Substance and Individuation in Leibniz

SUBSTANCE AND INDIVIDUATION IN LEIBNIZ

J. A. COVER JOHN O’LEARY-HAWTHORNE

CAMBRIDGE UNIVERSITY PRESS

S UBS TA NCE AN D IND IVI D UAT IO N I N L EI BNI Z

This book offers a sustained re-evaluation of the most central and perplexing themes of Leibniz’s metaphysics. In contrast to traditional assessments that view his metaphysics in terms of its place among post-Cartesian theories of the world, Jan Cover and John O’Leary-Hawthorne examine the question of how the scholastic themes which were Leibniz’s inheritance figure – and are refigured – in his mature account of substance and individuation. From this emerges a fresh and sometimes surprising assessment of Leibniz’s views on modality, the Identity of Indiscernibles, form as an internal law, and the complete-concept doctrine. As a rigorous philosophical treatment of a still-influential mediary between scholastic and modern metaphysics, their study will be of interest to historians of philosophy and contemporary metaphysicians alike. J. A. Cover is Associate Professor of Philosophy at Purdue University. He is co-editor of Central Themes in Early Modern Philosophy (Hackett, ), and co-author and co-editor of Philosophy of Science: the Central Issues (W. W. Norton, ). John O’Leary-Hawthorne is Associate Professor of Philosophy at Syracuse University. He is co-author of The Grammar of Meaning (Cambridge University Press, ).

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SUBSTANCE AND INDIVIDUATION IN LEIBNIZ J. A. CO VER J O HN O ’ LE A R Y - HA W TH O RN E

PUBLISHED BY CAMBRIDGE UNIVERSITY PRESS (VIRTUAL PUBLISHING) FOR AND ON BEHALF OF THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE The Pitt Building, Trumpington Street, Cambridge CB2 IRP 40 West 20th Street, New York, NY 10011-4211, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia http://www.cambridge.org © J. A. Cover and John O’Leary-Hawthorne 1999 This edition © J. A. Cover and John O’Leary-Hawthorne 2003 First published in printed format 1999

A catalogue record for the original printed book is available from the British Library and from the Library of Congress Original ISBN 0 521 59394 8 hardback

ISBN 0 511 00910 0 virtual (netLibrary Edition)

For Jonathan Bennett and Jose´ Benardete

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Contents

page ix

Acknowledgments



Introduction  Leibniz and the problem of individuation: the historical and philosophical context



 Relations



 Essentialism



 Haecceitism and anti-haecceitism



 Sufficient Reason and the Identity of Indiscernibles



 Law-of-the-series, identity and change



 The threat of one substance



Bibliography Index

 

vii

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Acknowledgments

We first began thinking about Leibniz’s philosophy at Syracuse University in the late s, with the encouragement and good help of Jonathan Bennett. Since then, we’ve fussed at various bits of Leibniz’s metaphysics, and tried to write about it. Some of those previous efforts have found their way – in various states of revision – into this book: we are grateful to the publishers of Nouˆs, Pacific Philosophical Quarterly, Studia Leibnitiana, and History of Philosophy Quarterly for permission to work that material into chapters –. It is a pleasure to acknowledge the support of our academic institutions and departments, at Purdue University and Syracuse University. We want to thank Pam Connelly (Purdue) for turning typescript material destined for chapter  into electronic form; we also thank Pam, and Sue McDougal and Lisa Mowins (Syracuse), for other efficient secretarial help. We are particularly grateful to the Purdue Research Foundation and the Center for Humanistic Studies at Purdue for financial help and a research fellows’ leave, and to the Research School of Australian National University for a Visiting Fellowship. We have benefited greatly from comments offered at meetings and colloquia where parts of the material in this book were presented: the University of California at Riverside, Purdue University, San Jose State University, Australian National University, Indiana Philosophical Association (Indiana University), Australian Association of Philosophers (Canberra), Midwest Seminar in Early Modern Philosophy (Washington University), the Leibniz in the s Conference (Virginia Polytechnic and State University), the Philosophy and its History Conference (Southern Illinois University), and the second Midwest Metaphysics Conference, MMM (University of Notre Dame). Our intellectual debts are manifold. We have learned too much philosophy and philosophical methodology from Jonathan Bennett and Jose´ Benardete not to say so, and too much about Leibniz from reading ix

x Robert M. Adams, Benson Mates, and Robert C. Sleigh not to say so. Welcome help came from discussing many of the issues treated in this book with various people, and we want to thank them, along with others who (as best we can recall) offered explicit help in the venues above: D. M. Armstrong, Jose´ Benardete, Gregory Brown, Mark Brown, Georges Dicker, Paul Eisenberg, Rudy L. Garns, Brian Garrett, C. L. Hardin, Nicholas Jolley, Manfred Kuehn, Mark Lance, David Lewis, Franklin Mason, Michaelis Michael, Brent Mundy, Alexander Rosenberg, William L. Rowe, Donald Rutherford, Robert C. Sleigh, Stephen Voss, and Timothy Williamson. For helpful written comments on earlier versions of material included here, we are grateful to Jonathan Bennett, Rod Bertolet, Andrew Black, Glenn A. Hartz, Mark Heller, Frances Howard-Snyder, Hide´ Ishiguro, Mark Kulstad, and Ronald J. Rudniki. We are very grateful to William P. Alston, Jose´ Benardete, Michael Gill, and Donald Rutherford for helpful discussion on our more recent efforts to write this book, and above all to Jonathan Bennett and Michael Murray for their careful and extensive written comments on the manuscript in its near-final stages. Special thanks go to Jonathan Bennett, Alfred J. Freddoso, Brian Leftow, and Manfred Kuehn for their assistance with various texts and translation. We are grateful to two anonymous readers for Cambridge University Press for their helpful suggestions, and to our editor Hilary Gaskin and copy-editor Christine Lyall Grant for their patience and assistance. Finally, our warmest gratitude and sincerest thanks to those whose encouragement and close friendship has sustained us throughout: Karen Cover, Michael Gill, Jonathan Bennett, Kimberly Barsema, Tamar Gendler, and Stuart Rachels. In Treatise  (‘‘Advice to Authors’’) of his Characteristics (), Shaftesbury bemoans that stratagem which in his day common practice had made ‘‘a necessary part of elegance,’’ whereby an author ‘‘pathetically endeavors in the softest manner to reconcile his reader to those faults which he chooses rather to excuse than to amend.’’ Some things don’t change. None of the good people mentioned above are very deeply responsible for mistakes in this book. A few of these colleagues have in particular cases given us fair warning: what we have got wrong – and a good bit of what we have got right – we have insisted upon.

Introduction

A lively renewal of interest in Leibniz studies over the past fifteen years has witnessed the publication of many important monographs touching on Leibniz’s metaphysics. The scope and tenor of these books is varied. Happily, Leibniz left plenty to go around – plenty enough to attract philosophers and historians of the early modern period, possessed of various temperaments and interests and talents, with a rich body of early writings,¹ stretches of correspondence or reaction to a contemporary,² sustained discussion of particular philosophical topics,³ broader thematic concerns,⁴ and so on. This book – predictably enough, given our own temperaments and interests – has rather focused historical and philosophical aims. To understand Leibniz’s metaphysics is, in some measure, to understand the historical ancestry of issues drawing his attention. Leibniz inherited a cluster of concerns about individuation that were prominent in the scholastic period; in his lifetime, he both shaped and refigured many of these concerns, and provided what he took to be a defensible treatment of them. Our historical objective is to gain some measure of appreciation for how Leibniz’s views on substance and individuation emerge in the context of certain scholastic themes, and to secure a better understanding of those themes and their place in Leibniz’s overall system. Most of the themes are there already in Aristotle, bequeathed to the ¹ Christia Mercer, Leibniz’s Metaphysics: Its Origins and Development. ² Nicholas Jolley, Leibniz and Locke: A Study of the New Essays Concerning Human Understanding; Robert C. Sleigh, Leibniz and Arnauld: A Commentary on Their Correspondence; Ezio Vailati, Leibniz and Clarke: A Study of Their Correspondence. ³ Mark Kulstad, Leibniz on Apperception, Consciousness and Reflection; Robert Adams, Leibniz: Determinist, Theist, Idealist; Laurence B. McCullough, Leibniz on Individuals and Individuation. ⁴ Benson Mates, The Philosophy of Leibniz: Metaphysics and Philosophy of Language; Catherine Wilson, Leibniz’s Metaphysics: A Historical and Comparative Study; Donald Rutherford, Leibniz and the Rational Order of Nature.





Introduction

medievals as a metaphysic of primary substance. Aristotle, too, left plenty to go around. The received metaphysic of individual substances took on rather the status of an agenda for its scholastic heirs, who fussed at their inheritance in myriad ways – variously polishing and leaving to tarnish and reconstructing the many elements of Aristotle’s scheme. To a great extent, ‘‘rational reconstruction’’ was the name of the game: take form and matter and essence and accident and secondary substance and . . . and do your best for yourself, given your own temperaments and interests. Scholastic interests almost always included bits of theology, themselves items of contention. In a period when one aimed to wed the deliverances of Aristotle (understood this way or that) with the deliverances of sacred Scripture (understood this way or that), one took also the Trinity and the Incarnation and the Eucharist and angels . . . and did one’s best for oneself. Thus on the topic of individuation, as on every other topic, the accounts rendered between the fifth and the sixteenth centuries were many. Boethius and Avicenna and Aquinas and Ockham and Scotus all, of course, had their own shots at it, as did other (by some reckoning) ‘‘minor,’’ less influential figures.⁵ By the time of Suarez’s Disputationes Metaphysicae (), there was a lot of sorting out to do. Inevitably, different philosophers had started with different views about what individuals there are, for which some general principle of individuation should account. Where moderate realists claimed that some things are individuals and others are not, extreme nominalists said that everything was, and extreme realists that nothing was. But granting that there are individuals, some philosophers sought a general principle of individuation for all, while others reckoned them to be of sufficiently different kinds to require distinct kinds of principles. And what is needed in a principle of individuation? Do we seek a general principle that explains the possibility of numerical diversity within a species, or an intrinsic principle by virtue of which this member of a species is distinct from that one, or an account of what it is that makes some member of a species the very individual member that it is, or something else again? Thus some philosophers polished the concepts of communicability and indivisibility, aiming to highlight the fact that individuals (unlike species) don’t divide into members or parts of the same kind; others polished the notions of distinction or numerical difference, aiming to account in the ⁵ For a helpful introduction to the topic of individuation, and excellent treatment of the main players in middle and later scholastic thought, see Jorge J. E. Gracia, ed., Individuation in Scholasticism.

Introduction



first instance for why (say) Plato and Aristotle are two. Whether such an account served as well to explain what it is for some individual to be the very individual it is would depend upon one’s view of extrinsic individuators, or primitive relations of division or difference. In these roles of intrinsic individuators, principles of numerical difference, and the possibility of division within a species entered the candidates of form and matter and essence and existence and accident and haecceity and more still. Suarez did the best for himself with all that, in the dusk years of Scholasticism. But Leibniz did too, in a much less mature and grand effort, in the Disputatio Metaphysica de Principio Individui (). The themes at work in this early document are the themes of scholastic thought; and the emerging ‘‘whole entity’’ doctrine of individuation that Leibniz adopts is unintelligible if viewed from the outside, or simply from the perspective of familiar mature Leibnizian doctrine. Ours is not a book on the Disputatio. Our historical aim is rather to understand those themes at work in it and emerging from it, as they figure – and, most importantly for us, are refigured and augmented – in Leibniz’s mature views of individuation. Perhaps it is true that ‘‘to the end of his life [Leibniz] never wavered in holding to the rather unusual and implausible doctrine that things are individuated by their whole being’. . .;’’⁶ perhaps it is true that Leibniz’s whole-entity account of individuation ‘‘amounts to a nonanswer’’⁷ to the question of individuation. Those are judgments of some confidence. Our hope is to approach their level of confidence, but in a somewhat different assessment, by offering a historically sensitive look at Leibniz’s views on individuation and their place in his larger metaphysic. If our focus is on Leibniz as a contributor to the historical metaphysics of the early modern period, it is no less on the topic of individuation itself. Most readers will have at least a rough working grasp of the cluster of topics we have in mind when speaking of ‘‘Problems of Individuation.’’ Questions of the form, ‘‘What makes a thing a thing of that kind?’’ ‘‘What is it for something to be the very individual that it is?’’ ‘‘What is essential to something’s being an enduring substance?’’ and, indeed, ‘‘What is it to be an individual (as opposed to something else)?’’ will have a ring of familiarity to anyone having even a cursory acquaintance with metaphysics, recent or less recent. Many will be honest ⁶ Benson Mates, The Philosophy of Leibniz, p. . ⁷ Ignacio Angelelli, ‘‘The Scholastic Background of Modern Philosophy: Entitas and Individuation in Leibniz,’’ p. .



Introduction

enough to admit, however, that their grip on such questions is rather tenuous. Some will find themselves having second thoughts about their very intelligibility; others, while relatively secure in their intuitive grip on such questions, will despair of a philosophical framework wherein the issues they raise can be engaged in any satisfactory way.⁸ The philosophical aim of this work is to grasp more clearly the metaphysical problems of individuation by taking seriously how these are played out in the hands of one influential philosopher standing as an important mediary between scholastic and modern metaphysics. One can scarcely hope to deliver on these historical and philosophical aims one at a time. There is no getting clear on the place of scholastic themes in Leibniz’s views about individuation without getting clear on the themes themselves, as the bits of serious philosophy Leibniz took them to be. Thus the question ‘‘What is it for something to be an individual?’’ will mean little or nothing without some grip on the problem of universals. And yet there is no getting clear on that problem without some grip on its historical nominalist glosses, including Leibniz’s (Suarezian) own. Or consider the question ‘‘What is it for something to be the very individual it is?’’ The question is too easily answered if one suspects, as many (in the grip of the Discourse on Metaphysics) wrongly have, that given Leibniz’s complete-concept doctrine, a substance is individuated by a complete list of all its properties. That popular answer emerges – but only after some philosophical trench-work – as inconsistent with any (i) serious essentialism, to some strong or moderate form of which Leibniz was surely committed; moreover that popular answer emerges – after a little historical digging – as inconsistent with a (ii) distinctively scholastic requirement on principles of individuation, to which Leibniz was also committed. The former, modal concern of (i) represents an important augmentation of Leibniz’s Disputatio account, and we shall attend to it at some length. The latter, historical point (ii) is crucial to understanding one source of Leibniz’s commitment to the Principle of the Identity of Indiscernibles, and to his general metaphysic of individual substance as involving active ⁸ One might expect encouragement for the project from Aristotle, if from no one else. But even here the verdict is mixed as to the viability of seeking – as Aristotle would put it – the cause of the unity of things. For after raising precisely that issue in Metaphysics , , he appears to retreat to the unsettling view that the only cause we can really ask after in this context is efficient: ‘‘But, as we have stated, the last matter and the form are one and the same; the one exists potentially, the other as actuality. Thus it is like asking what the cause of unity is and what causes something to be one; for each thing is a kind of unity, and potentiality and actuality taken together exist somehow as one. So there is no other cause, unless it be the mover which causes the motion from potency to actuality’’ (b–). Thanks to Jose´ Benardete for directing us to this passage.

Introduction



form or force. These issues will come clearer in later chapters, where our historical and philosophical aims are handled side by side. Others might approach Leibniz’s metaphysics differently, with different aims, given temperaments and interests and talents different from our own.⁹ While aspiring to advance the current discussion of Leibniz’s philosophy, this book is offered less as a scholarly historical study than as an interpretation and critical appraisal of a central issue in Leibniz’s metaphysics. Each of these three approaches – scholarly history, interpretation, and critical appraisal – has an important place in history of philosophy generally, though this is especially true in the case of a philosopher such as Leibniz. (a) Historical studies are needed in part because, unlike his contemporaries, Leibniz positively encouraged a return to ancient and scholastic accounts in which ‘‘there is much gold buried in the dross,’’ and because his own views witnessed development and contemporary influence. A full accounting of the medieval influences (neo-Platonic as well as Aristotelian) on Leibniz’s thoughts about individuation, tracing these influences within the context of seventeenth-century German university teaching generally, and at Leipzig (via Thomasius and Scherzer, and perhaps Daniel Stahl at Jena) in particular, would require a historical methodology more sophisticated than our own. We must leave it to others. (b) Interpretation, more widely systematic or more narrowly thematic, is needed because – again, arguably more than any other early modern thinker’s – Leibniz’s philosophy is a vast web of interconnected ideas, forming a wideranging system of remarkably broad vision. It is simply not always clear how these ideas are related to one another in forming the system (or even, if you like, systems) that Leibniz himself envisioned. In such cases, one must understand Leibniz as well as one can and try, sympathetically, to fill in the gaps, hoping to balance the textual data with the burden of explaining why Leibniz seems to say what he does. (c) Analysis and critical appraisal of Leibnizian doctrines are important not only because claims from a first-rate philosopher deserve as much, but also because certain of Leibniz’s proposals are in many respects only the first steps in an often complex philosophical proposal, inviting and indeed ⁹ And here perhaps we should note a third aspect of what appears in later chapters, not so much side by side with the historical and philosophical efforts as running through them. It is (by our lights) rather more difficult to think seriously and patiently about deep philosophical issues if one does not believe that there may well be important truths buried in them. Some of the threads pursued in this book may in any case be of serious intellectual interest only to someone who is committed to a Theistic world-view. No apologies here: we have a serious interest in those threads, and do have that commitment.



Introduction

requiring careful assessment of its prospects for being coherently advanced. This, in conjunction with the fact that many of the problems Leibniz confronts are of continuing interest to contemporary thinkers, recommends a serious look at the philosophical claims in their own right, as Leibniz himself approached the claims of his predecessors and contemporaries. Internal and external criticism are the stuff of Leibniz’s philosophical approach, and of our own. We are in the vicinity of warnings. It is perhaps best to issue three of them clearly, up front. () ‘‘Substance and Individuation in Leibniz’’ is somewhat misleading as a title, though we could think of none better. It shouldn’t be understood as analogous to, say, ‘‘Water Power and Steam Power in Early American Industry,’’ where one might fairly expect to get proper servings of each – about water power, and about steam power, in industrial production of the mid- to late -s. Our title is rather more like ‘‘Transportation and the Automobile in America,’’ where one expects a relatively thorough discussion of the latter from within some context of the former. Some context, but not the whole story; just as a treatise on the automobile might take certain liberties in setting out the broader context of (say) land transportation in America, foregoing efforts to settle the question of sea travel, so one might take certain liberties in setting out the broader context of (say) simple individual substance in the mature Leibniz, foregoing efforts to settle the question of corporeal substance in the middle years. While our topic is Leibniz’s views on the individuation of substances, we shan’t be offering a full accounting of Leibniz’s doctrine (or, if you read him this way, doctrines) of substance. Nor shall we offer an account of individual accidents. Those are topics of respectively broader and narrower concern to which others have much more to offer than we do. () The topic of individuation is not, in most books on Leibniz’s metaphysics, separated out as a distinctive issue of special concern to him. But it is always there below the surface – indeed, one might see us as arguing, at the foundations – of many familiar and well-worked Leibnizian doctrines. Thus, while ours is not intended as a book setting out yet again to trudge through familiar Leibnizian doctrines, they are nevertheless there front and center. What some will only regard as tiresome threads in the fabric of Leibniz’s metaphysics – essentialism, relations, the Identity of Indiscernibles, and so on – must figure in our account as the very warp and weft of his views on substance and individuation. So far as the interpretive task goes, that is where one must

Introduction



try to get things aright from the start: the added knots of color and their collective patterns come along the way. If we can only apologize for taking the liberty of narrowing our sights to simple substances, one can scarcely apologize for being patient with the foundations of Leibniz’s metaphysics. () Some rugs (e.g. the kelim) are like all tapestries: they are all warp and weave, with the color fixed at the very foundation itself. To our minds, much of the color in Leibniz’s metaphysics of individuation is located in the philosophical details arising from its foundations, in the most basic arguments connecting this thread to that. Appreciating those philosophical threads – and learning from them too – requires bending closer forward, not stepping further back. As we shall engage the interpretive and critical tasks noted above, being patient with the philosophy itself is all of a piece with doing history of philosophy. The reader can thus expect to encounter rather more frequent bits of ‘‘straight philosophy’’ along the way than is perhaps typical of most books being written on Leibniz nowadays. On those pages, we are doing little more than what Leibniz himself did, with what Leibniz himself, on a historically sensitive reading of him, seems to have left us. Historical sensitivity of course comes in degrees. Were we doing ‘‘straight philosophy’’ all the way through, we could do little more than what Leibniz – and (say) Galileo and Descartes and Kant – did, in large measure all the way through. We are doing history of philosophy on and with a historical systematic philosopher; they were creating systematic philosophy itself. Their extent of historical sensitivity could afford to be less than ours: What is more revolting . . . when someone is dealing with demonstrable conclusions, than to hear him interrupted by a text . . . thrown into his teeth by an opponent? If, indeed, you wish to continue in this method of studying, then put aside the name of philosophers and call yourselves historians, or memory experts; for it is not proper that those who never philosophize should usurp the honorable title of philosopher. (Galileo Galilei, Dialogues Concerning the Two Chief World Systems) Conversing with those of past centuries is much the same as traveling . . . But one who spends too much time traveling eventually becomes a stranger in his own country; and one who is too curious about practices of past ages usually remains quite ignorant about those of the present. (Rene´ Descartes, Discourse on Method) There are scholarly men to whom the history of philosophy (both ancient and



Introduction

modern) is philosophy itself; for these the present Prolegomena are not written. They must wait till those who endeavor to draw from the fountain of reason itself have completed their work; it will then be the turn of these scholars to inform the world of what has been done. (Immanuel Kant, Prolegomena to Any Future Metaphysics)

But if their historical sensitivity in doing straight philosophy could afford to be less than our own in doing history of philosophy, our philosophical sensitivity ought to be no less than theirs. One cannot hope to do good history of philosophy, in the company of good historical thinkers at any rate, without setting out to do good philosophy.¹⁰ There are, evidently, dangers in this methodology – dangers in approaching our historical and philosophical aims side by side, where the latter announces an explicit hope that we can learn from Leibniz, and (why not?) he from us. In his splendid book Leibniz and Arnauld: A Commentary on their Correspondence, Robert Sleigh distinguishes ‘‘philosophical history,’’ as illustrated best in the work of Benson Mates and Jonathan Bennett, from ‘‘exegetical history,’’ as illustrated best in the work of Robert Adams and Daniel Garber (and, to the extent we grasp the distinction, we would add Sleigh). The danger of philosophical history is that, in hands less capable than Mates’s or Bennett’s, ‘‘it degenerates into closet metaphysics . . . It allows the author a front for probing philosophical problems, presenting arguments, even reaching conclusions, without being held to current standards of rigor’’ (p. ). The potential vices are apparently two – doing metaphysics and giving arguments and reaching conclusions under the cover of doing something else, and failing to meet current standards of rigor. If the second of these refers to the always-current standards of valid philosophical argument, then we announce our intention to meet them. (It may refer to standards of scholarship for writing an intellectual history that primarily chronicles lineages of historical influence. Since that is not our aim, we ¹⁰ In fairness to Leibniz, who was every bit a systematic philosopher, it must be stressed that his historical sensitivities extended well beyond those of Galileo, Descartes, and Kant. Indeed, judging from his April  letter to Thomasius (which found its way into his preface of an edition of Nizolio’s De veris principiis . . ., at A ..–), for the early Leibniz at least ‘‘doing straight philosophy’’ meant showing how to reconcile Aristotle with the new philosophy. The temperament of Galileo, who tired of having Aristotle’s texts thrown into his teeth, wasn’t exactly Leibniz’s temperament. Nevertheless, even in a letter where (in its unpublished version: cf. A ..) Leibniz was prepared to describe his historical sensitivities toward the words of Aristotle as analogous with theological efforts to interpret sacred scripture, Leibniz was quick to criticize those philosophers ‘‘who are rather more skilled in antiquity than in learning [ars], and have given us lives rather than doctrines’’ (A ..: L ). Leibniz was above all concerned with ‘‘showing truth per se’’– if with the assistance of historical texts as well as ‘‘reason and experience’’ (ibid.). That is a balance worth striving for.

Introduction



shan’t announce any intention of meeting those standards.) The first vice is easily avoided with another announcement: we shall be doing metaphysics and giving arguments and reaching conclusions. It’s just not all that we shall be doing. The more we shall be doing is starting our arguments – and, if he is the philosopher we take him to be, typically ending them too – with the historical Leibniz, as best we can understand him. Philosophical historians are above all indebted to others who approach Leibniz more historically, more exegetically than we shall. But perhaps we can in some modest way try to return their good favor.

 

Leibniz and the problem of individuation: the historical and philosophical context

The metaphysics of individuation, like the historical and contemporary senses of ‘individuate’* and its cognates, is a complex web of difficult issues. The spin Leibniz gives to them can be properly traced out only against the scholastic backdrop that was his intellectual heritage. In this chapter we undertake a brief journey through the conceptual network in the vicinity of ‘‘individuation’’ – first as a means of distinguishing related questions that can be asked about our topic (§), and then as a means of highlighting similarities and differences between contemporary and scholastic ways of understanding them (§). With these introductory remarks in place, it will then be possible (§) to make vivid the central threads (as we see them) in the early Leibniz’s () Disputatio Metaphysica de Principio Individui,¹ anticipating finally two important themes in the mature Leibniz (§). Here – and indeed in the remaining chapters – we are not simply aiming to locate points of historical continuity. Much as contemporary readers are more comfortable with the mature Leibniz on substance and individuation as against the apparently contorted efforts of the scholastics to engage with roughly the same set of problems, one should not lose sight of ways that scholastic insights into problems and possible solutions were rejected and largely forgotten rather than refined and extended into the modern period. Then as now, continuity isn’t everything.

*Throughout this discussion we will use single quotations marks to indicate that words and phrases occur autonymously, reserving double quotation marks for their ordinary use as punctuation. ¹ At G ,–. We have profited from Laurence B. McCullough’s recent Leibniz on Individuals and Individuation, which contains along the way English translations of all sections of the Disputatio. We have used McCullough’s translation (with occasional revision) in what follows, using MLI followed by page in citing Disputatio texts. When treating of McCullough’s own discussion we shall cite McCullough, Leibniz on Individuals, with page. Readers are encouraged to consult the bibliography early on in their reading.



Approaches to the metaphysics of individuation

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                            Assume the bare bones of a substance/accident metaphysic. That is to say, assume that the world contains individual things that (can) endure through time – leaving aside for now whether they are material or immaterial –, and in which properties inhere – leaving aside for now whether properties are Platonic forms, mental abstractions, immanent universals, or individualized tropes. What general sort of approach might the philosopher take in articulating an account of individuation? We consider here two broad styles of approach to offering a metaphysic of individual substances that encode pictures of what the philosopher is up to when taking on problems of individuation – pictures that are in one form or another at work in the scholastic tradition. . The blueprint approach One way of getting clear about the nature of a thing or a kind of thing is to provide a sort of blueprint for bringing that thing, or a thing of that kind, into being. In (what we nowadays call) the philosophy of mind, for example, one might propose to come to grips with the nature of mind by trying to conceive some sort of blueprint for creating a thinking thing. The blueprint may of course be impossible to implement in practice for all sorts of reasons: one might not have ready access to the materials, one may have no ready means for recognizing the materials, and so on. Yet seeking such a blueprint may be thought – as many philosophers of the cognitive sciences have recently thought – to provide philosophical understanding nevertheless. Similarly, in fundamental metaphysics, the blueprint approach has enjoyed some popularity in the history of our subject, owing perhaps to earlier models of the relation between creatures and the Creator. When confronted with such abstract questions as ‘‘What is the nature of an individual substance?’’ one might hope to make some measure of progress by conceiving of a sort of blueprint – of God’s recipe book, so to speak. Just as a recipe in cookery will proceed by listing ingredients and modes of combination, so the blueprint for an individual substance would provide an account of the constituents of a thing, together with an account of the modes of unification whereby those constituents make up the thing or ontological kind in which one is interested. Suppose that a scholastic philosopher is taken with the blueprint picture and sets out to illuminate the metaphysical structure of in-

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Leibniz and the problem of individuation

dividual substances.² How will he proceed? He will not, of course, be working in an intellectual vacuum: scholastic philosophy begins with Aristotle. The struggle with individuation was, for medieval thinkers, a struggle to make good on the Aristotelian project of articulating the structure of substance, supplementing and refining Aristotle’s own account in response to perceived explanatory demands of various metaphysical and theological concerns. Three Aristotelian components were nearly always in play in discussions of individuation: form, matter, and accident. The familiar picture here, in broad brush-strokes, is that a form is a unifying principle³ in matter that yields the sort of unity in which accidents can inhere. The category of accident itself was typically regarded by the scholastics as ontologically posterior to that of substance – the reality of accidents in some deep sense presupposing the reality of substances in a way that substances do not presuppose accidents.⁴ That leaves matter and form, under some construal of which one or both will then – together perhaps with supplementary components to cover an explanatory shortfall – be put to work in settling questions about individuation. In addition to the historical influences of Aristotelianism are broadly theoretical constraints on the problem of individuation, variously implicit and explicit in medieval accounts of individuation. We note here three sorts of consideration that may constrain the search for a blueprint. First, in approaching an account of individuation, one may already be convinced of certain facts about the metaphysical structure of substances for reasons connected with other metaphysical or theological ² Here we set aside the possibility of construing substance as a mass noun: the issue will be discussed briefly in the environment of chapter . ³ Here using principle (principium) in the scholastic sense of origin or foundation or source, as inherited largely from Aristotle’s arche´ in the Metaphysics (cf. ,,bff): it was an established term, with this broad sense, by the thirteenth century. Having announced early in Disputatio § that he intends in that work ‘‘to treat of the principle of the individual’’ (G , : MLI ), Leibniz goes on to note that ‘principle’ has been understood in several ways (‘‘Principii quoque vox notat tum cognescendi principium, tum essendi. Essendi internum et externum’’) – opting himself in the Disputatio to avoid any epistemological or external glosses on a principle of individuation. ⁴ See for example Aristotle’s Metaphysics ,,a, echoed by Aquinas in his Expositio super librum Boethii De trinitate q., a.. That accidents are individuated by their substances was a common view of the middle scholastics (cf. Avicenna, Metaphysica v, c.  and Logica v, c. , and Aquinas, ST .); it was retained by many later figures, including John of St. Thomas (–), arguably the last of the major scholastics, who follows Aquinas in individuating accidents by the subjects in which they inhere (‘‘S. Thomae certissimum est individuationem acidentium sumi a subjecto, in quo sunt, seu in ordina ad illud’’: Cursus philosophicus . . . Reiser, p. ; cf. Gracia and Kronin, ‘‘John of St. Thomas,’’ p. ). This view was denied by some nominalists, Suarez later among them.

