaire seeing Fontenelle as a rival for leadership of the philosophes, and therefore wishing to diminish his importance. 26 The van Dale/Fontenelle argument was widely known and had a wide inﬂuence. It was taken up by Enlightenment thought in Catholic Spain, for example, receiving qualiﬁed support in the second volume of the work of the Benedictine, Benito Jero´nimo Feijo´o y Montenegro, Teatro Critico Universal (8 vols., Madrid, 1726–36). See Israel, Radical Enlightenment, 373.

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lives as well as in their teachings. Van Dale’s arguments were of a different order, however. De Oraculis was based on extensive knowledge of the primary and secondary sources, and van Dale mounted a detailed argument against the prevailing view, which was that the prophecies of the oracles were genuine prophecies, but were the work of the devil, and had miraculously come to an end with the advent of Christianity, which had replaced these false prophecies with true ones. But not only was it manifestly false that pagan prophecies miraculously came to an end with advent of Christianity, van Dale argued, they actually ﬂourished in an unprecedented way in the early centuries of the Christian era. He made it clear that magic simply does not exist—there had never been a single genuine demonstration of sorcery, divination, possession, communication with spirits, etc.—and the devil was incapable of affecting human beings in these ways. The culture of the Netherlands in which van Dale was writing was far more liberal and tolerant than that of France. Moreover he was an Anabaptist, and felt free to criticize not merely Roman Catholic superstitions, comparing Catholic priests with their pagan predecessors in promoting bogus miracles and wonders, but Lutheran and Calvinist practices as well. When Fontenelle takes up van Dale’s treatise, he softens its radical polemical edge by declining to draw any parallels with Christian practices, yet the central thrust of the work—the triumph of reason over superstition—remains in the attack on pagan superstitions and the behaviour of pagan priests in promoting them. Moreover, the Christian historiography set out in Bossuet’s Discours sur l’histoire universelle (1681), which was the standard treatment of these questions in France, was directly contradicted, in that Bossuet had offered a staunch defence of the traditional view that Christianity had miraculously rendered impotent the demons that inhabited the shrines and oracles of antiquity. In fact, Fontenelle argues, the shrines and oracles have a purely natural explanation. On the Delphic oracles, for example, he argues that there was a hole on Parnassus which emitted exhalations that inebriated those who encountered it, and as a result there arose the belief that it was divine: people began to approach the hole with respect, and little by little ceremonies were introduced.27 Naturalistic explanations of pagan beliefs and rituals can be traced back at least as far as Augustine, but Spinozism, deism, and new attempts to reconstruct religious texts meant that the climate of the 1690s was not as secure as it had been in Augustine’s time on the question of where naturalistic explanations stop. Moreover, Fontenelle introduced these considerations not to those able to immerse themselves in van Dale’s dense scholastic Latin, but to a broad reading public in an elegant and engaging French, opening up the issues to a wide audience who were being encouraged to make up their own minds on a wide range of cultural matters. 27

Fontenelle, Œuvres, ii. 370.

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At the time he published the Histoires, Fontenelle was working on his Origine des fables, although this was not committed to writing until the next decade and was not published until 1724. The two works are intimately connected: where the Histoires deals with premeditated imposture on the part of priests, the Origine deals with an unpremeditated universal tendency to evaluate the causes of things that affect us, even when we have no reliable information to work on.28 In the Origine, Fontenelle takes his starting point from a number of parallels between the mythologies of New World Indians and the Pelasgians (the pre-Hellenic inhabitants of Greece), and in virtue of these parallels and the way in which they were shaped in early civilizations—the Incas and the archaic Greeks respectively—he advances the thesis that, had they been left to themselves, the Amerindians would have developed a capacity to think that was equal to that of the Greeks: indeed, the increasing move towards rationality is a feature of all cultures. In other words, what is shared is not just the rationality that is the end point of the process but the primitive state of mind that is its origin. This primitive state of mind is universal, even though it comes to receive different mythical expressions. Modelling the development from primitive society to Enlightenment rationality on the development of a newborn child to full adulthood (a modelling which, it should be noted, Augustine had employed on a number of occasions), what Fontenelle is primarily interested in is less the move to rationality so much as the question of what we can learn from the original primitive state.29 D’Alembert’s interest, by contrast, is with what he presents as the tortuous journey to rationality. His reconstruction of this journey begins by distinguishing the order in which different forms of enquiry would be pursued if we were starting from scratch, and that in which they have been pursued since ‘the revival of learning’. By the latter, d’Alembert clearly means the Renaissance, for he tells us that, in the latter case, the progress has been from erudition, to belles-lettres, to philosophy, whereas in classical antiquity, when men were starting from scratch, philosophy was developed before belles-lettres. The discrepancy is due to the fact that ‘after a long Interval of Ignorance, preceded by Ages of Knowledge, the 28

See Manuel, The Eighteenth Century Confronts the Gods, 41–6. It was a widespread view among deists, defended for example by Toland, that priests had capitalized on human weaknesses in this respect. 29 Manuel (ibid., 132) sums up the situation admirably, when he writes that, among the philosophes, there was a general assumption that the real nature of man, of language, of writing, of political society, of inequality lay hidden in their ﬁrst expressions. Since these sons of Locke believed that no idea was innate and everything human had to be learned through the experience of pain and pleasure and by association with previous stimuli, they opened the whole ancient world to historico-psychological inquiry. To the philosophe the study of antiquity was not a mere academic exercise but an investigation of remarkable utility, for if modern man was befuddled by false notions, the philosopher, in the course of examining the genesis of beliefs, the development of acquired capacities, and the growth of customs and institutions, would establish the moment in time when error ﬁrst crept into human reasoning. The diagnosis in and of itself would exert a therapeutic effect.

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Reproduction of Ideas was necessarily different from their ﬁrst Generation.’30 The ability to make progress depends not just on individual genius, but on reading and conversation. In other words, there are social and cultural prerequisites for progress in learning. Such factors had been stressed by Bacon and repeated in Royal Society apologists such as Sprat, but they were wholly absent from the Cartesian tradition, and, as we have seen, although in Fontenelle they play a major role in the dissemination of scientiﬁc results, there is little consideration of their role in their production. D’Alembert is putting them at the fore, as Bacon had done,31 and he is historicizing the content of philosophical doctrines, so that lack of access to the works of antiquity meant that during the Middle Ages, philosophers, ‘instead of enquiring into Nature, and studying Man, . . . devoted themselves to frivolous Questions about abstract and metaphysical Essences; which often requiring too much Subtility, became an Abuse of Genius.’32 The idea that the times or culture that a person lives in can be invoked to explain their thought and behaviour was not completely unknown before the new travel literature of the late sixteenth century—the Greeks had, after all, characterized the ‘barbarians’ in such a fashion—but its systematic use was very rare. When Louis Le Roy, in arguing for the superiority of the modern era over classical Greece and Rome in his De la vicissitude ou varie´te´ des choses en l’univers (1575), used the case of Amerindians to show that all primitive societies are uncivilized,33 he was advancing a very radical thesis, not just in terms of the particular comparison, which was of course provocative, but in the very fact of contextualizing or historicizing a society like Athens or Rome. The importance of his equation of ‘early’ and ‘primitive’ lies less in what it asserts than in what it denies, and paramount in what it denies is the existence of a ‘Golden Age’ which provides a standard by which all later achievements are to be judged, yet which they can never attain. In one sense, Golden Age conceptions had themselves historicized or contextualized classical thought, in that they had seen Plato, Aristotle, Cicero, Seneca, etc., as ﬁgures who were representative of a particular time and culture in which things were possible that were no longer possible, and they had seen cultures largely in terms of the time at which that culture existed, that is, in terms of a stage in the historical process. The new historicizing tendency of sixteenth-century French humanists such as Bodin, Le Roy, and La Popelinie`re inverted this conception. It accepted these ﬁgures as being representative of a particular time and culture, and accepted the importance of their 30

Plan, 63; Encyclope´die, i. xxxii. See Stephen Gaukroger, Francis Bacon and the Transformation of Early Modern Philosophy (Cambridge, 2001), ch. 4. 32 Plan, 65; Encyclope´die, i. xxxiii. 33 Loys Le Roy, De la vicissitude ou varie´te´ des choses en l’univers, et concurrence des armes et des lettres par les premieres et plus illustres nations du monde, depuis le temps ou` a commence´ la civilite´, et memoire humain jusques a` presente (Paris, 1575), Book 10. 31

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being at a particular stage in a historical process, but offered a completely different assessment of this process and the cultures it generated. Time was now modelled not on some notion of Golden Age followed by a decline, but rather on growth from infancy to maturity and wisdom, so that the cultures of later times supersede those of earlier ones. We can ﬁnd this conception in English writers such as Gilbert,34 and it is indeed such a conception that lies behind Bacon’s defence of natural philosophy in the Redargutio Philosophiarum of 1608. In pursuing his discussion of the philosophers of antiquity, he says he is ‘holding to [his] rule of not entering into controversy on points of doctrine, but to judge by signs’.35 It is now ‘signs’, that is, the distinctive characteristics of a doctrine that enable us to evaluate its content, or, more generally, the distinctive characteristics of an age than enable us to evaluate the cultural products of that age, rather than the content of particular theories or doctrines, that guides Bacon’s interpretation of the philosophers of antiquity. In particular, the Greeks, Bacon tells us, were a nation ‘always mentally precipitate, and didactic by habit’.36 They chatter and argue, without ever producing anything. Moreover, their age was only one degree removed from fables, with little historical knowledge or knowledge of other regions of the earth and it lacked both a respect for earlier times and the wealth characteristic of modern times. The modern era, by contrast, has the beneﬁt of 2,000 years of history behind it, and has explored two-thirds of the globe. In the present context, the importance of the Redargutio lies in its use of a contextualization or historicization of knowledge to legitimate the pursuit of natural philosophy in the modern era. Using an evolutionary conception of societies and their intellectual cultures, Bacon is able to argue that it is reasonable to expect natural philosophy would ﬁnd better conditions for its nurturing in a culture which had reached maturity, rather than in one in which society was still in its childhood. He is able to argue that what is possible in the modern era far outstrips anything that was possible in antiquity without even making a comparative assessment of their achievements, because the point depends on what it is possible to achieve in particular cultures, not on what has actually been achieved. The issues came to a head in France later in the century with the ancients versus moderns controversy, and, as we have seen, by the middle of the eighteenth century even Jesuits were claiming that Aristotle would have believed little of what he did if he knew what we know now. But d’Alembert’s use of contextualization and historicization goes beyond that of his predecessors in ambition. On d’Alembert’s model, the development of language and history in the wake of the revival of learning should mirror the development of the faculties in a child, but there is something amiss in the order in which they were acquired, which distorts the structure and aims of knowledge. The thinkers of antiquity 34 35

William Gilbert, De mundo nostro sublunari philosophia nova (Amsterdam, 1651), 240. Bacon, Works, iii. 566. 36 Ibid., 563.

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had studied nature directly, having no aids to hand, but in the wake of printing, the new generations of thinkers had a surfeit of such aids, and merely read of the discoveries of the ancients in books, revering them without being in a position to evaluate them properly, and developing a sense of the acquisition of knowledge as a painless process. The next stage was that in which this misunderstanding of what knowledge consists in was recognized for what it is, and erudition gave way to belles-lettres, in which the ‘precious metal’ was separated from the dross, something which earlier indiscriminate scholars were unable to distinguish. The ancients were still admired above all others, but now with proper discrimination, so that, while they remained models to be imitated, this was no longer in a servile way.37 Nevertheless, such scholars believed that the only way to express oneself was in a learned language (Latin), and their skill consisted in part in the adopting an elegant classical style. Finally, however, writers abandoned the idea of copying or imitating the ancients, and in this way belles-lettres developed out of reﬁnement and renovation of erudition, only in the end to transcend it in signiﬁcant respects. The development of what d’Alembert refers to as philosophy, the core of which is natural philosophy, was a slower process however, and it was particularly obstructed by scholasticism. In the arts, poets and others had been allowed to celebrate pagan deities ‘as a matter of innocent amusement’, something that proved fertile ground for the imagination, and which was hardly a threat to Christianity, since no one was going to be led by this to revive the worship of Jupiter and Pluto. But things were different in philosophy. Here, ‘it was either apprehended, or pretended, that blind Reason might hence wound Christianity.’38 It was in this climate that religion, whose proper domain was restricted to faith and morals, began to take upon itself the teaching of philosophy, and natural philosophy in particular, and the policing of these areas by the Spanish and Roman Inquisitions. But ‘whilst ignorant or malevolent Enemies thus made open War on Science, Philosophy retreated under the Covert of some extraordinary Men, who, without entertaining the dangerous ambition of unveiling the Eyes of their Contemporaries, prepared, in Shade and Silence, that Light, which afterwards by insensible Degrees, enlightened the World.’39 Paramount among these ‘extraordinary men’ who pursued science in this hostile environment is Bacon, who is credited with inaugurating the new scientiﬁc approach, and whose plan of knowledge, d’Alembert points out, is the basis, updated and with modiﬁcations, for that presented for the Encyclope´die.40 Descartes is praised for acquiring knowledge for himself rather than deriving it from books, for his invention of algebra, for his application of geometry to natural philosophy in

37 39

Plan, 68; Encyclope´die, i. xxxiv. 38 Plan, 75; Encyclope´die, i. xxxvii. Plan, 78; Encyclope´die, i. xxxviii–xxxix. 40 Plan, 81; Encyclope´die, i. xl.