Approaches to the metaphysics of individuation

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concerns. A scholastic philosopher may, for example, have already convinced himself of the need to distinguish the matter of a substance from the substance itself, given a need to account for substantial change (a substance’s coming-to-be or going-out-of existence, as opposed to mere alteration).⁵ Yet, more obviously, a scholastic may well insist on distinguishing the proper accidents of a thing from other constituents of persisting individuals, as a means of explaining the diachronic identity of a substance through change (alteration). Further, that philosopher may already be convinced of the need to distinguish the essence of a created thing – which would exist whether or not God chose to bring the thing into being – and the existence of the thing, providing the differentia between the states of affairs of God’s actualizing, and God’s not actualizing, the essence in question. In such ways, the results of an inquiry into generation, corruption, creation, annihilation, diachronic change, and still other topics may already set our scholastic philosopher on the way toward a particular account of the metaphysical structure of substances. A distinct if related constraint would consist of various putative conceptual truths about substances as individuals – of what may be regarded as the ‘‘intension’’ of individual substances.⁶ Consider the notion of individuality itself–the notion of what it is to be an individual as opposed to being something else. Most of the intensional elements in terms of which that notion was variously analyzed by scholastic writers survive in some form or other to this day: Impredicability – on which condition an individual substance is not said of (does not inhere in) ⁵ Similarly, the modern philosopher may be convinced of a real distinction between, say, a statue and the hunk of matter that makes it up on account of the fact that the hunk of matter existed prior to the statue. Setting artifacts aside, the distinction itself here at issue was subject to various qualifications. The broad scholastic agreement with Aristotle on genuine substantial change was tempered by a theology of ex nihilo creation: where Aristotle had claimed that coming into being and ceasing to be in the absence of some persisting substratum was unintelligible, medievals viewed the Aristotelian requirement as at best correct for the realm of creaturely causes only. Leibniz follows the medievals here, though in the context of explaining how the mechanistic view of alteration (via motion) is consistent with Aristotelianism, the early Leibniz is cautious to remind us that ‘‘numerically the same change may be the generation of one being and the alteration of another’’ (G ,: L ) – citing among others the case of rusting iron (from Hooke’s Micrographia). ⁶ Or, more carefully, the intension of ‘individual’ simpliciter, as this terminology has been introduced and deployed by J. J. E. Gracia in his Introduction, pp. ff (see also pp. – of his ‘‘Introduction’’ (Ch. ) to Jorge J. E. Gracia, Individuation in Scholasticism.) The intension of ‘individual’ comes closest to what, in our reading of § of the Disputatio, Leibniz isolates as the sense of ‘individual’ applied in conceptu or formaliter: his announced purpose is to investigate that ‘‘real’’ principle of individuals (here applied in re or fundamentaliter) ‘‘which would serve as the foundation for the formal notion in the mind of ‘individual’. . .’’ (G ,: MLI ).

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Leibniz and the problem of individuation

anything in the way that properties are said of (inhere in) substances; Incommunicability – the core sense in which substances are indivisible, according to which individual substances are not common to many things (as universals are fully occurrent in many things at the same time); Identity – here construed diachronically as the capacity to endure under change (alteration); Division – which in scholastic terms is ‘‘a capacity to divide a species,’’ as individual dogs divide the canine species; and Distinction or difference – which is to say that substances are countable under the relation of numerical identity, as Socrates and Plato are said to be two. Whether deployed singly or in some combination, the role of such notions in a broadly conceptual analysis of what it is to be an individual will constrain the search for a blueprint for individual substance(s). A third constraint will be one’s sense of the paradigm cases of an individual substance, as well as one’s sense of the paradigm cases of non-substance. Here the question concerns the ‘‘extension’’ of ‘individual substance’. Alongside the well-worked distinction between substance and accident, of equal importance to medieval thought on our topic was a distinction between substances that exist at the metaphysical groundfloor, so to speak, and so-called enduring things that are metaphysically second rate. This idea too will not be altogether foreign to contemporary readers: each of us will have at least an initial temptation to think of a particular cat as enjoying a place in the metaphysical scheme of things that is of a rather different order to that enjoyed by Tabix, where Tabix is the aggregate of Tabby and Felix. With any such distinction in place – between what the medievals would reckon substances per se and substances per accidens⁷ – one’s search for a blueprint becomes more focused, here owing to a need to account for the sort of real unity enjoyed by first-rate substances but lacked by second-rate heaps. In contemporary philosophy, paradigm examples of individual substances are typically offered up (as just now) from within our folk, workaday, conceptual scheme. Needless to say, scholastic philosophy preceding Leibniz looked as much to theology as to the scheme encoded ⁷ The provenance of the distinction itself, traceable in large measure to Aristotle’s familiar doubts about whether heaps, parts of organisms, the elements, and so on are genuine substances (e.g.. Metaphysics ,), should not be too closely wedded to its taxonomic cousin in Metaphysics , and , about what is ‘‘accidentally one’’ versus what is ‘‘one by its own nature.’’ There, doubts about whether musical Corsicus – as opposed to rational Corsicus, say – is accidentally one represent concerns about proper differentia and the unity of definition. In this latter context, a bundle of sticks and an arm are alike said by Aristotle to be ‘‘one by its own nature’’ (bff); but alongside Physics ,,a– and the dominant sentiment of the Metaphysics, a bundle or an arm is one in at best a Pickwickian sense. Thanks to Patricia Curd and Martin Curd here.

Approaches to the metaphysics of individuation

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by natural reason for data that constrain metaphysical inquiry. Insofar as one takes the existence of God as source of all reality, or a being that is both human and divine, or the transubstantiated host, to be among the deliverances of special revelation, one will reckon such information as proper input into one’s search for a metaphysic of substantial individuals. Note in particular that for the scholastics it was largely nonnegotiable that some individual substances were purely spiritual, incorporeal beings: an account of individuation that only applied to corporeal substances would be at best an account of individuation of one kind of substance. As with all approaches to a full metaphysic of substantial individuals, the blueprint approach can proceed at different levels of generality. One may be after a schematic blueprint for substance qua substance – that is to say, a blueprint abstracting away from whatever is distinctive of any given particular substance and whatever is distinctive of any given particular kind of substance. Alternatively one might seek a portfolio of blueprints – one for each fundamental kind of substance taken to exist, where now each blueprint would abstract away from those features distinctive of any given particular substance. Yet again, one may be after a metaphysical blueprint for particular individuals – where the concern is not so much, say, a special fascination with what makes Socrates Socrates, but rather a concern to provide some recipe for a blueprint highlighting what it is, for any individual x, that makes x the very individual it is. Prima facie, then, one confronts at least three levels of blueprint approach, corresponding to the questions ‘‘What is it for a thing to be an individual substance?’’ ‘‘What is it for a thing to be the kind of substance that it is?’’ and ‘‘What is it for a thing to be the very individual substance that it is?’’ And here arises a fundamental methodological issue for approaching any metaphysic of individuation – namely where to begin. Does one start with the most general question and then descend in order of generality? In the case of the blueprint approach, this would amount to an initial search for the most abstract blueprint of substance qua substance, followed then by some filling-in of detail according to kinds (or else by some recipe for filling in detail according to kinds) – followed, finally, by filling in detail (or providing a recipe for doing so) according to the particular individual substance in question. Alternatively does one begin at a lower level, perhaps ascending later to one of the more general questions? Thus one might begin at the level of kind, adding individual differentia to each kind-blueprint to descend, abstracting what is com-

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Leibniz and the problem of individuation

mon to the kind-blueprints to ascend. It may of course arise that one of these levels of questioning presents itself as less coherent or otherwise less promising than the others. One may well reject the most abstract level, for example, owing to a conviction that there is nothing very useful to say concerning the metaphysical common ground between different kinds of individual substances. Thus it may emerge that kind A and kind B enjoy the intension of ‘individual substance’ via such different metaphysical routes that there is nothing much to offer by way of a general blueprint. (Here perhaps one thinks most naturally of Aquinas’s different accounts for compound [material] substances and angels.⁸) . The modal approach Questions about the nature of individual substances quite clearly have either an explicit or a tacit modal dimension to them. The question ‘‘What is the nature of an individual substance?’’ converts readily (again, since Aristotle) into the question ‘‘What must a thing be in order to be an individual substance?’’ Accordingly, one may fairly gloss the search for principles of individuation as the search for a certain class of necessary truths; in particular one is seeking the most fundamental truths (de re) about substances. In this connection, note that an assumption common to most medieval and contemporary thinkers alike is that substances are essentially substances: nothing is actually a substance but possibly a non-substance. Similarly, discussions at the level of kinds, to the extent that they are central to individuation, will concern kinds that are essential to substances. And, quite obviously, questions at the very lowest level of generality – concerned with, say, what makes this individual (say, Socrates) the very individual it is – are about de re necessities, it being assumed in such contexts that Socrates could not fail to be identical with Socrates. A natural place to look for answers to de re modal questions relevant to our topic will be to the intension of the general terms ‘substance’ and ‘individual’, to the intension of kind sortals, and to the intension of singular terms (names). One might object here that truths associated with intension must be de dicto.⁹ But illuminating de dicto truths of (say) the ⁸ See for example De ente et essentia §§–. ⁹ The de re/de dicto distinction is of course a medieval one. It was for example explicitly appealed to by Aquinas, notably in the discussion of divine foreknowledge in Summa contra gentiles .; but see also De veritate q., ar., ad. and De modalibus (cf. I. M. Bochenski, ‘‘Sancti Thomae Aquinatis de Modalibus Opusculum et Doctrina’’).

Approaches to the metaphysics of individuation

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form ‘Necessarily all Fs are Gs’ can readily be transformed into illuminating de re truths given the de re premise that such-and-such is necessarily F. Nevertheless it is a mistake to suppose that the modal approach itself amounts to no more than a conceptual analysis of intensions. Prior to converting any de dicto necessities into de re truths, for example, one must form some judgment concerning which truths are de re necessary – a judgment not settled by the de dicto necessities themselves. Moreover, it is unclear why some sort of high-level theory could not in any case supplement whatever modal truths are delivered by the intensions alone.¹⁰ Recall, inter alia, that from Aristotle to Kripke, metaphysicians have taken seriously the idea that a scientific, a posteriori inquiry into the nature of things may reveal de re modal truths altogether foreign to our pre-theoretic understanding of things. Putting the point now in scholastic terms: the real definition of thing or kind that places it in a taxonomic order of being may look nothing at all like the nominal definition that expresses the understanding that comes first in order of knowing.¹¹ In adopting what we might call the ‘‘simple modal approach’’ as so far conceived, one views the metaphysics of individuation as part of a high-level theory whereby one supplements the de dicto modal truths delivered by the intensions of relevant terms. The connection between the simple modal strategy and the blueprint approach is a mixed one. Some of the modal addenda about individual substances may implicitly say something about the contribution of its structural components to its ¹⁰ The need for such supplementation becomes particularly pressing to the extent that one doubts that a proper name or a term for a kind has much by way of an intension. Contemporary doubts (urged by Kripke in, for example, Naming and Necessity) arise from the recognition that many singular and natural-kind terms secure their reference by reference-fixers that are contingently true of their referents rather than by connotations that are uniquely and necessarily true of them. ¹¹ One cannot, however, straightforwardly equate the project of providing a theory of individuation for things with that of providing a real definition for them. Thomas Aquinas, while providing a principle of individuation for compound (corporeal) substances, was less than confident that they have a definition. He claims, notably, that signated matter ‘‘would be part of the definition of Socrates, if Socrates had a definition’’ (De ente et essentia §). Socrates has no definition if definitions by their nature must be in purely general terms, and if no purely general terms can succeed (fairly, without singular reference to Socrates himself or to individual regions/points of space) in uniquely singling out this signated matter here rather than that there. (Here, see Chapter .) A second point: Aquinas believed that once Socrates’ signated matter has individuated him (if you like, once it has individualized his form), God can keep him in existence without him having any matter at all. Think of the real definition as expressing components that are essential, and signated matter cannot be part of the real definition. But it can (in a way reminiscent of Kripke’s necessity of origins) figure in a story about individuation. Here is Aquinas (following Avicenna): ‘‘the individuation and multiplication of souls depends on the body in regard to its beginning, but not in regard to its termination’’ (De ente et essentia, §; cf. Summa contra gentiles .; Compendium theologiae ).

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Leibniz and the problem of individuation

nature¹² – as when one judges that (say) necessarily a human being always enjoys the numerically same soul at its helm. But some of them may not directly speak to issues of constituent structure – as when one judges that (say) an individual substance cannot enjoy a temporally gappy existence whereby it passes out of existence and then comes back into existence. The simple modal strategy, familiar in much of historical and contemporary metaphysics, represents a quite general approach to questions of substance and individuation. A fruitful and historically influential way of extending the approach as a methodological strategy is to take seriously Aristotle’s broad distinction between the order of knowing and the order of being. (i) For any theoretical inquiry there exists, on the one hand, an order of epistemic priority, whereby one proposition is known (or belief is judged to be warranted) on the basis of one’s knowledge or warranted belief of some other proposition. An order of epistemic priority may have a variety of sources. Q may be epistemically posterior to P if, in order to even grasp the proposition Q, one has already to know P. Thus, to understand the proposition that  +  = , one has already to know that four is the successor of three and that three is the successor of two. Alternatively, it may be that even though P and Q may be grasped independently, one can acquire good evidence for Q only by way of being epistemically secure about P. (ii) On the other hand (by contrast), the order of being has nothing to do with facts about cognitive grasp or evidence. To be convinced of an order of being is to be convinced that some truths obtain in virtue of other truths obtaining – and so, crucially, that certain truthmakers in the world obtain in virtue of other truthmakers obtaining. The philosopher who is comfortable with such a view of the world will typically have richer resources for making sense of the in virtue of relation than that provided only by efficient causal relations between distinct states of affairs, positing in addition other sorts of explanatory relationships that hold in the world – emergence, formal cause, emanation, supervenience, and so on. The scholastics were, of course, notable in their willingness to recognize such relations within the order of being. To anyone acknowledging the importance of such a distinction, the ¹² The implications may of course emerge in concert with the deliverances of intensional analysis. Prior to arguing in De ente et essentia that ‘‘matter is the principle of individuation’’ for composed material substances (§), Aquinas defends a crucial premise (§) on the basis of the meaning of ‘essence’ (analyzed in §§–). Concerning the issue of temporally ‘‘gappy’’ existence (below) and its relation to a constituent metaphysic of substances, see Summa contra gentiles .–.

Contemporary approaches to individuation

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answers delivered by the simple modal approach, even if they are correct, will not be fully satisfying. For one will still wish to understand the explanatory order of the modal facts. That is, according to what we might call the ‘‘modal-explanatory approach,’’ one should like to make explicit the ranking of all relevant modal facts vis-a`-vis the order of being. And having the Aristotelian distinction firmly in hand, one will not assume that the epistemic order marches in lockstep with the order of being.¹³ Thus, for example, the intension of ‘substance’, while perhaps primordial in the order of knowing about substances, may in many respects emerge as derivative in the order of being. That is to say, the analytic truths belonging to the intension of ‘substance’ may be true of members of its extension by virtue of facts that do not at all belong to the intension of ‘substance’. Moreover, there may be a de re hierarchy vis-a`-vis the order of being even within those intensional truths, where that hierarchy is not internal to the intension itself.                                                   When approaching Leibniz’s writings about individuation, it is tempting to locate them within a contemporary framework in which discussions of individuation take place. In our view there is much to be learned from doing so. But one should not forget that the mature Leibniz evolved from an earlier self that was very much immersed in a scholastic approach to our topic. Insofar as there are deep but often subtle differences between scholastic and contemporary frameworks for thinking about individuation, one should be aware of them, allowing where necessary the residue of Scholasticism to explain certain peculiarities of Leibnizian thought, particularly when they remain opaque when viewed through contemporary glasses. As a means to better appreciating Leibniz’s views on individuation, it will be helpful, we think, to look at contemporary approaches through scholastic eyes. . Criteria of identity In contemporary accounts, questions most closely approximating traditional concerns about individuation are often posed in terms of so-called ¹³ As clearly the mature Leibniz himself did not assume when claiming that ‘‘we are not concerned with the sequence of our discoveries . . . but with the connection and natural order of truths’’ (NE .vii.: RB ).

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Leibniz and the problem of individuation

‘‘criteria of identity.’’ In some cases the sought-after criteria specifically concern diachronic questions: for example, under what conditions is some F-thing (x) at t identical with some F-thing (y) at t (where F could be ‘enduring substance’ but is typically a more restricted kind sortal)? On other occasions the sought-after criteria are not specifically diachronic: for example, under what conditions is some x that is F identical with some y that is F? Consider two familiar examples of this sort of account that have been offered, disregarding what might be said for or against them: (P) Person x at t is identical with person y at t iff y is psychologically continuous with x. (E) Event x is identical with event y iff x and y have the same causes and effects. One point to note about both sorts of identity criteria is that neither begins to exhaust the modal questions one would hope to have answered by a theory of individuation. Clearly, answers to diachronic questions are not designed to provide answers to questions of synchronic counting, providing at most truth conditions for putative necessary truths of the form ‘a is the same F as b’ when that claim involves tacit reference to different times. Criterion (P) doesn’t begin to tell one what it is for there to be a single person at a time. The second style of identity criterion is also limited in its modal ambit. Recognize the tacit necessity operator at the front end of (E) and it is clearly not restricted to the actual world. Nevertheless its focus remains intra-world, concerning what can and cannot be shared by a pair of events within a single world: (E) does not, as it stands, yield an answer to the question ‘‘How could a particular event have been different and nevertheless be the numerically same event?’’ Such modal limitations as these may, of course, be eliminated by the right sort of transworld identity criteria. Thus: (E') Event x in W is identical with event y in W iff x and y have the same causes and effects – for better or worse reckoning the causes and effects of any particular event to be essential to it. Nevertheless, there would be, for the scholastic, very obvious limitations to a story of individuation that satisfied itself with a transworld identity criterion of this familiar sort. One complaint with such approaches, enjoying some contemporary

Contemporary approaches to individuation

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voice but scarcely any scholastic sympathy, is an epistemic one: modal issues aside, the likes of (E') may not enable one to recognize whether some event x is numerically the same as some event y because we may be able to settle the causal facts only alongside of or posterior to settling identity facts.¹⁴ The typical run of scholastic philosopher will not much care if an account of individuation for Fs refers to what is posterior in the order of knowing, so long as the claim about order of being for Fs is otherwise acceptable. A complaint that would arise from this latter scholastic perspective, one with which we should all be able to muster some sympathy, is this: the transworld identity criterion (E') does not tell us what it is to be an event in the first place. Given event x and event y and the relevant causal facts about x and y, the criterion will enable us to infer whether x and y are numerically the same or not. But until one is provided with some account of what it is for something to fall under the concept event, the criterion is not something one could begin to deploy. Shall we count Adam – the first man – as numerically the same event as Adam, on the basis of the fact that Adam and Adam have the same effects (none at all or identical agent-causal ones) and the same causes (none at all or a particular volition of God)?¹⁵ This latest complaint signals the kind of misgiving a typical scholastic philosopher would have about contemporary, ‘‘criteria-of-identity’’ approaches to individuation: they are at best incomplete metaphysical accounts. Clearly such criteria presuppose some general account of individuality – some prior accounting of what metaphysical facts-of-thematter (sortal-specific or otherwise) ground the division, impredictability, and incommunicability of individuals. But supposing a stock of individuals to be safely on board, such criteria (by contraposition) speak to the intensional element of individuality we earlier called numerical distinction or difference, inviting one to complete the schema ‘At time t, individual x is numerically distinct from individual y iff —’ (sticking here with the synchronic version and setting modal and sortal distractions aside). The philosophical temperament of the scholastic will incline ¹⁴ Here see the discussion of § in chapter  of Jonathan Bennett, Events and Their Names. In his Haecceity: An Ontological Essay, Gary S. Rosenkrantz is careful early on in chapter  (‘‘The Problem of Individuation’’) to warn that his sought-after ‘‘formal criterion of individuation,’’ which must specify a condition that is logically necessary and sufficient for numerical diversity, ‘‘should not be confused with the notion of an epistemic principle of individuation’’ (p. , n. ). ¹⁵ One is reminded here of Frege’s concern in the Grundlagen (§§–) about whether Julius Caesar could be the number two, or whether England could be identical with the direction of the earth’s axis.



Leibniz and the problem of individuation

again to the complaint of metaphysical shallowness: ‘‘All this,’’ the scholastic might wonder, ‘‘as if to simply assume that some positive account or other must be available as filler: there is some quality that x has which y lacks, or there is some causal ancestry and progeny that x enjoys which y does not, or there is some material stuff associated with x that is not associated with y, or x is in some spatial location that y is not, or x has some form that y lacks, or . . .’’ What is here simply assumed should, by scholastic lights, be earned in the context of a deeper metaphysics. Thus: ‘‘However prior they may be in the order of knowing, the accidents of quality are posterior to individuals in the order of being, and so cannot play the needed role in individuation. Spatial location is either an (internal) accident or external relation. But accidents are out, and an appeal to external relation – spatial, causal or otherwise – is merely an appeal to yet a further presumed instance of numerical distinction or difference, itself as yet unexplained. Matter is pure potentiality, indifferent to this or that individual substance. Form is general, common, sharable. Thus, there is no positive principle in individual substances grounding numerical diversity. Negation is the principle of individuation: numerical diversity or difference is the negation of identity or sameness.’’¹⁶ Never mind our choice of this particular response, nor its chances of succeeding. The general point is that a scholastic will be much more concerned to push very hard on both structural and explanatory questions. Even settling modal and sortal distractions of the sort noted above – even supposing that one’s identity criterion is transworld adequate and that one specifies conditions for falling under the relevant sortal – the scholastic will yet push on such questions as ‘‘By virtue of what does everything falling under that sortal satisfy that criterion?’’ and ‘‘By virtue of what is that criterion of identity true of all possible Fs?’’ Answering such questions will lead the scholastic to seek the relevant explanatory truth-makers within the internal metaphysical structure of individuals, to enlist the modal contribution of such constituents – whether a ‘‘negative’’ principle or, more typically, some ‘‘positive’’ principles such as form, matter, accident, or something else again – in at least partially explaining the de re modal truths of individuals. ¹⁶ Arguments similar to this one, attacked by Scotus, are laid out and criticized by Christian de Ramoneda (in Disp. de materia, a.), by Archangelus Mercenarius (in De principio individuationis , ch. ), and others cited by Leibniz: see McCullough, Leibniz on Individuals, chapter  for references and texts.

Contemporary approaches to individuation



. Modern essentialist semantics Consider a typical subject–predicate sentence of the form ‘a is F’. And consider now the following, fairly standard semantic story offered by the contemporary essentialist: ‘F’ expresses a function from possible worlds to sets of individuals. If the predicate-function corresponding to ‘F’ delivers a set containing a when the actual world is given as argument, then ‘a is F’ is true. If, for each world in which a exists, the predicatefunction corresponding to ‘F’ delivers a set containing a when that world is given as argument, then ‘a is essentially F’ is true. (Let us say that in this case, the predicate-function is essential to a.) If a is F but it is not the case that a is essentially F, then ‘a is accidentally F’ is true. If a is not-F but it is not the case that a is essentially not-F, then ‘a is accidentally not-F’ is true. Here ‘not-F’, like ‘F’, expresses a function from worlds to sets.¹⁷ The essence of any particular thing is given by the set of predicatefunctions that are essential to it. The essence of any kind is given the set of predicate-functions essential to every possible member of that kind. The essence of substance qua substance is given by the set of predicatefunctions essential to every possible substance. That familiar story will, of course, get supplemented with yet further details. But even at this stage, it bears striking and fundamental differences from the scholastic framework. We consider here two important differences that are especially worthy of note. First, the modern essentialist schema neglects, by scholastic lights, the distinction between the real definition and the proper accidents, where the essence is given by the real definition. Both the real definition and the proper accidents are essential to the thing, in the contemporary sense of the term ‘essential’ just noted. But only the real definition gives the essence, in the scholastic sense, which is that of the true inner nature of the thing. The proper accidents flow ineluctably from the true inner nature but do not constitute that nature. As a rough first pass (of its deficiency, more later): the real definition can be regarded as specifying some core or ‘‘nuclear’’ set of properties that are essential in the contemporary sense, and which are such that the remaining properties that are essential in this sense hold in virtue of one or more members of the core.¹⁸ The distinction is an Aristotelian one. After explaining that a ¹⁷ If one dislikes function talk, one can mirror the story by talking about a property expressed by each predicate and then deploying talk of instantiation, actual and possible, in place of talk of function, argument, and value. ¹⁸ Where a necessary (but not sufficient) condition for a property A holding by virtue of B is that, necessarily, if B then A.



Leibniz and the problem of individuation

(real) definition ‘‘signifies a thing’s essence’’ (Topics ,,b), Aristotle says that distinct from what is expressed by the definition are its ‘‘properties’’ (proper accidents), which ‘‘do not indicate the essence of a thing, but yet belongs to that thing alone, and is predicated convertibly of it’’ (a). His example: if x is a man then x is capable of learning grammar; and if x is capable of learning grammar then x is a man. The capability of learning grammar is not the essence of man, though man has it of de re necessity by virtue of being essentially (Aristotelian/ scholastic sense) rational. The distinction – including Aristotle’s preferred taxonomy of essence vs. property – was apparently commonplace enough even in the early modern period for Spinoza to remind his readers of what he supposed ‘‘no one fails to see.’’ From his account of definition in the Tractatus de Intellectus Emendatione (§): To be called perfect, a definition will have to explain the inmost essence of the thing, and to take care not to use certain propria in its place . . . If a circle, for example, is defined as a figure in which the lines drawn from the center to the circumference are equal, no one fails to see that such a definition does not at all explain the essence of the circle, but only a property of it . . . [T]he properties of a thing are not understood so long as their essences are not known.¹⁹

Second, the modern essentialist gives the same metaphysical treatment to every grammatical predicate – by associating a function from worlds to extensions for each. From a scholastic point of view, such a treatment would blur distinctions of fundamental metaphysical import. In particular, the scholastic would insist on a distinction between those predicates that are made true of a thing by virtue of an accident inhering in the subject, and those predicates that are not. Consider what might make a predicate true of a thing without its being made true by an accident inhering in the thing: (i) it could be made true by some mental abstraction that is warranted by the thing without corresponding to any ontologically sanctioned principle in the thing, or (ii) it could be made true by some metaphysical constituent of the thing that is nevertheless of a different ontological kind from the thing or an accident, or (iii) it could be made true by the thing itself. Category (ii) here is particularly ¹⁹ CWS . The early Leibniz either failed to see it or used ‘essence’ in something closer to the contemporary sense: in arguing that form cannot be increased or decreased and (hence) that one circle cannot be (so to speak) more circle than another, Leibniz writes to Thomasius in  that ‘‘the essence of a circle consists in the equality of all lines drawn from its center to its circumference’’ (G ,: L ; cf. also the ms. ‘‘Ad Christophori Stegmanni metaphysicam unitariorum’’ translated in Jolley, Leibniz and Locke, at p. ). For Locke’s version of essence and properties, see Essay .vi..

Contemporary approaches to individuation



important, given the scholastic tendency to proliferate (by contemporary standards) metaphysical constituents of an individual substance. Thus the predicate ‘is a man’ is made true by the lights of many scholastics by the substantial form of a thing, which is not at all conceived as being of a piece ontologically with the accidents of the thing.²⁰ From the perspective of one who takes seriously the requirement to be selective in one’s pairing of predicates with accidents and, relatedly, to find other kinds of truth-makers for those predicates not associated with accidents, the contemporary semantic model – whereby each predicate alike is associated with a function from worlds to sets – will seem to neglect altogether the most important aspects of the ontological structure of a substance. And in failing thus to give a sufficiently fine-grained representation of the manifold (truth-making) relations between language and the world, it will thereby neglect some of the most important explanatory relationships that are needed for an adequate metaphysic – between immanent substantial form and the thing itself, between substantial or other forms and accidents, between form and matter, and so on. In light of this second point, our first pass at taking account of the distinction between proper accidents and real definition (essence) would appear unsatisfactory from a scholastic point of view. That rough account took for granted that the predicates of the real definition and predicates corresponding to proper accidents both express entities of the same ontological genus, namely, properties – the distinction itself being drawn in terms of explanatory relationships internal to the genus. The typical scholastic would be loath to assume that the essence of a thing can be analyzed in terms of members of the same ontological genus to which accidents also belong, perhaps even thinking that the explanatory relationship holding between an essence and its proper accidents will be of a sort that never holds in intra-accidental reality. ²⁰ To speak of ‘‘the substantial form’’ here in fact under-represents the extent of metaphysical proliferation by most scholastics before and after (but not including) Aquinas, for whom there were many substantial forms in living things. Aquinas himself – perhaps to preserve his conviction that the unity of a creature must imitate the simplicity of the divine essence – argued that there is only one substantial form in an individual composite (material) substance: the presence of any substantial form in prime matter suffices to bestow existence on the composite. Arguments against the Thomistic view were manifold. The authority of Aristotle’s tripartite division of the soul into the essential but distinct nutritive, sensitive, and intellectual powers sufficed for many. Others, holding that the intellectual soul in humans is caused by God, left the substantial form of the body to be contributed by the parents; others argued that since (at death) the body of a creature remains when the form of the soul does not, it must be said that the form in virtue of which one is corporeal is distinct from the form in virtue of which one is animated; still others argued that the doctrine of the Incarnation requires that we admit the compresence of human and divine substantial forms; and so on.



Leibniz and the problem of individuation                :                 

In method and historical purview, Leibniz’s early dissertation of  is squarely in the scholastic tradition, and is directly concerned with problems of individuation. In what follows, we first lay out some important threads of that work, and then discuss the positive doctrine of the Disputatio in light of those threads, with an eye to understanding the ways that his mature views bear traces of his scholastic heritage. In the final section of this chapter we take an initial glance at the mature Leibniz against the background of the Disputatio. . Four themes in the ‘‘Disputatio’’ Much of the Disputatio itself is devoted to articulating historically influential accounts of individuation, and to Leibniz’s critical evaluation of them. The scholastics participating in debates about individuation – given its historical development in the  years preceding Leibniz and its relevance to a wide range of philosophical and theological stances – had inevitably cast their various nets in various ways. Thus (i) certain items emerging as intensional aspects of ‘individuality’ – division, impredicability, incommunicability, identity, and distinction or difference – might receive more or less emphasis, and might, for some participants but not others, stand to one another in asymmetric explanatory relations. Among the later scholastics, for example, Suarez was perhaps most explicit in reckoning incommunicability as the ‘‘essence’’ of individuation, and in arguing that distinction or difference is a sort of consequence of it.²¹ In § of the Disputatio Leibniz notes in addition that ²¹ ‘‘Essence’’ in quotes because, on Suarez’s account, only natural kinds and their members have real essences. That incommunicability – indivisibility – is the essence of individuation for Suarez emerges at the very outset in Section  of the Disputationes metaphysicae  (‘‘On Individual Unity and its Principle’’), where his immediate concern is to argue that, ‘‘that is called ‘one in number’ or ‘singular’ or ‘individual’ which is one being in such a way that...it is not communicable to many’’ (§: Berton, vol. , p. ), and that the very notion of a singular individual consists (consistet) in its being indivisible (§). The explanatory priority of incommunicability to numerical distinction or difference arises most clearly in Section  of Disputation . On the heels of rejecting the Thomistic view that the principle of individuation is a team effort – matter yielding incommunicability and quantity yielding numerical distinction – Suarez claims that no team effort is needed: a thing’s being a singular individual unity is ‘‘by nature prior to its being distinct from others,’’ and moreover ‘‘the latter follows intrinsically from the former without any positive addition being made to the thing itself that is one’’ (§: Berton vol. , p. ). Numerical distinction or difference supervenes, comes along for the ride: whatever immediately grounds the incommunicable unity of an individual suffices mediately to ground its numerical distinction. ‘‘The same positive [thing] that is the foundation of unity with respect to the first negation, i.e.

The early Leibniz: ‘‘Disputatio Metaphysica’’



(ii) accounts of individuation may proceed with a use of ‘individual’ to express every individual, or only substances, or just created substances, or even simply material substances; that (iii) an account of individuation may seek a principle of knowing or a principle of being; and that (iv) a principle of individuation may be an external principle or an internal one. The focus of Leibniz’s own project reflects a philosophical temperament not unlike that of his mature years: [W]e treat of something real and what is called a physical principle, which would serve as the foundation for the formal notion in the mind of ‘individual’, understood as individuation or numerical difference. We shall address individuals, particularly created and substantial individuals . . . Since we shall here abstract from material and non-material substance . . . we shall examine only the general opinions. (§§,: G ,: MLI –)

(i') Leibniz’s concern in the Disputatio (like Suarez’s in the Metaphysical Disputations) is with indivisibility (incommunicability) and numerical difference. There is no special attention devoted to identity through change or to impredicability, both central to Aristotle’s conception of primary substances. And it is (ii') individual substance itself that is Leibniz’s principal target. That leaves one item in the traditional ontology out of his sights: while there are accidents, which by Leibniz’s reckoning are numerically distinct and incommunicable individuals, he devotes no energy to discussing principles of individuation for accidents in the Disputatio.²² But if focusing on individual substances in particular over individuals generally is a methodological choice, a further decision is philosophically motivated: in offering principles of individuation, ‘‘[t]here are . . . two kinds of opinions. Some have held hypotheses that were applicable to all individuals, like Scotus. Others, like Thomas, held a different view’’ (G ,: MLI ) – treating bodies in one way, angels in another. Here Leibniz sides with Scotus, judging it possible to ‘‘abstract from material and non-material substance’’ in locating a general principle of individuation applicable to all individual substances. (Or anyway, to all finite [created] individual substances, as Leibniz is careful to note.) (iii') In seeking ‘‘something real and what is called a indivision itself, is subsequently the foundation of the later negation, i.e. distinction from another.’’ ²² ‘‘[W]e have left accidents and incomplete beings out of the scope of our undertaking’’ (Disputatio §: G ,: MLI ) – this unlike Suarez, who devotes a full third (Sections  – ) of Disputation  to the individuation of accidents. We shall briefly address ‘‘incomplete beings’’ in §. below.



Leibniz and the problem of individuation

physical principle, which would serve as the foundation for the formal notion in the mind of ‘individual’,’’ Leibniz focuses on the order of being, not the order of knowing. He is doing metaphysics, not epistemology or linguistic analysis. A. A Principle of Individuation as Internal And what of (iv) internal vs. external principles of individuation? The distinction might have been more immediately relevant, in the early going of the Disputatio, were Leibniz to have divided his labor between substances and accidents – the latter, but not the former, being typically individuated by reference to something else²³ – or were Leibniz to have sided with Thomas in reckoning matter under dimensive quantity an individuating principle of material things – it being argued by some that this requires appeal to an external principle. After noting the internal–external distinction, Leibniz in any case makes no further mention of it, and one can scarcely doubt that his aim to locate a purely internal principle was too obvious to deserve special mention. It is absolutely fundamental to Leibniz’s thinking on individuation that whatever individuates a substance must be something wholly internal to that substance itself. That basic assumption is quietly but resolutely at work throughout the critical parts of the Disputatio. Thus, for example, when approaching arguments (similar to that devised in §. above) for the claim that one or more negations must the serve to individuate a substance, Leibniz writes: This can be easily opposed: the individual is constituted by negations, either outside the mind or in the mind. If the latter, their answer has nothing to do with the issue in question; if the former, how can positive being be constituted by negative being? (§: G ,: MLI )

On the latter horn of the dilemma as presented, the negation account is damned straightaway on the grounds that it invokes something external to the substance itself (in this case a mind). The problem isn’t that this makes the putative individuator only contingently connected to the thing; after all, the mind might be the immutable and eternal mind of God. What Leibniz insists upon is not merely that the individuator be non-contingent but that it be internal to the thing itself. The latter individuality-by-negation proposal has nothing to do with Leibniz’s question, since he is seeking an internal principle of individuation. As we are reading him, Leibniz is requiring in the Disputatio what would later be expressed more explicitly – in First Truths, where he claims that whatever ²³ See note  above.

The early Leibniz: ‘‘Disputatio Metaphysica’’



grounds the numerical diversity of individual substances ‘‘must be sought in some differences within themselves’’ (C –: L ), and on into the New Essays, where we’re told that quite apart from ‘‘the relations to what lies outside’’ different individual substances ‘‘there must always be an internal principle of distinction’’ (NE .xxvii: RB ). The general intuition is powerfully motivated. Consider some bona fide existing individual substance. That substance would it seems be the very individual it is even were it alone in the world. Take that idea seriously and it immediately becomes impermissible to bring in individuators of a substance that involve relation, or that make reference to other substances – indeed, even a relation of numerical difference to other things. Relatedly, one’s groundfloor story about what makes substance a different from substance b shouldn’t, by the present lights, concern a relation between a and b, since a would be what it is even if there were no b and b would be what it is even if there were no a. Take now the correct story about what makes a a and the correct story about what makes b b, each member of the pair proceeding without reference to the other: the relation of difference will supervene on the elements that make each story true. Hence the relation of difference will not be a primordial, inexplicable fact. That, recall, is Suarez’s picture of Disputation V, where a thing’s being a singular individual unity is ‘‘by nature prior to its being distinct from others’’ and where ‘‘the latter follows intrinsically from the former without any positive addition being made to the thing itself that is one.’’²⁴ B. All Unity is Grounded in Numerical Unity An equally strong current in early Leibnizian thought is that metaphysical unity must be explained in terms of numerical unity. By thus rejecting the idea that numerical unity is a mere species of the genus unity, Leibniz in effect closes the door on any approach to individuation that attempts to explain numerical unity ²⁴ See note . Powerfully motivated as the general intuition may be, it is far from unanimously embraced in the context of contemporary metaphysics. According to the Kripkean necessity of origins story, what makes corporeal substances the very substances that they are is, at least in part, their origin – sperm and egg in the case of mammals, hunks of matter in the case of material artifacts, and so on. For the record, we have some sympathy with the scholastics and Leibniz, though now is not the time to defend such a conviction at length. (But, not at length: suppose that two duplicate organisms arise ex nihilo. In that case, there will presumably be a metaphysical ground of the relation of numerical difference between the two. And presumably, each organism would be the very organism it is even without the other existing, so the relation of difference isn’t primitive. Intuitively, then, there is a sufficiently individuating bit of metaphysical detail for each individual that grounds the numerical distinction between each. Won’t the kind of differentia we invoke here also [a] be present in the case of organisms with a history and [b] be sufficient to explain what makes each of them the very organisms they are?)



Leibniz and the problem of individuation

in terms of some other sort(s) of unity posited to coexist at the metaphysical groundfloor. In relation to scholastic accounts, this commitment of Leibniz’s is rather more controversial than the previous one. Anticipating his mature view that ‘‘what is not truly one being is not truly one being either’’ (; G , : LA ), Leibniz flatly says of unitas and entitas ‘‘in re idem est’’ (Disputatio §: G ,: MLI ). His point is to reject pictures according to which some common entity, having less than numerical unity, combines with an individuator or contracting difference to yield a singular individual enjoying numerical unity. Thomistic matter and form might have been the target, but wasn’t in this context: that approach had been scuttled in favor of a more general one, and Thomas was in any case possessed of sufficient nominalist scruples to acknowledge that communicable universals are the work of the intellect (ST a, q., a.). In Disputatio §, Leibniz cites an argument against his own view of individuation – that the whole entity, the individual substance itself, individuates – from Paulus Socinas (Quaestiones Metaphysicales), the first premise of which is that ‘‘[t]he proper unity of essence, namely the formal or specific unity, is less than numerical entity’’ (G ,: MLI ). Leibniz’s response here, namely to ‘‘deny the antecedent concerning unity outside the intellect,’’ applies as well to Scotus. According to Scotus, indeterminate but determinable common nature – which in combination with a particular thisness or haecceity yields a numerically unified singular individual – is a real entity, in re not in mente, possessing less than numerical unity.²⁵ That Scotistic endorsement of a formal ²⁵ Leibniz’s response applies to Scotus, but is applied to Scotists: in the Disputatio itself Leibniz identifies the position with Scotus and only explicitly cites texts of Fonseca, Pererius, and Bassolis. In withholding numerical unity and applying formal unity to common nature(s), it might seem that while the humanity of Socrates is formally one with the humanity of Plato, there is simply no fact of the matter about whether the humanity of Socrates is numerically one with that of Plato (in the way that many conceive of full-blown universals) or numerically distinct from that of Plato (in the way that many would conceive of individual accidents). Thus, Scotus: ‘‘According to me, [common nature] is not ‘one of itself ’, as in numerical unity, nor is it ‘many of itself’, with a plurality opposite that [numerical] unity...’’ (‘‘Intelligo: non est ‘ex se una’ unitate numerali, nec ‘plures’ pluralitate opposita illa unitati . . .’’ at Ordinatio , d., no. ). But this latter claim, about common nature considered in itself, is all on a par with Thomas’s view that nature considered absolutely is neither one nor many, but becomes one when considered by the intellect as a universal and becomes many outside the intellect in the concrete individuals having the nature. Aquinas and Scotus would say that there is a fact of the matter about whether Plato’s humanity is Socrates’: it isn’t (cf. note ). What is distinctive about Scotus’s position, and explicitly denied here by Leibniz (as it would have been by Thomas), is that common nature has a special sort of being and unity outside the intellect and considered in itself, something less than numerical unity. It is this Scotistic extravagance which Leibniz later describes (§) as an extreme realism: we shall return to this.

The early Leibniz: ‘‘Disputatio Metaphysica’’



unity prior to and independent of any numerical unity is just the sort of thing Leibniz rejects. To anticipate, briefly: what is Leibniz’s view of specific unity, generally said to be less than numerical unity? Sticking to the Disputatio, Leibniz endorses a qualified Suarezian nominalism,²⁶ claiming that there is nothing common or universal save what is subsequently abstracted by the intellect from singular individual substances themselves, these located first in the order of being. Given that there is no real distinction in res, but only a distinctio rationis separating out what is said to be common and to have specific unity, Leibniz’s fundamental position against the Scotists is in place: since ‘‘there are no universals before the operation of the mind, there is no composition from the universal and the individuating [principle] . . . There is no real composition, not all of whose members are real’’ (Disputatio §: G ,: MLI ). Thus, insofar as ‘‘the principle of individuation is taken to be either the whole entity or less-than-whole entity’’ (§), Leibniz is unambiguously opting for whole entity. But now – removing our nominalist hats and permitting ourselves the luxury of peering beyond the Disputatio – what about the metaphysics of individual substance itself, and its relation to specific unity? Recall the deep thread in Leibniz’s thought noted earlier, stretching from ‘‘unity and entity are the same in things’’ () to ‘‘what is not one being is not one being either’’ (to Arnauld, ). This thread looks to be woven alongside another (if, in , one more thinly spun), beginning with Leibniz’s explicit note in Disputatio § (G ,) that for Aquinas, the principle of individuation for angels is their whole entity. That Leibniz should, in the Discourse of  and to Arnauld the same year, say ‘‘of all substances’’ what Thomas ‘‘says about angels or intelligences (that every individual is an infima species)’’ (G ,: L ), would look to require of Leibniz the view that lowest species, at least, enjoy nothing less than numerical unity. One can only suspect that Leibniz had a glimpse of this requirement in the Disputatio; immediately after claiming that unity and entity ‘‘are the same in things,’’ Leibniz writes ‘‘Neither does numerical entity differ really from specific’’ (§: G ,: MLI ), echoing his earlier claim that ‘‘there is no real unity of a species except numerical unity’’ (§). C. Universals A third current in early Leibnizian thought is that talk of universals or common natures is not talk about something real, existing ²⁶ Suarez’s nominalist response to the (Scotistic) ‘‘realist’’ account of the unity of common nature can be found in Disputationes metaphysicae , ‘‘On Formal and Universal Unity.’’



Leibniz and the problem of individuation

in things independently of the intellect. The point isn’t one of Platonism vs. Aristotelianism. Like most parties in the medieval realism debate, Leibniz conceives of universals in Aristotelian rather than Platonic terms: were they to exist, universals would not be items confined to Platonic heaven, with only participants or instances located here and there, but rather would be fully present here and there within individual substances. So far as universal expressions themselves go, it was agreed on pretty much all hands that ‘man’, ‘white’ and the like do refer at least to intelligible concepts and typically also to something else distinct from concepts. The real issue of debate concerned whether or not any metaphysical entity in re ipsa was signified by a universal expression. As one might expect, Leibniz’s nominalism is most apparent in his critique of the Scotistic account of individuation. Unlike the Thomists, Scotus understood the nature of things as a real entity existing in individual substances quite independently of the intellect – a fundamentum in re by virtue of which individuals are the kind of things they are and share their membership in a common species. Being formally the same in, or common to, each member of a species, the quidditative common nature (natura communis) is indifferent to its determination in this or that individual and hence cannot serve as a principle of individuation. Thus it is some other positive entity, some ‘‘individuating difference’’ or haecceity, that together with common nature makes for an individual substance. Here is Leibniz on Scotus: Now it is known that Scotus was an extreme realist, because he held that universals have true reality outside the mind, while Thomas would prefer their formal character to originate in the mind . . . [B]ecause he [Scotus] supposed universals to be something real (either out of zeal for argument or because he thought that Thomas’ opinion was inexplicable or that of the nominalists incredible), it was necessary that singulars originate from a universal with something added. (Disputatio §: G ,: MLI )

Leibniz’s polemic against the Scotistic account of individuation is thus directed not only against the idea of constituent individuating differences (haecceities), but against Scotistic common natures: ‘‘If there are no universals before the operation of the mind, then there is no composition from the universal and the individuating [difference] before the operation of the mind . . . But the first is true. Therefore, etc.’’ (§: G ,: MLI ). Elsewhere Leibniz argues that since whatever things differ before the operation of the mind are separable,²⁷ to believe in ²⁷ x is separable from y iff x can exist independently of y. The separability relation itself isn’t symmetric, and so doesn’t entail a real distinction: substances are separable from modes but not

The early Leibniz: ‘‘Disputatio Metaphysica’’



communicable genus and species as real entities distinct from individuals apart from the intellect is akin to believing that there could be a line that is neither straight nor curved, or an animal that is neither rational nor irrational, ‘‘which is absurd’’ (§§, ). As noted earlier, Leibniz is here siding with Suarez in denying that the universality or communicability of natures is independent of the intellect. Where Scotus was clear that ‘‘community affixes to [convenit] the nature outside of the intellect, as does singularity,’’ Suarez insisted that ‘‘the disposition to exist in many things is not a real property belonging to the common nature of its own apart from the operation of the understanding.’’²⁸ But whatever the hostility to accounts of individuation positing real communicable natures in things, it says nothing against recognizing in individuals real natures. For Leibniz, as for Suarez, the nature in Socrates is individual to Socrates himself. ‘‘There is a nature, for example, in Socrates, which is intrinsically determined outside the mind to him’’ (§: G ,: MLI ) – a nature that, Leibniz goes on to say, is not ‘‘indifferent’’ to being determined as a nature of Socrates or of Plato or of someone else, indeed a ‘‘nature of Socrates [which] individuates itself.’’ And for Leibniz that claim of self-individuation is in fact the core thesis of the Disputatio itself: ‘‘every individual is individuated by its whole entity’’ (§: G ,: MLI ). Since ‘‘one adds nothing to being,’’ that by means of which a thing is one in number is that by means of which it is (§) – that is, self-individuated natures are individuated singular substances. Suarez had connected these same points in just that way: ‘‘the nature insofar as it exists in reality is individual, and is in fact entirely indistinct from the individual.’’²⁹ It is in view of just this thesis that one should understand Leibniz’s later refusal in Disputatio §§– to distinguish essence from existence as separate components of the being of a substance. conversely. In the context of denying that there is any (Scotistic) formal distinction preceding an operation of the intellect, Suarez says that any true and actual distinction ex natura rei will be either between real entities or between a real entity and its mode (Disputation ..). In the latter case Suarez will speak of ‘‘non-mutual separation, as it is commonly called, i.e. a separation in which one extreme can remain without the other, but not conversely’’ (Disputation ..: Berton vol. , p. ). ²⁸ Scotus, Opus oxoniense , d., q., n. and Suarez, Disputationes metaphysicae . .. In Disputatio § Leibniz pokes fun at ‘‘those who drag Suarez into Scotus’’ (. . . sunt qui Suarium ad Scotum trahant) – that is, he pokes fun at those who write as if they had altogether ignored Suarez’s insistence that only by a distinction of reason could one speak of an individual as adding something to the ‘‘common nature,’’ which for Suarez is of course not common nature at all. (Leibniz’s § reference to Suarez here, rendered by Gerhardt [G ,] and retained by McCullough [MLI ] as ‘‘Disp. Met. , sect. , n. ,’’ is in fact to sect.  [i.e., two, not eleven], number , of Disputationes metaphysicae .) ²⁹ Disputationes metaphysicae .. (Berton, vol. , p. ).

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Leibniz and the problem of individuation

We pause briefly here to note the claim of Laurence B. McCullough that Leibniz’s reading of Scotus involves a ‘‘fundamental blunder,’’ one that ‘‘colors all the remaining criticisms that he offers of haecceity in the Disputatio.’’³⁰ The blunder, on his reading of Leibniz, was to construe Scotus as claiming that common natures are universals (§) and can exist apart from haecceity (§). What about that? McCullough is certainly right that Scotus did not countenance a realism about universals sufficiently robust as to posit either a common nature that is numerically one in many substances or common natures that might exist independently of haecceities. Avicenna had said that ‘‘Equinity is just equinity – of itself it is neither one nor several, neither universal nor particular.’’ The text from Scotus cited earlier (see note ), in connection with the claim that natures possess less than numerical unity, is in fact a comment on this equinity passage from Avicenna’s Metaphysica ., and Scotus (who was by his own reckoning much influenced by Avicenna) proceeds in just the same way: nature in itself is not ‘one’, nor is it ‘several’ as the opposite of numerical unity – ‘‘nor’’ he continues, ‘‘is it universal . . . nor particular in itself.’’³¹ Now Leibniz understood very clearly that for the Scotists, the terms of the formal distinction are not really separable relata. Thus consider the two potentially offending passages in the Disputatio. First: ‘‘it is known that Scotus was an extreme realist, because he held that universals have a true reality outside the mind’’ (§). Leibniz’s complaint is not that Scotus believed common natures to enjoy individual numerical unity. He knew full well that the Scotists (like Scotus) wished above all to avoid any such commitment. That is why, after attributing an ‘‘extreme realism’’ to Scotus, he says straight away that Scotus ‘‘contrived the ‘formal distinction’ to hide his error’’ (G ,: LMI ). Leibniz’s primary concern is simply that once one grants common natures reality outside the mind, one must then locate an extra ingredient to combine with common nature to secure an individual – these ingredients being the differentia of individuals, serving to individuate them. And so Leibniz goes on to point out that ‘‘because he supposed universals to be ³⁰ McCullough, Leibniz on Individuals, pp. –; see also pp. , , . ³¹ Duns Scotus, Ordinatio , d., no. , continuing the passage from note . So, is the humanity of Socrates the same as the humanity of Plato? For Scotus, the question is ambiguous. If you mean ‘‘specifically the same’’ by ‘the same’ the answer is ‘‘yes’’. If you mean ‘‘really the same’’ the answer is probably ‘‘no.’’ On Scotus’s account, Socrates’ humanity is really identical with (though specifically/formally distinct from) Socrates; it follows that Plato’s humanity, which is really identical with Plato, is really distinct from Socrates’ humanity. Leibniz’s complaint (earlier, and below) concerns the reality and unity said by Scotus to be enjoyed by common natures considered in themselves and apart from the intellect.

The early Leibniz: ‘‘Disputatio Metaphysica’’

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something real . . . it was necessary that singulars originate from a universal with something added.’’ Notice here that Leibniz’s complaint does not trade on any illicit presumption that universals enjoy the relation of numerical unity and real difference with other things; rather, it trades only on the assumption that universals have reality outside of the mind. The second offending passage reads: ‘‘according to [Scotus] species exist apart from [praecisa] haecceity’’ (§: G ,: MLI ). Leibniz is not attributing to Scotus the claim that species are separable from haecceities, thus emerging as really distinct: he knows very well that Scotus and his followers intend them to be only formally distinct. Rather, Leibniz intends to attribute to Scotus the view that common natures are real and other than haecceities – with his ‘apart from’, like our own ‘other than,’ being the best one might do by way of a neutral term not explicitly bringing the language of numerical distinctness to bear. If Leibniz meant ‘‘really distinct, and so separable,’’ he had that taxonomy available to him, and used it in the Disputatio. Moreover, Leibniz goes on in § to represent one of the Scotists’ arguments for haecceity as involving this inference: since unity follows upon entity, and since numerical unity cannot follow from specific unity, some further individuating difference must be added to species to secure an individual. By attributing the second premise to the Scotists, Leibniz can hardly be charged with having understood them to believe that species are numerically distinct, really separable. In short, the ‘‘extreme realism’’ with which Leibniz charges the Scotists is a position according to which common natures are real, enjoying a reality and unity independent of any operation of the intellect. D. No Formal Distinctions A fourth strain in early Leibnizian thought is his denial of the formal distinction. The distinction itself was meant to be of service in cases where – granting that no act of the intellect can render distinct what is numerically one and the same – one’s unwillingness to claim that a and b are really distinct things (res) is matched by reasons for saying that a is thus and b is so.³² Such formally distinct entities ( formalitates) are neither really distinct nor mentally distinct: as Suarez characterizes the Scotistic opinion, ‘‘there is [said to be] in things prior ³² Such reasons were often theological. One might wish, consistently with affirming the doctrine of the simplicity of the divine essence, nevertheless to distinguish God’s mercy and God’s justice (for example, avoiding the inference from ‘‘He forgave me on account of His mercy’’ (true) to ‘‘He forgave me on account of His justice’’ (false)). Scotus himself made heavy use of the formal distinction in discussing the Trinity.



Leibniz and the problem of individuation

to intellectual activity a certain actual distinction, which accordingly is greater than a mental distinction but still not so great as the real distinction between thing and thing.’’³³ Leibniz is prepared to accept only the real and the mental distinction – here setting aside the modal distinction emphasized by Suarez (concerning the relation of properties/accidents to substances), given Leibniz’s decision to leave accidents out of his undertaking in the Disputatio.³⁴ The real distinction, on the one hand, holds between numerically distinct separable res, ‘‘between thing and thing,’’ independently of any act of the intellect. Thus Leibniz says that ‘‘Everything that before the operation of the mind really differs from another, such that neither is part of the other either wholly or partly, can be separated from the other.’’³⁵ On the other hand, there is the mental or rational distinction, which is made by the mind and does not map onto any really distinct separable res. It would be a mistake to suppose that for Leibniz, or for Suarez before him, such a distinction is a pure fiction of the mind. In saying (for example) that ‘‘genus and species are distinguished mentally’’ (§), Leibniz is allowing that certain distinctions not mapping onto real distinctions in the world are nevertheless proper for the intellect to make. Suarez had marked off the ‘‘purely fictional’’ from the ‘‘proper’’ by noting two kinds of rational or mental distinction: One, which has no foundation in reality, is called a distinction of the reasoning reason (distinctio rationis ratiocinantis), since it arises entirely from the reflection ³³ Disputationes metaphysicae .., citing Scotus’s In I Sent., d., q., and elsewhere. Leibniz says that the distinction is attributed to Scotus ‘‘as a middle between the real [distinction] and [that] of reason’’ (§: G ,: MLI ). ³⁴ Suarez introduces his third (‘‘modal’’) distinction in Disputationes metaphysicae .. (cf. note ). So far as we are aware Leibniz does not explicitly discuss the modal distinction itself. Descartes adopted the three-fold taxonomy of real, modal, and rational distinctions – its provenance for him tracing perhaps no more directly to Suarez than to Eustachius a Sancto Paulo (cf. Gilson, Index Scolastico-Carte´sien, pp. –), whose Summa philosophica quadripartita... () was familiar to Descartes (AT ,–: CSMK .–). (It was at least indirectly familiar to Leibniz as well, who cites the Breviarium Eustachianum of his teacher, Johannes Scherzer, in Disputatio §, and Eustachius himself in Disputatio §.) It should be noted that in a letter to an unknown correspondent Descartes says that his distinctio rationis ‘‘is perhaps better called formal’’ (AT ,: CSMK .), summarizing at the end of the letter: ‘‘So, then, I postulate three kinds of distinction: first Realem . . .; and then Modalem and Formalem . . .’’ Descartes would not have been the first to equate the rational (mental) distinction with the formal distinction (see Suarez, Disputationes metaphysicae .. and ..); nor apparently would he be the last (see McCullough, Leibniz on Individuals, p. , n.). ³⁵ Disputatio §. Leibniz’s comment that for really distinct things ‘‘neither stands in need of the other for its own esse’’ (G , : MLI ) calls attention to the fact that our earlier formulation – that x is separable from y iff x can exist independently of y – needs to be restricted to creatures, to render the truism ‘‘Finite substances are really distinct from God’’ consistent with orthodoxy. That was effectively Descartes’s route in Principles . (AT ,: CSM .).

The early Leibniz: ‘‘Disputatio Metaphysica’’

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and activity of the intellect. The other, which has a foundation in reality, is called by many a distinction of the reasoned reason (distinctio rationis ratiocinatae). This kind of mental distinction can be understood as pre-existing in reality, before the discriminating operation of the intellect, and only requires the intellect to recognize it, but not to constitute it . . . [I]t does not arise entirely from the mere operation of the intellect, but rather from the occasion offered by the thing itself, on which the mind is reflecting.³⁶

Like Suarez (and Descartes), Leibniz is prepared to acknowledge distinctions that reality in some way obliges the reasoning mind to make even though they do not correspond to a real distinction between numerically distinct individuals.³⁷ While the reasoned-reason account of the rational/mental distinction is clearly more robust than a distinction of purely fictional origin, the fact remains that for Leibniz the only distinction on the side of the world is the real distinction. This feature of early Leibnizian thought is central to his various attacks on views of individuation alternative to his own. Thus Scotistic haecceity, meant to individuate the substance while being only formally distinct, will to Leibniz’s thinking prove difficult to distinguish from the individual itself – implying in § that since species is not really separable from individuating (haecceitistic) difference we are left simply with the individual. Of course, having argued (§: G ,: MLI ) that ‘‘If there is no formal distinction, haecceity falls; but the first is true; therefore . . .’’ it remains open for Leibniz to accept the species–haecceity distinction as one of the reasoned reason. But this still precludes haecceity from figuring in an account of what, in the world, serves as the principle of individuation – of what marks off any individual substance as numerically distinct from others and makes it the individual it is. Nothing essentially involving a relation to the intellect can be a principle of individuation, which must instead be internal to the individual itself (point A above). This feature in Leibniz’s thought comes into play once again in his discussion of the putative distinction between esse and essentia. That distinction, viewed by earlier scholastics as an instance of the more general act/potency distinction, had apparently come to figure in accounts of individuation: as essence would correspond to what is merely potential, so the ‘‘terminating act of existence’’ would individuate an ³⁶ Disputationes metaphysicae , ‘‘On the Various Kinds of Distinctions,’’ Part , § (Berton, vol. , p. ). ³⁷ A very rough analogue in contemporary terms: one thing with two modes of presentation, each mode being compelling for the mind on account of the world.

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Leibniz and the problem of individuation

actual individual substance. Leibniz argues that essence cannot be really distinct from existence. If ‘‘whatever things really differ can . . . be separated from each other’’ (§), then a really separated essence would exist but apart from existence (§: G ,: MLI ), which is silly.³⁸ But Leibniz is prepared to embrace what on his view is the only alternative (short of denying the distinction altogether): ‘‘if [existence] differs only mentally from essence, [this position] agrees uncommonly well with us.’’³⁹ That is, existence as the principle of individuation will then amount to whole entity as individuator. Before moving to some philosophical reflections on Leibniz’s positive, ‘‘whole entity’’ doctrine of the Disputatio, we note two points in connection with earlier discussion. First, it is worth emphasizing here the deep and important alliance between Leibniz’s separability requirement for real existence and his commitment to the idea that a principle of individuation must be internal. Suppose a principle to be external. It will either be contingently related to the individual substance or noncontingently related. If the individuator is contingently related to the substance, then it cannot serve to individuate after all. But if the individuator is non-contingently related to the substance, then we should have posited a real distinction without separability, which Leibniz cannot allow. Second, recall again Leibniz’s departure from Aquinas in aiming to give a general account of individuation, ‘‘abstracting from material and non-material substances.’’ Given Leibniz’s insistence that the only distinctions in the world are real, and given that a real distinction entails separability, it is prima facie surprising that he takes his account to square perfectly well with an Aristotelian matter-plus-form account of substance. Thus: ³⁸ Of essence and existence Ockham had said: ‘‘[I]f they were two things [extra-mentally distinct], then no contradiction would be involved if God preserved the essence of some thing in the world without its existence . . . which [is] impossible’’ (Summa logicae, .ii.c xxvii). ³⁹ Disputatio §: G ,: MLI . Suarez argues that the essence/existence distinction is neither real nor modal but rather a distinction of reason in Disputation  (‘‘On the Essence of Finite Being As Such, On the Existence of that Essence and their Distinction’’), devoting Section  to separability considerations. Although he includes Aquinas among his representatives of ‘‘The First Opinion Affirming They are Really Distinguished’’ (Section ), Suarez was surely aware of the debate among later Thomists – indeed especially those at Salamanca – about whether a separability gloss on the real distinction is faithful to Thomas himself; and in the separability discussion of Section  Suarez is overtly cautious about attributing the dua res reading only to ‘‘one or another of the moderns’’ (..: Berton, vol. , p. ; here see Kennedy, ‘‘Thomism at the University of Salamanca in the Sixteenth Century’’). However keen Suarez and Leibniz are to deny any metaphysically robust distinction between essence and existence, the separability challenge itself probably cannot be directed at Aquinas.