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his optics, and, even though the theory was no longer accepted, for his account of vortices. The only egregious error ascribed to Descartes is his advocacy of the doctrine of innate ideas, and his outstanding merit was that he couragiously ventured to shew men of Genius how they might shake off the Yoke of the Schools, the Tyranny of Opinion, Authority, Prejudice, and Barbarism. He may be considered as the Head of a Party, or a Leader, who had the Courage to stand up ﬁrst against Arbitrary Power; and by projecting a glorious Revolution, laid the Foundation of a just and happy Government, which he could not live to see established.41

The third great ﬁgure picked out for special attention is Newton, whose natural philosophy is identiﬁed as the ﬁrst and only permanent one. It relies not on conjectures but on experiment and geometry alone. Newton is credited with sharing the invention of the calculus with Leibniz, and his contributions to celestial mechanics and optics are spelled out, and brieﬂy defended against various objections such as the claim that gravitational attraction is an occult quality. The last great ﬁgure discussed in any detail is Locke, who, as we have seen, is credited with supplying a ‘rational metaphysics’ that vindicates Newton’s natural philosophy, and which, ‘like Natural Philosophy, consists in carefully collecting Facts, reducing them into a Body, explaining them by one another, and distinguishing those that ought to precede, and serve as a Basis to the rest’.42 What d’Alembert provides in the Discours is much more than a rational reconstruction of the history of philosophy. It is a vindication of the project of the Encyclope´die in the distinctively Baconian genre of a legitimating genealogy.43 What is at issue is primarily a question of establishing a historical sequence in which one can follow a progression that starts with the origins of knowledge and traces a process of growth—while uncovering and analysing various false starts— which can be shown to culminate in the present, so that the present, as represented by the Encyclope´die, provides both a secure vantage point for scrutinizing the past and a secure starting point for further enquiry.44

41

Plan, 85–6; Encyclope´die, i. xlii. Plan, 91; Encyclope´die, i. xlvi. 43 In his 1753 Essai sur la socie´te´ des gens de lettres et des grands, d’Alembert adds a political dimension to this account. Here we are told that Louis XIV gradually conquered the traditional predilection of the nobility for ignorance, and natural philosophers and others engaged in intellectual pursuits were taken out the solitude to which they had been accustomed and raised to the standing of ‘greats’. See d’Alembert, Œuvres, iv. 338–43. 44 Note in this respect Condorcet’s entry on integral calculus, ﬁrst published in the 1776 supplement to the Encyclope´die, in which he draws attention to what he considers the lack of progress in ‘knowledge of the system of the world’ between 1686, the year of publication of Newton’s Principia, and 1747, when ‘d’Alembert, Euler, and Clairaut found their analytical solutions of the three-body problem’ (Encyclope´die, xviii. 887). 1747, the year when the consolidation of the Newtonian understanding began on this reckoning, also happens to be the year in which Diderot and d’Alembert started work on the Encyclope´die. 42

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There cannot be a stronger contrast with d’Alembert’s promotion of reason in understanding than Hume’s account of the relation between reason and sensibility. ‘Reason is, and ought only to be the slave of the passions, and can never pretend to any other ofﬁce than to serve and obey them’, Hume tells us in his Treatise of Human Nature, published in 1739.45 On its title page, he announces that the work is ‘an attempt to introduce the experimental Method of Reasoning into Moral Subjects’, and in the Introduction he sets out what this amounts to in these terms: For it seems to me evident, that the essence of the mind being equally unknown to us with that of external bodies, it must be equally impossible to form any notion of its powers and qualities otherwise than from careful and exact experiments, and the observation of those particular effects, which result from its different circumstances and situations. And tho’ we must endeavour to render all our principles as universal as possible, by tracing up our experiments to the upmost, and explaining all effects from the simplest and fewest causes, ’tis still certain we cannot go beyond experience; and any hypothesis, that pretends to discover the ultimate original qualities of human nature, ought at ﬁrst to be rejected as presumptuous and chimerical.46

A little later into the book, in comparing his doctrine of the association of ideas with the Newtonian account of gravitational attraction, he writes: Here is a kind of ATTRACTION, which in the mental world will be found to have as extraordinary effects as in the natural, and to shew itself in as many and as various effects. Its effects are every where conspicuous; but as to its causes, they are mostly unknown, and must be resolv’d into original qualities of human nature, which I pretend not to explain. Nothing is more requisite for a true philosopher, than to restrain the intemperate desire of searching into causes, and having establish’d any doctrine upon a sufﬁcient number of experiments, rest contented with that, when he sees a farther explanation would lead him into obscure and uncertain speculations. In that case his enquiry wou’d be much better employ’d in examining the effects than the causes of his principle.47

This is a thoroughly Lockean appraisal, as is Hume’s remark in the Appendix to the Treatise that what is characteristic of Newtonian philosophy is ‘a modest scepticism to a certain degree, and a fair confession of ignorance in subjects, that exceed all human capacity’.48 45 Hume, A Treatise of Human Nature (3 vols., London, 1879), 295. Earlier in the Treatise, he describes reason as ‘nothing but a wonderful and unintelligible instinct in our souls’ (179). 46 Ibid., xxi. 47 Ibid., 12–13. 48 Ibid., 639. Equally Lockean in tone is Hume’s statement in the Essay on the Sceptic in his Essays, Moral, Political, and Literary: ‘There is one mistake to which [philosophers] seem liable, almost without exception; they conﬁne too much their principles, and make no account of that vast variety which nature has so much affected in all her operations.’ Essays and Treatises, i. 162.

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The Treatise was written in France, during a four-year sojourn at La Fle`che, where Hume was able to make free use of the library of Pluche, who was busy working on his Spectacle de la nature. He arrived in 1734, the year of publication of Voltaire’s Lettres, and some of the central concerns of the work turn on the questions at issue between Locke and Malebranche that we looked at in Chapter 4. Malebranche is treated by Hume as the archetypical systematic metaphysician: which he was, given that the systems of his two competitors, Spinozean and Leibnizian metaphysics, had each been very effectively marginalized—at least outside the German states in the latter case—by the 1730s. He does not argue against the Malebranchean position, however, but sets it out as an apparently coherent way of approaching its subject matter, to the extent that it may look as if he is actually adopting this position as his own. In fact he does reject it: it is just that his rejection comes at the meta-level, in that the Malebranchean position is taken as indicative of philosophical reasoning, and Hume’s point is to draw attention to the limits of a particular kind philosophical reasoning per se, not just in its Malebranchean variety.49 Consider the most striking case of this: Hume’s treatment of causation in Book I, Part 3, section xiv of the Treatise.50 Here, the account of cause that Hume sets out, as McCracken has shown in detail, is straight out of Malebranche:51 as well as extensive passages that pre´cis Malebranche’s La recherche, there are other passages that can only be described as word-for-word translations of Malebranche. Hume reiterates the Malebranchean doctrine that we get no idea of power from our notions of body, mind, or the union of the two, and he uses the same example as Malebranche to show the vacuity of an appeal to powers and forces; he repeats Malebranche’s view that we are not aware of a power in ourselves when we move our arms, as well as using his example of a paralytic person willing his arm to raise without the effect being produced; he follows Malebranche explicitly in arguing that the variety of philosophical opinions about power is evidence that we lack a clear idea of it. Malebranche explains that a true cause is a ‘necessary connection’, a distinctive doctrine which—by contrast with Descartes, Locke, or Berkeley for example—he stresses on a number of occasions, with a view to arguing that there are no such necessary connections between natural things: a view that Hume, who likewise stresses the 49 This is in accord with the stategy set out in the Treatise: ‘Reason ﬁrst appears in possession of the throne, prescribing laws, and imposing maxims, with an absolute sway and authority. Her enemy, therefore, is oglig’d to take shelter under her protection, and by making use of rational arguments to prove the fallaciousness and imbecility of reason, produces, in a manner, a patent under her head and seal,’ (Book I, Part IV, sect. i). 50 Cf. Malebranche, La recherche, XVe E´claircissement. 51 McCracken, Malebranche and British Philosophy, 257–69. The issues are not conﬁned to the metaphysics of causation. Gracyk, for example, has argued that ‘Hume’s alleged aesthetic scepticism may be no more than his summary of the consequences of Hutcheson’s theory, put forth in order to criticize and subsequently modify it.’ Theodore Gracyk, ‘Rethinking the Standard of Taste’, Journal of Aesthetics and Art Criticism, 52 (1994), 168–82: 170.

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idea of cause as a necessary connection, adopts. The one signiﬁcant difference between the two is that Malebranche believes that there are indirect connections between things which are determined by God, a doctrine that Hume ignores, leaving us with no connections. There is much dispute over Hume’s degree of commitment to the rejection of necessary connections, and whereas earlier commentators had construed him as denying any real causation in the world, asserting that there is merely constant conjunction, there has more recently been a move to see Hume as a ‘sceptical realist’, that is, someone who accepts that there are real causes in the world, but who denies that we can have a philosophical grasp of them.52 This makes a good deal of sense of his use of Malebranche. Hume is not plagiarizing Malebranche: not only does he refer to La recherche in passing, but Malebranche was a very familiar philosopher to both French and English audiences, and one whose views on causation were well known. Rather, he employs a slightly pared-down version of Malebranche’s view to represent the epitome of philosophical reasoning on this question.53 On the Lockean/Newtonian account, there are forms of enquiry in which one can seek underlying causes, but there are realms of enquiry in which this is the wrong way to proceed, not only because it gets nowhere but, more importantly, because it cuts off productive avenues of research which a phenomenal approach reveals. This is a view that Newton and Locke held about natural philosophy. Hume, whose concern is with the ‘moral sciences’ rather than natural philosophy as such, generalizes the question to include any form of cognitive enquiry, including metaphysics, as indeed Locke had done. His argument seems to be that one can always pursue systematic enquiry, and it remains a perfectly legitimate exercise: indeed, he characterizes this kind of philosophical search as something that is part of human nature. However, one ultimately pays a price for pursuing this path, and in the case of causation, as in the more general case of scepticism, the price of drawing matters to their logical conclusion is a denial of something that we not only know to be the case, but without which we could not proceed in our daily lives. Systematic metaphysical enquiry takes on a life of its own, becoming increasingly disconnected from the world as it proceeds: Malebranche, Spinoza, Leibniz, and Berkeley had all been criticized in these terms, but Hume is the ﬁrst to offer a considered diagnosis of what has gone wrong. There are two connected questions at issue here that can help us understand what Hume is proposing, the ﬁrst touching on the nature of scepticism, the 52 See in particular John P. Wright, The Sceptical Realism of David Hume (Manchester, 1983); and Galen Strawson, The Secret Connection: Causation, Realism, and David Hume (Oxford, 1989). 53 For Hume, doubt is an instrument of reason that can make us aware of its limits, but only when it is carried through to the end, that is, so long as various prejudices and assumptions are not smuggled in as immune, as he believes they invariably are. He would have regarded Malebranche’s introduction of God as an example of such prejudices and assumptions, so to make the power of sceptical argument clear, his ‘paring down’ is necessary.