The early Leibniz: ‘‘Disputatio Metaphysica’’

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Ramoneda erroneously attacks those who claim that the individual individuates itself and those who say that matter and form supply it [the principle of individuation] as contradicting each other, for they could instead be understood to be subordinate views, as special instances under the general view. For what is matter and form united except the whole entity of the composite? (§: G ,: MLI )

Here Leibniz seems to be expressing the sentiment that one should bring all the components into an account of individuation, not that we shouldn’t multiply them. But how can the distinction between matter and form be acceptable in a way that makes it suitable for purposes of a story about individuation? Does Leibniz think that matter and form are really distinct and separable?⁴⁰ After all, ‘‘there is no real composition, not all of whose members are real’’ (§: G ,: MLI ); and in connection with Leibniz’s insistence that all unity is grounded in numerical unity, recall his concern to reject pictures according to which things having less than numerical unity could yield a singular individual enjoying numerical unity. Within two pages Leibniz clarifies his position somewhat: ‘‘the material and the formal element of the individual . . . do not differ really’’ (§: G ,: MLI ). If one suspects him here of ignoring his later concern not to ‘‘make sport of the authority of Aristotle’’ (§), Leibniz might remind us that Aristotle too had said that ‘‘the proximate matter and the form are one and the same thing.’’⁴¹ Nevertheless, one should not think that Leibniz’s remarks about matter and form – apparently urging a rational distinction between them – make for a perfectly happy union with his general approach in the Disputatio. Leibniz’s standard way with rational distinctions is that they involve a relation to intellect, and so cannot figure in any principle of individuation which must be internal to the substance. In reckoning the matter/form distinction a rational one and thus, in effect, irrelevant by his lights to a theory of individuation, the bedrock of most scholastic ⁴⁰ The reader will perhaps have noticed a via media for reconciling a real distinction of matter and form with a claim of insubstantiality for each considered in itself. Suppose that matter requires a form but no form in particular in order to exist, and that a form requires some matter but no particular quantity of matter in order to exist. Neither form nor matter will in this context have the stand-alone characteristics of the medieval conception of substance; but nevertheless each particular form and each particular quantity of matter will be separable and hence really distinct. This view is not a defensible piece of early Leibniz interpretation, given his insistence that matter and form are not really distinct (§: G , ). But it stands as a philosophical option worth noting – one indeed that Scotus entertained and rejected. ⁴¹ Metaphysics , , b – though (not unexpectedly) Aristotle fudges, in a direction that Leibniz should be less eager to point out, by adding later ‘‘the potential and the actual are somehow one.’’

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Leibniz and the problem of individuation

accounts of individuation crumbles. If this is correct, Leibniz should be rather less sanguine about welcoming on board the traditional matterplus-form account of numerical unity. . The whole entity doctrine: reflections on Leibniz’s positive account Set aside this latest concern, and assume a general component-style account of individuation: individuals are numerically distinct and are the very individuals they are in virtue of their components. This style of account can take two forms: things are individuated by the totality of their components, or by some of them. Early in the Disputatio Leibniz says that traditionally a principle of individuation is taken to be ‘‘either the whole-entity or less-than-whole-entity’’ (§). The whole-entity thesis is, at least at a first pass, the thesis that things are individuated by all of their components, the less-than-whole entity thesis claiming that things are individuated by some of them. We should like here to reflect a bit more carefully on what the whole entity thesis amounts to. Is Leibniz saying, for example, that my fingernail must figure into what individuates me? Relatedly, is he saying that my fingernail is essential to me? And if it isn’t essential, how can it individuate me, even in part? Leibniz doesn’t explicitly address such mundane questions in the Disputatio. Judging from the concerns of the Disputatio itself, the whole-entity doctrine in our view makes rather less sense if understood in this way, as bringing with it all of (say) Socrates’ accidents. The whole entity, we suggest, is what one gets when one strips away the accidental accouterments of the individual – trappings understood by all to be other than genuinely internal to the ultimate subject of predication underlying the accidents. Taking this line, it now makes reasonable sense to ask which of the components of a whole entity are those by virtue of which the thing is (say) Socrates. Suppose a scholastic thinks that x, y, and z are essential to Socrates. Perhaps x is substantial form, y quantity of matter, z Scotistic haecceity. The following question naturally arises: ‘‘Is it by virtue of all or only some of these components that Socrates is the very individual Socrates is?’’ Prima facie, one isn’t obliged to think that all of the components must be invoked in connection with such questions of individuation as these. Perhaps one component explains the thing’s qualitative nature, another its numerical distinctness from colleagues, another its being Socrates himself, and so on – a view that given the above list will be very natural. The approach Leibniz is keen to reject in the Disputatio is the view that, among the

The early Leibniz: ‘‘Disputatio Metaphysica’’

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non-accidental components of a thing, only a subset of them need be invoked in order to explain Socrates’ individuality. (It must be admitted here that Leibniz never clearly distinguishes the question ‘‘What accounts for the numerical distinctness of a thing?’’ from ‘‘What accounts for its being the very individual that it is?’’ Thus for example he lumps together the double negation doctrine with the Scotistic haecceity account as less-than-whole entity approaches to individuation. But the double negation view – that a substance gets its numerical unity by the negations of indivisibility and difference – could at best account for what makes a thing a genuinely individual substance, and not what makes a substance Socrates as opposed to Plato. This failure [to some extent a weakness of Suarez, in our view] is partially explained by the fact that on Leibniz’s positive account, it will come to seem like the same thing – the whole entity – that does both sorts of explanatory work. Nevertheless one cannot help but think that having those questions more clearly distinguished would have proven instructive in Leibniz’s treatment of alternative views.) Abstracting from the particular scholastic offerings, how might one argue in a general way for the whole entity view as opposed to the less-than-whole entity view? One tempting line of argument invokes the thesis that an individuator – one entity or metaphysical principle in the world – can’t individuate numerically distinct things, coupled with the axiom that an individuator must be internal to the thing individuated. Suppose there are components x, y, and z of Socrates. One seems to confront the option of including all or less-than-all of the intrinsic components in an account of what individuates Socrates. If it is all, then that is equivalent to the whole entity doctrine. Assume for reductio less-than-all – a less-than-whole entity doctrine. Suppose it is z that individuates. Presumably, the whole entity doctrine is true of z, it being always illegitimate to look for extrinsic individuators. But z cannot individuate z and Socrates unless Socrates is z: if one assumed that z individuates z and Socrates, but that Socrates is not z, then the putative individuator could not account for the relation of numerical difference between z and Socrates. So z must be Socrates. Hence the whole entity doctrine would be true of Socrates after all. Tantalizing as the preceding argument is, and despite its Leibnizian premises, we do not find explicit traces of it in the early Leibniz. Instead, the basic argument for whole entity, offered by Leibniz and nearly all others endorsing the view (§§,), is parasitic on themes already noted: that by virtue of which an individual substance is, or has being, is that by

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Leibniz and the problem of individuation

virtue of which it is numerically one, and the being of a substance just is its whole entity (G ,–: MLI –). To suppose, as Bassolis and Mercenarius supposed, that something distinct and (so by Leibniz’s reckoning) separable from the individual entity secures its numerical unity, is to suppose that something necessary but not sufficient for there being the entity itself is nevertheless sufficient for there being one entity – this latter role simply is not playable by anything less than whole entity. We pursue briefly this latter line of thought. Suppose there are n components of the whole entity (where possibly n = ). None of those components can be this way – neither necessary nor sufficient for the individual substance: again, the whole entity is what one is left with when one strips away the accidental accouterments of the substance. So the components will include members from the following pair of categories: (i) Necessary and Sufficient for the individual and (ii) Necessary for the individual. Suppose, on the one hand, that there is at least one component C* that is necessary and sufficient for the individual. C* will be sufficient for each of the components that are necessary. If there are other components apart from C*, then C* will be sufficient for them. But then C* will not be separable from them, since C* can’t exist without them. If there is just one component that is necessary and sufficient, then one can preserve the separability of components only by taking the entity to be identical with that component. Thus assuming that there is at least one necessary and sufficient component, one arrives at the view that the entity has one component – itself. This speaks in favor of the whole entity view. Suppose, on the other hand, that there is no component that is necessary and sufficient, but instead a number of components c to cn that are necessary. No subset of those components will be sufficient; for, given separability, no subset will guarantee the existence of the rest. And since the existence of the rest is necessary for the existence of the thing, no subset will guarantee the existence of the thing. Hence one won’t be able to individuate the thing in terms of some, but not all, of its components. Once again this speaks in favor of the whole entity view. Thus: . The components of the whole entity are non-accidental and so each necessary for the individual substance. . Either one of the components is necessary and sufficient or it isn’t. . If one component is necessary and sufficient, then there is only one component altogether (and thus the less-than-whole entity view fails).

The early Leibniz: ‘‘Disputatio Metaphysica’’



. If no component is necessary and sufficient, then no subset of the components will suffice for the thing (and thus the less-than-whole entity view fails). . Therefore the less-than-whole entity view fails. Given that separability looks able to carry most of the load, why does Leibniz lean so heavily on a denial of universals? As nominalists – even those of the attenuated Suarezian stripe – had long seen, to the extent one believes in universals, it is difficult to maintain that on the side of the world there are only really distinct things. Suppose one believed that there is a species-component of us – say humanity. One is then almost compelled to throw in other components to individuate a substance. But then, given that humanity is essential to the substance and that the full story of individuation involves at least two components, the thesis that everything on the side of the world (rather than the reasoned reason) is really separable will be violated. Leibniz can only defend himself here by denying the existence of genuinely common universals. Thus, from Disputatio § (G ,: MLI ): [It is said that] species is not contracted either through form or through matter, or through accidents, etc. Therefore there remains haecceity. I answer that it is contracted through nothing, because there is no [species] outside the mind. [It is said that] species contract genus through specific difference. Therefore, the individual [contracts] species through numerical difference. I answer by denying the antecedent as true outside the mind.

There are, of course, for Leibniz as for Suarez, rationally distinct universals components. But since they exist only in relation to the intellect, they are irrelevant to individuation. What would contemporary philosophy make of this discussion? If one were to think (as many do) that there are immanent universals, one would of course object to Leibniz’s project. But suppose for better or worse one is charitable enough to play the game by roughly Leibnizian rules: is there any way that the contemporary might think of the discussion as altogether wrongheaded? To anticipate bits of later discussion, we mention two sorts of reaction: (A) ‘‘The requirement that individuation be explained by some component or plurality of them is altogether on the wrong track. Whatever the correct account, it must be able to preserve our intuitions about particular issues of identity and difference, including diachronic ones. Take personal identity for example. The identity of person A at t with B at t concerns some relation of

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Leibniz and the problem of individuation

continuity between A and B, and not any common component that survives over change from t to t. It may well have been axiomatic for the scholastics that identity of individual substance through change requires something numerically identical throughout; but that is ultimately indefensible.’’ (B) ‘‘Identity is not to be explained in terms of components of an individual at all. Properties account for individuation – indeed perhaps haecceitistic properties such as being identical with Socrates. But however the property-story goes, properties are had by the thing, instantiated by the thing: they are not components of a thing in any scholastic sense.’’

Our concern is not with the cogency of these remarks, but rather with their departure from the requirement that a principle of individuation be internal to the thing. Suppose that A and B are people. By Leibniz’s reckoning, what makes an individual A and what makes an individual B will be wholly internal to each. If A is B, then what makes an individual A is what makes an individual B, and this will explain A’s being B. From the scholastic perspective, to invoke the intended continuity relations as fundamental is to suppose that B would not be the individual it is without its history, or that A would not be the individual it is without its future. But this threatens to contravene the fact that a thing’s individuality is internal to it – unless, perhaps, one’s metaphysic of substance provides for a thing’s history and future being somehow packed internally into it . Similarly, on the side of properties, a Platonic haecceity (etc.) view would seem to violate the requirement that a thing’s individuality is internal to it. Now, of course Leibniz will allow accidents, which will for him be unique to their subjects; but the secondary metaphysical status of accidents prohibits them from explaining the individuality of a subject – of being that in virtue of which this individual is the very individual it is. Perhaps haecceitistic accidents are permissible, with Socrates yielding the trope Socrateity by virtue of being Socrates. But to posit a form Socrateity that grounds this individual’s being Socrates without being an internal component of the substance Socrates is to assert necessary connections between really distinct existences – a thesis that, in its own way, seems to us as important to Leibniz’s philosophy as to Hume’s.⁴²

⁴² Of course, while Leibniz (like Hume) will affirm this thesis for created things, he would be careful to qualify it when God’s relation to the world is in view.

The early Leibniz: ‘‘Disputatio Metaphysica’’



. Simplicity Does the early Leibniz’s story, or the resources he deploys, secure the view not only that substances are individuated by their whole entity but moreover that individual substances are simple? The answer is ‘‘no’’, and it is worth understanding why. If the requirements of separability are taken seriously, then insofar as there is just one necessary and sufficient component, that component will be identical with the individual substance itself, and the whole-entity will lack any plurality of components. In this way, one secures not only the whole-entity view, but a simple-entity view. The alternative we noted was a plurality of components, each being necessary and no subset being sufficient. And the question is whether this is a possible structure of substances by the lights of the early Leibniz. Recall the early Leibniz’s insistence that there is no entity having less than numerical unity. Insofar as composite substances have constituents, then, a feature that constituents must enjoy is numerical unity. And that is to say that they must themselves be bona fide individuals. So Leibnizian composites will have to be bona fide individuals enjoying bona fide individuals as components. The viability of any such composite was a much-debated issue from the time of Aristotle, who bequeathed to his scholastic offspring grist for a philosophical debate. In On the Soul ., after reminding us that we speak of substance sometimes as matter (which is not a this), sometimes as form (in virtue of which a thing is a this), and then sometimes ‘‘in the sense of that which is compounded of both,’’ Aristotle says of paradigm individual substances – living things – that they are ‘‘substances in the manner of a compound’’ (a), of which the soul is the form. To that hylomorphism add the claim of Metaphysics . that ‘‘no substance is composed of substances’’ (a), and one is left with deciding whether (permit us say) the substance that Socrates is comes from his matter being a substance but not his form, comes from his form being a substance but not his matter, or somehow comes from the combination of non-substantial form and non-substantial matter. Aristotle wasn’t prepared to speak of matter itself, uninformed matter, as a substance; but if ‘‘it is clear that the soul is inseparable from its body’’ (a), then, given his own separability requirement for substance, perhaps neither is ‘‘un-mattered’’ form a substance. The question in any case arose for the scholastics whether a genuinely individual substance, numerically one per se, could in any way be composed of things enjoying a substantial unity themselves.

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Leibniz and the problem of individuation

Suppose that Leibniz were to allow composite substances of this sort. The logic of the Disputatio says a good deal about what they would have to be like. Keeping Leibniz’s separability gloss of the real distinction in place, the only kind of necessary but not sufficient component that appears to be allowable is the sort of component that can exist independently of the other components. Since the other components are, by hypothesis, necessary for the existence of the composite, this requires that each component can, so to speak, survive corruption of the substance – rather like a parcel of matter or an immaterial ego, for example. Suppose there is a plurality of necessary components that are all of this sort. The mere coexistence of those components won’t suffice for an individual substance – for then the thing would be a mere aggregate, having nothing like the substantial unity sought for genuine substances by all scholastic thinkers. So the substance, while having those components, must itself be something ‘‘over and above’’ simply those components. Furthermore, this over-and-above cannot be a distinct component of the substance. For the over-and-above as component would have to be necessary and sufficient for having the existing individual (none of the other components being sufficient, save collectively for an aggregate); but then this would rule out the other components as necessary, on pain of violating the requirement of separability of components. Thus one must say that the substance is over and above the components, but that there is nothing real apart from the substance itself that constitutes its being over and above the components. This sort of position is not foreign to contemporary metaphysics. Consider, for example, David Armstrong’s view on states of affairs. The state of affairs of a’s being F is something over and above a and F. Yet there is nothing really distinct from the state of affairs itself that provides the differentia between a, F, a’s being F (on the one hand) and a, F, a’s not being F (on the other).⁴³ Is this a viable picture for the early Leibniz? Only if separability is somehow restricted. After all, the whole substance isn’t separable from all or each of its components. Since each component, by hypothesis, is necessary for the whole,⁴⁴ the whole cannot exist without that component existing. If separability is taken in an unrestricted form, namely: ⁴³ See D. M. Armstrong, A World of States of Affairs, chapter . ⁴⁴ Aren’t some components accidental to the whole? Recall that the whole-entity view, as we understand Leibniz’s conception of it, is what you get when you strip away the accidental accouterments.

The early Leibniz: ‘‘Disputatio Metaphysica’’



(US) For all x and y, if x and y are numerically distinct, then x can exist without y and y without x,

then composites with necessary ingredients are ruled out straight away. But recall Leibniz’s clearest statement of separability: ‘‘Everything that before the operation of the mind really differs from another, such that neither is part of the other either wholly or partly, can be separated from the other’’ (§ our emphasis). This clearly embraces a restriction on generalized separability, namely: (RS) For all x and y, if x and y are numerically distinct, then x can exist without y and y without x, unless x is a component of y or y is a component of x. If x is a component of y, then x can exist without y but not y without x. If y is a component of x, then y can exist without x but not x without y.

Assuming this restricted separability, then, the logic of the Disputatio admits the intelligibility of substantial individuals having per se components. But note that the Disputatio hardly requires a substantial unity to have components. At best it permits them. Component diversity is on no reading of the early Leibniz somehow integral to substantial unity as such. To this extent, any commitment on Leibniz’s part to a component metaphysic of substance is at best half-hearted. Nevertheless, if the picture just sketched is a coherent one, room is made for a composite individual substance, albeit a composite substance with substantial unities within it. If one were to attempt to put scholastic meat on the bones of the composites permitted by the logic of the Disputatio, one would undoubtedly look to the medieval conception of ‘‘incomplete substances.’’ For it was through this conception that the idea of a per se individual with per se components found its distinctive expression in the tradition inherited by the early Leibniz. We divert briefly to recall how the picture of incomplete substance took shape in response to the problematic bequeathed by Aristotle. For his own part, Aquinas held that all created (non-angelic) individual substances are composed of prime matter and substantial form, prime matter being the substratum in which forms inhere – now the form of humanity (Socrates alive), now the form of corpse (Socrates dead). If one should object that, insofar as prime matter can persist now-informed-thus, now-informed-so, it is a really separable substance, Aquinas would note that matter isn’t a this, but merely exists in potentiality relative to some form or other – only forms themselves enjoying actual existence. So any composite substance has at most one com-

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Leibniz and the problem of individuation

ponent with actual existence, at most one substantial form. Scotus departed from Aquinas here, urging that matter couldn’t be the persisting substratum for substantial change unless it had some actual being of its own. Indeed, since Aristotle taught us that substances are compounds, matter is no less a genuine component with actual being than is form – both no doubt possessed of a natural inclination to be joined with the other, but in some sense really distinct and separable from one another.⁴⁵ And why stop there? Many scholastics didn’t, arguing that one must indeed recognize corporeal forms, quite distinct from animating forms, and also (according to some) distinguish sensory from intellectual forms.⁴⁶ Here then is the scholastic idea of incomplete substances (substantia incompleta). Suarez deployed the notion often in the Metaphysical Disputations – referring for example to the rational soul and prime matter as incomplete substances (Disputation ..), that is, distinct substantial components of the complete substance that is a particular corporeal organism. So the soul is incomplete insofar as it is ‘‘by its nature set up [made ready: institutus] to inform matter,’’ and is a substance in being prior to and necessary for the complete substance, having the status of incomplete substance ‘‘even if separated from the body’’ (..–: Berton v. , –; compare Aquinas, ST  .). The idea is that an individual substance could be a composite, having incomplete substantial components or forms that are completed in the unified whole.⁴⁷ Contrast this genuine complete substance with a heap or aggregate. The ‘‘inferior’’ substantial forms figuring as parts of an aggregate are all the forms one needs to have the mere aggregate; but in the case of a ⁴⁵ Scotus says that matter is ‘‘really distinct from form’’ at Opus Oxoniense , d., q. Ockham took pretty much the same line: see Marilyn McCord Adams, William Ockham, pp. –. Chapter  of Adams’s work, on which we’ve drawn here (including the Scotus reference just given), contains a rich discussion of composite substance in the scholastic period (prior to Suarez). (NB: ‘‘substantia composita’’ in the scholastic tradition, while perhaps most often used in reference to the composition of form and matter, was also used to express other forms of ‘‘composition’’ such as that of genus and difference, essence and existence, substance and accident, and so on. We use the expression here to speak of the relation between complete substances that are one per se and their logically prior incomplete substances or substantial forms, their components.) ⁴⁶ See note . ⁴⁷ Descartes, in the Fourth Replies, is prepared to speak of incomplete substances in this sense – ‘‘in the sense that, although it has nothing incomplete about it qua substance, it is incomplete in so far as it is referred to some other substance in conjunction with which it composes something that is one per se . . . [T]he mind and the body are incomplete substances when they are referred to a human being which together they compose; but considered on their own, they are complete’’ (AT , : CSM .). But Descartes distanced himself from the scholastic notion that incomplete substances have a natural disposition or inclination to be joined in a compound substance: see the letter to Regius of December  (AT ,: CSM(K) .).

The early Leibniz: ‘‘Disputatio Metaphysica’’



complete substance, the substantial forms figuring as components of the substance are not alone sufficient for having the complete substance itself – here needing some further substantial form to complete the substance. Thus a substance is incomplete if it enjoys a substantial form and is by its nature fitted to participate in a further substantial form that gives something else its nature. A substance is complete if it enjoys a substantial form that gives it its nature and doesn’t participate in a further substantial form that gives something else its nature. Both are concrete individuals, both are substances. Is this view consistent with the whole entity account? In the hands of the Disputatio Leibniz, any incomplete substance doctrine would have to satisfy a number of distinct requirements. First, one would not be permitted to think of a substance as a composite of one or more incomplete substances coupled with something or other that lacked numerical unity. Second, one would be required to think that the incomplete substances (for example, soul and body) comprising a complete substance could each exist apart from the other (so that the separability requirement is respected). Third, rehearsing now a familiar Disputatio thought about natures, the forms would have to be individualized: Disputatio nominalism would not permit one to think of forms as common to many substances. Fourth, one would not be permitted to think of the individual form that completes one or more⁴⁸ incomplete substances as an ingredient of the complete substance numerically distinct from it. This by now is a familiar thought: to admit an individuating differentia of a complete substance that is distinct from it is to violate separability, to grant a difference without a real difference. Suppose then that Socrates is a complete substance. It follows that (i) Socrates has one or more⁴⁹ necessary components, none of which are sufficient for the existence of Socrates – whether considered individually (else separability would be violated) or severally (else Socrates would be a mere aggregate); (ii) these components enjoy substantial unity, though are incomplete substances because caught up in a further substantial form; (iii) each of these components can exist independently of the others; (iv) Socrates’ form is individual to him, since forms aren’t universal; and (v) Socrates is identical with the substantial form in which ⁴⁸ As we have presented it, the logic of the Disputatio permits a complete substance to have one numerically distinct incomplete component. The trick, if you like, is to resist the temptation of thinking that some ingredient, distinct from the complete substance combines with the incomplete substance, to yield the complete substance. Whether one or many incomplete substances are in view, it is the complete substance itself, not the addition of an ingredient, that completes the incomplete substance(s). ⁴⁹ See note , above.

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Leibniz and the problem of individuation

the components are caught up. Here, all of the early Leibniz’s key doctrines about individuation are readily preserved. Individuation is internal; all unities are at bottom numerical per se unities; there are no universals; and there is real separability of all components that are not related as component to whole. The early Leibniz’s doctrines of individuation, we conclude, are neutral as to whether there are non-simple substances. This is how things should be. Leibniz explicitly flags the issue of incomplete substances as postponed to another occasion, claiming that ‘‘we have left incomplete beings out of the present undertaking’’ (§: G ,: MLI ). As we read his whole-entity account, there are thus two sorts of substances allowed by the early Leibniz: simple substance that individuate themselves, and composite substances that individuate themselves (their components, even taken as coexisting, being insufficient to individuate them).                     Far from abandoning the logico-metaphysical assumptions of the Disputatio, those assumptions are fully integrated into Leibniz’s mature metaphysic. Their presence there is not always fully apparent. Part of the effort of our later chapters is to isolate these assumptions, and highlight their importance to Leibniz’s thought. Before sketching our plan to articulate and develop the mature Leibnizian metaphysic of individuation in those chapters, we pause briefly to indicate something of its focus. Reference to ‘‘the mature Leibnizian metaphysic’’ will seem to many already in need of added precision, shy of any sustained historical or textual argument for a univocal reading of Leibniz’s philosophy from  onward (which is not among our purposes). Our pause, then, is a brief look at the thorny issue of corporeal substance, approached now (as it generally is not) from Leibniz’s distinctive Disputatio allowance for non-simple substances. . Composite beings? Here are two possible pictures of the substantial world that are left open by the Disputatio: a world of only simple substances, and a world including composite substances having simple substances as their only components while being somehow over and above them. On one interpretation of certain texts, the mature Leibniz might have

Preliminary remarks on the mature Leibniz



been tempted by something approaching the second, compositional, story. Suppose there are simple substances, monads: ‘‘Monads do not constitute a complete composite substance, since they do not make up an unum per se but merely an aggregate . . . ’’ – ‘‘unless,’’ Leibniz added in this May  letter to Des Bosses, ‘‘some substantial bond is added’’ (G ,: L ). As late as the Des Bosses correspondence, Leibniz may be seen to entertain the idea that ‘‘[i]f corporeal substance is something real in addition to monads, as a line is known to be something more than points, it will have to be said that corporeal substance consists in a kind of union or, rather, in a real unifier superadded to the monads’’ (G ,: L ) – thus introducing the vexing idea of a monadum substantiale vinculum. Now it seems to us that, in identifying the real unifier added to monads with what the corporeal substance consists in, Leibniz is not conceiving the vinculum as an individualized ingredient distinct from the composite substance itself – no more than one would conceive of something that, when added as an ingredient to points, combines with them to produce a line. Rather, what is superadded to the monads is the substance itself (to the points, the line itself ). The composite substance, Leibniz tells Des Bosses, ‘‘consists in that unifying reality which adds something absolute and hence substantial’’ (G ,: L ), referring later to the ‘‘union constituting a new substantiation (unione substantiatum novum constituente)’’ (G ,). What there is over and above the monads is the corporeal substance, the unifying reality in which that corporeal substance consists. Certainly there is little doubting that the vinculum substantiale was to enjoy many of the properties Leibniz reserved for substances: it was to explain metaphysical unity (G ,: L ), to have the status of a substantial form (G ,: L ), and to consist in the primitive active power from which all actions of a substance arise (G , : L ; G ,: L ). Leibniz’s commitment to the vinculum, initially offered in response to Des Bosses’s request that he explain the substantial change of transubstantiation, is at least as doubtful as his commitment to transubstantiation itself.⁵⁰ It is in any case inconsistent with what, to an increasing extent before and after the Des Bosses interlude, comes to dominate Leibniz’s later metaphysic – namely the first picture of a world con⁵⁰ See G , , . Of course, Leibniz’s reluctance here in  and  – that ‘‘we [Lutherans] who reject transubstantiation do not need such things’’ – cannot be the whole story, given his willingness to pursue the vinculum account beyond expressly eucharistic discussions, and to take up the issue of transubstantiation charitably elsewhere. For an extremely helpful and wellbalanced treatment of the Des Bosses correspondence and the vinculum substantiale, see Robert M. Adams, Leibniz: Determinist, Theist, Idealist, pp. –.

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Leibniz and the problem of individuation

taining only simple substances. That is the picture we shall be keeping primarily in our sights in this book, one according to which ‘‘there is nothing real in things except simple substances, and in them perception and appetite’’ (G ,: L ). The expedient of narrowed focus comes with a risk. The Des Bosses interlude aside, our focus on simple substance pays little heed to other talk of ‘‘corporeal substance’’ between  and the early s – a period of texts from which we shall be borrowing freely in subsequent chapters. Now an exclusive focus on simple monadic substances in the context of our study would be straightforwardly in order were all the corporeal-substance texts to invite what Robert Adams calls a ‘‘qualified one substance’’ reading of them.⁵¹ Many texts permit that reading: a corporeal substance is nothing more than a monad qua possessor of an organic body, not some further, compound entity with a monad (and the monads or corporeal substances of the aggregate-body) as component(s). By way of analogy, suppose we call some rational creature a King. Calling him a King will draw attention to the fact that he enjoys a kingdom. But of course (i) we should resist thinking of the elements of the kingdom over which the rational being has dominion as components of the King, and moreover (ii) we should recognize that the King is simply identical with the rational individual to whom the kingdom belongs. Suppose the one-substance reading captures much of Leibniz’s intent. Then corporeal substances are identical with dominant monads and the ultimate de re metaphysic of the latter transfers immediately to the former. What renders an individual worthy of the description ‘King’ may be different from what makes an individual worthy of the description ‘rational being’; but the de re metaphysic of Kings will not be a special subject-matter distinct from the de re metaphysic of rational beings. Likewise, the de re metaphysic of corporeal substances is not a special subject-matter distinct from the de re metaphysic of simple monads. Alas, the texts are far from speaking in one voice for the onesubstance account. Robert Adams has made a persuasive case for thinking that in the s and s, Leibniz allowed corporeal substances to be per se unified substances distinct from their dominant monads, whose per se unity consists in the harmony of perceptions between their dominant monads and the monads that compose their organic body.⁵² Of course no one doubts the importance to Leibniz of his anti-Cartesian ⁵¹ Adams, Leibniz, pp. –.

⁵² Ibid., pp. –.

Preliminary remarks on the mature Leibniz



polemic against extension as a principle of per se unity in any substance. Nevertheless, according to the picture under consideration, there remain two distinct sources of per se unity in substances. On the one hand, the per se unity of simple substances is constituted by a unified active form or force; on the other hand, the per se unity of compound substances is constituted by the right kind of harmony. But this harmony is not a superadded ingredient; rather it is a relation secured by God creating the right kind of simple substances in the first place. (We shall address the issue of harmony in chapters  and .) As Adams points out,⁵³ the mature Leibniz finally, by , had second thoughts about the idea that harmony can ground per se unity, conceding to Rene´-Joseph de Tournemine’s criticism of the pre-established harmony that, just as the agreement that the Cartesian God maintains between soul and body cannot ‘‘bring about a true Union,’’ so also ‘‘my pre-established harmony could do no better’’ (G ,: AG ). In this period, Leibniz believed that it would take an irreducible union – later, a vinculum substantiale – to confer substantial unity on a monadic aggregate; and his preparedness to endorse per se composite unities in that context was, as indicated by the Des Bosses correspondence, at best tentative. By our lights, this shift in Leibniz’s mature thought, away from the idea that harmony between simples can confer per se unity on an aggregate being, is to be applauded. Sentiments on the side of historical precedent for corporeal substances notwithstanding, Leibniz’s concession to non-simple substances has little motivation from and does little work within his systematic metaphysics itself. Indeed, when viewed against the backdrop of the oft-repeated conviction that ‘‘a unity founded on the relations of true substances’’ constitutes only a ‘‘being by aggregation’’ (G ,: LA ), the introduction of composite corporeal substances seems to us rather a botch. If so-called organic substances turn out to be constituted by no more than relations of perceptual harmony among what is otherwise an aggregate of simple substances, then what Leibniz said to Tournemine expressed what he should have said all along. ‘Corporeal substance’ turns out, from this perspective, to be an oxymoron, a misleading shorthand for ‘‘simple substances related thus-and-so.’’ Suppose that the particular relational facts of harmony at a world supervene on the creation of the right simple substances. If this is in fact ⁵³ Ibid., pp. –.



Leibniz and the problem of individuation

Leibniz’s considered picture, matters are worse still for any concession to corporeal substance. For it now turns out that the mere co-existence of certain simple substances is sufficient for the existence of a so-called corporeal substance – a tell-tale sign for the scholastics, and for us, of a second-rate being per accidens rather than per se unity, the corporeal substance being nothing over and above the members of the aggregate. There lies the way of botch to be sure, for it is Leibniz’s considered picture that the relational facts of harmony at a world supervene on the creation of the right simple substances, as we shall see in chapters  and . (And, insofar as our discussion in those chapters succeeds in showing that the harmony-theoretic facts true of any individual substance are strictly speaking extrinsic and do not express intrinsic metaphysical necessities de re, the connection between monads and bodies required by the commitment to composite substances whose per se unity consists in the harmony of perceptions between dominant monads and the monads composing their organic body would seem rather tenuous. Indeed Leibniz denies that monads necessarily have bodies (G ,; G , ). How likely is it that per se unities are to be grounded in de re contingencies?) Some readers will agree with us that Leibniz’s affair with corporeal substances represents an ill-considered and not especially serious metaphysical commitment, composite substances being metaphysical danglers with little underpinning.⁵⁴ We invite those readers to treat subsequent chapters – exclusively focused as they are on simple substances – as a study of all the substances finding a place in Leibniz’s considered account of things. Despite a confessed lack of fit with some wayward thinking on Leibniz’s part, one may yet think of the onesubstance view as a good first pass at both what Leibniz ought to have thought and what from  on Leibniz – flirtations with the vinculum substantiale aside – did think.⁵⁵ ⁵⁴ Donald Rutherford is one who takes such a line, diagnosing Leibniz’s flirtations with corporeal substance in the s to be explained by either a failure to ‘‘have thought through the full consequences of his doctrine of pre-established harmony for the unity of the soul-body composite’’ or else an attempt to accept ‘‘the advantage of seeming to defend the orthodox position that the soul–body composite is an unum per se, when, strictly speaking, he could claim that only of the soul itself ’’ (Donald Rutherford, Leibniz and the Rational Order of Nature, p. .) We recommend to readers chapter  of Rutherford’s excellent book for a discussion of Leibniz’s passes at – but deep reservations about – the idea that corporeal substances could enjoy per se unity. ⁵⁵ A view that dispensed with ‘corporeal substance’ altogether, adopting instead ‘organism’ as shorthand for ‘‘simple substances perceiving one another in the right way’’, would serve Leibniz’s considered purposes just as well.

Preliminary remarks on the mature Leibniz



Other readers will insist that Leibniz’s considered view required two sorts of per se unities – the simple substances whose individuation we examine in later chapters, and the harmoniously constituted complexes we choose to ignore. Those readers are invited to treat what follows as an account of the most foundational class of per se unities – the simple perceiving monads. It being well beyond the concerns of this work to undertake a systematic treatment of Leibniz’s views of corporeal substance, we leave it to others to offer an account of what those readers will purport to be a second class of per se unities. (Perhaps we would be pleasantly surprised by the payoffs of such a project. For now, we are very skeptical indeed.) . Leibnizian monads and individuation: looking ahead If the Disputatio is neutral about the extension of ‘individual substance,’ the considered and mature Leibniz’s positive metaphysic of unextended mind-like substances is not at all neutral. To take up the extensional question is to accept the task of saying what substances there are. Doing so, as Leibniz saw well, requires a theoretical account of individual substance sufficiently rich to explain something of their nature, to tell one what kinds there are, and to say how many there are. On the matter of how many substances there are, the most basic ‘‘How many?’’ question is of course raised by the perennial monism versus pluralism debate, a debate on which the whole entity doctrine itself would appear perfectly neutral. Leibniz’s engagement with this debate, like Spinoza’s, is part and parcel of his entire metaphysic: it will occupy us in chapter . On this score at least, the extent of Leibniz’s agreement with Spinoza went little further than the thesis that substances aren’t divisible. Leaning heavily on the claim that no two substances could be alike in respect of attributes, Spinoza concluded that there is exactly one substance, extended and thinking. Leibniz objected by claiming not only that whatever is extended is divisible, concluding that there are no extended substances, but also by claiming that two substances might be alike in respect of some but not all attributes (G ,: L ). This latter claim (granting that each property falls under some principle attribute or other) anticipates Leibniz’s commitment to the famous Principle of the Identity of Indiscernibles. Here, notoriously, Leibniz has in hand what is perhaps the most obvious of his mature efforts to preserve the intension of ‘individual substance’ deeply important to him: numerical distinction goes with qualitative difference, and



Leibniz and the problem of individuation

numerical sameness with exact qualitative similarity. This approach to answering ‘‘How many?’’ in a world of more than one finite substance, and Leibniz’s prospects for justifying it, will occupy us in chapter . The approach is a purely synchronic one. But having indicted purely passive Cartesian extension as explanatorily unable to ground a metaphysics (and, ultimately, a physics) of dynamic, changing individuals, the role of causally active ‘‘form or force’’ (G, ,: L ) loomed large in the mature doctrine of substance. Thus will Leibniz come to explicitly address an intensional aspect of ‘individual substance’ that is absent from the Disputatio, namely the identity of substance through change over time. Leibniz’s commitment to a primitive force or law of change that is permanent in enduring substances is the focus of chapter . A proper accounting of these mature themes depends on a good deal else that is absent from the Disputatio and prominent in the mature period. Leibniz had left accidents out of his early account. How are individual substances related to their qualities, and ultimately to the qualitative manifold? It is in connection with Leibniz’s answer to this question that his metaphysic of individual substances becomes maximally difficult, indeed maximally confusing. For the mature story about the qualitative character of individual substances figures in what is now a distinctively modal approach to individuation, crucial details of which threaten to undo Leibniz’s axiomatic commitments about substance itself. The modal requirement of separability placed on really distinct substances appears threatened by Leibniz’s view that the whole universe is somehow contained in the qualitative character of each substance. That appearance of threat comes to seem all the more real alongside an emerging story about substances linking them closely to their individual accidents. The modal strength of the link is forged, primarily, with the complete concept doctrine, which apparently claims that to grasp an individual substance is to have an algorithm by which one can contrive, at the limit, a complete list of its qualities. To this Leibniz adds what is a natural ally of that doctrine – the Identity of Indiscernibles recently noted – which apparently claims that numerical sameness and difference of individual substance is grounded in qualitative similarity and dissimilarity. These mainstays of Leibniz’s mature account put considerable strain on what we have identified as guiding presuppositions of his metaphysic of individual substances. Insofar as the ground of numerical sameness and difference is given in terms of the category of accident, the idea that substance is prior to accident in the order of being gets undone. Insofar as one accounts for

Preliminary remarks on the mature Leibniz



numerical unity in terms of qualitative similarity, the view that numerical unity is primordial in the order of being gets challenged. Insofar as qualitative character includes the category of relation (to secure mirroring), the picture of the separability of substances, as well as the picture of the ground of individual unity being internal, are put under great pressure. Here then is an agenda, a cluster of concerns that need addressing before we approach the themes of chapters – sketched above. The latter challenge, concerning relations, is clearly an important one. The thorny issue of Leibniz’s view on the status of inter-substantial relations will occupy us in chapter . Its relevance to modal issues – including separability – is clear enough. Such issues are (cf. §. above) at least tacit in any account of the nature of substances, where the most fundamental truths (de re) about substances are to be given; they are explicit in any modal approach to individuation itself. The extent of modal involvement in Leibniz’s own case is due in large measure to the claim that corresponding to each individual substance is its complete concept in which are contained all truths about the substance. Thus arises the question of Leibniz’s essentialism – of de re modal constraints on the qualitative clothing substances enjoy. If the full range of predicates contained in an individual substance’s complete concept in some sense define that substance, marking it off not simply from other substances but all other possible substances, then it would appear that no substance could possibly have different properties from the ones it actually has; and indeed if relational properties are among them, it would appear that no substance could exist in a world populated by any substance distinct from all actual ones. This issue will occupy us in chapter . Properties and the concepts expressing them, even if construed in nominalist fashion as abstractions in the mind, are by their nature general, ‘‘common’’ in at least the formal if not material sense. Aquinas doubted that Socrates had a definition (§.), apparently worrying that no concatenation of purely general or common terms or concepts could secure genuinely singular reference to a unique this. Can the purely general and descriptive resources of a complete concept serve to ground the distinctively de re modal claims of Leibniz’s essentialism, by which he is committed to judging ‘This individual is necessarily sinful’ and ‘Socrates could have been long-nosed’ as literally true or false? This theme will occupy us in chapter . Scotus, of course, had answered ‘‘no,’’ judging it necessary to go beyond common natures to recognize in individual substances a distinct entitas individualis or haecceity. That, apparently, is not a route Leibniz can take.

 

Relations

In the old days¹ it was said that Leibniz endorsed a kind of reducibility thesis about inter-monadic relations. Nowadays we are invited to recognize that no such reduction is available and that Leibniz never intended one.² Unfortunately, the issue is obscured by a lack of clarity on the part of Leibniz and his commentators: one is never quite sure whether the reducibility thesis is a claim about relational constructions in a language, a thesis about concepts figuring in propositions expressed by those constructions, a metaphysical doctrine about individual substancescum-accidents, or something else again; and it is never quite clear, given items from any one of those options, in what sort of ‘‘reduction’’ they are to figure as terms. In this chapter we propose a return to the old days. Leibniz was a reductionist about inter-monadic relations, and we shall say in exactly what sense or senses of ‘reduction’ that is so. Why should a discussion of Leibniz’s views of relations figure so prominently in a book on Leibniz on individuation? The reader will discover that Leibniz’s reductionism about relations figures centrally in later chapters: his views on relations are integral to the project of modal individuation generally and to the stripe of essentialism to which he was committed in particular; they underlie his views on the Identity of Indiscernibles; they inform his negative views on the role of spatiotemporal relations in constituting the identity and difference of things; and, as we shall argue in a final chapter, they render him prone to a Spinozistic world view. In short, Leibniz’s stance on relations forms the backdrop for much of his mature thinking about individuation. Getting ¹ Of Bertrand Russell (A Critical Exposition of the Philosophy of Leibniz) and Louis Couturat (‘‘Sur la Me´taphysique de Leibniz’’), primarily – though the view we discuss here trickles down to G. H. R. Parkinson and Nicholas Rescher. ² See, for example, Jaakko Hintikka, ‘‘Leibniz on Plenitude, Relations and the ‘Reign of Law’ ’’; Hide´ Ishiguro, ‘‘Leibniz’s Theory of the Ideality of Relations’’; Mark Kulstad, ‘‘A Closer Look at Leibniz’s Alleged Reduction of Relations’’; and Laurence B. McCullough, Leibniz on Individuals and Individuation, pp. –.



Early Leibniz



clear about the former will pave the way for an enriched understanding of the latter. In § below, we attend briefly to the views of the early Leibniz, highlighting the strongly anti-reductionist flavor of some early works and sketching some reasons for the shift to reductionism in his later work. Turning to the mature Leibniz, we argue in § that current treatments of Leibniz succeed in establishing very little about his view of inter-monadic relations; this is so because very little can be squeezed from the subject–predicate terms in which skeptics about reducibility have conducted their discussions. Thus § moves to more suitably metaphysical territory, where we argue that Leibniz’s account of individual substances and their perceptual accidents underwrites a reductive account of inter-monadic relations. That account is developed and defended in § as a kind of supervenience thesis.          The Disputatio puts the topic of accidents to one side. A fortiori it has little to say about whether there are relational accidents and, if so, what they are like. Insofar as there is anything in the Disputatio bearing on the topic of relations, it is the following important undercurrent, one that we have already made explicit: the principle of individuation of a thing is wholly internal to it. This idea, axiomatic to much of scholastic philosophy, renders inter-substantial relations irrelevant to the most fundamental metaphysical questions concerning the individuation of substances. The requirement of separability for individual substances underscores a related theme: if any substance is wholly separable from any other, then positive instances of relations between substances cannot explain what makes any substance the very individual that it is. Relations, then, cannot individuate according to the Disputatio Leibniz. That much seems clear. As to the question whether relational facts are something over and above facts about what is intrinsic to each substance, the Disputatio Leibniz has nothing to say. Strikingly, however, as Leibniz retreated from the scholastic style of doing things in the period immediately following the Disputatio, relations acquired considerable importance in his philosophical thought. Early on in this period, not only is it evident that he is no reductionist about relations; he explicitly endorses the idea that, pace virtually the whole of the scholastic tradition, relations can individuate substances. The first of these views – that relations are not reducible to the



Relations

intrinsic qualities of things – is apparent in De Arte Combinatoria () where Leibniz writes ‘‘Variation is here a change of relation. For some change is of substance, some of quantity; some makes no change in a thing, but changes only its relation, its situation, or its conjunction with something else’’ (A ..: PLP ). Leibniz’s most startling use of the category of relation, however, occurs in the early (c.) Confessio Philosophi,³ where he explicitly attends to issues of individuation. There, Leibniz’s spokesman narrates views on individuation that, as his interlocutor puts it, ‘‘have not entered into the mind of any scholastic even in a dream.’’ Engaged with the issue of whether there are two eggs ‘‘so similar to each other that not even an angel . . . can observe a difference,’’ Leibniz allows that a judgment of difference can have as its ultimate grounding a perception of time and place, i.e. of movement of the thing in question with respect to something already determined, either our own movement (e.g. a hand or finger by which we demonstrate) or some pre-determined thing, like a baton, pointed toward the thing in question. (A ..)

Leibniz is fully aware of committing himself thereby to the idea that the principle of individuation of a thing is not internal to it: There you have it, what amazes you, the principle of individuation, outside the thing itself. For among these eggs no difference can be assigned either by an angel or, I have the audacity to say, by God (given the hypothesis of the greatest similarity possible) other than that at the present time this one is at place A, the other at place B. That is why – in order to be able to distinguish them continuously, which is what a designation (i.e. a perpetual determination) consists in – it is necessary (supposing that one has permitted nothing spread on them, no mark attached to them, no sign printed on them, by which they cease to be similar) either that you keep these eggs in some container that is immobile, where they themselves remain unchanged; or you bring it about that their site or container, if it is mobile, nevertheless is not breakable, and they are fixed in it, so that they retain the same relationship always to certain previously determined marks imprinted on parts of the container; or, finally, if [you] are going to allow them complete freedom from restraint, it will be necessary that, at each moment of time during which they move, you continuously follow the motion of each, through each place, either with your eyes or hands or some other kind of contact.⁴ ³ We thank Robert C. Sleigh, Jr. for drawing our attention to the passage noted below, and for providing us with his unpublished translation of the Confessio. ⁴ A ... These remarks, including the previously quoted passage where Leibniz says that determining a particular individual is our singling it out demonstratively in relation to some previously-determined object like our finger (‘‘ . . . nisi sensus temporis et loci, seu motus aut rei datae, ad nos vel rem jam determinatam, aut noster (manus puta aut digiti quo demonstramus) vel

Early Leibniz



One encounters here a partial blurring of epistemology and metaphysics. There is on the one hand the epistemological issue of how one can keep track of a thing assuming its complete similarity to another thing. On the other hand, there is the metaphysical issue of what would ground the difference between two intrinsically indiscernible individuals. But it is clear, at any rate, that Leibniz intends to (a) allow for intrinsically indiscernible things and (b) let spatio-temporal relations do the work both for the purposes of epistemology and metaphysics. Does Leibniz intend this relational view of individuation to apply only to objects like eggs rather than (what would later be ‘‘first rate’’) objects like minds? The text is clear on this point too: souls, or as I prefer to call them, minds, are also individuated, or, as it were, become these, by place and time. This posited, the entire question vanishes. For to ask why this soul rather than another is subjected from the beginning to these circumstances of time and place (from which the entire series of life, death, salvation or damnation arises), and why, consequently, it passes from one set of circumstances to others – when the series of things external to itself brings forth in this manner – is to ask why this soul is this soul. Suppose another soul began to exist in this same body (that is a body located at the same time and place) at the same time and place as that in which this one had begun; then this very soul that you call another, will not be another, but will be this one. (A ..)

In effect, Leibniz offers a style of answer very similar to his own later ‘‘switching’’ arguments against indiscernibles, to be discussed in chapters  and . In brief, the relevant strand of Leibniz’s later thought ran: ‘‘If there were two intrinsic duplicate eggs or leaves (say), God would have no reason to create this world rather than another in which they are switched.’’ The Confessio anticipates this kind of puzzle, answering it thus: the relations of time and space are at least part of what makes each thing the thing that it is. To suppose the possibility of switching is to rei jam determinatae, ut baculi, ad rem datum demonstrandam . . .’’), resemble a similar claim of Avicenna, who also lets the mode of demonstration play a role in individuating a thing: ‘‘So if you say: Zayd is the handsome, tall, literate so-and-so [man] – as many attributes as you like, still the individuality of Zayd has not been determined for you in the intellect. Rather it is possible for the concept consisting of the totality of all that to belong to more than one. Rather, however, existence and the demonstration of an individual concept determines Zayd, as when you say that he is the son of so-and-so, is what is existent at a certain time, is tall, is the philosopher. And then it would have occurred that at that time there is not something sharing with him in those attributes, and you would have already had this knowledge also by this occurrence, that is through a consciousness analagous to what is demonstrated by sensation, in some mode demonstrating the very same so-and-so at the very same time. Here you would be verifying the individuality of Zayd, and this statement would be significative of his individuality.’’ (Logica, v, col., quoted and discussed at pp. – of Allan Ba¨ck, ‘‘The Islamic Background: Avicenna and Averroes.’’) We shall not conjecture if and to what extent there was any channel of direct or indirect influence here.



Relations

suppose that each could have been the thing that it is even if each had had a very different spatio-temporal trajectory. Therefore there is no world where they are switched, since a thing cannot lose what is essential to it. One can hardly fail to notice a decisive shift between Leibniz’s thinking in these early works and his mature thought. Consider for example the striking contrast between the  De Arte Combinatoria remark that ‘‘some [variation] makes no change in a thing, but changes only its relation, its situation, or its conjunction with something else’’ (A ..: PLP ) with the remark in  to Des Bosses that ‘‘Relations in themselves cannot change, and are the result of absolute things’’ (G ,). Meanwhile, as far as individuation goes, we shall argue that in the mature Leibniz relations drop out of any metaphysical role, retaining only the epistemological role of standing as a means by which we can keep track of a thing. The mature position on relations in regard to individuation is nicely summed up in the New Essays: . . . although time and place (i.e. the relations to what lies outside) do distinguish for us things which we could not tell easily apart by reference to themselves alone, things are nevertheless distinguishable in themselves. (NE .xxvii.: RB )

It is not hard to see, at least in broad outline, the reason for the shift. A popular position among the scholastics was one according to which, in Thomas’s words, ‘‘The same accident is not in different subjects.’’⁵ This bit of scholastic orthodoxy enjoyed a happy marriage with another one, viz. that relations between substances have some sort of ‘‘foundation’’ in the substances themselves, where ‘‘[t]he foundation is another accident by the intercession of which the relation inheres in the subject.’’⁶ Posit the foundations and one is able to say that, even though the same accident is never in two subjects – and so, there are no two-place accidents, as it were – there is a sort of basis in the world for relational truths, namely, the foundations for those truths existing in the substances themselves. While the Leibniz of the Confessio era was (it seems to us) aiming to put ⁵ In quatuor libros Sententiarum, , d., q., ar., echoing (as often he did) Avicenna’s view: ‘‘Igitur nullo modo putes quod unum accidens sit in duobus subjectus’’ (from Liber de philosophia prima sive scientia divina –, in Avicenna latinus, p. , discussed in Henninger, Relations: Medieval Theories –, p. ). ⁶ From Conrad Horne’s Compendium dialecticae succinctum et perbreve (), quoted by Massimo Mugnai at p.  of his Leibniz’ Theory of Relations. Mugnai notes that Horne’s Compendium was in Leibniz’s library. See chapters  and  in Mugnai for an extended discussion of the scholastic heritage of the ‘no accident in two subjects’ and ‘all relations have a foundation’ doctrines.

Relations and subject–predicate expressions



some distance between himself and scholastic philosophy, there is no doubt that this pair of scholastic theses about relations were absolutely integral to his mature philosophy. He is emphatic that a single accident cannot straddle two substances: famously, ‘‘I do not believe that you will admit an accident that is in two subjects at the same time’’ (G ,: L ; cf. G ,). Relatedly, he is equally emphatic that relational truths have a foundation in what can be predicated individually of the relata: famously, ‘‘On my view, all extrinsic denominations are grounded in intrinsic denominations.’’⁷ As we shall see, however, very different glosses have been put on Leibniz’s conception of the foundations for relational truths.                  –            Bertrand Russell, notoriously, held that Leibniz is primarily concerned to draw out metaphysical consequences from logical ones. Given Leibniz’s endorsement of a subject–predicate logic, Russell suggests that the ultimate reducibility of all propositions to ones attributing a predicate to a subject commits Leibniz to the following view: claims that putatively express relational facts about substances are reducible to subject–predicate forms which do not. Parkinson and Rescher adopt this reading well.⁸ Russell’s argument – that anyone committed to a subject–predicate logic must endorse the reducibility thesis as presently understood – has force only if ‘predicate’ is construed narrowly, to exclude what recent commentators have called ‘‘relational predicates.’’⁹ So long as Leibniz’s final and considered logic admits both non-relational predicates (‘is wise’) and relational predicates (‘is wiser than Caius’), he can allow relational subject–predicate propositions. On that reading of him, we mustn’t ⁷ VE ; cf. C . In his reflections on Aloys Temmik’s Philosophia vera Theologiae et medicanae ministra (), Leibniz had written, ‘‘The foundation of the category of relation appears to be an absolute accident, or a modification’’ (VE ). ⁸ See Russell, The Philosophy of Leibniz, pp. –. Says Parkinson, ‘‘[Leibniz] seems to believe that to talk in relational terms is meaningful, but unnecessary, being another way of saying what could have been said in subject–predicate terms’’ (Logic and Reality in Leibniz’s Metaphysics, pp. –). In his first book on Leibniz, Rescher formulates what he calls Leibniz’s Thesis, which says that all relations obtaining among individual substances are reducible to predications about the respective substances (The Philosophy of Leibniz, p. ). ⁹ The commentators we have in mind include primarily those cited in note . The need for somehow deflecting the force of Russell’s argument toward a reducibility thesis presumably gains urgency in the light of Russell’s critique – in § of The Philosophy of Leibniz – of Leibniz’s (and Bradley’s) eliminative handling of relations. Far from an embarrassment facing Leibniz, the whole affair is, we shall argue, pretty much a red herring.



Relations

see Leibniz as reducing relations to non-relations in any sense that has all relational facts about individual substances go over to monadic ones: while he may well reduce items of the relational form ‘xRy’ to nonrelational expressions of the form ‘Fx’ (or truth-functional constructions therefrom), he is not committed to a reduction of all relational facts about substances, for ‘F’ may be a complex relational predicate of the form ‘R(y)’. Does Leibniz allow relational predicates? A textual argument that he does adduces evidence of the following sort:¹⁰ God on the other hand, seeing the individual notion . . . of Alexander, sees in it at the same time the foundation of and reason for all the predicates which can truly be stated of him – as, for example, that he is the conqueror of Darius and Porus. (G ,: L , emphases added)

Since this passage and others like it contain reference to predicates that are undoubtedly relational, it follows that Leibniz does not endorse the thesis that all relational propositions are reducible to non-relational ones. We confess to finding this textual argument weak. First, it does of course present grounds for saying that some predicates are relational, but that is not what we need. Leibniz and everyone else will agree that ‘is the conqueror of Darius’ is indeed a predicate, no less a predicate than ‘is a more swift conqueror of the former king of Persia than conqueror of a youthful Indian ruler of land stretching from the river Hydaspes to the river Acesines’ (or whatever other monstrous predicate you like). What we need and don’t yet have are grounds for saying that in Leibniz’s final, considered lingua philosophica they emerge as genuinely irreducible predicates. Second, the argument plays too quickly into the hands of the Russell–Couturat attempt at wringing metaphysical blood from a logico-linguistic turnip. We shall say more about such attempts later. For now it suffices to ask: Are states of monads, properly understood in terms of individual accidents, irreducibly relational in whatever monstrous way predicates may be? That rings distinctly un-Leibnizian to our ears. Third, a glance at the scholastic background to Leibniz’s views about relations hardly lends much encouragement to this textual argument. Let us turn to the scholastic background.

¹⁰ From Discourse § . The argument and text (emphases added) are taken from Kulstad, ‘‘A Closer Look at Leibniz’s Alleged Reduction of Relations,’’ p. .

Relations and subject–predicate expressions



. Some scholastic background Following Aristotle, the scholastics certainly treated it as a step in the right explanatory direction to analyze a relational statement of the form ‘aRb’ into two subject–predicate statements, one attributing a relational predicate to a, the other attributing a different relational predicate to b. But the project of giving relations an analysis in terms of accidents hardly came to a halt at that point. In particular, a distinction was standardly made between two aspects of any such relational accident – an aspect of inherence in the subject (the esse-in) and the aspect of pointing towards a different subject (the esse-ad). As Mark G. Henninger’s admirable treatise on medieval treatments of relation makes very clear, the variety of medieval views on relations can be seen as offering various attempts to resolve the tension that ‘‘springs from the need to do justice to both of these characteristics: a relation’s alleged reality as an Aristotelian accident (esse-in) and its peculiar character of involving somehow more than the subject (esse-ad).’’¹¹ The scholastics were patently aware that, at least prima facie, relational predicates do not straightforwardly correspond to accidents inhering in a subject. For example, they wished to recognize real (but not substantial) change as change in accidents and noticed that it does not appear that every change in a relational predicate amounts to a real change. It is not hard to be sympathetic here. If I am equal in height to you and you grow so that I am no longer equal in height, that does not seem to amount to a real change in me in the way that relief of a headache amounts to real change. Supposing now that one takes seriously that idea that real change is change in accidents, one will certainly be rather more reluctant to think of ‘being equal in height to Parmenides’ as corresponding to an individual accident that inheres in me in the way that ‘having a headache’ may correspond to an individual accident that inheres in me. Consider, by way of example, how the sorts of ideas that we have just briefly explored play themselves out in Aquinas. Continuing on from Aristotle’s observation in Physics ,  that in the case of relation ‘‘ . . . when one correlative changes, the other can truly be said not to change at all’’ (b–), Aquinas notes that ‘‘if someone through a change in him becomes equal to me while I am not changed, that equality was first in me in some way, as in its root from which it has real being.’’¹² This ¹¹ Henninger, Relations, pp. –. ¹² In V Phys., lect. , quoted by Henninger, Relations, p. .



Relations

required him to posit an accident that stands as the root of the relational predicate, but which falls short of being sufficient for it. Sometimes a relational predicate can come upon one without one’s acquiring any new roots so to speak: in such a case, there is no real change. Under these circumstances, what is new is the esse-ad aspect of the relation, not the esse-in aspect. Can relations change without any esse-in changes occurring anywhere in the world? As Henninger interprets him, Aquinas holds against this that ‘‘a comes to be or ceases to be really related to b through some change of the foundation that is or is in a and/or of the foundation that is or is in b.’’¹³ Aquinas, then, does take relational predicates that apply to a single subject as the focal point for his analysis. But his analysis of the foundations for relations hardly ends by a resolution of relations into relational predicates. Indeed, that is little more than the beginning of his analysis. When viewed in the light of such well-known scholastic analyses of how relations enjoy a foundation in the subject, it would be surprising at the least had Leibniz permitted his analysis of relation to bottom out at relational predicates that were supposed to unproblematically express accidents inhering in the subject. The scholastics were driven in their treatment of relations not merely by logico-linguistic considerations but moreover by metaphysical considerations about the nature of accidents, their mode of inherence, and the nature of change. As we read (and shall be reading) him, Leibniz was clearly sensitive to that range of considerations in his own thinking. . Relational predicates We’ve spoken as if the idea of so-called ‘‘relational predicates’’ is a clear one. Leibniz never uses such terminology, and commentators inventing it on his behalf leave obscure both what counts as relational and what counts as a predicate. We are given plenty of examples: ‘is wise’, ‘runs’, and the like are non-relational; ‘is wiser than Caius’, ‘loves Helen’, and the like are relational. In the common run of philosophical treatment, predicates are frequently viewed as (incomplete or schematic) linguistic ¹³ Henninger, Relations, p. . The reason for Henninger’s disjunctive ‘is or is in’ is that he wishes to allow, on Aquinas’ behalf, that substantial forms as well as accidental forms may serve as the foundation (so that substantial generation and corruption as well as accidental change will all be kinds of changes that can yield a change of relation).