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second, which is what I particularly want to focus on, touching on the relation between reason and sensibility. On the question of scepticism, it is important to draw a distinction between ancient scepticism, for which we can use the generic title of Pyrrhonism, and modern Cartesian scepticism. Pyrrhonism is doxastic scepticism, that is, it questions whether we are entitled to our beliefs, typically by trying to show that for any belief we have there is an equally good opposing belief, so that we cannot decide between the two.54 Cartesian scepticism, by contrast, is epistemological scepticism. It does not question our beliefs, but rather our knowledge claims. It questions whether any of our beliefs can be called knowledge, typically on the grounds that knowledge is justiﬁed true belief, and that, when pressed, we cannot provide the requisite justiﬁcation for any of these beliefs. In short, doxastic scepticism questions whether any of our beliefs are true; epistemological scepticism questions whether any of our beliefs (whether true or not) are justiﬁed. The former was associated with a distinctive way of life in antiquity: not merely a Socratic-style life which questioned everything and was free from dogmatism (something also distinctive of the Cynics), but one in which peace of mind was associated with a conception of enquiry not as something that seeks the ultimate truth, but as something in which one sees the strengths of, and can balance, mutually opposing views. Epistemological scepticism, because it did not bear on beliefs, could be more radical and is not the kind of thing that could support a way of life. It could be more radical because, as far as the question of justiﬁcation was concerned, it allowed a form of hyperbolic doubt in which even beliefs about which we are certain—beliefs like the existence of the external world, and simple arithmetical truths—can be subjected to question, because what is at stake was not whether these beliefs are true, but whether they could receive the requisite justiﬁcation. It could not support a way of life because it would be impossible to live in accord with such hyperbolic doubts. Epistemological scepticism was not designed to provide us with a new set of beliefs in its own right, but to sweep away various prejudices and assumptions so that one could start afresh. In terms of what they set out to achieve, and how they achieve it, doxastic and epistemological doubt are quite different. Hume is as concerned with Pyrrhonism as he is with epistemological scepticism, and what is distinctive about his approach is that he runs together doxastic and epistemological considerations in an idiosyncratic way. It is not that he simply conﬂates the two: rather, what he does is to assess the value of doubt generally both with respect to doxastic and epistemological criteria. The oddity of this way of proceeding is that hyperbolic doubt comes to be assessed by 54 See my ‘The Ten Modes of Aenesidemus and the Myth of Ancient Scepticism’, where I explore the distinction between doxastic and epistemological scepticism in detail. I argue there that Pyrrhonism is strictly speaking a form of relativism rather than a form of scepticism, but Hume treats it as a form of scepticism, and the distinction does not bear on the discussion here.

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doxastic criteria, which of course it fails to satisfy. Consider the case of cause. One can question whether one’s belief that there are necessary connections meets the highest standards of justiﬁcation, and indeed one may conclude that they do not, if only because these standards of justiﬁcation, for whatever reason, can never be met. But one cannot, on philosophical grounds, genuinely believe that one is mistaken about necessary connections, any more than one can genuinely believe that one is mistaken about the existence of an external world.55 By applying doxastic criteria to hyperbolic doubt, Hume inevitably ﬁnds himself in a dire position where ‘I am ﬁrst affrighted and confounded with that forelorn solitude, in which I am plac’d in my philosophy, and fancy myself some strange uncouth monster, who not being able to mingle and unite in society, has been expell’d all human commerce, and left utterly abandon’d and disconsolate.’56 It is hard to imagine that philosophical speculation could lead to such a state of psychological distress, although it is of interest that Hume’s description does in fact capture the psychological state of patients suffering from Cotard’s syndrome, caused by a brain lesion in which cognitive and affective pathways in the brain which normally work in tandem are separated, as a result of which the patient experiences the world, or even himself, as not really existing, a condition accompanied by severe psychotic depression. In other words, the inability to associate or align what might be described, in eighteenth-century terms, as reason and sensibility, is what leads to this state, rather than a defect of either taken separately.57 This is exactly the kind of claim (allowing for difference of context) that Hume wants to make. The issue of the nature and limits of human enquiry turns in Hume as much on sensibility as on reason. In An Enquiry Concerning the Principles of Morals, Hume takes issue with Montesquieu, who he tells us supposes all right to be founded on certain rapports or relations; which is a system, that, in my opinion, never will be reconciled with true philosophy. Father Malebranche, as far as I can learn, was the ﬁrst that started this abstract theory of morals, which was afterwards

55 The two are in fact connected, because scepticism about causation leads to scepticism about the external world: ‘Thus there is a direct and total opposition betwixt our reason and our senses; or more properly speaking, betwixt those conclusions we form from cause and effect, and those that perswade us of the continu’d and independent existence of body. When we reason from cause and effect, we conclude, that neither colour, sound, taste, nor smell have a continu’d and independent existence. When we exclude these sensible qualities there remains nothing in the universe, which has such an existence.’ Treatise, 231. 56 Ibid., 264. But compare the remark in the Introduction to the Treatise that ‘nothing is more certain, than that despair has almost the same effect upon us as enjoyment, and that we are no sooner acquainted with the impossibility of satisfying any desire, than the desire itself vanishes’. Treatise, xxii. 57 See A. W. Young, K. M. Leafhead, and T. K. Szulecka, ‘The Capgras and Cotard Delusions’, Psychopathology 162 (1994), 226–31.

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adopted by Cudworth, Clarke, and others; and as it excludes all sentiment, and pretends to found everything on reason, it has not wanted followers in this philosophic age.58

That there is a more general point at stake here is evident from the remark in the Treatise that: ‘the understanding, when it acts alone, and according to its most general principles, entirely subverts itself, and leaves not the lowest degree of evidence in any proposition, either in philosophy or in common life.’59 Trying to live in accord with reason alone is misguided: Philosophy on the contrary, if just, can present us only with the mild and moderate sentiments; and if false and extravagant, its opinions are merely the objects of a cold and general speculation, and seldom go so far as to interrupt the course of our natural propensities. The CYNICS are an extraordinary instance of philosophers, who from reasonings purely philosophical ran into as great extravagancies of conduct as any Monk or Dervise that ever was in the world. Generally speaking, the errors in religion are dangerous; those in philosophy only ridiculous.60

Yet the solution to this does not lie in renouncing abstract, systematic reasoning, for to do so would be to ‘cut off entirely all science and philosophy’ and would ‘subvert entirely the human understanding’.61 Hume is able to offer no solution to this dilemma. ‘For my part’, he tells us, ‘I know not what ought to be done in the present case.’62 There are a number of ways of thinking about the problem raised here. One is to try to explore the question of the relation between reason and sensibility in an abstract way which forces some kind of commensurability between the two, an approach that would inevitably involve translating the questions into terms of some overarching discipline. This is what Kant will do, turning the problem into one in epistemology, but this would certainly not have satisﬁed Hume. Another approach is to treat the dilemma as a genuine dilemma, not something that can be overcome, but as telling us something about the human condition. In concentrating on doxastic doubt, Hume’s deployment of scepticism is not part of an epistemological project, but one designed to reveal how to live, just as it was for the Pyrrhonists.63 It is important for this project that we understand how the idea of causation in nature has its origins in human nature. For Hume, as for many of his contemporaries, the means that we employ to divine what the dilemma posed by reason and sensibility tells us are historical. And since coming

58 David Hume, Enquiries Concerning the Human Understanding and Concerning the Principles of Morals, ed. L. A. Selby-Bigge (2nd edn., Oxford, 1902), 197n. 59 Hume, Treatise, 267–8. 60 Ibid., 272. 61 Ibid., 268. This is also true of morals: see Appendix 1, ‘Concerning Moral Sentiment’ to the Inquiry concerning the Principles of Morals: Hume, Enquiries Concerning the Human Understanding, 285–94. 62 Treatise, 268. 63 The point is explored in detail in Livingston, Philosophical Melancholy and Delirium.

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to terms with this dilemma is a crucial part of coming to understand human nature for Hume, our understanding of human nature necessarily has a historical dimension. From the last decades of the seventeenth century, history became to the moral or human sciences what observation and experiment were to natural history. History had traditionally acted as source of guidance in moral and political questions, but not in the cases of what we might characterize as psychological or anthropological questions (with rare exceptions in the travel literature). Its scope now widens radically, and it begins to act as a form of investigation that runs parallel to philosophical analysis, sometimes complementing it, at other times at odds with it. THE VARIETIES OF UNDERSTANDING D’Alembert’s genealogy was by no means the only way in which the history of knowledge was pursued, and there were other forms of historical enquiry that found more in myth and religion than a mere history of error which had to be overcome if knowledge was to triumph. In particular, there were attempts to explore just what light mythical and religious thought threw on knowledge more generally. Some of these worked in terms of a stark contrast between mythology and reason, but others, such as those of Vico and Hume, had a direct bearing on the idea of a natural-philosophical model for knowledge.64 I want to focus on the case of Hume, for Hume raises two fundamental issues. First, he questions whether there is any single form of critical enquiry that allows one to stand back from the various kinds of cognitive projects and pass judgement on them, and in particular whether this is a task to which philosophy, in the form of metaphysics, is ﬁtted. Hume argues that there is no such single form of enquiry.65 64

Vico, for example, offered a profound analysis of mythical thought, and he set out a very different model of knowledge from the predominant natural-philosophical one. But he looks more promising in this context than he actually is, because he does not engage with natural-philosophical models except in the most abstract terms (those of Cartesian metaphysics), and the connection between his two enterprises is marginal at best. His model of knowledge turns on the idea of ‘maker’s knowledge’. That is, he argued that we have special access to the civil world, a kind of access that we do not have to the natural world, which is due to our having created the former but not the latter. This is because making something puts one in a special cognitive relation to what one has made, and the general importance and interest of the ‘maker’s knowledge’ principle derive from the fact that history and society can be considered to be human artefacts (by contrast with nature, which is a divine artefact), which means that we can have a special kind of understanding of these, not available in natural knowledge and more secure than it. See Stephen Gaukroger, ‘Vico and the Maker’s Knowledge Principle’, History of Philosophy Quarterly 3 (1986), 29–44. 65 It is interesting that doubts about this role for metaphysics were being raised around the same time in the Wolfﬁan metaphysical tradition. In his Aesthetica (Frankfurt, 1750), Baumgarten on the one hand treats both the understanding and sensation as leading to higher metaphysical truths, while on the other treating them as autonomous and possibly conﬂicting. See the brief discussion in Ted Kinnaman, ‘Aesthetics before Kant’, in Steven Nadler, ed., A Companion to Early Modern Philosophy (Oxford, 2002), 572–85: 578–82.

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Second, where such a question had been answered in the afﬁrmative in those eighteenth-century projects traditionally associated with ‘the Enlightenment’, it was on the assumption that such a critical task was the duty of ‘reason’, however that was identiﬁed. But Hume raises the fundamental question, inherent in the eighteenth-century sensibility tradition, whether understanding of the world and our place in it is exhausted by reason, and he answers that it is not. Reason requires marshalling understanding of the world into a propositional form, but Hume argues that understanding is in fact a balance of propositional and nonpropositional forms, where this contrast is to a large extent associated with one driven by speciﬁcally natural-philosophical concerns, that between systematic and natural-historical kinds of understanding. It is therefore a crucial part of his project that he examine both religion and philosophy in terms of what, in the former case, he explicitly calls ‘a natural history’. Although the term ‘natural history’ does not denote a history in the modern sense, that is, a diachronic account,66 it is worth stressing from the outset not only the important role that history proper plays in Hume’s thinking, but also the importance of identifying just what role this is. Hume’s approach was resolutely historical, but by contrast with the genealogical approaches of the philosophes, in which the aim was as often as not a reduction of Christianity to a ‘conspiracy of priests’, his treatment of religion was more along the lines of the experimental or phenomenological versions of natural philosophy. That is to say, it was primarily a matter of establishing connections between phenomena, and paramount among the phenomena connected were religious and philosophical thought and practice, for it is one of the distinctive features of Hume’s treatment that Christianity, in its contemporary forms, turns out to lie at the intersection of philosophical and religious thought and practice. What is distinctive about his account is that he uses this historicization of religion and philosophy to open up questions about the nature of propositional understanding. He manages to transform what at ﬁrst looks like yet another criticism of the limits of systematic understanding into a far more profound and difﬁcult form of enquiry, into the limits of a propositional understanding of the world. The appraisal of sensibility in our understanding of the world and our place in it no longer hinges on the existence or otherwise of innate ideas, but is now a conceptual issue about the forms of understanding available to us and in what circumstances it is appropriate to draw on them. The procedure he uses can be glimpsed most fully in what is by far its most elaborate version, his history of British politics. Following the lack of response to his Treatise, Hume turned his intellectual talents to essays—concentrating on political and economic questions—and a multi-volume history of England: these, especially the latter, were very successful, and it was through them that 66

On what he identiﬁes as the ‘temporalization of history’ in the early modern era, see Reinhart Koselleck, Futures Past: On the Semantics of Historical Time (Cambridge, Mass., 1985), 21–38.