Relations and subject–predicate expressions

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items: relationality in these simplest cases might then be fairly ‘‘read off’’ the structure of such items as also bring with them a singular term, as in the examples just noted. But there is something distinctly unsatisfying about using purely syntactic categories to specify the proper arena in which to conduct discussions of reducibility. Current Leibniz scholarship has inherited much of its talk of ‘‘relational predicates’’ by engaging, from within precisely this syntactic arena, efforts to couch relationality safely within a subject–predicate logic – by (as we saw above, for example) first rewriting statements expressing a relation R between individuals a and b to have a syntactic form like statements which do not, and then reconstruing the predicate term to express something best rendered by the syntactic form ‘being R to b’. No historically sensitive or philosophically rewarding mileage is gained by those efforts, and in anything but the simplest cases they are useless. Is the statement ‘Leibniz believes that snow is white’ relational? Opponents of the reducibility thesis have said it is, as we’ll see: but on what syntactic grounds is one barred from simply deciding that it isn’t, rewriting it in the form ‘Fa’ as ‘Leibniz [believes that snow is white]’? What is unsatisfying about syntactic criteria for relationality is that they quite ignore whether or not anything in the world answers to them. Witness: one can, if one chooses, let any of our paradigmatically monadic predicates define a relational predicate in syntactic terms. One can let a be red if a is shmaller than x – that is, let ‘shmaller than x, for any x’ be truly applicable to a just in the case that a is red. But of course one can’t do that, precisely because there aren’t relational ways things are, out in the world, wherever one chooses to find them, even if on syntactic grounds there are relational expressions in our language, wherever one chooses to parse or define them. Certain commentators, when discussing Leibniz on inter-monadic relations, seem to have something other than syntax in mind, a more conceptual something less faithfully revealed by the structure of linguistic items. We are told that when Leibniz uses the sentence ‘A wise man is a believer’ to illustrate subject–predicate form, he commits himself to relational predicates, since ‘‘one cannot be a believer without being a believer in something.’’¹⁴ Never mind that adverbial theories of belief needn’t buy into that. The principle apparently at work here does not look obviously true – that if ‘x is F’ cannot be true unless ‘x is G’ is true, ¹⁴ Kulstad, ‘‘A Closer Look at Leibniz’s Alleged Reduction of Relations,’’ p. .

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Relations

then somehow the relational content of the latter must be packed into the conceptual guts of the former.¹⁵ Even if it is true, the principle is of no use as a non-syntactic criterion for relationality: it tells one to look at the semantic or conceptual progeny of ‘x is F’ for evidence that F is relational, presuming one already knows what non-syntactic evidence to look for. A more generous attempt goes like this. Following the simplest examples, a predicate F is relational if and only if it is not possible that both (i) there exists some substance x that is F and (ii) there exists no y distinct from x. The criterion is not without difficulties. It makes what one might have called reflexive relational predicates non-relational after all, and it commits anyone believing that a Spinozistic substancemonism is logically impossible to saying that all predicates are relational.¹⁶ The second of these difficulties may be avoided by reading ‘not possible’ in the criterion as expressing something stronger than logical impossibility – as expressing a kind of ‘‘analytic’’ impossibility: F is relational if and only if someone couldn’t understand F unless she believed that at no worlds is it the case that (i) and (ii). Despite its shortcomings, the criterion comes suggestively close to capturing our best intuitions about relations.¹⁷ Suppose one sticks with dyadic relations, and intuitively grasps their doubly unsaturated nature: if one also has the notion of propositions resulting from relations when – so to speak – they’re doubly saturated, one can think of relational concepts as ¹⁵ Our worries are of the sort that makes one doubtful about whether (say), for any A and B, B implies A is packed into the conceptual or semantic guts of necessarily A. ¹⁶ Because, for any x, it is impossible that there be no y distinct from it, hence (ii) above is always impossible, thus the conjunction of (i) and (ii) is always impossible, for any predicate F. Hide´ Ishiguro, on p.  of her Leibniz’s Philosophy of Logic and Language, implies that Leibniz believes it is a logical truth that there is more than one substance. (We have chosen this counterexample because of its relevance to the historical case at hand, but one needn’t choose anything quite so esoteric: ‘is odd’, ‘is even’, and the like will be relational, on the present criterion, for the same reason just given.) We are not attacking a straw criterion: in her ‘‘Space: An Abstract System of Non-supervenient Relations,’’ Carol E. Cleland defines any property P as non-relational iff ‘‘it is possible that there exists an x such that x has P and no individual physical thing wholly other than x exists’’ (p. ). And David Wong, in ‘‘Leibniz’s Theory of Relations,’’ has it that a relational predicate expression is one which makes ‘‘essential reference to some other thing other than the one to which it is attributed’’ (cf. pp. –). ¹⁷ See David Lewis, ‘‘Extrinsic Properties’’ for a discussion of a range of subtler problems. Lewis notes that this style of criterion makes being alone in the world an intrinsic property, which intuitively it isn’t. The positive view expressed in that essay is that intrinsic properties are ones shared by all possible duplicates; duplication itself, if explicated, would have to be explicated in terms of intrinsic properties. But, according to Lewis, that tight little circle is tolerable. Explanations have to come to an end somewhere. More recent, unpublished work by Lewis takes a different tack, though this is not the place to pursue it: our stated criterion is a good enough approximation to the truth for our purposes here.

Relations and subject–predicate expressions

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fitting somewhere midway between those. This is just a model, usefully restricted to relational predications involving two individual substances, and usefully close to the earlier inclination to think of relational predicates as concepts that could be expressed by open sentences with a free variable and singular term.¹⁸ We argued earlier that a commitment to irreducibly relational facts about individual substances does not follow from the use of relational predicates. Why should it? Unless one thinks that how we speak gives really reliable insight into the deep nature of what there is, room is left for denying on purely metaphysical grounds that such predicates are irreducible, or that corresponding to all such predicates are irreducibly relational ways things are. We do not, in any case, wish to concede a view that most treatments of Leibniz on relations seem to have conceded – that, as Russell and Couturat insist, Leibniz’s metaphysics must be understood as issuing from his logic and language. Indeed recent discussions of Leibniz’s predicate-in-subject principle indicate that we should read him quite the other way round.¹⁹ Thus while Leibniz and some of his commentators move uncritically back and forth between speaking of predicates and subjects now in the formal, now the material, mode, we want to refrain from that. In particular, we want to leave discussion of the reducibility thesis in terms of language behind, and move on to the more suitably metaphysical territory of substances and their accidents. Before doing so, however, it will be helpful to anticipate that transition by considering an objection yet in the formal mode: hasn’t Leibniz committed himself to irreducibility relational facts about substances, not by merely using relational predicates, but by explicitly saying that they are contained in the complete concept of the individual falling under them? On anything but the most superficial reading of containment, he hasn’t. Leibniz does sometimes speak of all the predicates being in the subject. But, in the first place, one is free to read ‘in’ here as expressing a properly logical connection of relational concepts to basic nonrelational attributes, such that one could (perhaps in conjunction with ¹⁸ There might be linguistic means for expressing them otherwise. Two points: first, the ‘‘believes’’ case noted earlier is not one we’re interested in here, since it does not involve inter-monadic relations. Second: the slightly deviant case of reflexive relations is not ruled out by the linguistic rendition of the present model, since no restriction is placed on the range of the free variable and singular term. This rendition is equivalent to what we get with lambda abstraction in moving from the proposition expressed by ‘aRb’ (if there is one) to the property expressed by ‘(kz)zRb’ (if there is one): we don’t know what to say to someone denying that ‘(kz)(kx)zRx’ expresses a relation. ¹⁹ See, for example, Noel Fleming’s ‘‘On Leibniz on Subject and Substance.’’

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Relations

certain generalizations) deductively crank out the derivative relational facts. As we shall urge below, this won’t be the whole story about complete concepts and the relational notions they ‘‘contain,’’ but it serves much of the reductive purpose Leibniz has in mind. In the second place, Leibniz clearly does not want to hold that everything the vulgar say – of Alexander, for example – is outright false: in the passage quoted earlier from Discourse §, recall, the relational ‘conqueror of Darius’ is a predicate truly statable of him. Yet this does not commit Leibniz to saying that our relational claims cannot be given reductive treatment in terms of more basic non-relational concepts on which such predication depends (and not conversely). Indeed, we think Leibniz sometimes refrains from saying that all the predicates are in the complete concept precisely because he has such a treatment in mind. Look again at the passage from Discourse §, used by skeptics against the reducibility thesis: there, Leibniz hasn’t said that all Alexander’s predicates are in his individual notion, but rather God sees in it ‘‘the foundation of and reason for all the predicates which can be truly stated of him.’’ The reductive tone of that passage is echoed in Leibniz’s claim that ‘‘. . . it is in the nature of an individual substance to have such a complete concept, whence can be inferred everything that one can attribute to it’’ (G ,: LA ; our emphasis). And after telling Arnauld that strictly speaking not all of the predicates that are true of Adam need to be packed into his individual concept, Leibniz continues: For all the predicates of Adam depend or do not depend upon other predicates of the same Adam. Setting aside, therefore, those which do depend on others, one has only to consider together all the basic predicates in order to form the complete concept of Adam adequate to deduce from it everything that is ever to happen to him . . . (G ,: LA –)

A fully sympathetic account of Leibnizian reduction would attempt to exploit the idea that some facts about substances ‘‘depend’’ on more basic or foundational ones. Leibniz exploits something like it in his explicit rejection of ‘‘purely extrinsic denominations’’ (at C –: L –, and elsewhere). Reading reductively Leibniz’s claim that intrinsic denominations are the basis or ground (fundamentum, in most cases) of extrinsic denominations, the most plausible explanation of what he is up to when saying that ‘‘there is no denomination so extrinsic that it does not have an intrinsic denomination as its basis’’ is simply this: extrinsic denominations are relational properties or concepts, intrinsic denominations are monadic properties or concepts, and no individual falls

Relations and subject–predicate expressions

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under an irreducibly extrinsic denomination. Benson Mates argues for that: ‘‘Leibniz’s dictum that ‘there are no purely extrinsic denominations’ becomes, therefore, the assertion that every relational property of an individual is reducible, in some sense of ‘reducible’, to nonrelational properties to that and other individuals . . .’’²⁰ . Relational construals of intrinsic denominations In §, we shall gesture at one way of fleshing out that ‘‘in some sense of ‘reducible’. . .’’: for now let us note an argument on intrinsic denominations from Mark Kulstad, who doubts that such fleshings-out repay close attention.²¹ Since Leibniz asserts that every predicate is intrinsically connected with its subject (G ,), one must say that (i) every predicate designates an intrinsic denomination. But – as the textual argument considered earlier is meant to show – (ii) Leibniz uses ‘predicate’ to include relational predicates. Hence, his requirement that all denominations be intrinsic still allows intrinsic relational properties. That is not a good argument, one can now see, partly because (ii) is either harmless against the reducibility of relational facts about individual substances or else begs the question against it. Moreover the argument leaves one wondering what Leibniz is up to when he does speak of extrinsic denominations, arguing that none lacks an intrinsic denomination as its basis. The idea that there may be two kinds of relational predicates, reducible ones (to which Leibniz’s purge applies) and irreducible ones (to which it does not) is a textual non-starter. Lawrence B. McCullough endorses Kulstad’s view that relational accidents are bona fide intrinsic denominations as they stand. In addition ²⁰ Mates, The Philosophy of Leibniz, p. . Parkinson takes this line, saying that Leibniz understands ‘extrinsic’ and ‘intrinsic’ in the scholastic sense, ‘‘an extrinsic denomination being a relation, and an intrinsic denomination a [non-relational] predicate’’ (Parkinson, Logic and Reality in Leibniz’s Metaphysics, p. ). Professor Ishiguro has warned us that a more plausible reading is available which does not support reduction. When Leibniz says that there are no purely extrinsic denominations, he is both distinguishing them from intrinsic denominations and saying that we cannot have the former kind of denomination without the latter. Thus, if one says that there are no purely Doric temples, one implies that every temple with Doric features has some features which are not Doric but which are something else, e.g. Corinthian, and one does not imply that Doric features can be reduced to others. Fair enough, so far as it goes: the relevant Leibnizian expression needn’t imply that, though it is consistent to read it as having that implication, and our point on these pages is to argue that in fact it does. As for Ishiguro’s reading itself, rather too much weight rests on ‘purely’: we can’t align it with passages where Leibniz explicitly says (for example, at LH vii C  – ) that ‘‘. . . speaking rigorously there is no extrinsic denomination in reality . . .’’ (cf. G ,: L ), nor especially with his claim that ‘‘In my opinion all extrinsic denominations are founded in intrinsic denominations . . .’’ (LH viii , our emphasis). ²¹ Kulstad, ‘‘A Closer Look,’’ p.  fn. . The argument to follow is at p. –.

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Relations

to commending Kulstad’s work to the reader, McCullough offers his own – in our view unsatisfactory – gloss on the connection between Leibniz’s view (as he sees it) and the scholastic problematic.²² Having noted the scholastic challenge of making sense of both the esse-in and esse-ad features of relations, he interprets Leibniz as solving the problem by having relational accidents – in the form of perceptions that drag in other bits of the world – inhering in each monad as the foundations for relational predicates. This is hardly a solution to the scholastic problem. For the whole problematic, as conceived by the scholastics, was precisely the worry as to how a relational accident could at once embrace other bits of reality and yet genuinely inhere in a single subject. McCullough’s Leibniz comes close to the views of Richard of Mediavilla. But (notably), while embracing relational accidents as real and irreducible, Richard felt the need to appease the worry just noted by denying that relational accidents inhere in substances in the way intrinsic accidents do, so that ‘‘the being of a relation’’ is not ‘‘being in something.’’²³ McCullough goes on to align Leibniz’s view that ‘‘the relation common to each of these relations [sic] is a merely mental thing’’ with Peter Aurioli’s mentalism about relations. In fact, all of the scholastics thinkers with whom we are familiar denied that relations, construed as two place entities with a foot in two different subjects, have a real existence. What is distinctive about Aurioli’s views is that he does not even permit relational accidents any extra-mental reality either, and thus is thoroughgoingly conceptualist about all relational modes of representation. ²² By way of a distinct, non-scholastic consideration in his favor, McCullough (Leibniz on Individuals, p. ) notes that in the Des Bosses correspondence, Leibniz famously affirms that ‘‘paternity in David is one entity, filiation in Solomon is another entity, but the relation common to each of these relations is a merely mental thing, the foundation of which would be the modifications of singulars.’’ Part of the point of the quoted passage is to underscore the fact that, for Leibniz, as for the scholastics, a healthy first step when confronted with a relational claim – in this case ‘a is the father of b’ – is to analyze it into two relational predications, one concerning a, another concerning b, with the two-place relation being treated as a merely mental construction. For us however, but not for McCullough, this is but the first stage in a fully reductive analysis whereby only intrinsic accidents lie at the groundfloor (of which more later). What then should we make of Leibniz’s willingness to call David’s paternity a thing (or if McCullough prefers, an entity)? The Des Bosses passage itself does not force one to concede that, according to Leibniz, the modification that stands as the foundation of, say, David’s paternity, is most perspicuously described by a relational predicate. On the account we develop in §, one can think of David’s paternity as identical with a modification readily enough without yet thinking of the modification as fundamentally relational. We note here that McCullough’s ‘‘ . . . but the relation common to each of these relations is a merely mental thing’’ (our emphasis), which translates Leibniz’s ‘‘sed relationem communem utrique esse rem mere mentalem’’ may obstruct a proper understanding of the matter. The Latin is surely better rendered by ‘‘but the relation common to both is merely a mental thing.’’ ²³ Quodl. , q. , quoted by Henninger, Relations, p. .

Substances and perceptual accidents

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                     If the final story of Leibniz’s groundfloor metaphysics includes relational facts about the substances David, Socrates, and Paris falling under irreducibly relational concepts or properties, then there must be in those substances individual accidents that essentially have, respectively, Solomon and Theatetus and Helen (or their haecceitistic proxies) as constituents. Now whatever that might amount to, it sounds odd coming from Leibniz: are we to believe that he rejects accidents with one leg in one substance, the other in another, but welcomes accidents with one leg in one substance and a full-nelson hug around another? And yet, how else could Leibniz do justice to those vulgar relational claims in terms of accidents in substances? Socrates, apparently without (relevant) changes in himself, becomes shorter than Theatetus when Theatetus undergoes changes in height. Reflecting on this puzzle of Theatetus a–b, Leibniz writes that ‘‘when someone, by growing, becomes bigger than me, then some change occurs in me as well, since a denomination of mine is changed. In this way, all things are in a certain way contained in all things.’’²⁴ He later summarizes Plato’s Phaedo (b–a) treatment of relational predication by agreeing that Socrates now has tallness, and now shortness, in him, these being individual accidents falling under the forms Tall and Short. But the shortness of Socrates cannot be shortness simpliciter, surely, for Socrates is shorter than lots of people but also taller than lots of people: that shortness by virtue of which it is true that Theatetus stands taller than Socrates is not what makes it true that Socrates is shorter than Simmias. Mustn’t this individual shortness-accident bring Theatetus with it, and mustn’t Socrates be thereby intrinsically and irreducibly related to Theatetus by containing in him a relational accident with Theatetus (or his proxy) as constituent? Not on an informed Leibnizian view of accidents. Notice his earlier claim that ‘‘everything is in a certain way contained in everything.’’ That is a helpful clue, directing one to Leibniz’s view that every individual perceives every other. ‘Perception’ is a general term covering the entire range of mental states or activities of Leibniz’s spiritual substances: the accidents of an individual substance at a moment are thus how it is or what is happening to it at that moment, which consist of its perceptions. ²⁴ A ..: DSR –. Leibniz was clearly thinking about Plato’s Theatetus paradox during the period around April  when this was written (cf. A ..); see also Hector-Neri Castan˜eda, ‘‘Leibniz and Plato’s Phaedo Theory of Relations and Predication.’’

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Relations

Says Leibniz: ‘‘this is the only thing – namely, perceptions and their changes – that can be found in simple substance . . .,’’ and elsewhere that ‘‘nothing can in fact happen to us except thoughts and perceptions,’’²⁵ these following upon one another ‘‘from within,’’ according to the particular law-of-the-series specified by one’s complete concept. Leibniz’s ‘‘containment’’ here, then, is such that substances contain others not formaliter but rather objective – that is, representatively – and it is important to see that this requires nothing like intrinsic relational states of substances. On Leibniz’s treatment of perception as expression, specifying completely the perceptual states of a monad will bring with it no overt commitment to the things that are perceived, or even to there being something that is perceived at all.²⁶ Perceptual states are monadic: that they count as expressions of a thing outside it cannot be derived from anything intrinsic to that state, and they count as such only insofar as pre-established harmony guarantees merely that they correspond in suitable ways with monadic states of other substances. Pre-established harmony is not properly understood in terms of relational accidents in substances, but rather as a general truth (a very long conjunction, perhaps) decreed by God in his creation of the best world. On our view, then, when Leibniz speaks of ‘‘some change occurring in me, when someone, by growing, becomes bigger than me, since a denomination of mine is changed,’’ he does not mean that (a) it follows with absolute necessity that a denomination of mine is changed (because something that was previously not sayable of me is now sayable of me), but rather means that (b) it follows with moral/theological inevitability that there is a change ²⁵ G , and G ,. That Leibniz wants the set of perceptual accidents to be materially adequate to facts of monadic individuation is recommended in his (nearly over-stated) claim that ‘‘Monads are nothing else than representations of phenomena with transition to new phenomena; it is manifest that representation in them is perception . . . ’’ (G ,). A full discussion of Leibniz on accidents can be found in Kenneth Clatterbaugh, Leibniz’s Doctrine of Individual Accidents. ²⁶ Is the most fundamental description of monadic states non-intentional, then? Two models: according to the first, (i) the intrinsic states enjoy a most basic level of description that is non-intentional, and the laws of expression determine for those states both representational contents and veridicality. According to a second model (ii) what the monad perceives, taken as the intentional content rather than material object of perception, is intrinsic to it (for a modern analogue, consider the adverbial view of seeing as, which takes perceptual content to be intrinsic and monadic), and the laws of expression determine what things are perceived de re, together with the veridicality of those contents. There is little evidence that Leibniz thought much about this contrast. We needn’t adjudicate on his behalf here, but permit us a hunch – that the second model, which assumes with Descartes that intentional description gets in at the groundfloor of mind qua mind, is the more natural for a rationalist of Leibniz’s stripe.

Substances and perceptual accidents



not merely in what is truly sayable of me but in my intrinsic state.²⁷ Some texts will help to firm things up a bit here. On pre-established harmony: [I]t follows from what we have just said, that each substance is a world apart, independent of everything outside of itself except God. Thus all our phenomena, that is to say, all the things that can ever happen to us, are only the results of our own being. And since all these phenomena maintain a certain order which conforms to our nature or, so to speak, to the world which is within us . . . this would be sufficient to enable us to say that these phenomena are true, without being put to the task of inquiring whether they are outside of us and whether others perceive them also. Nevertheless it is true that the perceptions or expressions of all substances intercorrespond . . . It is only God . . . who is the cause of this correspondence between their phenomena . . . (Discourse § at G ,: L )

And more explicitly on expression: ‘‘one thing is said to express another if it has properties that correspond to the properties of the thing expressed . . .’’ (G ,: L ). The relational element here is not packed into these properties, but rather rides over them as mere correspondence. In this same passage we get illustrations of expression, which include the expression of a particular figure by an algebraic equation or the expression of a three-dimensional solid by a plane diagram. The diagram or the equation doesn’t have built into it essential reference (so to speak) to some solid or some drawn figure. But doesn’t all this make perception as expression solipsistic? It does, rather: this emerges already from Leibniz’s telling Arnauld that a monad takes on its perceptual states according to an internal principle, its ‘‘succeeding state [being] a sequel . . . of its preceding state, as though only God and it existed in the world’’ (G ,: LA ). That Leibniz intends nothing like relational accidents in substances is evident in his even stronger claim to Des Bosses that ‘‘there would be no deception of ²⁷ Objections: (A) But don’t I contain in my concept the laws of expression, in which case it is absolutely necessary that these denominations in me express what they do? (B) When Leibniz speaks of some intrinsic change in me on the occasion of your growing ‘‘because some denomination of mine has changed,’’ he seems negatively not to be relying on harmony, and positively to be endorsing the traditional Kulstad et al. view. Replies: (A') As we shall argue in the next chapter, Leibniz’s considered view holds that while my inner law of the series constitutes my essence, the intermonadic laws grounding the harmony of perceptions do not. (B'): The earlier Paris passage, we concede, doesn’t itself recommend the mature position we’re mapping out for Leibniz in these pages. The full resources of pre-established harmony and universal expression were not in place in –, though presumably Leibniz was then grasping for something to fill their role (cf. Leibniz’s ‘‘Notabilis est haec difficultas’’ note to the Theatetus puzzle at A .., the gestures toward expression and harmony at A .., etc.).



Relations

rational creatures even if everything outside of them did not correspond exactly to their experiences, or indeed if nothing did, just as if there were only one mind. . .’’ (G,). Hide´ Ishiguro believes that Leibniz is caught up in ‘‘a strange inconsistency’’²⁸ with talk of that sort: ‘‘if substances are individuated by their perceptual states . . . it is a logical truth that there is more than one substance in the world . . .,’’²⁹ since the individual concept of substances includes relational predicates. Here, perhaps, one person’s reductio is another’s modus tollens: Leibniz’s avowedly non-relational account of accidents entails that substances do not fall under irreducibly relational concepts. The picture we have just sketched – whereby each intrinsic history (the intrinsic history being what is internal to the monad) expresses each other via the laws of harmony – connects in interesting and straightforward ways with the scholastic problematic. Recall the view, shared by Aquinas and others, that each relational feature of a substance has a root in that substance, the esse-in component of that substance. The hypothesis of such a root is not easily defensible for every relational feature. If I am such as to be in a world where Socrates drank hemlock, it seems far from obvious that there is any root whatsoever in me of that relational feature. The difficulty is not simply that one cannot find a root that is sufficient for the relational feature. That wouldn’t be a problem ²⁸ Ishiguro, Leibniz’s Philosophy of Logic and Language, pp. ff. Mates might have found an inconsistency here too, between the passage just quoted and his own view (The Philosophy of Leibniz, p. ) that substances are not, as they were for Aristotle, independent (separable). We’ve seen Leibniz’s commitment to separability in the Disputatio, and will return to it again in chapter . We note here that its connection with Leibniz’s claim that substances have no parts represents a strong indirect argument in favor of the reducibility thesis. Whether or not Leibniz understood the Aristotelian view that ‘‘substance is that which is neither predicable of nor present in anything else’’ (Categories a) as entailing that substances cannot be parts, Leibniz clearly does believe that substances cannot have parts. When he says (explaining the part–whole relation at GM VII,) that ‘‘if the whole is posited, the part is immediately posited thereby . . .’’ and that ‘‘we cannot say – with complete fidelity to the truth of things – that the same whole continues to exist if a part of it is lost’’ (NE .xxvii.: RB ), Leibniz clearly means that wholes are not separable from parts. Thus we can argue safely from the reducibility thesis, which entails separability of substances, to Leibniz’s favored doctrine of the simplicity of substances. Bodies are not unities per se precisely because there are no intrinsically relational ways substances are; since bodies constitute a unity only ‘‘per accidens or by an external denomination’’ (G ,), bodies are no more a part of Leibniz’s considered metaphysic than are relational facts about monads. Similarly, perhaps, for corporeal substances: see chapter , §.. ²⁹ So it is a logical truth that there can’t be a single thing with contentful states? According to standard semantics, insofar as ‘‘I think there are ten green bottles’’ is relational at all, it involves a relation between myself and a proposition or representation, not between me and other substances (bottles, for instance). (Whether substances are properly said to be ‘‘individuated by their perceptual states’’ [Ishiguro] is a separate matter, addressed in chapters  and ; it would suffice for her proposal to say, as we did above, that the set of perceptual accidents is materially adequate to facts of monadic individuation.)

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

for a scholastic, as there was no commitment to the idea that the esse-in feature suffices for the esse-ad feature. The problem is rather that there appears to be no esse-in feature at all. It is only in the Leibnizian framework that the idea that each relational predicate that I enjoy has a root in me finds a secure defense. If my intrinsic states express – via the laws of harmony – every nook and cranny of the world, then one of them (or a group of them) will express Socrates’ fatal act. When thought through, it appears that the thesis that every relational feature of a thing has an esse-in root requires something like Leibniz’s view that each thing expresses the whole world. Seeing this, the mature Leibniz frequently connects the thesis of intrinsic foundations for extrinsic denominations with pre-established harmony, as when he tells us in the New Essays that ‘‘in metaphysical strictness there is no wholly (pure) extrinsic denomination, because of the real connections amongst all things’’ (NE .xxv.: RB ). The thesis of harmony provides the requisite philosophical grounds for saying what many of the scholastics wanted to say – that every relational feature of me has an esse-in root. It also permits Leibniz to say something that the scholastics were understandably reluctant to say, namely that every relational change that I enjoy is tantamount to a real change in me. The threat of purely relational changes is undercut by the fact that every change in the world is – if only in my insensible unconscious constitution – perceived by me. Thus in De Termino, Praedicato, Relatione (c. ) Leibniz is careful to qualify his claim that ‘‘if I move and Peter stands still, surely Peter’s distance from me changes, though without any change taking place in Peter’’ by adding ‘‘–unless in virtue of the universal connection of all things’’ (VE –). Elsewhere, he is more forthright. After reminding us that ‘‘all existing things have an intercourse with each other,’’ he asserts outright that ‘‘no one becomes a widower in India by the death of his wife in Europe unless a real change occurs in him’’ (G ,–: L ).          We have been arguing that if skeptics about the reducibility thesis hunt carefully for relational facts about substances in Leibniz’s groundfloor metaphysical story, they won’t find them. We want now to suggest that skeptics about reducibility have misguided reasons for thinking that there must be such facts: in doing so we’ll deliver in a modest way on the promise to flesh out Leibnizian reduction.



Relations . Reduction and equivalence objections

Leibniz tells us that similars are things having the same quality (GM ,: L ). Thus, supposing that (A) and (B) are true, (A) Caius is wise (B) Titius is wise it is then true – and in no possible world at which (A) and (B) are true will it be false – that (C) Caius is similar to Titius. The relational (C) is thus entailed by the monadic truths (A) and (B). This appears to provide the beginnings of a model for reduction, then. Relational claims are made true by monadic facts; God has instantiated a world of monadic facts from which relational truths follow, and to which relational truths are reducible; relations between substances ‘‘result’’ from monadic states of them; (C) reduces to (A) and (B) conjoined, of the form ‘Fx and Fy,’ for a genuinely monadic F. It may be objected that, say, no reduction of (C) to (A) and (B) is workable unless we explicitly add that (*) For some F, if c is F and t is F, then c is similar to t, which vitiates the reduction by its explicitly relational element. The objection surfaces in the literature most frequently in connection with asymmetric relations. Of the thesis that ‘‘all relations . . . must be reduced to the properties of the apparently related terms’’ Russell says ‘‘there are many ways of refuting this opinion,’’ offering as an example the fact that a’s being greater or less in some respect than b reduces to a statement of the magnitude of a, and likewise of b, plus the (necessary) relational claim that those measures stand in the greater-than relation.³⁰ The objection seems off the mark, insisting as it does that the relevant monadic truths can entail the relational ones only if we add something – a necessary relational something. But this confuses entailment with deductive consequence (relative to a syntactic system): given the relational claim R and relevant set M of monadic claims, our present formulation of the reducibility thesis has it that every model which satisfies M is one ³⁰ Bertrand Russell, Our Knowledge of the External World, pp. –. Less flagrantly, Nicholas Rescher (The Philosophy of Leibniz, p. ) says that a reduction of the relational truth ‘Titius is wiser than Caius’ to the monadic predicative facts (i) ‘Caius is somewhat wise’ and (ii) ‘Titius is very wise’ is incomplete without adding that wiser = superior in point of wisdom and ‘‘very’’ represents a degree superior to ‘‘somewhat.’’

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

where R is satisfied. A Leibnizian reduction of relations between substances to their monadic states requires nothing like the addition of all necessary truths needed as rules in a syntactic system, or as premises of a formal deductive argument, or as statements of what someone must accept as true if she sees that M entails R. Requiring that we add (*) to (A) and (B), above, is demanding what the Tortoise demanded of Achilles,³¹ and we ought not to fall for it. Somewhat different versions of this ‘‘presupposed relation’’ objection have arisen from slightly different territory. Proper reductions, it will be said, must be expressed as logical equivalences: this being so, the presupposed relational element is required, and cannot be treated as we have just treated it. Thus C. D. Broad criticizes Leibniz’s attempts at reducibility by saying that ‘‘a true relational sentence expresses something genuine which would be left unexpressed if one merely made statements about the [monadic] qualities of the term,’’ insisting that ‘L is longer than M’ is ‘‘plainly not equivalent to’’ the monadic truths about the relata L and M, but rather properly reduces to its logical equivalent ‘there is some i and j such that L has length i and M has length j and i is greater than j.’³² (It is unclear whether Rescher is echoing the need for equivalence, or introducing a new reservation about it, when he asks, ‘‘When aRb is said to be ‘reducible’ to predicational information about a and b, do these predicates not include relational predicates themselves?’’ A solution that he claims is workable requires that such relational predicates be ‘‘analytically equivalent’’ to some complex of genuinely monadic ones.) There are two issues here – of reduction as logical equivalence (again), and of meaning-equivalence. With the first of these yet on board, we pause to note the following objection: since first-order monadic predicate logic is decidable while first-order predicate logic with relations is not decidable, isn’t a reduction of relational expressions to monadic ones impossible on purely logical grounds? We think not. A first step toward seeing why not is made already in recognizing that Leibniz’s reducibility thesis about putative inter-monadic relations is a thesis about contingent truths, while decidability results are purely about logical truths. (Of course the ‘‘contingent’’ truths at issue are [for Leibniz] also in a certain sense analytic, but this shouldn’t and wouldn’t stop Leibniz from holding that there is an important distinction here.) ³¹ In Lewis Carroll’s ‘‘What the Tortoise Said to Achilles.’’ ³² C. D. Broad, Leibniz: An Introduction, p. . The items cited below from Rescher are at pp. – of his The Philosophy of Leibniz.



Relations

To develop this point a bit further, we can sketch out how one might generate examples that intuitively present a reduction of relational claims to monadic claims which are consistent with decidability results. Consider a certain uninterpreted first-order language LR containing relational and monadic predicates, a fragment LM of which contains only monadic predicates. LM is decidable and LR is undecidable. It is a trivially simple task to give interpretations for the language – that is, models for LR – in which all relational expressions are equivalencereducible to monadic expressions in a fairly clear and unobjectionable sense; these will simply be models according to which any expression of the form ‘xRy’ is true if and only if x is F and y is G, or x is H and y is J . . . for genuinely monadic F, G, H, J . . . But our concern with reduction here is not merely with sentences of a formal system, but with reductions properly specified by an intended interpretation. Thus (repeating now an earlier lesson) questions about reducibility cannot be settled in purely syntactic terms; for whether or not some or all relational claims reduce to monadic ones is a question about claims, about interpreted sentences with truth values, which no result for formal languages or systems can answer. And the Leibnizian interpretation before us has it that relational claims about substances are true if and (for the moment) only if substances are monadically thus-and-so. Concerning the second issue of meaning-equivalence, it is far from clear on what grounds Broad (and perhaps Rescher) should demand that equivalence-reductions be ‘‘meaning-preserving’’ ones. Leibniz certainly doesn’t believe that logically equivalent expressions must have the same meaning (recall his discussion of Triangularity and Trilaterality in New Essays .ii.: RB ), and we are aware of no evidence in his writings for the view that reducing items must express what the reduced item expresses (Broad), or that relational items in the end must be analytically equivalent to complexes of monadic ones (Rescher). Indeed one gets prima facie evidence to the contrary from his claim that ‘Peter is similar to Paul’ is reduced (reducitur) to ‘Peter is A now’ and ‘Paul is A now’ (C ). Also relevant here perhaps is Leibniz’s view that relational propositions are in some sense an abstraction in the divine mind of a sort that their monadic truthmakers are not – thus further distancing him from the notion that relational propositions are equivalent in meaning to their reductive base. As Leibniz puts it in the New Essays, relations are ‘‘to some extent ‘beings of reason,’ although they have their foundations in things; for one can say that their reality, like that of eternal truths and

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

of possibilities, comes from the Supreme Reason’’ (NE .xxv.: RB ). The best reply to equivalence-objections, in any event, is recommended by our earlier sketch at Leibnizian reduction in terms of one-way entailment. Why demand logical equivalence? Mates has called attention to this, alongside textual evidence that Leibniz’s reductions seem to make no effort to meet it.³³ We think Mates is right: when Leibniz reduces (as he does) ‘A is similar to B’ to ‘A is red and B is red’, [he] is surely not telling us that two things are similar if and only if they are both red. The point again must be that whenever ‘A is similar to B’ is true, there will be a couple of true propositions of the form ‘A is C’ and ‘B is C’ that imply it and are made true by the same substances-with-accidents that are the ground of its truth.

There is a quite general thesis lurking here, worth filling out a bit. Leibniz is fond of saying that reduced relational propositions ‘‘arise’’ from monadic reducing propositions (LH , vii C ), that relations obtain merely as ‘‘results’’ of states of things or changes of states (C ; G ,: L ; LH , vii C ), or again that they have their ‘‘foundation’’ in the relata. This avowedly asymmetric view of a dependence between relational facts and apparently monadic ones finds indirect support in Leibniz’s use of the quatenus and eo ipso formulations in reductive contexts.³⁴ Titius is wiser than Caius, that is, Titius is wise, and qua wise is superior insofar as [quatenus] Caius qua wise is inferior. (C ) Paris is Helen’s lover, that is, Paris loves and by virtue of that fact [eo ipso] Helen is loved. (C )

We reduce ‘Paris loves Helen’ to some non-relational propositions of the form ‘F(helen)’ and ‘G(paris)’, where now the facts making ‘Paris loves’ true also make ‘Helen is loved’ true. But of course ‘Paris loves Helen’ itself is made true by, or is true in virtue of, those relevant facts grounding it, just as the fact that Caius is similar to Titius arises from and obtains in virtue of the facts that Caius is wise and Titius is wise. ³³ See Mates, The Philosophy of Leibniz, pp. – and –; the quotation below is from p. . The present sub-section, inspired by Mates’s discussion, may be viewed as an attempt to develop and defend it. ³⁴ Our reason for drawing attention to these constructions differs somewhat from those given by Rescher (The Philosophy of Leibniz, pp. –), where he is properly concerned to draw out their role as a syncategorematic connective expressing relations between propositions (rather than individual substances).



Relations

Generally, then: monadic facts simply determine relational ones; reduced relational facts obtain because the monadic, reducing ones obtain. And conversely? No. Suppose we grant recent commentators their ‘‘relational predicates’’ discussed earlier in §. Thus it is said³⁵ that: (a) ‘David is the father of Solomon’ reduces in part to something ascribing paternity to David, and paternity is relational. (b) ‘L is no longer than M’ can, ‘‘in the first way of considering it’’ (G ,: L ) be reduced to something in which L is the subject and greater than M is the relational accident. (c) ‘Paris loves Helen’ reduces in part to something ascribing ‘is a lover’ to Paris, and that predicate is relational. (d) ‘A wise man is a believer,’ according to Leibniz, has ‘wise man’ as subject and ‘is a believer’ as predicate, and since one cannot be a believer without believing in something, that predicate is relational. Now the facts expressed in these (italicized) cases aren’t irreducible relational facts, in the asymmetric sense of reduction with which we’re now concerned. The relational fact that Caius is similar to Titius, recall, reduces to – is grounded by, arises or results from, obtains in virtue of, is made true by – the facts that Caius is wise and that Titius is wise. Any world where the two monadic facts obtain is one where the relational fact obtains, but not conversely. A similar reduction applies to (a) – (d).³⁶ In all these cases, the relational fact obtains because of facts about the relata: in any world where those facts about the relata obtain, the relational fact obtains, but not conversely. There are many things that can make it true that David has paternity: David’s having paternity entails none of them, but all of them entail David’s having paternity. There are many things that could ground the fact that ‘greater than M’ applies to L: L’s being longer than M implies none of them, but all of them imply that L is longer than M. ‘Is a lover’ applies to Paris in virtue of some facts about Paris and Helen: in any world where those facts ³⁵ That is, said by the following in these sources for (a) – (a) below: (a) from Ishiguro, Leibniz’s Philosophy of Logic and Language, p. ; Kulstad, ‘‘A Closer Look,’’ p. ; McCullough, Leibniz on Individuals, p. . (b) from Kulstad, p. ; McCullough, p. . (c) from Hintikka, ‘‘Leibniz on Plenitude, Relations,’’ p. . (d) from Kulstad, p. . ³⁶ As in the earlier example of similarity, we’re avoiding familiar complexities needed to distinguish relations of connection from relations of comparison. For the moment we simply acknowledge the difference in plausibility between reductions of comparative relations (‘is similar to’) and connective ones (‘loves’): we’ll deal with this shortly.

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obtain Paris is a lover, but in plenty of worlds where Paris is a lover, those facts don’t obtain. And so on. . A supervenience model Contemporary resources provide a handy way of treating the stripe of reduction that our Leibniz is committed to. Supervenience, as a determinative relationship between properties or families of properties, brings with it no proof-theoretic or conceptual equivalence: mightn’t we understand Leibniz’s reductive treatment of inter-monadic relations in that way?³⁷ As a model it seems not far off. In terms roughly hewn: to say that inter-monadic relations or relational properties supervene on monadic properties, is to say that for any relation R or relational property R (y), necessarily if x is R to y or has the property R(y), then there are monadic properties F, G . . . of x and y, and necessarily if any x and y have F, G . . . then x is R to y or x has R(y). That reading captures the intuitive idea behind Leibniz’s saying that intrinsic denominations are the basis or foundation of extrinsic relational ones, that relations or relational facts ‘‘result’’ or ‘‘arise’’ from states of the relata. And by adding not implausible content to the idea that certain relational facts obtain in virtue of other monadic ones but not conversely, it helps to fill out Mates’s insight that Leibnizian reduction requires nothing like logical equivalence. The supervenience reading does a bit more than fill things out, however. It points to an important informal line of argument against skeptics about reducibility, best posed to them as a question: do you really think that Leibniz believes God could have actualized a world which, so far as monadic states are concerned, maps onto our world exactly, but where the relations are different? By our lights, the correct answer is clearly ‘‘no.’’ That returns us to our earlier discussion of complete concepts, which are supposed to completely determine exactly one possible individual: if the more finely sliced monadic properties determine the relational ones (via the laws of expression) as Leibniz ³⁷ Others have agreed with our supervenience proposal of ‘‘Relations and Reduction in Leibniz’’ (from which parts of this chapter are drawn). Robert C. Sleigh, Jr. expresses it this way (bracketing the reference to modality, our topic in chapter ): ‘‘The basic idea is that when you have said what there is to say about the distribution of intrinsic denominations among individual substances in a given world, you have said it all; that is, any other contingent truths about that world (except truths about God’s relation to it) must supervene on what has already been said’’ (Leibniz and Arnauld, p. ).



Relations

seems clearly to hold, then no additional work toward specifying exactly one possible individual can be done by putting those derived properties into the complete concept. We haven’t argued that Leibniz is right about all this, but rather have recommended it as a plausible way of interpreting Leibniz on relations – one siding with the old-fashioned view that he had in mind some sort of reducibility thesis about inter-monadic relations. Even on this more modest score, a lot of work remains: in particular, one needs to show how one or two of the more difficult ‘‘connective’’ cases – like the ‘Paris loves Helen’ case, say – can be spelled out in more detail, with explicit appeal to only Leibnizian resources. A preliminary sketch might go as follows. First move: for Paris to love Helen is for Paris to be in such-and-such a state, and this is caused in him by Helen. One could in principle express this first move in terms of a quatenusstyle analysis, so long as one is careful to make sure that the states referred to in each of the connecting sentences refers to a genuinely intrinsic state. It must be acknowledged that Leibniz is not always careful to ensure this of the quatenus-style analyses produced in the context of logico-grammatical analysis, as when ‘Caius is killed by Titius’ goes to ‘Insofar as Titius is murdering, therefore Caius is murdered’ (VE ). Here ‘murdering’ is not clearly an intrinsic description. For purposes of illuminating the metaphysical groundfloor, the most perspicuous kind of quatenus-style analysis of relations of connection would look something more like: ‘Joe strangled Bill’ becomes ‘Insofar as Joe squeezed, Bill choked’ (and in the end, of course, a maximally perspicuous quatenus-style analysis would involve mental predicates). But notice in any case why this style of analysis – even in its less perspicuous versions – is a step in the right direction: it dissolves the need for Titius himself (or his haecceitistic proxy) to figure in the predicate ascribed to Caius. Instead of including ‘Caius’ in the predicate itself (or Caius in the concept it expresses), one captures the esse-ad contribution of Caius via the quatenus-style connection. Notice, moreover, that the quatenus strategy makes no sense if, as the Kulstad–McCullough view would have it, other-substance-embracing relational predicates can straightforwardly figure in an individual’s complete concept. Leibniz’s view of relations is clearly not one according to which business is completed once ‘Titius murdered Caius’ is rendered as the pair ‘‘Titius is such that ‘murdered Caius’ is true of him’’ and ‘‘Caius is such that ‘is murdered by Titius’ is true of him.’’ By contrast with the Kulstad–McCullough view, the

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reductive program we are ascribing to Leibniz renders the quatenus-style of analysis intelligible and worthwhile. The first step, recall, still leaves us with a relational, causal-explanatory element, manifest by the stressed items in ‘Paris is in such-and-such a state, and this is caused in him by Helen’ and in ‘Insofar as Joe squeezed, Bill choked.’ So, second move: cash out this so-called inter-monadic ‘‘causality’’ exactly as Leibniz would, in terms of states of Helen, states of Paris, and pre-established harmony. Those states are monadic, so step three should finish things off: for there to be pre-established harmony is simply for the monadic facts about the world to be such that whenever a so-and-so fact obtains, other such-and-such facts obtain (where from here the story goes over to matter about true propositions and eventually over to divine psychology). We’ve included some promissory notes there, but don’t see an obvious dead-end. One thus arrives at a picture according to which, first, (a) relational truths about the world supervene on the global monadic facts (the central thesis of this section); and second, emerging from § and now framed in terms of a supervenience thesis, (b) relational truths about an individual substance supervene on the monadic truths about that substance alone together with the laws of expression. Items (a) and (b) are connected by this: facts of expression as between substances supervene on the distribution of monadic facts. . Relations and relational accidents We have said plenty about relational facts, but not much about relations themselves. Let us end by addressing the ontological issue head on. It is clear enough that, when construed as things having a foot in many subjects, Leibniz believed that there are no such things as relations. Thus he writes The relations which connect two monads are not in either the one or the other, but equally in both at once; and therefore properly speaking, in neither . . . I do not think that you would wish to posit an accident which would inhere simultaneously in two subjects . . . (G ,; our emphasis)

In connection with this theme, Leibniz frequently says (to Foucher, to de Volder, to Bayle in his ‘‘Rorarius’’ reply, to Princess Sophia, to Des Bosses, to Clarke) that relations are ideal, and he says no less frequently that what is neither a substance nor an accident must be an ideal thing.³⁸ ³⁸ For references, and for discussion of Leibniz’s use of ‘ideal,’ see Glenn A. Hartz and J. A. Cover, ‘‘Space and Time in the Leibnizian Metaphysic.’’



Relations

But while Leibniz denies reality to two-footed relations, as it were, one must reckon with his willingness – even while noting that the relation common to both David and Solomon ‘‘is merely a mental thing’’– to affirm the existence of ‘‘the paternity in David’’ and the ‘‘filiation in Solomon.’’ What, then, of relational accidents? Leibniz typically uses ‘relation’ as a term for the ideal two-footed things, but sometimes (if much less frequently) follows the scholastic willingness to use ‘relation’ to name relational accidents, as when (to Clarke) he refers to a relational accident as ‘‘what philosophers call a ‘relation’ ’’ (G ,: L ). It may seem from our discussion so far that we are committed to denying the existence of relational accidents on Leibniz’s behalf. That’s not quite right. The reductionist program we have sketched on Leibniz’s behalf can perfectly well permit an identification of some relational accident with an intrinsic modification. Just as on one model of corporeal substance, a corporeal substance is identical with a monad insofar as it has a body³⁹ – our favorite analogy being the identity of a person with a king, where a king is a person insofar as he has a kingdom – so a relational accident can and should be regarded as identical with an intrinsic accident insofar as certain facts of expression hold of it. A relational designation like ‘‘paternity’’ will apply to some modification – not merely by virtue of the intrinsic character of that modification, but also, ultimately, by virtue of the laws of expression governing it. Our point is not to deny the existence of relational accidents thus understood. There are such accidents, and they are identical with their esse-in foundations. In thus permitting relational accidents, Leibniz needn’t admit inter-monadic relational facts into his metaphysical groundfloor. And it is clear to us that he did not admit them. ³⁹ Recall what Robert M. Adams has called the ‘qualified one substance’ view, discussed briefly in chapter , §..

 

Essentialism

How are individual substances related to their qualities, and ultimately to the qualitative manifold? Anticipating the transition from Leibniz’s early discussion in the Disputatio to his mature account of simple individual substances, we noted at the close of chapter  that it is in connection with Leibniz’s answer to these questions that his metaphysic becomes maximally difficult. The issue of relational properties (chapter ), perplexing enough in its own right, is just one – albeit crucial – thread in a larger web that is Leibniz’s answer. At the center of Leibniz’s answer is the complete concept doctrine, from which emerge various modal strands intersecting other parts of the Leibnizian metaphysic. The greatest tension is focused at their intersection with our workaday modal claims about individuals, and with the dominant themes in Leibniz’s account of individuation – the requirement of separability or independence for individual substances, and the requirement that whatever individuates a substance must be wholly internal to it. Suppose that individual concepts are indeed complete in their specification of the properties enjoyed by each substance; and suppose, as Leibniz seems clearly to hold, that no substance could have a complete concept different from the one it in fact has – complete concepts in some sense ‘‘defining’’ possible substances. The resulting de re modal constraints on the relation between any substance and its qualitative clothing would look to imply that no substance could have properties other than those it in fact has. If relational properties are among them, all alike essential,¹ then the defining complete concepts for individuals look to threaten both the separability and internal-individuator requirements for individuation. In the contemporary idiom, any particular substance would look to be world-bound, so that there is no possible world, ¹ That is, essential in the contemporary sense. See chapter , §..





Essentialism

different in any way from the actual world, where that particular substance also exists.² Thus we have, in what is apparently Leibniz’s extreme essentialism, the first of two problems of (let us call it) modal individuation, to occupy us in this chapter. A second and deeper problem, concerning the ability to ‘‘define’’ individual substances by way of complete concepts, will be reserved for chapter . Together, these problems form a cluster of issues relevant to what we earlier called the modal approach to individuation – that bit of high-level theory supplementing de dicto truths delivered by the intensions of ‘substance’ and ‘individual.’ If (as we believe) the texts leave room to doubt whether Leibniz consciously developed anything like a considered theory meant to handle questions of de re modality, as contemporary modal metaphysicians seek to develop, there is no doubting Leibniz’s deep concern with modal issues, and throughout his lifetime Leibniz struggled to give a satisfactory treatment of them. The scope of his treatments ranges wider than our topics in these chapters. Our task is not to give a full-dress accounting of Leibniz on modality, much of which involves broadly semantic and proof-theoretic doctrines, but instead to discuss the modal dimension of Leibniz’s theory of simple substances and their individuation. Doing so will go some distance toward fleshing out that bit of high-level theory that Leibniz’s metaphysics of individual substance is in fact capable of providing. There can be little question about the importance of the complete concept doctrine (and its attendant predicate-in-subject account of truth) for Leibniz’s mature picture of individuation; and there can be little question about their relevance to de re modal predication. But the exact relation of the complete concept and predicate-in-subject doctrines to Leibniz’s views of modal individuation – to the strength of his essentialism and its consequences for claims of trans-world identity – is not at all straightforward. This is in large measure because Leibniz’s own statements of the complete concept doctrine, and its intended grip on the metaphysics of modality, are open to a good deal of filling out. We shall discuss three views, associated with three ways of filling out the modal strands emerging from the complete concept doctrine: superessentialism, strong essentialism, and moderate essentialism. The first of these is a well-worked bit of Leibnizian lore, no less important for its ² Entertain, as David Lewis does in chapter  (passim) of the Plurality of Worlds, the somewhat frivolous idea that two numerically distinct worlds may nevertheless be indiscernible, and the inference from ‘‘I couldn’t exist if the world had been different in any way’’ to ‘‘I am worldbound’’ isn’t mandatory. For (inter alia) Leibnizian reasons, we shall ignore this idea in what follows.

Superessentialism vs. strong essentialism



influence in discussions of Leibniz on modality than for its naturalness as an interpretation of what Leibniz in fact says. In § to follow we shall briefly lay out the superessentialist view, and evaluate its credentials alongside those of strong essentialism. After a passing interlude in § comparing Leibniz’s account with so-called ‘‘counterpart semantics,’’ we consider in § the case to be made for moderate essentialism. Finally in § we take up a challenge to the strong essentialism we favor, issuing from the problem of compossibility.              .            We’ve permitted already talk of world-bound individuals (WBI) and trans-world identity (TWI), and shall continue doing so. The idiom of possible worlds, at home in contemporary modal semantics and unquestionably there in the Leibnizian taxonomy, was not Leibniz’s preferred vehicle for posing modal issues. Although he was willing to deploy the idiom of worlds in modal contexts (of which more in §), Leibniz himself used possible worlds primarily, if not exclusively, for discussing theological issues associated with this doctrine of creation, tending rather more to the use of conditionals with contrary-to-fact antecedents when posing modal questions of the sort concerning us here. But granting that the de re modal commitments of a philosopher do not bring this or that particular semantics with it – and so far as we are aware, Leibniz had no well-developed modal semantics – there is no particular danger in using the vehicle of possible worlds to frame the issues before us, to grapple with the content of relevant modal claims when Leibniz’s intentions are sufficiently clear. Moreover it is an interesting question whether Leibnizian worlds can be fairly said to express possible ways things could have been (so that x’s being essentially F will entail that x is F at every world at which x exists) while nevertheless departing from the contemporary construal of possible worlds. That question, and the more immediate connection between Leibniz’s essentialism and the individuation of substances in the context of various modal scenarios, can be approached safely if cautiously enough in the idiom of possible worlds. . Superessentialism The texts in which Leibniz is most forthcoming about issues crucial to his essentialism³ come from the correspondence with Arnauld. In that



Essentialism

exchange, the notion of a ‘‘possible Adam’’ figures crucially in Leibniz’s effort to defend the complete concept doctrine of the Discourse and to articulate its consequences. Corresponding to Adam, Leibniz says, is his complete individual concept, the content of which is identical with ‘‘the knowledge God had of Adam when he determined to create him’’ from amongst an infinite number of (other) possible Adams (G ,: LA ). [His complete concept is] a perfect representation of a particular Adam who has particular individual conditions and also is thereby distinguished from an infinite number of other possible persons who are very similar yet different from him . . . There is a possible Adam whose posterity is thus, and an infinite number of other possible Adams whose posterity would be different; is it not true that these possible Adams (if one may so call them) differ among themselves and that God has chosen just one who is precisely our Adam? (April : G ,: LA –)

Arnauld approached that with an understandable sympathy for TWI firmly in hand (cf. G ,–: LA –): the modal status of a scenario in which God creates him, this particular individual Arnauld that he is (identical with), as a doctor with children rather than a celibate theologian, must surely be possible. Arnauld thus construes Leibniz as claiming that ‘‘other possible Adams’’ picks out Adam – our Adam – at other possible worlds, possessing some properties in those worlds not exemplified by him at the actual world (cf. G ,–: LA ). But then (Arnauld wonders), how can Leibniz treat complete concepts as he has, understanding them to specify the individual nature or essence of substances? If the individual concept of the actual Adam is a ‘‘perfect representation’’ of him and the properties ascribed by that concept are essential to him, then how can that concept denote possible Adams with different properties? This, at any rate, plausibly explains what Arnauld was thinking when he replies: I do not know how by taking Adam as the example of a singular nature one can conceive of many possible Adams. It is as though I were to conceive of many ³ It has become standard practice in the philosophical literature to reserve the term ‘essentialism’ for the view that some but not all of an individual’s properties are essential to it. Insofar as the super-essentialist reading here under discussion regards Leibniz as having said that all of an individual’s properties are essential to it, the term ‘super-essentialism’ as a description of his position departs somewhat from common usage. Care in recognizing this departure is especially important when discussing the ascription of world-bound individuals (WBI) and counterpart theory to Leibniz: ‘essential’ in this case can only mean ‘‘what is shared by all of one’s counterparts.’’ Unless specifically indicated in the text, we avoid using ‘essential’ in any such derived sense.

Superessentialism vs. strong essentialism



possible varieties of myself; . . . [But] I cannot think of myself without considering myself as an individual nature, so distinct from any other, existing or possible, that I can as little conceive of different varieties of myself as of a circle whose diameters are not all of equal length . . . Thus one of these varieties of myself would necessarily not be me; which is manifestly a contradiction. (May : G ,: LA )

Arnauld looks to regard the complete concept doctrine and its threat to TWI as a package: if my singular nature is expressed by a complete concept as Leibniz says, then I am numerically distinct from every individual in any other possible world, however similar they might be to me. Leibniz doesn’t deny this. He does deny being committed to the ‘‘manifest contradiction’’ of many Arnaulds and many Adams, explaining that other possible Adams aren’t (our) Adam, but rather possible inhabitants of other worlds that are ‘‘very similar but distinct from him’’ – Adam counterparts so to speak. In thinking about possible Adams, says Leibniz, we must not ‘‘conceive of an indeterminate Adam . . . but we must attribute to him a concept so complete that all which can be attributed to him may be derived from it.’’⁴ Thus, when Leibniz says that his complete concept is that ‘‘by virtue of which all my predicates pertain to me as their subject’’ (G ,: LA ), he is claiming that the truth of ‘x is F’ can be accounted for in terms of x’s having the complete concept it does, and thereby that any individual in whose concept F is not contained cannot be x.⁵ Had God created an individual exemplifying properties even slightly different from the properties given in your individual nature or complete concept, He would have created some individual numerically distinct from you: [O]ne must attribute to [Adam] a concept so complete that everything that can be attributed to him can be deduced from it . . . It follows that he would not have been our Adam, but another, if he had experienced other events, for nothing prevents us from saying that he would be another. He is therefore another. (G ,: LA ) ⁴ From the long memorandum for the  July letter, ‘‘Remarks upon M. Arnauld’s letter in regard to my statement that the individual concept of each person involves, once for all, all that will ever happen to him’’ at G ,: LA –. ⁵ Thus Leibniz views the complete concept doctrine of substances and the predicate-in-subject account of truth as very closely connected. One cannot help but think that the latter entails the former, and that the former entails the latter when one adds the Leibnizian premise that the subject concept of subject-predicate propositions are complete individual concepts. Leibniz is in any case clear about how he regards the close connection between them: ‘‘In saying that the individual concept of Adam involves all that will ever happen to him, I mean nothing else than what all philosophers mean when they say that the predicate is present in the subject of a true proposition (praedicatum inesse subjecto verae propositionis)’’ (G ,: LA ). Cf. also G ,: LA .



Essentialism

But, someone will object, whence comes it then that this man will assuredly sin? The reply is easy. It is that otherwise it would not be this man.⁶ You will object that it is possible for you to ask why God did not give you more strength than he has. I answer: if he had done that, you would not exist, for he would have produced not you but another creature. (Grua )

Thus Leibniz views complete concepts as materially adequate to the role of a modally robust individuator, identifying the complete concept of x with the haecceity of x in Discourse §.⁷ This brief review of a familiar exchange and some relevant texts captures the main elements in what many have judged the preferred and most natural reading of Leibniz’s position. The view may be characterized by the following three theses, together with a fourth to be added shortly. Since Leibniz views complete concepts to express singular natures or essences of individual substances, () an individual could not have a different individual concept than the one it in fact has; and since individual concepts are complete, Leibniz endorses a kind of superessentialism, according to which () all the properties of an individual substance are essential to it. Hence Leibniz denies TWI: on his view, () created substances are world-bound individuals (WBI).⁸ But here one must exercise the due caution recommended earlier. For Leibniz to say, as the superessentialist reading has it, that Arnauld exists only at the actual world, will on the typical possible-worlds ⁶ G ,: L  – here departing from the usual ‘‘otherwise he would not be this man’’ of L and AG, which is less faithful to the French and is rather more awkward. ⁷ At G ,. Leibniz doesn’t have Scotistic haecceities in mind, of course: exactly what he does have in mind is addressed in chapter . It should be noted that the role of complete concepts as (materially adequate) modally robust individuators or Leibnizian haecceities is not yet fully in place from the texts cited thus far. Appropriating Arnauld’s apt description of a complete concept as expressing an individual substance’s ‘‘singular nature’’, while a ‘‘nature’’ is such that no one substance could enjoy two of them, it is ‘‘singular’’ only if two substances cannot enjoy one of them. We shall return to this presently. ⁸ Thus Fabrizio Mondadori, from p.  of ‘‘Leibniz and the Doctrine of Inter-World Identity’’: ‘‘Leibniz’s theory of complete concepts entails precisely that no actual individual could have had different properties than the properties he does have, hence, that no actual individual can belong to more than one world.’’ Leibniz’s reply (in the Discourse at G ,: L ) to the question, ‘‘How does it come about that this man will certainly commit this Sin?’’ was a quick ‘‘The reply is easy: it is that otherwise he would not be this man.’’ Discussing this reply in his ‘‘Reference, Essentialism, and Modality in Leibniz’s Metaphysics,’’ Mondadori summarizes: ‘‘In other words: it is not possible that this man should have had different properties than the properties he in fact had . . . There is no possible world of which ‘Peter exists but does not sin’ is true (I owe this way of putting the matter to Benson Mates, personal communication). Hence, Peter exists nowhere but in the actual world’’ (pp. –). See also Benson Mates, ‘‘Individuals and Modality in the Philosophy of Leibniz,’’ and chapter , ‘‘Cross-World Identity’’ of his The Philosophy of Leibniz. See also Baruch Brody, Identity and Essence, pp. –.

Superessentialism vs. strong essentialism



semantics entail that Arnauld could not have married: Arnauld is celibate at every world at which he exists. Now it is one thing to say, as we have suggested one fairly can, that if x is necessarily F then x is F at every world at which x exists, and quite another to assert the converse. Leibniz didn’t go in for Spinoza’s necessitarianism. Famously, Leibniz denies the converse, arguing in many texts that while F is contained in the complete concept of x, it does not follow that x is necessarily F. To preserve the truth value that most of us think work-a-day modal claims deserve (e.g., ‘‘Arnauld could have married’’) the super-essentialist encourages us to see that Leibniz has recourse to the counterparts of Arnauld at other worlds. According to this last element of the superessentialist picture, () Leibniz employs a counterpart-theoretic account of de re modal claims, on which talk about ways some actual individual x might have been is to be understood as talk about possible, non-actual individuals that are similar to but not identical with x.⁹ . Relational properties and superessentialism Beyond its prima facie plausibility alongside certain texts, what more can be said about the superessentialist reading of Leibnizian modality? There is, of course, the question of what Leibniz in fact believed. No mean Leibnizian himself, he certainly does endorse Leibnizian essentialism: singular individual concepts are complete, and no individual could have fallen under a different complete concept. So far as we are aware, Leibniz never explicitly enunciates or argues for WBI. If the texts are not unambiguous on this latter question, they are – as is clear in the representative texts already cited – at least suggestive. As Robert Adams summarizes the relevant portion of the Leibniz–Arnauld debate, Arnauld affirms transworld or counterfactual identity . . . In his response, as in a number of other places in his writings, Leibniz made clear that he did not accept Arnauld’s assumption of counterfactual identity. He held that no actual individual creature would have existed if anything at all had gone differently from the way things go in the actual world – that if Arnauld, for example, had ⁹ ‘‘In the framework of Leibniz’s theory of complete concepts, counterpart theory provides a neat way of making sense of de re modal predications, as well as of counterfactual conditionals – a way, moreover, which is consistent with superessentialism, and which does not make all of them uniformly false’’ (Mondadori, ‘‘Leibniz and the Doctrine of Inter-World Identity,’’ p. ). See also Hide´ Ishiguro, Leibniz’s Philosophy of Logic and Language, pp. –. Thus: ‘‘What Leibniz meant by saying that the opposite of ‘Caesar crossed the Rubicon’ is possible, is that there could have been – in a different world – a person like Caesar in all respects except that of crossing the Rubicon, with its attendant consequences’’ (p. ). Much less explicitly, see also Mates (The Philosophy of Leibniz, chapter  passim), to whom we hesitate to ascribe the full counterpart-theoretic reading of Leibniz.