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he was known. The History of England provides a concrete narration of the practice of politics (including ecclesiastical politics), in which the theme of liberty and authority discussed in the Treatise and in the Essays is developed in a distinctive way. The treatment is twofold. Hume explores the origins of liberty both in human nature and in the contingent circumstances of the history of England (and to a lesser extent Europe), with a view to building up the concept on a ﬁrm basis, from which he can then criticize what he considers to be mistaken conceptions of liberty, particularly those espoused by radical democratic elements among the philosophes. What emerges from the Essays is that there must always be a balance between liberty and authority, and the History shows that that balance is shifting, depending on the historical circumstances, and always precarious. As for the writing of history itself, in his essay ‘Of the Rise and Progress of the Arts and Sciences’, Hume develops his idea that the relation between cause and effect is a matter of inference67 rather than direct perception, arguing that such connections are more easily established when changes in human conditions produce changes in large-scale human behaviour, as in the case of the rise and progress of the arts and sciences, or that of the rise and progress of commerce, rather than on an individual level, and he distinguishes two forms of history corresponding respectively to cultural change and to individual actions.68 By contrast with the attempt of the Encyclope´dists in France to promote conjectural history at the expense of other forms of history, both Hume’s History of England and William Robertson’s equally ‘philosophical’ History of Scotland (1759) combined the two forms of history that Hume distinguishes: a narrative of deeds with an account of the development of forms of collective progress in the arts, sciences, and commerce.69 Given Hume’s broader aims, the idea of ﬁnding a way to accommodate or balance competing considerations, rather than forcing a choice of one set over another, is not simply an issue about how to write history, but an integral aspect of his conception of what understanding the human condition consists in. Livingston puts the point well, noting that much of Hume’s philosophy is an attempt to show that ‘what we would call rationality in science, morals, politics, and religion is the result of a long, gradual, and largely unreﬂective evolution of conventions, the end of which is the coordination and satisfaction of conﬂicting human needs and desires.’70 The example that Hume works out in detail along these lines is that of the British constitution, which is not the work of conscious design: rather he sets out to show that its provisions were, as Livingston notes, largely unintended results of painful and unwilling adjustments forced by over a century of political chaos. 67 Such inference is to be guided by ‘rules by which to judge of causes and effects’, given in the Treatise, Book I, Part III, sect. xiv. 68 Hume, Essays and Treatises, i. 111–37. 69 See the discussion in Pocock, Barbarism and Religion, ii. 184–5 and, more generally, 177–98. 70 Livingston, Philosophical Melancholy and Delirium, 38.

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To understand how this approach works in the case of religion and philosophy, it will be helpful to begin by considering the two fundamental questions that Fontenelle had opened up, and which were to provide a focus for much eighteenth-century anthropological thinking about religion. The ﬁrst, raised by the Histoires, was whether modern religion might in fact be a form of superstition: a criticism that Christians had unhesitatingly used to dismiss other religions—and which Protestants had unhesitatingly used to criticize Roman Catholicism—is now turned on Christianity itself. The idea was that perhaps superstition was not a perversion of Christianity after all, but in large part constitutive of it, as Hobbes and Spinoza had earlier argued. Hume is not particularly concerned with this question, not because he does not identify various beliefs as superstitions, for he does, but rather because the issues do not turn on the question of reason versus superstition for him. Fontenelle’s second question, raised in his Origine, was whether the development of religion took the form outlined in the bible and reinforced by Christian theology. Although he regarded primitive myth-making as hopelessly puerile, and consequently of no interest in its own right, Fontenelle argued that myths are important because they reﬂect a universal human tendency to project into nature one’s own experience, so that gods and goddesses emerge as magniﬁed anthropomorphic projections.71 The interesting thing about these projections is that they reﬂect particular fears and aspirations, and in tracing the origins of religion to such myths, he rules out the idea of a primitive monotheism. This was a radical conclusion, denying something that was widely held by defenders of orthodoxy72 and by deists alike, with Voltaire, for example, rewriting ancient paganism so that it was deist rather than polytheist.73 If polytheism was the original form of religious thought, then the widely held view that even the most primitive peoples had a natural—perhaps innate—understanding of God was in jeopardy. After all, such a ‘primitive man’ had Adamic and indeed Noachian origins: the culture in which he lived could hardly have completely forgotten the monotheism of his ancestors (especially given the small number of generations allowed by biblical chronology).74 On Fontenelle’s reconstruction, it would seem 71 Fontenelle is explicitly aware of the great difﬁculties facing the exercise of uncovering a primitive mentality, for all ‘primitive’ societies that we have access to are at least at the mythological stage, and so are not genuinely primitive in the strict sense. 72 It is, for example, a pressing issue in Noe¨l-Antoine Pluche, Histoire du ciel conside´re´ selon les ide´es des poe¨tes, des philosophes, et de Moı¨se (2 vols., Paris, 1739). Note also Cudworth’s insistence that all forms of polytheism—he identiﬁes Orphism, Zoroastrianism, and ancient Egyptian religion as the main forms—asserted the existence of one supreme deity, which he evidently assumes to be effectively tantamount to monotheism: The True Intellectual System of the Universe, i. 308. 73 On Voltaire, see Pocock, Barbarism and Religion, ii. 107. 74 There were various orthodox responses to this problem. The abbe´ Antoine Banier, in his Histoire ge´ne´rale des ce´re´monies, mœurs, et coutumes religieuses de tous les peuple du monde (Paris, 1741), for example, suggests that idol-worship was an extreme reaction of people to the Flood, who, terriﬁed, unthinkingly resorted to this form of polytheism. Some writers—De Brosses, Vico, and

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that monotheism was in fact a later development, the innate and ‘natural’ idea, if there were such a thing, being polytheism. Whereas eighteenth-century atheism or deism confronted Christianity very much on its own terms, the very idea that polytheism might be a, or even the, original form of religious belief historicized Christianity, and opened up the possibility that it might merely be a stage in human development. In The Natural History of Religion, Hume explores—in a way that an account which focused on superstition could not—the advantages and disadvantages of polytheism. His concern, he tells us in the Introduction, is with the origin of religion in human nature, not with any rational grounds that might be adduced for or against it. Religious belief, he notes, is and has always been widespread, but not universal, and, more importantly, the content of the belief has varied so radically that there are no two cases where it has been identical. But one thing, he argues, is manifest from the literature on ‘primitive’ religions: the original forms of religion are always polytheist.75 He sets out, therefore, to reconstruct why this might have been the case, and why we witness a subsequent transition to monotheism. Primitive religion arose, he argues, not from a search for fundamental truths but as a practical way of dealing with and controlling the fear and dread arising from a hostile environment.76 It results from a form of projection of human qualities onto inanimate things, and the move from polytheism to theism has nothing to do with rational argument. There is no general progress towards ‘reason’ in the development of religious belief. This is evident in the present day, he argues, and ‘since the vulgar, in nations which have embraced the doctrine of theism, still build it upon irrational and superstitious principles, they are never led into that opinion by any process of argument, but by a certain train of thinking, more suitable to their genius and capacity.’77 This prompts the question of why monotheism has replaced polytheism. In weighing the beneﬁts and disadvantages of polytheism and monotheism, Hume devotes considerable attention to the inherent toleration of polytheists and the lack of it among theists, noting that ‘if, among Christians, the English and the Dutch have embraced the principles of toleration, this singularity has proceeded from the steady resolution of the civil magistrate, in opposition to the continued efforts of priests and bigots.’78 Moreover, the idea of an inﬁnitely superior God Boulanger—preserved Adamic monotheism by default, by beginning their accounts with postdiluvian polytheism. See Manuel, The Eighteenth Century Confronts the Gods, 139–40. 75 Hume, Essays and Treatises, ii. 401–14 (Natural History, Sect. I to III). 76 Ibid., ii. 408 (Sect. II). 77 Ibid., ii. 428 (Sect. VI). In other words, while there may be good arguments for monotheism, this is not what conduces people generally to monotheism. Instead, ‘though the original notions of the vulgar represent the Divinity as a limited being, and consider him only as the particular cause of health or sickness, plenty or want, prosperity or adversity; yet when more magniﬁcent ideas are urged upon them, they esteem it dangerous to refuse their assent.’ Ibid., 432 (Sect. VII). 78 Ibid., ii. 439 (Sect. IX).

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fosters submission and abasement, whereas when gods are conceived as only ﬁnitely superior the virtues which ﬂourish are those of ‘activity, spirit, courage, magnanimity, love of liberty’.79 Given that there are such signiﬁcant social beneﬁts to polytheism, and given that polytheism is such a natural system, we can imagine its having ﬂourished, so Hume asks why it has not in fact ﬂourished. The chief objection, he argues, is ‘that it is not ascertained by any just reason or authority’, whereas where ‘theism forms the fundamental principle of any popular religion, that tenet is so conformable to sound reason, that philosophy is apt to incorporate itself with such a system of theology.’ The problem is that philosophy soon ﬁnds itself ‘unequally yoked with her new associate; and instead of regulating each principle as they advance together, she is at every turn perverted to serve the purposes of superstition.’80 It is perhaps not remarkable that, when he turns, in the Dialogues Concerning Natural Religion, to a philosophical account of the nature of a single God, something that sums up Christian theology both in content and tenor, it is Malebranche’s account that he quotes.81 Again it is Malebranche who is the archetypal metaphysician, just as he was on causation. And the conclusion is the same in both cases, namely that: ‘All the philosophy, therefore, in the world, and all the religion, which is nothing but a species of philosophy, will never be able to carry us beyond the usual course of experience, or give us measures of conduct and behaviour different from those which are furnished by reﬂections on common life.’82 By tying in his account of religion with an account of philosophy, Hume makes the critical evaluation of religion feed into a critical evaluation of philosophy, conceived no longer simply as the language of criticism from which it itself is immune, but rather as something deeply problematic in its standing, for philosophy must retain an autonomy as the vehicle of criticism of nonphilosophical thought, while at the same time taking its place as a form of practice which, like religion, has its roots in human nature and as such develops in various ways which can be analysed. The new task that Hume identiﬁes is not to analyse philosophy at the level of doctrine, however, for this is uncontentious and is indeed part of any philosophical programme, but rather to undertake an analysis at the level of the philosophical enterprise itself, an analysis that describes phenomenologically—as a ‘natural history’—rather than acting as a neutral arbiter, for as we have seen Hume deems the latter enterprise impossible, and not just in the guise of metaphysics, but simpliciter. It is helpful to understand the parallels with the investigation of religion here. For one important strand in the late seventeenth-century historicization of religion, that exempliﬁed in Bayle for example, the point was not to investigate the development of religious doctrine, something that scholars had been doing for centuries, but rather to enable one to stand back from religion in general, and Christianity in particular, and to 79 82

Ibid., ii. 441 (Sect. X). 80 Ibid., 443 (Sect. XI). 81 Ibid., 489–90. Enquiries Concerning the Human Understanding, 38 (Sect. XI).

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consider it as an object of study without any assumptions as to the validity of its claims to truth. Hume in effect adapts this procedure, suitably reﬁned, to philosophy: that is, to metaphysics, which he treats as constitutive of philosophy for these purposes. This is not to deny legitimacy to metaphysics, or more generally to an a priori systematic discourse, however. Hume thinks that to do without systematic enquiry would be to ‘cut off all science and philosophy’,83 and this is something that he is not prepared to give up: the difference between barbarism and civilization is that between living what Hume terms the ‘common life’ unreﬂectively, and engaging critically with it. The point is rather that putting ourselves at a critical distance, devising a language and a set of resources by which we can analyse the respective merits of natural philosophy and Christian teaching for example, cannot be a matter of metaphysics, or indeed any single form of enquiry.84 Hume’s view on metaphysics, and philosophical reﬂection generally, is that it puts us in a position to participate critically in our culture. Indispensable as it is in this respect, however, it is not unique. Moreover, participation is quite different from, and indeed stands in contrast to, the idea of an autonomous discipline standing above others in judgement on them. In this way, Hume can be seen as developing the insights of the attempts to understand sensibility and its relation to reason, attempts that dominated natural philosophy in the second quarter of the eighteenth century. Hume himself connects his work to natural philosophy, describing the Treatise in its subtitle as ‘being an attempt to introduce the experimental method of reasoning into moral subjects’. His models here are Boyle and Newton. Because of the way in which Boyle integrated theological and natural-philosophical considerations, he was considered the pre-eminent natural philosopher at the University of Edinburgh while Hume was a student there, and we know that Hume was very familiar with his writings.85 As for Newton, Hume knew his Opticks, above all the work on colours, but there is no reason to think that he had a signiﬁcant grasp of the Principia, or of the mathematics required for understanding it. The central contrast here is that between the ‘experimental method’ and systematic enquiry. 83

Cf. the Enquiry on how to deal with scepticism: ‘My practice, you say, refutes my doubts. But you mistake the purport of my question. As an agent, I am quite satisﬁed in the point; but as a philosopher, who has some share of curiosity, I will not say scepticism, I want to learn the foundation of this inference.’ Enquiries Concerning the Human Understanding, 38 (Sect. IV, Part ii). 84 The incapacity of metaphysics here is fundamental for, he tells us, it is ‘impossible upon any system to defend either our understanding or senses’. Treatise, 218 (Book I, Part IV, Sect. 2). 85 See Michael Barfoot, ‘Hume and The Culture of Science in The Early Eighteenth Century’, in M. A. Stewart, ed., Studies in the Philosophy of Scottish Enlightenment (Oxford, 1990), 151–90. See also James E. Force, ‘Hume’s Interest in Newton and Science’, Hume Studies 13 (1987), 166–216; Eric Schliesser, ‘Hume’s Missing Shade of Blue Reconsidered from a Newtonian Perspective’, Journal of Scottish Philosophy 2 (2004), 164–75; John P. Wright, ‘Metaphysics and Physiology: Mind, Body and the Animal Economy in Eighteenth-Century Scotland’, in M. A. Stewart, ed., Studies in the Philosophy of Scottish Enlightenment (Oxford, 1990), 251–301; and Eric Schliesser, ‘Newtonianism and Anti-Newtonianism in Hume’, Stanford Encyclopedia of Philosophy (2007): .

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Experimental natural philosophy and systematic natural philosophy come on either side of the divide, and Newton’s Opticks and his Principia were taken as representing the two streams in the eighteenth century.86 The systematic enterprise that Hume wants to examine is not a naturalphilosophical one, however, but metaphysics. Starting with Descartes’ Principia Philosophiae, there had been an intimate connection between systematic metaphysics and natural philosophy. Those metaphysical systems that appeared in the wake of Descartes—those of Spinoza, Malebranche, and Leibniz—each had its own intimate connection with natural philosophy. Hume rejects both the (originally Thomist) idea that metaphysics provides a neutral language, or a neutral set of resources, by which to adjudicate the competing claims of cognitive disciplines such as natural philosophy and theology; and he rejects the (originally Scotist) idea that metaphysics provides a fundamental form of discourse in which the competing claims of cognitive disciplines such as natural philosophy and theology can be grounded. In both these forms of metaphysics, a combination of a priori postulates and a highly systematic—typically deductive—form are taken to secure that nothing falls outside their scope: a search for closure is an integral part of the exercise. It is precisely this search for closure that is questioned in Hume. The stress on the important role of sensibility in our thinking generally, and the attempt to think through what a form of comprehension that was not the product of a single system would be like, are combined, so that they become transformed into a questioning of the idea that all understanding takes a propositional form. Although the questions of sensibility and non-systematic understanding can be traced back to Locke, and were a feature of the French culture in which he composed the Treatise, Hume’s work was either completely ignored, or, later, effectively neutralized, in that the reaction to it was to treat Hume as a sceptic, as someone who (a` la Berkeley) ingeniously questioned something we all know to be true, such as the existence of causes, thereby representing a ‘dead end’ in the history of philosophy, as Bertrand Russell was to put it.87 But this is to miss the profoundity of Hume’s solution, which is not a sceptical one. At the most general level, what Hume is questioning is the attempt to found any cognitive enterprise—natural philosophy, morals, politics, and religion—on the basis of an autonomous reason or rationality. He is not denying that natural philosophy paradigmatically embodies reason. Rather, he is arguing that it is an egregious and dangerous error to imagine that, were something to embody reason paradigmatically, that would thereby entitle it to act as a model for all human understanding. He is offering an account of ‘human understanding’ whereby it is a judicious balancing of propositional and non-propositional considerations, of considerations of reason and sensibility. To the extent to which natural 86 87

This is established in detail in Cohen, Franklin and Newton. Bertrand Russell, A History of Western Philosophy (New York, 1945), 660.

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philosophy offers a model for understanding here, it takes the form of what Hume terms ‘natural history’, something deriving from the experimental philosophy tradition and its empiricist successor, and which he uses to naturalize enquiry on the one hand while denying both systematicity or even a uniﬁed programme to natural philosophy on the other. It is entirely destructive of the idea that natural philosophy constitutes a single form of understanding, and therefore of the idea that it can act as a model for knowledge in the sense in which its proponents, from Fontenelle onwards, intended.

Conclusion By the middle of the eighteenth century, a paradoxical situation had arisen regarding the standing of natural philosophy. On the one hand, the elevated place it had achieved remained secure, and indeed was reinforced as naturalization became a dominant explanatory strategy. Above all, the introduction of considerations of sensibility into the understanding of natural philosophy began to allow the naturalization of moral and political philosophy. On the other hand, those features of natural philosophy that had been considered, most notably by mechanists, to mark it out as a cognitive paradigm in the ﬁrst place were not only now considered by most natural philosophers to be mistaken, but natural philosophy itself had largely fragmented into different disciplines, holding out no hope for a single, uniﬁed model for knowledge. Seventeenth- and early eighteenth-century thinkers would have considered this an admission of failure: as would many in the late eighteenth and nineteenth centuries, as a commitment to the idea of natural philosophy as an essentially systematic enterprise was revived. Such a failure would, moreover, have been taken to undermine the ability of natural philosophy to act as a cognitive model. But in the mid-eighteenth century, the situation was not so clear cut, and many thinkers took the lack of unity of natural philosophy to reﬂect facts about the nature of understanding, and about the nature of the world. The fragmentation of knowledge, for example, reﬂected the fragmentation of the world, as revealed in those disciplines devoted to empirical exploration, as opposed to attempting to impose artiﬁcial systems on the world. It is within the context of such a conception that the naturalization of the traditional humanistic disciplines proceeded, rather than in the context of an attempt to understand human behaviour on a reductive model derived from some supposedly canonical form of natural philosophy. Nevertheless, if, as I have suggested, the arguments of Diderot, Hume, and others that understanding consists in a balance of reason and sensibility offer us an insight into how we might ﬂesh out such a position in a satisfactory way, then it cannot be denied that the situation reached by mid-century was highly unstable, and that this kind of solution to the problem of human understanding soon began to be seen as less a solution and more a sharpening of the dilemma. At this point, we enter a new era in the development of a scientiﬁc model for understanding, one in which there is a revival in the fortunes of systematic understanding. Whether or not this marks an advance will be a matter for future volumes.

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Yeo, Richard. Encyclopedic Visions: Scientiﬁc Dictionaries and Enlightenment Culture (Cambridge, 2001). ——‘John Locke and Polite Philosophy’, in Conal Condren, Stephen Gaukroger, and Ian Hunter, eds., The Philosopher in Early Modern Europe: The Nature of a Contested Identity (Cambridge, 2006), 254–75. Yolton, John W. Perceptual Acquaintance from Descartes to Reid (Oxford, 1984). ——Locke and French Materialism (Oxford, 1991). Young, A. W., Leafhead, K. M., and Szulecka, T. K. ‘The Capgras and Cotard Delusions’, Psychopathology 162 (1994), 226–31. Young, Brian W. Religion and Enlightenment in Eighteenth-Century England: Theological Debate from Locke to Burke (Oxford, 1998). Yushkevich, Adolph Pavlovich. ‘The Concept of Function up to the Middle of the 19th Century’, Archive for History of Exact Sciences 16 (1976), 37–85. Zammito, John H. Kant, Herder, and the Birth of Anthropology (Chicago, 2002).

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Index Abbot, George, Archbishop (1562–1633) 378n.72 Abra de Raconis, Charles Franc¸ois de (1580–1646) 20n.15 abstraction 4, 11, 20, 27–8, 30, 98, 125, 141–7, 210, 236, 244–7, 251, 269, 280, 283–4, 285, 289, 194, 301, 303, 306, 320, 325, 369, 372, 389, 392–3, 408–16, 434, 442–3, 444n.64 Acade´mie d’Architecture 234 Acade´mie des Arts 234 Acade´mie des Inscriptions et Belleslettres 233, 234, 258, 374 Acade´mie des Jeux Floraux 234 Acade´mie des Peinture et Sculpture 234 Acade´mie des Sciences 210, 212–17, 229–56, 267–8, 274–5, 294, 317–18, 321n.35, 343–4, 357, 369, 376, 387 Acade´mie Franc¸aise 234, 236n.16, 236n.17, 241, 273 Acade´mie Royale des Beaux-Arts 234 Aepinus, Franz Ulrich Theodesius (1724–1802) aether 83–94, 185, 322–3, 335, 326, 329, 331, 334–5, 340, 346 Aldrovandi, Ulisse (1522–1605) 277 Alembert, Jean Le Rond d’ (1717–83) 4, 27n.35, 156, 211n.75, 235, 274–6, 279–87, 306–27, 420, 423, 427–8, 433–7, 444 Alexandre, Noe¨l (1639–1724) 428 Amerpoel, Johannes ( ﬂ. 1667) 35n.52 analysis 27–8, 243–3, 246, 251, 286, 311, 324, 302n.4 anatomy 34, 163–4, 380, 396 ancients versus moderns 233, 241–2, 245 Anglicanism 42, 51, 262 Anselm of Canterbury (1033–1109) 40 Apollonius (262–190 BCE) 136, 138

a priori truths 29, 72n.32, 142, 145–7, 149, 215, 266, 295–6, 306–27, 336, 403, 450, 451 Aquinas, Thomas (1225–74) and Thomism 17, 19, 25, 33, 106, 244–5n.42 Arbuthnot, John (1667–1735) 87n.78 Archimedes (c.287–12 BCE) 136 Arianism 265 Aristotle (384–22 BCE) and Aristotelianism 11, 25, 47, 106, 164, 435; natural history 188–9, 366, 378, 380; matter theory 331–2, 336; metaphysics 17–18, 23, 108, 122; natural philosophy 5, 6, 23, 30, 57, 58, 59, 152, 244, 250, 297–9, 366; sensory knowledge 176–81 Arnauld, Antoine (1612–94) 122, 140, 159, 170, 175, 182–3, 409–10 Artedi, Peter (1705–35) 192n.19 astronomy 22, 181, 235, 251n.66, 274, 361 atheism 13, 46–8, 50, 258, 260, 448 atomism: see micro-corpuscularianism Augustine of Hippo (354–430) and Augustinianism 25–6, 28–9, 105, 171, 432 authority, scientiﬁc 2, 232–47 authority, religious 24–5, 33, 34, 50–1, 167, 259–60 Averroes [Ibn Rushd] (1126–98) 245 Bacon, Francis (1561–1626) 31n.41, 232, 234, 277, 280, 284, 335, 419, 422, 434–5 Baglivi, Giorgio (1668–1707) 355, 396 Baillet, Adrien (1649–1706) 240 Baltus, Jean (1667–1743) 431n.25 Banier, Antoine (1673–1741) 447–8n.74 Bauhin, Caspar (1560–1634) 189

494

Index

Bayle, Pierre (1647–1706) 42, 48, 150n.3, 231, 240–1, 259, 267, 271–3, 288, 403, 422, 424, 430, 431n.25, 449 Beccaria, Giambattista (1716–81) 349 Beeckman, Isaac (1588–1637) 111 Benedict XIV, Pope (1675–1758) 245 Bentley, Richard (1662–1742) 37, 46–7, 90, 334 Berkeley, George (1685–1753) 125n.73, 141–3, 156–7, 171, 284, 412–13, 439, 451 [Berlin] Academy of Sciences and Belles-lettres de Prusse (Societas Regia Scientiarum to 1744) 275, 288n.92, 320n.30 Bernoulli, Daniel (1700–82) 304–5, 318–19, 322, 324, 371–2n.50 Bernoulli, Jakob (1654–1705) 56–7, 70, 134–5, 147, 244, 302, 305, 318, 324, 380n.75 Bernoulli, Johann [ Jean] (1667–1748) 57, 70, 75n.46, 134–5, 145, 147, 244, 248, 253, 255, 286, 302, 304–5, 318–19, 324 bible, the: Berleburger Bible 40n.71; biblical chronology 372–4; biblical philology 25, 40; Genesis 2, 32–40, 375; Wertheim Bible 39n.69; scriptural interpretation 50–1 Bignon, Jean-Paul (1662–1743) 236, 242 biomechanics 58, 190, 328, 355, 387–8, 394–5 Birch, Thomas (1705–1766) 87n.78 Bisterfeld, Johann Heinrich (1605–55) 106n.19 blindness 409, 411–16 Blome, Richard (d.1705) 428 Blount, Charles (1654–93) 431–2 Bodin, Jean (1530–96) 434 Boerhaave, Hermann (1668–1738) 338–40, 396 Bolingbroke, Henry St John, 1st Viscount (1678–1751) 260–1

Bonnet, Charles (1720–93) 357–8, 360, 414n.75 Bordeu, The´ophile (1722–76) 396, 399–401 Borel, Pierre (c.1620–71) 237n.21 Boscovich, Roger Joseph (1711–87) 305, 345–7 Bossu, Rene´ le (1631–80) 106n.19 Bossuet, Jacques–Be´nigne (1627–1704) 260, 425, 432 Bossut, Charles (1730–1814) 324 botany 187–97, 332 Bouguer, Pierre (1698–1757) 256 Boulanger, Nicolas–Antoine (1722–59) 366–7n.53, 447–8n.74 Boyle, Robert (1627–91) 86, 165–6, 171, 213, 219, 245, 344; colour 181, 299–300; experimental natural philosophy 332, 450; physicotheology 30–2; pneumatics 6, 153–5, 157–61, 173, 201, 204–5, 209, 217, 301 Brahe, Tycho (1546–1601) and the Tychonic system 62, 152 Brerewood, Edward (c.1565–1613) Breynius, Johann Philip ( ﬂ. 1680–1764) 377n.67 Brissot de Warville, Jacques–Pierre (1754–93) 235n.15 Browne, Thomas (1663–1704) 199 Brucker, Jacob (1696–1770) 276–7n.51 Bruno, Giordano (1548–1600) 237 Buffon, Georges Louis Leclerc, Comte de (1707–88) 194–6, 283–4, 344–5, 350, 356, 363–83, 389, 400 Buonanni, Filippo (1658–1723) 367 Burnet, Thomas (c.1635–1715) 2, 32, 34–40, 86, 367, 372 Butler, Charles (d. 1647) 401n.35 calculus 27n.36, 57, 70, 125–45, 242–4, 252, 316–17, 437n.44 Cambridge Platonists 19; see also Cudworth

Index Carre´, Louis (1662–1711) 134n.96 Cartesianism 5, 13, 21–30, 58, 92, 140, 170–84, 214–17, 234, 235, 251, 264, 330, 355, 409–10, 434 Cassini, Jacques (1677–1756) 234n.10, 253, 255 Cassini, Giovanni Domenico [ JeanDominique] (1625–1712) 78, 147n.138 Catholicism 42, 50, 243–6, 259, 262, 278, 357, 372, 429–30 causation 28, 153–5, 164–6, 171–84, 185, 217–25, 294–304, 307–17, 333 Cavalieri, Bonaventura (1598–1647) 127–8 centrifugal force 14, 87–8, 306 centripetal force 66, 87–8, 247–9 Cesalpino, Andrea (1519–1603) 188–9, 366 Chambers, Ephraim (1680–1740) 273–4, 276 Charlemagne (742–814) 425n.9 Charleton, Walter (1619–1707) 85 Chaˆtelet, Gabrielle E´milie Le Tonnelier de Breteuil, marquise du (1706–49) 263, 285n.84, 304 chemistry 6, 7, 149, 187–8, 252, 289, 331–6, 345, 350–4, 355, 361, 362, 387, 394 Cheselden, William (1688–1752) 415–16 Cheyne, George (1673–1743) 16, 334 China 48, 260, 373, 402, 403, 425–6 Christianity 1–3, 11–16, 30–54, 160, 266–7, 375n.60, 421 chronology 372–6, 424 Cicero, Marcus Tullius (106–43 BCE) 31, 47, 423 Clairaut, Alexis (1713–65) 134n.96, 135n.101, 254, 255–6, 304, 319, 437n.44 clarity and distinctness, criterion of 23, 26, 32, 83, 107, 174, 209, 243–4, 246, 258, 289, 302n.4, 310, 316 Clarke, Samuel (1675–1729) 11, 13, 42, 48–9, 119, 252, 334–5, 443

495

classiﬁcation: see taxonomy Clauberg, Johannes (1622–65) 170 Clement of Alexandria (c.150–c.215) 430 cognition and cognitive values 1, 3, 4, 7, 24–5, 33, 54, 230–1, 267, 282, 387–420 Colbert, Jean–Baptiste (1619–83) 232–4, 236, 242, 318 Coleridge, Samuel Taylor (1772–1834) 185 College of Physicians 161, 162, 387 Collins, Anthony (1676–1729) 52–3 collision 15, 27, 68, 81, 109, 117–19, 123–4, 307–17 colour 26, 175–7, 181–4, 197–8, 299–300, 410 comets 14–15, 38, 48, 259, 376 Condillac, E´tienne Bonnot de (1715–80) 231–2, 275, 284–5, 381–2, 389, 409, 413–15, 417 Condorcet, Marie Jean Antoine Nicolas de Caritat, marquis de (1743–94) 236n.16, 327, 437n.44 Confucius (551–479 BCE) 260 Connaissance des Temps 235 Conring, Hermann (1606–81) 140 conservation principles 88, 109, 117–20, 123–4, 347–8, 394 Conti, Antonio Schinella (1677–1749) 374 Copernicus, Nicolaus (1473–1543) and Copernicanism 152 Cordemoy, Ge´raud de (1626–84) 170, 214n.91 Corneille, Pierre (1606–84) 236 cosmology 14, 56, 214, 294 Coste, Pierre (1668–1747) 150 Cotes, Roger (1682–1716) 85n.68, 250 Cousin, Victor (1792–1867) 244–5n.42 Coyer, Gabriel Franc¸ois (1707–82) 417n.85 Craig, John (d. 1731) 16 creation 16, 17, 30, 32–3, 58, 88, 100, 107, 118, 244, 358n.6, 366, 368n.37, 369, 373, 376

496

Index

Croft, Herbert (1603–91) 36n.55 Crousaz, Jean-Pierre (1663–1750) 260n.9 Cudworth, Ralph (1617–88) 110, 443, 447n.72 Cumberland, Richard (1631–1718) 49–50 Dale, Anthonie van (1638–1708) 431–2 Daubenton, Louis-Jean-Marie (1716–99) 363 De Clave, Estienne ( ﬂ. 1620s) 212–13 De la Fayette, Marie-Madeleine, Comtesse (1634–93) 392 Delisle, Joseph-Nicolas (1644–1720) 255 Democritus (c.460–c.360 BCE) 110 Dennis, John (1657–1734) 184 Denyse, Jean ( ﬂ. 1717) 260n.8 Derham, William (1657–1735) 15n.5 Desaguliers, John Theophilus (1683–1744) 205–6, 257n.1 Desargues, Ge´rard (1591–1661) 100 Des Bosses, Bartholomew (1668–1738) 244, 447–8n.74 Descartes, Rene´ (1596–1650) 17, 152, 156–7, 159, 245, 268, 280, 380–1, 419, 437, 439; algebra 126, 136–8, 302n.4; botany 190; cosmology 55–60, 105–13, 237; development of the foetus 361, 369; earth and planets, formation of the 2, 35, 367, 371–2; epistemology 32, 280–2; laws of nature of 67–8, 306, 347; magnetism and electricity 198–200; mechanics 117–32; mechanism 5–6, 21–6, 55–60, 107–13, 218, 298, 314; optics and vision 68, 175–6, 180, 197; passions 391, 417; sense perception 409–11; weight 80–1, 86; see also Cartesianism Desgabets, Robert (1610–78) 24n.26 Desmarets, Jean Sieur de Saint-Sorlin (1595–1676) 241 Diderot, Denis (1713–84) 4, 232, 269–71, 274–80, 284, 286–7, 324,

363, 382, 389, 393, 401, 407, 409, 413–20, 423, 453 Digby, Kenelm (1603–65) 199 Dilthey, Wilhelm (1833–1911) 156n.10 Dirac, Paul (1902–84) 136n.107 Dolland, John (1706–61) 326 Dubos, Jean-Baptiste (1670–1742) 426n.11 Duclos, Charles Pinot (1704–72) 417n.85 Du Clos, Samuel Cottereau (1598–1685) 213 Dufay, Charles-Franc¸ois de Cisternai (1698–1739) 339–40 Du Hamel, Jean-Baptiste (1624–1706) 106n.19, 236 Du Marsais, Ce´sar Chesneau, Sieur (1676–1756) 419n.95 Duns Scotus, John (c.1265–1308) and Scotism 18, 106, 122 Dupleix, Scipion (1596–1661) 20n.15 Du Roure, Jacques (d. c.1685) 106n.19 Du Verney, Guichard Joseph (1648–1730) 398 dynamics 34, 55–94, 115–25, 134, 304–27, 345–7 earth, formation of: see geology and theory of the formation of the earth; shape of the 247–56, 265 eclecticism 46, 122, 244–5, 276–7, 280 Edinburgh, University of 397, 450 Edwards, John (1637–1716) 430n.23 electricity 6, 91–2, 149, 187, 196–206, 217, 286, 289, 323, 336–50, 355, 356–7, 387, 394 empiricism and experimental natural philosophy 98, 150–86, 204, 217–25, 264, 438–44, 450–2; see also rationalism and empiricism Encyclope´die, the 4 Epicureanism 13, 37, 42, 59, 109, 297–8, 331, 375n.60, 395, 402–3 epigenesis 359–65 Epitectus (55–135) 280 equilibrium 14, 61–2, 69, 309–10, 349 ethics 20, 21, 48–9, 280, 402–20

Index Euclid ( ﬂ. 300 BCE) 127, 136 Euler, Johann Albrect (1734–1800) 323n.38 Euler, Leonhard (1707–83) 143n.127, 148n.141, 288n.91, 304–27, 437n.44 Eustachius a Sancto Paolo (d. 1640) 20 experimental natural philosophy: see empiricism and experimental natural philosophy explanation 6–7, 217–25 Fabri, Honore´ (1607–88) 245 Fall, the 49, 140–1, 404 Fatio de Duillier, Nicolas (1664–1753) 57, 145, 321 Feijo´o y Montenegro, Benito Jero´nimo (1676–1734) 431n.26 Ferguson, Adam (1723–1816) 408 Feynman, Richard (1918–88) 136n.107 Ficino, Marsilio (1433–99) 18–19 Fischer, Kuno (1824–1907) 155–6 Flood, the 34–40, 277–8, 366–7, 374 ﬂuids, the mechanics of 14, 60, 72–6, 145, 317–21 Fontenelle, Bernard le Bouvier de (1657–1757) 3–4, 146, 210, 212, 214, 233, 240–7, 259, 267, 269, 302n.6, 357, 391, 424, 431–4, 447–8, 452 force 27n.35, 28, 72–3, 107–25, 304–27, 345–7; see also centrifugal force, centripetal force, gravity, inertia Formey, Johann Heinrich Samuel (1711–97) 274n.44 fossils 367–8, 374 foundations for knowledge 99 Francke, August Hermann (1663–1727) 287 Franklin, Benjamin (1706–90) 340, 343–4, 347–9 Freind, John (1675–1728) 334 Fre´ret, Nicolas (1688–1749) 258 Froude, William (1810–79) 320n.31 Furetie`re, Antoine (1619–88) 271–3

497

Gale, Theophilus (1628–78) 430 Galenism 161–2, 165 Galiani, Celestino (1681–1753) 186 Galileo Galilei (1564–1642) 58–9, 80, 128, 152, 245, 338; heliocentrism 21–2; mechanics 59–64, 112, 114, 147, 218, 305, 306, 325, 333 Galison, Peter 303–4 Gallois, Jean (1632–1707) 243 gas laws 348 Gassendi, Pierre (1592–1631) 21, 30, 109, 164, 198, 218, 245, 297–8 Geoffrin, Marie The´re`se Rodet (1699–1777) 423 Geoffroy, Franc¸ois E´tienne (1672–1731) 186–7, 206–18, 332, 352–3 geology and theory of the formation of the earth 2–3, 34–40, 366–8, 371–9 geometry 26, 27, 97, 100–1, 126–8, 136, 141–2, 210, 243–4, 280, 309–10, 383 Geulincx, Arnold (1624–69) 24n.26 Gibbon, Edward (1737–94) 1 Gilbert, William (1544–1603) 198, 435 Glanvill, Joseph (1636–80) 157n.15 Glasgow, University of 408 Glisson, Francis (c.1599–1677) 396 God 13–16, 17, 28, 30, 35–40, 49, 107, 174, 282 Godin, Louis (1704–60) 256 Gordon, Andreas (1712–50) Go¨ttingen, University of 396 Grandjean de Fouchy, Jean-Paul (1707–88) 267–8n.28 Grassi, Orazio (1582–1654) 152 Graunt, John (1620–74) 380n.75 Graverol, Jean (1647–1718) 36n.57 Gravesande, Willem Jacob van’s (1688–1742) 186, 285n.84 gravity 6, 14, 28n.37, 56–7, 63–4, 67, 79–94, 116, 144, 145, 147, 154, 185–6, 248, 251–3, 305, 321–3, 331, 333, 337, 345, 362, 396, 438

498

Index

Gray, Stephen (1666–1736) 187, 203–6, 217–18, 300, 301, 339 Gregory, David (1659–1708) 90, 145 Grotius, Hugo (1583–1645) 49 Guisne´e, N. (d. 1718) 134n.96 Habermas, Ju¨rgen 239n.25 Hales, Stephen (1677–1761) 337–8, 356 Halle, University of 287 Haller, Albrecht von (1708–77) 396–9 Halley, Edmond (1656–1742) 64, 81, 376n.63 Harris, John (c.1666–1719) 90n.87, 273–4 Harvey, William (1578–1657) 396 Haug, Johann Friedrich ( ﬂ. 1726) 40n.71 Hauksbee, Francis (c.1666–1713) 91–2, 201–5, 323, 336–7, 340, 342 heat 26, 87, 92–3, 200, 212–16, 337–42, 348, 351–4, 376–8 Hegel, Georg Wilhelm Friedrich (1770–1831) 156n.10 Helmont, Jan Baptista van (1577–1644) and Helmontianism 86, 162, 213 Helve´tius, Claude Adrien (1715–71) 417–18 Herbert of Cherbury (1583–1648) 431 Herder, Johann Gottfried (1744–1803) 32n.43 heredity 360–1, 365–6 heresy 41, 47 Hermann, Jacob (1678–1733) 62n.13, 134, 149 Hesiod (8th century BCE) 430 Hobbes, Thomas (1588–1679) 44–5, 50, 109, 111, 127, 161, 164, 218, 421 Homberg, Wilhelm (1652–1715) 214–16, 351–2, 361 Homer (8th century BCE) 242 Hooke, Robert (1635–1703) 65, 73n.36, 192n.20, 325, 366 Hoˆpital, Guillaume de l’ (1661–1704) 57n.6, 104, 133–4, 144n.131, 145, 248, 304

Houtteville, Aexandre Claude-Franc¸ois (1686–1742) 260n.8 Huet, Daniel (1630–1721) 240, 430n.21 humane learning 380 humanism 4, 12 Hume, David (1711–76) 156–7, 171, 172, 268n.29, 393, 408, 419–20, 453; causation 439–40; metaphysics 439–52; religion 53, 444–52; scepticism 438n.48, 440–4, 451; sensibility 438–52 Hutcheson, Francis (1694–1746) 407–8, 421 Huygens, Christiaan (1629–95) 22, 28, 78–9, 107, 129–30, 138, 154, 157–8, 181, 234; collision 68, 220n.99, 306; magnetism 200n.46; mechanics 28, 56n.5, 61, 111–14, 118–19, 147, 174, 301–2; shape of the earth 252–3 Hyde, Thomas (1636–1703) 428 hydrodynamics: see ﬂuids, the mechanics of hydrostatics 14, 61–2, 333 hylozoism 362 impenetrability 83, 88–9, 108–9, 122–4, 222–3, 311–15, 346–7, 362, 365 Index of Prohibited Books 23, 186, 245 inertia and inertial states 63, 66, 74, 80, 88, 91, 93, 114, 243, 308–17, 333, 362 innate ideas 4, 26, 47, 49, 166–8, 171, 258, 264, 285, 382, 402, 404, 406–8, 411–12, 417, 421, 437, 445, 447–8 inoculation 263 Investiture Controversy (1050–1122) 34 irritability 390, 394–402 Islam 17, 31, 40–1, 47, 103, 421 James, Robert (1705–76) 274 Jansenism 243n.36 Jardin du Roi 212, 369 Jaucourt, Louis de (1704–79) 276n.49

Index Jesuits 22, 47, 234, 235, 243–6, 259, 273, 280, 373, 402, 435 Journal de Tre´voux 243–4, 250, 252, 258, 259, 357, 407 Journal des Sc¸avants 76, 235, 252 Judaism 17, 41, 47, 103, 421, 428, 430 Jupiter (god) 436 Jupiter (planet) 78, 82 Jurin, James (1684–1750) 143n.126 Kant, Immanuel (1724–1804) 98, 156, 186, 239n.25, 244n.42, 286–7, 305, 314, 443 Keill, John (1671–1721) 34, 38, 334 Kepler’s laws 62–3, 77, 82, 114, 116–17, 145, 180, 247, 255, 265, 322 kinematics 28, 60–4, 107, 112, 119–20, 130, 147, 174, 301, 309, 311, 315, 333 Kircher, Athanasius (1602–80) 245 La Chalotais, Louis-Rene´ de Caradeuc de (1701–85) 417n.85 La Cre´quinie`re, Sieur de ( ﬂ. 1704) 428 La Condamine, Charles Marie de (1701–74) 256, 261 La Coste, Betrand de ( ﬂ. 1670s) 235n.15 La Forge, Louis (1632–66) 170 Lagrange, Joseph Louis (1736–1813) 143n.127, 148, 320n.30, 324–5 Lalande, Je´roˆme de (1732–1807) 237n.22 La Mettrie, Julien Offray de (1709–51) 396, 398–9 Lamoignon de Malesherbes, Guillaume-Chre´tien de (1721–94) 278n.60 La Popelinie`re, Lancelot du Voisin de (1541–1608) 434 La Peyre`re, Isaac de (1596–1676) 36 Laplace, Pierre Simon (1747–1827) 14n.4, 325, 327 law 44–5, 180–1 Le Breton, Andre´ (1708–79) 279 Le Camus, Antoine (1722–72) 417

499

Le Clerc, Jean (1657–1736) 243 Leechman, William (1706–85) 408 Leeuwenhoek, Anton von (1632–1723) 359 Le Grand, Antoine (1629–99) 23 Leibniz, Gottfried Wilhelm (1646–1716) 2, 11, 13, 15–16, 19, 29, 89, 97–149, 150–7, 171, 210, 244, 248, 252, 265–6, 283–4, 285, 330–1, 346, 451; calculus 57, 70, 125–41, 210, 244, 249, 302; dynamics 84, 98, 107, 111, 115–25, 220, 305, 306; monads 106, 124n.71, 125, 307–8, 359–40; perspectivalism 2, 99–101; preformation 359–40; politicotheology 42–6, 48, 105; substance, theory of 100, 104, 105–15, 121, 122, 124–5, 196; unity of knowledge 101–4, 121–2, 266, 283–8 Leland, John (1691–1766) 260n.12 Lelarge de Lignac, Joseph Adrien (1710–62) 344–5, 368, 370 Le´mery, Louis (1677–1743), 216–17 Le´mery, Nicolas (1645–1715) 213–15, 361 Leo XIII, Pope (1810–1903) 244–5n.42 Le Roy, Louis (1510–77) 434 LeSage, George-Louis (1724–1803) 321–2 Lescarbot, Marc (c.1570–1641) 428 Lesclache, Louis de (1620–71) 237n.22 Leslie, Charles (1660–1722) 52n.105 Le´ry, Jean de (1536–1613) 47 Leyden jar 206, 342–9 Liceti, Fortunio (1577–1657) 358n.7 life and vital phenomena 6, 58, 331–2, 350, 355–83, 387–8; see also biomechanics Linnaeus, Carl (1707–78) 192n.19, 194–6, 235, 380 Livy (59 BCE – 17 CE) 423 Locke, John (1632–1704) 4, 6, 7, 98, 149, 150–187, 197, 209–11, 217–8, 225, 229, 231, 239n.25, 245, 269,

500

Index

Locke, John (cont.): 274, 288, 299–300, 304, 307, 335, 381, 407–8, 420, 438–40, 451; botany 190–4; Essay Concerning Human Understanding 49, 141–2, 150–1, 157, 159, 163–86, 190–1, 402–6, 421; Essays on the Law of Nature 49, 159, 161; on Christianity 11, 16, 42, 49–53; reception in France 7, 187, 229, 231–2, 257–86, 366; perception 410–12; sensationalism/ sensibilism 4–5, 231–2, 380, 389; species nominalism 190–3, 363, 381; Two Treatises of Government 421–2 logic 20, 21, 280 Louis XIV, king of France (1638–1715) 23, 51, 229, 231, 251, 423, 437n.43 Louis XV, king of France (1710–74) 425 Lovell, Archibald ( ﬂ. 1696) 36n.57 Lull, Ra´mon (c.1232–1315) 40, 100, 103 Luther, Martin (1483–1546) 141n.120 Mach, Ernst (1838–1916) 114n.38 Machiavelli, Niccolo` (1469–1527) 380 Maclaurin, Colin (1698–1746) 143, 185–6, 307, 335, 427n.15 Macquer, Pierre (1718–84) 351 Mabillon, Jean (1632–1707) 424n.7 magnetism 6, 67, 80–1, 149, 198–9 Maillet, Benoıˆt de (1656–1738) 367, 375–6 Mairan, Jean-Jacques Dortous de (1678–1771) 251, 253, 376–7 Malebranche, Nicolas (1638–1715) 2, 89, 107, 140–1, 157, 159, 170–84, 209–12, 243, 284, 307, 344, 392–3, 442, 451; causation 28, 159, 171–84, 209, 220, 439–40; Malebranche circle in the Acade´mie 125, 134, 144, 146–7, 246, 251, 317–18; mathematics 248, 251; metaphysics 24–9, 104–5, 170–84, 439–40, 449; perception 159,

409–10; preformation and pre-existence 359, 379; primary and secondary qualities 298–9 Mallet, Edme´-Franc¸ois (1713–55) 277 Mariotte, Edme´ (c.1620–84) 213, 319 Marsili, Luigi Ferdinando, Count (1658–1730) 368n.37 mass 60, 64, 66, 69, 72–3, 80, 98, 118–19, 124, 253, 196, 308, 309–17, 318, 320, 321, 322, 332, 346, 353, 365, 372 mathematics 1, 28, 59, 70, 73, 171, 209, 243, 274, 289; see also analysis, calculus, geometry, practical mathematics matter theory 5–7, 34, 57–64, 196–206, 211–25, 296–304, 328–83, 387–8, 394, 395–6 Maupertuis, Pierre-Louis Moreau de (1698–1759) 4, 254–6, 263, 267, 344, 354, 360–2, 365–6 mechanics 5–7, 15n.7, 28, 31, 34, 54, 55–94, 146–9, 218–25, 252, 355, 366, 394; rational mechanics 147–9, 171, 246–7, 286, 293–327, 328, 387 mechanism 13–14, 31, 38, 57–64, 97–125, 164–86, 190, 196–206, 213–14, 243, 293–304, 338, 353–4, 366, 387–8, 396; see also biomechanics, micro-corpuscularianism medicine 161–3, 233n.6, 356–7, 387–8, 390, 391, 396 Melanchthon, Philip (1497–1560) 141n.120 Mencius (c.371–c.289 BCE) 260 Me´nuret de Chambaud, Jean Jacques (1733–1815) 401 Mercure galant 236, 240, 241, 242 Mercury 78n.54 Mersenne, Marin (1588–1648) 190, 198 metaphysics 2, 12, 17–30, 43–6, 67, 97–125, 266, 280, 284–5, 287, 347, 439–52 micro-corpuscularianism 6, 7, 26, 57–64, 97–9, 108–9, 153–5, 163–86,

Index 197–203, 216–7, 294–304, 330–54, 357, 387–8; see also mechanism microscope 140–1, 358–9, 364 Middleton, Conyers (1683–1750) 429n.19 mind 26, 107–8, 164, 166–7, 174–84 Molyneux, Thomas (1661–1733) 375 Molyneux, William (1656–98) 191, 411–12, 414–15 momentum 28, 58, 66, 68, 76, 118n.49, 198, 220n.99, 307, 347 monotheism and polytheism 41, 47, 447–9 Montaigne, Michel de (1533–92) 407 Montesquieu, Charles de Secondat, Baron de (1689–1755) 231, 245n.44, 261–2, 275, 381–3, 421, 442–3 Montfaucon, Bernard de (1655–1741) 424n.7 moon, the 78–80 moral sciences, the 380n.75, 383, 389, 393, 440, 444–52 morality 12, 13, 25, 33, 41–2, 46–52, 230, 262, 402–20, 421–2 More, Henry (1614–87) 237n.21 More´ri, Louis (1643–80) 273 Morison, Robert (1620–83) 191 Moses 37–8, 430n.21 motion, transfer of 28, 58, 76; see also momentum Mundinus Mundinius (c.1275–c.1326) 358n.7 Musschenbroek, Pieter van (1692–1761) 186, 342 mythology 33, 34, 39, 42 natural history 30–1, 34, 188–96, 251, 278, 344–5, 355–83, 409, 445, 449–52 natural theology 2–3, 16, 30–40, 230 Needham, John Tuberville (1713–81) 350, 364 Nemeitz, Joachim Christoph (1679–1753) 262 Neoplatonism 18–20, 29, 58, 59, 100, 171, 299 Nestorianism 41

501

Newton, Isaac (1642–1727) 11–16, 35–37, 38, 55–92, 119, 157–9, 174, 184–6, 225, 234n.10, 245, 263–5, 280, 284, 296, 299, 305, 314, 325–6, 330–1, 338, 363, 367, 368, 376–7, 409, 437–40, 450; alchemy/ chemistry 84–6, 89–90; calculus 125–6, 135–40, 146, 243, 255, 305; Chronology of Ancient Kingdoms 373–4; De aere et aethere 88; De gravitatione 55, 88–9, 113, 346; De motu corporum 56, 64–6, 309; De natura acidorum 84n.64, 90; dynamics 61–83, 107, 113–15, 117, 119–20, 145, 147, 148, 248, 253–6, 305–11, 315–16, 371; experiments on the spectrum 6, 94, 153–5, 173, 181, 197–8, 205, 209, 217, 300, 301; magnetism and electricity 200–1, 337, 344; Opticks and Optice, 16, 91–4, 184, 210–12, 251–2, 329, 331, 333–5, 340, 450–1; Principia, 7, 13, 16, 31, 37, 55–92, 97, 115–16, 125–6, 146, 184–6, 219, 247, 250, 251, 294, 304–5, 309, 318–20, 332–3, 345, 376, 437n.44, 450–1; Questiones quaedem philosophicae 84–5 Newtonianism 3–4, 7, 184–6, 229, 261, 267, 274, 334–5, 345–6, 351; in France: 97, 229, 247–56, 257–8, 304–17, 344, 360–1, 437n.44 Nice´ron, Jean-Franc¸ois (1613–46) 101 Nicole, Pierre (1625–95) 169 Nieuwentijdt, Bernard (1654–1718) 135n.102, 141, 243 Noah’s ark 277–8 Nollet, Jean Antoine (1700–70) 206, 332, 339–44, 349–50, 356–7 Nouvelles de la Re´publique des Lettres 240, 273, 431n.25 objectivity 27, 152 occasionalism 26–7, 89, 159, 172 occult qualities 82, 93, 116, 198, 247, 248, 250–1, 265, 437

502

Index

Ockham, William of (c.1285–c.1349) 122 optics and the theory of light 6, 8–19, 34, 197–8, 206; chromatic aberration 325–6; reﬂection 68; refraction 197–8, 251–2, 325–6 Origen (c.185–c.254) 31 paganism 41, 47, 430, 447 Palissy, Bernard (c.1510–90) 367 Paman, Roger (1688–1748) 143 Pappus’ locus-problem 138 Paracelsus (Theophrastus Bombastus von Hohenheim) (1493–1541) and Paracelsianism 162, 188, 212, 214 Paris, University of 234, 278n.58 Pascal, Blaise (1623–62) 100, 130, 139, 257, 264–5 passions 47, 391, 406, 413, 417–18, 438 Patin, Charles (1633–93) 424n.7 Patrizi da Cherso, Francesco (1529–97) 19 Pelagianism 33 Peletier, Jacques (1517–82) 127 pendulum, the 306, 348, 383 Pereira, Benedictus (1535–1610) 22n.20 Perrault, Charles (1628–1703) 213, 233, 241–2 persona of the philosopher 12, 230–2, 235, 268–9, 276–7, 286–7, 416–20 Petty, William (1623–87) 380n.75 philosophe 3–4, 230–2, 268–83, 276–7, 286, 419n.94, 419n.95, 433n.29 phlogiston 353–4 physico-theology 2–3, 12, 15n.7, 17, 30–40, 48–9, 230, 264, 267, 277–8, 372, 374 physics 1, 7, 20, 280, 317–27 physiology 34, 149, 161–3, 289, 331, 355–83, 390, 394–402 Picard, Jean (1620–82) 252 pietists 287–8 planetary orbits 13–16, 28, 61–94, 107, 116 Plato (c.428–c.348 BCE) 21, 26, 48, 105, 268, 419

Pluche, Noe¨l–Antoine (1688–1761) 278n.57, 439, 447n.72 pluralism 7, 42, 154, 266, 288, 304 Poleni, Giovanni (c.1683–1761) 255 politico-theology 24, 43–54, 266 polyp, freshwater (hydra) 358, 362–3, 379 polytheism: see monotheism and polytheism practical mathematics 59, 83, 218, 325 Prades, Jean-Martin de (c.1720–82) 278 preformationism 359–65 Priestley, Joseph (1733–1804) 344n.31 primary and secondary qualities 27, 54, 58, 147, 161, 170–84, 209, 298–9, 328 probability 181, 268–9, 369–40, 371–2, 380n.75, 383n.79 Protestantism 32n.43, 51, 212, 259, 429–30 Pseudo-Dionysios the Aeropagite ( ﬂ. c.700) 19 Pufendorf, Samuel von (1632–94) 44–5 Purchas, Samuel (1577–1626) 401n.35 Puritanism 42 Pyrrhonism 402–3, 424, 441–4 quadrature of the circle 140 race 382 Raey, Johannes de (1622–1702) 106n.19 rationalism and empiricism 98, 155–7; see also empiricism Ray, John (1628–1705) 34, 38, 187–94, 196, 217, 332, 367n.36 reason 4, 40–54, 294, 387–420 Re´aumur, Rene´ Antoine Ferchault de (1683–1757) 251, 343–5, 350, 357, 368, 370 Redi, Francesco (1626–97) 359 Redlhamer, Josef (1713–61) 245 reduction and uniﬁcation 6–7, 12, 97, 150–86, 196–225, 294–304, 317–27, 328–83 Re´gis, Pierre-Sylvan (1632–1707) 24n.26, 76, 214n.91

Index Regius, Henricus (1598–1679) 21 religion 3, 24–5, 40–1, 47, 48, 243–4, 417, 421, 429–33, 447–52 Re´mond, Nicolas (d. 1716) 104, 150 representation 175–84, 298–9, 409–10 Republic of Letters 3–4, 229–56, 257–60, 271–3, 390–1, 393 revelation 3, 11, 17, 22, 24–5, 31 Reyneau, Charles (1656–1728) 134n.96 Richer, Jean (1630–96) 252–3 Rivinus [Bachmann], August (1652–1723) 192–4 Robertson, William 721–93) 446 Robins, Benjamin (1707–51) 143, 318 Roger, Abraham (d. 1649) 428 Rohault, Jacques (1620–65) 21, 28n.37, 214n.91, 334–5 Rolle, Michel (1652–1719) 242–3 Rosmini, Antonio (1797–1855) 244–5n.42 Rousseau, Jean-Jacques (1712–78) 275, 401, 417n.85 Rowning, John (c.1701–71) 247–8n.54, 345 Royal Society 30, 157n.15, 190n.11, 210, 211–12, 253, 275, 387, 421, 434 Russell, Bertrand (1872–1970) 451 sacred texts 17, 31, 430 Sallust (86–34 BCE) 423 salons 163n.31, 214, 237, 239, 240, 393, 423 Sanderson, Robert (1587–1663) 77 Saturn 78 Saunderson, Nicholas (1682–1739) 415–16 Saurin, Joseph (1659–1737) 248 scepticism 243, 282, 438n, 48, 440–4 Schleiermacher, Friedrich Daniel Ernst (1768–1834) 33n.44 Schmidt, Johann Lorenz (1702–49) 39n.69 Schott, Gaspar (1608–66) 245 scientia 18, 20 Scude´ry, Madeleine de (1607–1701) 391–2

503

self, the 412–20 Senac, Jean-Baptiste (1693–1770) 351n.50 Seneca, Marcus Aurelius (c.4 BCE – c.65 AD) 280 sensation and sense perception 26, 49, 150–86, 264, 280–3 sensibility 4–5, 294, 387–420 Shaftesbury, Anthony Ashley Cooper, 1st Earl of (1621–83) 161 Shaftesbury, Anthony Ashley Cooper, 3rd Earl of (1671–1713) 405–8, 418, 421 Shaw, Peter (1694–1763) 351n.50 Shuckford, Samuel (1694–1754) 430 Sibbald, Robert (1641–1722) 424n.7 Sigorgne, Pierre (1719–1809) 247–8n.54 Simon, Richard (1638–1712) 50–1 Simpson, Thomas (1710–61) 144n.128 Sloane, Hans (1660–1753) 203, 212 Smith, Adam (1723–90) 408, 427–8n.15 Socinianism 279 Socrates (469–399 BCE) 268 solar system: see planetary orbits Sorbie`re, Samuel de (1615–70) soul 17, 19, 58 Southey, Robert (1774–1843) 262n.17 Spencer, John (1630–93) 430n.23 Spinoza, Baruch (1633–77) 2, 24–5, 33, 42, 43, 45, 50, 104–6, 154, 156–7, 171, 260, 284, 388n.2, 421, 432, 451 spontaneous generation 350, 359–60, 364, 367n.36 Sprat, Thomas (1635–1713) 16, 30, 236n.19, 434 Stahl, Georg Ernst (1660–1734) 351–2, 360, 394–6, 398 Stanyan, Temple (c.1667–1752) 274 statics 59, 119–20, 309–10 statistics 379, 383n.79 Steno, Nicolas (1638–86) 366 Stillingﬂeet, Edward (1635–99) 404 Stoicism 59, 287, 331, 402–3, 405, 419n, 95

504

Index

Sua´rez, Francisco (1548–1617) 18, 21, 99, 106 Swammerdam, Jan (1637–80) 359 Sydenham, Thomas (1624–89) 157–9, 161–3, 168, 174 systems and systematic understanding 5–8, 18, 22, 31, 97–149, 150–86, 169–70, 269, 283–9, 294–304, 328–83, 438–52, 453 taxonomy 189–97, 217, 332 telescopes: refracting versus reﬂecting 325–6 theology 2, 12, 16, 252, 278; see also natural theology Theophrastus (371–287 BCE) 189 Thomasius, Christian (1655–1728) 44, 267, 287–8 Thorley, John ( ﬂ. 1744) 401n.35 Tillotson, John (1630–94) 52 Toland, John (1670–1722) 42, 52–3, 186, 433n.28 Tolomei, Giovanni Battista, Cardinal (1653–1726) 244 Torricelli, Evangelista (1608–47) 128–9, 245, 318 touch, sense of 382, 411–15 Tournefort, J. Pitton de (1656–1708) 192–4 travel books 402, 409, 421 Trembley, Abraham (1710–84) 358, 361, 363 Trenchard, John (1662–1723) 429 truth 36, 44, 269, 282 Tschirnhaus, Ehrenfreid Walther von (1651–1708) 215 Turgot, Anne Robert Jacques, Baron de Laune (1727–81) 275, 371n.48, 426n.12 uniﬁcation: see reduction and uniﬁcation Uppsala University 288n.92 Ussher, James (1581–1656) 373, 376 Vanini, Lucilio (1584–1619) 260 Varenius, Bernhardus (1622–51) 87

Varignon, Pierre (1654–1722) 28, 144–9, 212, 236, 242–3, 248–9, 251, 304–5 Vausenville, Guillaume Roberger de ( ﬂ. 1770s) 235n.15 Vico, Giambattista (1668–1744) 426–7, 444, 447–8n.74 Vie`te, Franc¸ois (1540–1603) 136 Villemot, Philippe (1651–1713) 247–9 vis viva 68, 118–19, 263n.22, 306, 347 vital phenomena: see life and vital phenomena Voltaire, Franc¸ois Marie Arouet de (1694–1778) 3–4, 229–31, 245, 246, 256, 273, 275, 278–9, 280, 287–8, 344, 345, 383, 389, 422, 423–7, 447; Dissertation sur les changements 367–8; Essai dur les murs 366, 389, 423, 425–6; Le sie`cle de Louis XIV 423, 425; Lettres philosophiques 186, 257–89, 409, 439 vortex theory 14, 28, 56, 74–6, 79, 87, 246–56, 265, 318 Vossius, Gerhard Johann (1577–1649) 431 Vries, Gerhard de (1648–1705) 237n.21 Wallis, John (1616–1703) 57n.6 Warburton, William (1698–1779) 261–2n.15 Warder, John ( ﬂ. 1688–1718) 401n.35 Warren, Erasmus ( ﬂ. 1690) 36n.55 Watson, William (1715–87) 357n.4 Weigel, Erhard (1625–99) 106n.19 Westphalia, Treaty of 43–5 Wheler, Granville (1701–70) 206 Whiston, William (1667–1752) 34, 37–8, 372 White, Thomas (1593–1676) 199 Whytt, Robert (1714–66) 396–400 Wilkins, John (1614–72) 191, 278 will, the 47, 164, 395–6, 397, 401, 407, 412, 439

Index Willughby, Francis (1635–72) 192n.19 Wolff, Christian (1679–1754) 146, 283–8, 329, 444n.65 Woodward, John (1665–1728) 34, 35–6, 367, 372 Worster, Benjamin (1685–1726) 345

Wren, Christopher (1632–1723) 68, 91 Yvon, Claude (1714–91) 278n.58 zoology 379–80

505