Essentialism

married, he would not have been Arnauld [or more precisely, that anyone who got married would not have been Arnauld (cf. Grua )].¹⁰

If Arnauld and Leibniz disagree about the complete concept doctrine, they seem to agree about its apparent entailment for TWI – the denial of TWI being precisely the rub for Arnauld. An actual substance’s individual concept, being at once a singular nature and complete, looks to require that had anything at all gone differently from the way things go in the actual world, the substance would not exist. It is one thing to ask what Leibniz believed, and another to ask what Leibniz’s pronouncements commit him to. So, again: beyond its prima facie plausibility given certain texts, what more can be said about the superessentialist reading of Leibnizian modality? In particular, is Leibniz committed to claiming that ‘‘no actual individual creature would have existed if anything at all had gone differently from the way things go in the actual world’’? First, and crucially, there is this: the claim that an individual could not have fallen under a different complete concept (Leibnizian essentialism) does not by itself entail the denial of TWI. The former tells us that for any x, x has the same complete concept at any world at which x exists. But that is neutral with respect to the claim that x exists at more than one world, and so is consistent with it. Nor does Leibnizian essentialism, together with TWI, violate Leibniz’s principle of the Identity of Indiscernibles: were Leibniz to allow that you exist at other worlds and claim that your complete concept could not have been different, he is committed at most to the existence of indiscernibles that are trans-world identical, not to indiscernibles that are trans-world distinct.¹¹ Thus arguments of the sort ‘‘there is no possible world of which ‘Peter exists ¹⁰ Robert M. Adams, Leibniz: Determinist, Theist, Idealist, pp. –. Adams frames the debate in terms of the predicate-in-subject doctrine, though the relevant passages on which he is commenting focus on the complete concept doctrine, which Leibniz sees the former to have entailed (see note  above). Later Adams says that ‘‘Leibniz and Arnauld appear to have assumed that the denial of transworld or counterfactual identity follows from Leibniz’s [predicate-in-subject] theory of truth. This is a natural assumption to make, but it is incorrect’’ (p.). Adams is right on both counts. What we want at the moment is that the assumption is a natural one to make; our reasons for denying that it is a correct assumption, presented at length below, are quite different from the reason Adams offers (which, we note, depends crucially on the completeness of concepts). ¹¹ Nor does Leibnizian essentialism and TWI commit one to transworld indiscernibles if ‘indiscernible’ means ‘‘sharing all properties.’’ But as Mates (The Philosophy of Leibniz, pp. –, and p. ) points out, it would trivialize the principle of the Identity of Indiscernibles to construe it as saying that x and y are identical if x and y share every property, including relational properties in particular. Leibniz sometimes formulates the principle as claiming that the sharing of a complete concept is sufficient for identity; it is on that construal that the two doctrines commit one to transworld indiscernibles.

Superessentialism vs. strong essentialism



but does not sin’ is true; hence, Peter exists nowhere but in the actual world’’¹² are at best enthymematic. Elements () – () of the superessentialist view are not so tight a package as all that. If Leibnizian essentialism, however ‘‘naturally’’ (to use Adams’s apt phrase) associated with the denial of TWI, is not so closely connected with WBI as to immediately entail it, then it remains to be shown exactly what, wittingly or unwittingly, Leibniz or superessentialists writing on his behalf have wedded to Leibnizian essentialism so as to get WBI. Leibniz hints at an argument in the passage to Arnauld cited earlier. After stating the complete concept doctrine, Leibniz immediately continues: ‘‘It follows that he would not have been our Adam, but another, if he had experienced other events, for nothing prevents us from saying that he would be another. He is therefore another’’ (G ,: LA ). Commentators have not responded favorably to this argument of Leibniz’s, which appeals to the Principle of Sufficient Reason (PSR). The argument deserves closer attention and more respect than it has been given; lacking the resources here to say why, let us set it aside until chapter , and look elsewhere. Looking elsewhere won’t mean looking for explicit proof-texts: the texts, as we have noted, are suggestive but not conclusive. Here is perhaps the most obvious proposal for connecting Leibnizian essentialism to WBI: If one attempted to envision an actual substance x existing at some other, non-actual world, what one would at minimum envision is x in a different environment, and this difference (by the ‘‘interconnection of all things’’) would be registered in the states of x. The argument can be put in terms of a substance’s ‘‘relational properties.’’ Since all the properties specified by my complete concept are essential to me, all my relational properties are essential to me, and this entails that I exist only at one (i.e., the actual) world. For suppose that I don’t exist only at the actual world W. I then exist at some non-actual world W*, which necessarily differs from W by containing some nonactual individual s*, or at very least in exemplifying some property F not exemplified in W.¹³ In W* I thereby have in my complete concept some relational property that I don’t exemplify at W – of being R-to-s*, or at very least of being in an F-world. So, not all the of properties contained in my complete concept are essential. But that contradicts ¹² Thus see note . ¹³ This follows from an application of the Identity of Indiscernibles (PII) to worlds. The application of PII to worlds will be taken up in chapter .



Essentialism

Leibnizian essentialism; hence, by reductio, I cannot exist at any other world. Leibnizian essentialism entails WBI. As we have argued in chapter , the evidence falls strongly on the side of attributing to Leibniz a reducibility thesis about intermonadic relations – that is, on the side of claiming that (i) Leibniz did not accept relational facts about individual substances as irreducible, fundamental truths of his groundfloor metaphysic, and (consequently) that (ii) relational properties needn’t appear in the complete concepts of substances. Syntactic considerations, including the ability of Leibniz’s subject– predicate logic to accommodate relational predicates, count little or not at all against (i); and counting in favor of (i) are various metaphysical considerations drawn from Leibniz’s views of individual accidents and intrinsic denominations. One consequence of this for (ii), recall, is that if the basic, more finely sliced monadic properties in complete concepts of individuals at our world determine the relational truths about those individuals, then no additional work can be done towards uniquely specifying those individuals by packing derived relational properties into individual concepts. In the spirit of Leibniz’s view that something is complete if adding to it is ‘‘superfluous’’ (C : PLP ), one may think of God as thus observing a kind of redundancy criterion for the singular natures of substances, in accordance with PSR: since the non-relational properties had by individuals at a world determine the relational truths about that world, God has no reason to include such properties in the complete concepts of individuals. The suggestion here – that if relational properties ‘‘needn’t’’ appear in complete concepts then they don’t – is supported (recall again) by Leibniz’s claims that what God sees in complete concepts is the foundation for all of Alexander’s predicates, and that setting aside those predicates which depend on others, He need only consider all the basic predicates of Adam in order to form his complete concept. We shall return to these themes shortly: there are details left to be settled. For the moment it suffices to note that if relational properties of individual substances are not part of their complete concepts, then arguments proceeding from their inclusion in complete concepts to superessentialism and thence to WBI are unsatisfactory. Leibnizian essentialism is true: Adam’s complete individual concept does specify the singular nature of Adam, and at every world at which Adam exists, he has just those properties expressed by his concept. But since Adam’s complete concept does not contain properties like is R-to-s, or is in a non-F-world, it remains to be shown why he cannot exist at another

Superessentialism vs. strong essentialism



world. (Or better – to avoid the doubly stacked modal expression ‘cannot exist at another world’: it remains to be shown why every world containing some non-actual substance s*, or instantiating some property F not instantiated at the actual world, fails to contain Adam.) Thus far, it would seem that Leibnizian essentialism can permit Adam’s complete concept to be co-instantiated with a set of complete concepts differing from that instantiated at our world. More generally, if, following the account of chapter , relational properties obtaining at a world supervene on the basic monadic properties included in the complete concepts instantiated at that world, then the thesis of () Leibnizian essentialism is weaker than () superessentialism. Nevertheless () is quite strong: all intrinsic monadic properties are part of the singular nature of each individual substance, thus drastically restricting but not excluding nonactual worlds at which Adam exists. . Harmonious correspondence and superessentialism The case is far from settled. The sub-text in standard arguments for superessentialism, involving relational properties, may admit of a somewhat different if suitably Leibnizian gloss to secure the route from () to () by other means. Fair enough: individual substances are not genuinely connected with other substances in any robust sense. Leibniz makes it clear that simple windowless substances cannot causally interact, for example (G ,: L ). Still, Leibniz clearly thinks that there are relational truths involving distinct substances, and moreover he employs an explicitly relational taxonomy for describing states of substances. Each monad mirrors (reflects) the entire universe from its own point of view (G ,: L ); its states, Leibniz says, are ‘‘perceptions or expressions of external things’’ (G ,: L ); indeed he claims that ‘‘a monad always expresses within itself its relations to all others’’ (G ,: L ). Thus even if complete concepts do not strictly include relational properties, it can hardly be said that substances remain altogether dead to their environment. For while God has created substances so as to ‘‘get their perceptions out of their own store, so to speak,’’¹⁴ undergoing their changes without any genuinely causal connections to things outside them, He nevertheless instantiates complete individual concepts of substances whose perceptual states correspond exactly and harmoniously to all other substances, detail for detail, ¹⁴ As Des Bosses nicely described Leibniz’s position at G ,: L  – a passage to which we shall return presently.



Essentialism

change for change (cf. Discourse §). Since this correspondence with the careers of distinct substances external to them is guaranteed by their complete concepts, and complete concepts express singular natures essential to them, no actual individual can exist at a world even slightly different from the actual world. The mirroring doctrine is important to Leibniz’s picture of the actual world: such mirroring he took to be constitutive of the harmony that God chose to instantiate in creating the best of all possible worlds. So there is no doubting Leibniz’s commitment to the view that each monadic history in some sense reflects every other. But in what sense? Parts of chapter  anticipate our judgment that this refined version of the superessentialist reading presses into service a superficial view of Leibnizian perception. On Leibniz’s own account of perception as expression, a complete specification of the perceptual states of a monad brings with it no overt commitment to the things that are perceived, nor even to there being something that is perceived at all. Perceptual states of Leibnizian substances are monadic: that they count as expressions of a thing outside it cannot be gotten from anything intrinsic to that state, and they count as such only insofar as a pre-established harmony guarantees that they correspond in suitable ways with monadic states of other substances. This pre-established harmony is a general fact about our world that supervenes on the primitive monadic facts of our world, specified by the complete concepts of substances that God in His wisdom and goodness has chosen to create. Recall again Leibniz on pre-established harmony: it follows from what we have just said, that each substance is a world apart, independent of everything outside itself except God. Thus all our phenomena, that is to say, all the things that can ever happen to us, are only the results of our own being. And since all these phenomena maintain a certain order which conforms to our nature or, so to speak, to the world that is within us . . . this would be sufficient to enable us to say that these phenomena are true, without being put to the task of inquiring whether they are outside of us and whether others perceive them also. Nevertheless it is true that the perceptions or expressions of all substances inter-correspond . . . It is only God . . . who is the cause of this correspondence between their phenomena . . . (G ,: L )

And (again) concerning expression, Leibniz writes in an early fragment that ‘‘one thing is said to express another if it has properties [habitudines] that correspond to the properties of the thing expressed’’ (: G ,: L ), later echoing the same theme in his response to Arnauld’s query about expression: ‘‘One thing expresses another (in my

Superessentialism vs. strong essentialism



terminology) when there exists a constant and fixed relationship between what can be said of the one and of the other’’ (October : G ,: LA ).¹⁵ The relational element here isn’t built into those properties, but rather rides over them as mere correspondence. Thus Leibniz’s relational idioms (‘‘perception,’’ ‘‘expression,’’ ‘‘mirroring’’ and so on) are not reliable indicators of anything intrinsic to a substance that necessarily brings its environment with it. If this is correct, then the superessentialist reading may be fairly resisted as capturing Leibniz’s intentions. For God to create a world in which states of substances maximally harmonize, as Leibniz believes they do at the actual world, is for Him to create a world in which this particular set of individual concepts is instantiated rather than some other. At other worlds (none of them the best possible, of course), perceptual states of substances will correspond less perfectly, less harmoniously, than they do in ours.¹⁶ This is, again, a weakening of superessentialism in the direction of a strong essentialism, away from any absolute necessity of a particular environment, toward a proper moral or hypothetical necessity of the actual-world environment. That is, where the refined defense of superessentialism under consideration must judge inter-monadic correspondence itself as somehow internal to the life of each individual substance (at a world), strong essentialism would have it supervene on all of them as a consequence of God’s benevolent choice to instantiate this set of individual concepts rather than some other. However, for perceptual states of monads to mirror one another and harmonize as they do at the best of all worlds, it is sufficient simply that there be a relational law or set of laws made true by God’s instantiating a certain set of intrinsic monadic histories. This is what Leibniz intends when he warns: ¹⁵ Leibniz is fond of the following examples of expression – the genus of which perception is a species: algebraic equations express geometrical figures, projective (plane) drawings express solids, maps express geographical regions. There are of course no intrinsic features of equations or drawings or maps entailing that certain figures, solids, or geographical regions exist, to which they stand in ‘‘a certain precise and natural relationship of correspondence’’ (cf. NE .viii.: RB ). On perception as expression, see Robert McRae’s Leibniz: Perception, Apperception, and Thought, esp. pp. –. ¹⁶ That description and our treatment below of relational laws of order gloss over a number of distinctions crucial to a proper account of harmony. We should not be taken for claiming that (a) the doctrine of expression, as a claim about the existence of laws of order at a world, is equivalent to the doctrine of universal harmony, nor that (b) the doctrine of perfection is equivalent to the doctrine of harmony. (a) is false and (b) is controversial. Our point here is simply that God’s choice to create a world in which those relational virtues obtain just is a choice about what monadic histories to instantiate (and upon which those relational laws will supervene). On (a), see Robert C. Sleigh, Jr., ‘‘Notes on Harmony’’; on (b), see esp. pp. – of Gregory Brown, ‘‘Compossibility Harmony, and Perfection in Leibniz.’’



Essentialism

But it must not be thought that, when I speak of a mirror, I mean that external things are always depicted in the organs and in the soul itself. For it is sufficient for the expression of one thing in another that there should be a certain constant relational law . . .¹⁷

Leibnizian essentialism plus harmonious correspondence does not entail WBI, because laws of harmony are not absolutely necessary. The questionable view implicit in superessentialism (that the entailment does hold) is an old one: Des Bosses had it, and Leibniz explicitly corrects him. In his letter of  April , Des Bosses wrote: If the monads of the universe get their perceptions out of their own store, so to speak, and without any physical influence of one on the other; if, furthermore, the perceptions of each monad correspond exactly to the rest of the monads which God has already created, and to the perceptions of these monads, and are harmonized so as to represent them; it follows that God could not create any one of these monads which thus exist without constructing all the others which equally exist now . . . (G ,: L )

To the charge that God cannot create any one of these monads without creating all the others, Leibniz answers: My reply is easy and has already been given. He can do it absolutely; he cannot do it hypothetically, because he has decreed that all things should function most wisely and harmoniously. There would be no deception of rational creatures, however, even if everything outside of them did not correspond exactly to their experiences, or indeed if nothing did, just as if there were only one mind . . . ¹⁸

We shall return to the issue of harmony when discussing the compossibility threat to strong essentialism, in § below: that threat arises in connection with a related challenge, about the relation of laws to ¹⁷ C : MP –. Or, returning to the geometrical example (see note ), the relations of correspondence between a sphere and its (projected) ellipse are the basis of expression, ‘‘since any point whatever on the ellipse corresponds to some point on the circle according to a definite law’’ (G ,: L ). The role of laws will be taken up in §. below. ¹⁸ G ,: L . Leibniz’s denial here of the absolute or per se impossibility of any actual monad existing without all other actual substances forms part of the reason for saying that actual laws of harmony are not absolutely necessary. The relational truths of correspondence about any substance at a world are only hypothetically necessary, and this, for Leibniz, entails that such truths follow only on the supposition of other facts external to it, not from its own nature. Comparing absolute with hypothetical necessity, Leibniz says that ‘‘there is a hypothetical necessity when a thing’s being other than it is can indeed be understood through itself, but it is necessarily as it is non-essentially (per accidens), on account of other things outside itself already presupposed’’ (cf. Grua ). We say this forms part of the account of the contingency of the laws of harmony: in addition to grounding contingency on the notion of what is possible ‘‘in its own nature,’’ independent of God’s particular volitions, Leibniz also believes that God’s creation of this world, equally possible in the first sense, is a contingent matter. For a splendid treatment of these broader issues, see Adams, Leibniz, chapter , ‘‘Leibniz’s Theories of Contingency.’’

Superessentialism vs. strong essentialism



complete concepts. But before moving to the question of laws, witness in the Des Bosses reply above Leibniz’s commitment to a central element of traditional Aristotelian-scholastic accounts of substance and individuation – a mature commitment to the separability requirement at work already in the early Disputatio (see chapter ). Traceable to Aristotle’s discussion in the Categories, the notion of substance in the hands of Descartes, Spinoza, and Leibniz comes in large measure to be the notion of that which is independent of other things.¹⁹ Descartes invokes it at Principles .–, famously weakening ‘‘depend[s] on no other thing for its existence’’ (AT A,: CSM .) to ‘‘no other thing except God’’ for the case of created substances. If there is an implicit weakening in Descartes’s claims that substances are able to ‘‘exist on their own’’ (AT ,: CSM .) or are ‘‘capable of existing independently’’ (AT ,: CSM .), Spinoza maintains the strong version of independence in Id of the Ethics, insisting that substance is conceived ‘‘through itself’’ (CWS ) – that is, is such that the concept of it requires no appeal to the concept of any other thing. The separability or independence requirement for really distinct substances is a deeply and firmly entrenched element of the early modern conception of individual substances. Des Bosses’s worry may be fairly viewed as a worry that Leibniz is committed to denying what is deeply and firmly entrenched. And Leibniz’s reply is that his metaphysic of perceiving substances entails no such denial, even in the morally inferior counterfactual situation where there is no correspondence: internal monadic states would be what they are even in the absence of external relata to complete the intensional features of perceptions, ‘‘as if there were only one mind.’’ An earlier letter to Des Bosses, like the reply above, highlights the hypothetical necessity of external substances answering to internal states: ‘‘That one substance should exist alone is one of those things not agreeing with divine wisdom, and so will not happen, even if it could happen’’ (G ,). In his remarks on the article Rorarius, Leibniz is even more forthright about the possibility of any substance existing apart from the others: ¹⁹ The separability or independence requirement is one of four in the Aristotelian-scholastic tradition: substance is (a) that which is independent of other things; (b) that which is the subject of predication, but is not predicated of another; (c) that which contains within it a principle of activity; and (d) that which endures through change. The route from various Aristotelian pronouncements (see, for example, (a) Categories , a and Metaphysics aff; (b) Categories , a; (c) Physics , a-b; (d) Categories , a), through scholastic thought into the early modern period, is an interesting and difficult one, the reconstruction of which we leave to more capable hands. Each of (a) – (d) are to be found in Leibniz: (a) G , : L ; G ,: L ; (b) G ,: L ; (c) G ,: L ; G ,: L ; (d) G ,: L ; G ,: L .



Essentialism

It is true that if God were able to destroy all the things that are outside of the soul, and conserve the soul alone with its affections and modifications, they would bring it by its own dispositions to have the same sensations as before – as if the bodies remained – although in that case it would only be like a kind of dream. But since that is contrary to the designs of God, who has willed that the soul and the things outside of it are in agreement, it is clear that this pre-established harmony destroys such a fiction, which is a metaphysical possibility, but which does not accord with the facts and their reasons. (G ,, our emphases)

The Cartesian weakening of the independence requirement is implicit in each of Leibniz’s replies, though it is explicit in Discourse §: ‘‘each substance is a world apart, independent of everything outside of itself except God’’ (G ,: L ). What we want from Leibniz’s replies and the related passages is simply his commitment to a consistent pair – a modally strong separability requirement and a modally weak correspondence thesis. In chapter  we argued that the scholastic sentiment favoring a principle of individuation that is wholly internal to the substance is a well-motivated one. For the general run of scholastics, it was obvious that a substance would be the very individual it is even if it were alone in the world. Taken seriously, that sentiment must reckon any project of accounting for the individuality of substances in terms of its relations to other individuals to be off on the wrong foot. Now the Disputatio context of Leibniz’s insistence on an internal principle grounding the individuality of distinct substances was not an explicitly modal one. But if we are at all correct to recognize in the mature Leibniz a distinctively modal approach to individuation, then the unnegotiable separability of really distinct substances – itself a modal requirement through and through, present in texts early and late – can only look to render the superessentialist construal a less plausible account of Leibniz’s position. You are a substance, and co-exist with other substances at this world. If, following the superessentialist reading, every world at which you exist is a world at which they exist, then your existence is not independent of their existence. But you are a substance, really distinct from them, and your existence does not depend upon theirs. Hence there is a world where you exist but they do not. Thus you are not a world-bound individual. In addition to separability considerations, Leibniz’s famous commitment to the Identity of Indiscernibles (PII) provides further Leibnizian grounds for affirming TWI. Whether or not Adam is world-bound, it seems that God could create an individual in W* that is intrinsically the

Superessentialism vs. strong essentialism



same as our Adam (in Leibnizian terms: has the same history of intrinsic denominations). Suppose, for reductio, that such an individual – Adam*, call him – would nevertheless be distinct from our Adam (because, say, the relational properties of Adam* are different from Adam, or because the laws of nature are packed into individual concepts). So Adam* would be numerically distinct from Adam despite having the same history of intrinsic denominations. But PII tells us that if a and b have the same intrinsic denominations, then a and b are one (Monadology §). So, by reductio, Adam* is identical with Adam after all. As before, WBI isn’t in the cards. Note that here and elsewhere our emphasis is and must be that Leibniz’s considered stance is a strong essentialist but not a superessentialist one, not that strong essentialism squares with the letter of every text taken at face value. Leibniz does say after all that the fact of his undertaking a journey is such that if he did not take it, it would ‘‘destroy’’ the individual concept of him (G ,: LA ). At that moment Leibniz certainly did not have a strong rather than superessentialist picture clearly in mind. Our efforts here are to show that the architectonic of Leibniz’s own metaphysic is properly captured by strong essentialism, that the important and deepest threads of his thinking better hang together on that construal. At bottom, speaking in the lingua philosophica, there will be no talk of journeys to Paris, there being no Paris or space at the groundfloor to take journeys to or through. Will it now be the intrinsic perceptions in me that are correlated with the journey which are essential to me (as we would have it), or in addition (as we wouldn’t have it) are the relations that I bear to the colony of monads that confusedly appear as a spatial destination also essential to me? Here, and elsewhere, only broader considerations about the structure of Leibniz’s metaphysic will permit a considered answer as to what the story, now conducted in the lingua philosophica, would be. That is the sort of project we are engaging. . Laws and strong essentialism Recall again the main theses of the superessentialist reading of Leibniz: () an individual substance could not have a different individual concept than the one it in fact has; and since individual concepts are complete, Leibniz endorses superessentialism, according to which () all the properties of an individual substance are essential to it. Hence Leibniz denies TWI: on his view, () created substances are world-bound



Essentialism

individuals. To preserve the truth value that most work-a-day modal claims deserve (e.g., ‘‘Arnauld could have married’’), () Leibniz employs a counterpart-theoretic account of de re modal truths, according to which claims to the effect that some actual individual x might have been otherwise are to be evaluated in terms of possible, non-actual individuals that are similar to but not identical with x. Setting the counterpart thesis () aside for the moment, a strong essentialist reading of the texts proposes that although Leibniz is committed to () Leibnizian essentialism, his complete concept doctrine does not bring with it a commitment to () superessentialism or () the denial of transworld identity; rather, that doctrine represents a commitment to the thesis that all intrinsic monadic properties of an individual are essential to it – a strong essentialism that is yet weak enough to be logically consistent with TWI. While the case for a strong essentialist construal of the texts has, in our judgment, the most to be said for it, strong essentialism is far from plain sailing. In approaching the problem of laws, recall again Leibniz’s claim to Arnauld that ‘‘one has only to consider together all the basic predicates in order to form the complete concept of Adam’’ (G ,: LA ), and the thesis (recommended earlier) that a complete concept includes only predicates expressing basic, intrinsic monadic properties of an individual substance. The extent of difficulty in carving out Leibniz’s commitments from texts relevant to modal individuation might be gauged by noting that this thesis, at work in defending strong essentialism (above), finds a home as well within the superessentialist and moderate essentialist camps. From its latter, less surprising appearance one is encouraged to ‘‘associate with each individual substance in some world W its strict complete individual concept, including all and only its primitive intrinsic denominations.’’²⁰ In the former, more surprising appearance it recommends that ‘‘a complete concept is to be identified with a core set of properties . . . from which all of the (remaining) properties of the individual in question can somehow be deduced.’’²¹ ²⁰ Robert C. Sleigh, Leibniz and Arnauld, p. : we shall discuss Sleigh’s moderate essentialism in § below. It is clear from pp. – of Sleigh’s account that this formulation of the thesis – unlike its appearance in super-essentialist contexts (see note  below) – is meant to exclude relational properties. See chapter , footnote . ²¹ Fabrizio Mondadori, ‘‘Leibniz and the Doctrine of Inter-World Identity,’’ p. . Since Mondadori is not explicit about the presence or absence of relational properties in what he calls the ‘‘core set of properties,’’ we hesitate to ascribe to him precisely the thesis we (and Sleigh) adopt.

Superessentialism vs. strong essentialism



Just so. But how so? That is, how could those remaining – for us, relational – properties be somehow deduced? If we can infer the relational predications true of x from the complete concept of x, then x cannot exist at other worlds. For at other worlds x must instantiate the same complete concept and will yet have different relational properties; but that is impossible, because it is impossible to deduce both P and not-P (for any relational truth P about x) from any single complete concept. And yet, if Leibniz sees the predicate-in-subject account of truth is all of a piece with the complete concept doctrine²² – that is, if one can be sure that in any true proposition about Caesar the predicate concept is contained in the subject concept, since the subject concept is Caesar’s complete concept – then one can scarcely deny that relational properties true of Caesar are sufficiently ‘‘contained’’ in his complete concept to be derivable from it. Thick complete concepts would permit a strict and univocal sense of containment applicable across the board, rather like a list; thin complete concepts require something weaker or less than that, something more complicated. We shall face up to just how complicated the story must be in chapter . In the present context, it suffices to recommend that derived, relational truths about x at a world follow from its complete concept only in conjunction with certain generalizations true at that world – intuitively, only in conjunction with the global laws of nature describing the sequence of harmonious changes in substances at that world. Thus Leibniz agrees that Caesar’s crossing the Rubicon can indeed be derived from his concept, acknowledging ‘‘[that] this demonstration of the predicate of Caesar is not as absolute as that of numbers or of geometry but that it presupposes the sequence of things which God has freely chosen’’ that is, the contingent laws of our world (Discourse §). It is to laws of nature that one might finally turn in measuring the credentials of a strong essentialist reading, as against superessentialism. For ease of exposition, let us presume that the laws of nature at a world are the particular laws of harmony at that world.²³ And suppose one confronted the following sort of argument for a superessentialist reading of Leibniz, which recommends that laws of nature supervene on complete concepts: ²² See note . ²³ It doesn’t affect the thrust of our discussion or arguments below if one opts for either of the following alternative construals of laws of nature: () Laws of nature include laws of harmony in conjunction with individual laws-of-the-series; or () Laws of nature are determined by the laws of harmony, but are not identical with them.



Essentialism

had God chosen a different set of laws than the set required by the relevant complete concepts, a different set of complete concepts would have been actualized in place of the set which was in fact actualized by God. And this is just another way of saying . . . that things could not have been otherwise than they are.²⁴

What about that? The argument seems to depend upon the following inference: if God had instantiated a different set of laws at some non-actual world W*, then He would have instantiated a different set of complete concepts; hence W* contains no actual individuals. But that is mistaken, for while there being different laws of nature at W* does entail that not all of the complete concepts of our world are instantiated at W*, it doesn’t entail that all of the complete concepts of our world are not instantiated in W*. Of course, if by ‘‘could not have been otherwise’’ is meant ‘‘could not have been intrinsically monadically otherwise,’’ then the conclusion is unobjectionable by the lights of strong essentialism, and fails to support either WBI or superessentialism. Indeed this emended conclusion is entailed, not by the supervenience of natural laws on complete concepts, but by strong essentialism itself. A non-actual world at which an actual individual exists would be governed by laws different from actual laws. To deny this would be to deny that one can infer all the relational truths about this world from the complete concept of that individual in conjunction with the natural laws.²⁵ If the superessentialist reading is to be preferred, then, what must be shown is that no actual individual substance could exist at a world at which the laws of nature are different. Now it may be suggested²⁶ that the laws of nature are contained in the complete concept of any actual individual. This, conjoined with () Leibnizian essentialism, would indeed secure () superessentialism and () WBI. We have argued (above, ²⁴ Mondadori, ‘‘Leibniz and the Doctrine of Inter-World Identity,’’ p. , in the context of defending superessentialism (§). ²⁵ Granted, then, that no pair of worlds with the same laws could share a common individual, is it also true that no pair of worlds could share the same laws? On this we are less clear. Analogy: Assuming the Identity of Indiscernibles for worlds, no pair of deterministic worlds could share the same laws and a common time slice. But we can still allow that there be a pair of deterministic worlds with the same laws. (Might a Leibnizian argue that the laws describing the actual world are not instantiated by any other world in the following way? ‘‘Any other world W* that was governed by the same laws of nature as the actual world would be equally perfect. If there were such a world W*, our world wouldn’t be the best possible world. But our world is the best possible world. Hence no other world W* instantiates the laws at our world.’’ Although certain of Leibniz’s letters to Wolff might recommend the first premise of this argument (see GLW ff: AG ff, where Leibniz comes close to identifying perfection with lawful harmony), the typical view that perfection is a function of simplicity of laws and richness of effects hardly recommends it: perhaps a non-actual world could fall short of perfection on the second account.) ²⁶ See Mondadori, ‘‘Leibniz and the Doctrine of Inter-World Identity,’’ p. .

Superessentialism vs. strong essentialism



§.) that laws of nature – whether they include laws of harmony operative at our world (in conjunction with individual laws-of-the-series) or are determined by but not identical with them – are not written into each complete concept: we shall return to this presently. But to whatever degree the superessentialist reading is meant to acknowledge that God can ‘‘read off’’ those laws²⁷ from the core intrinsic monadic histories making up a world, to this extent it becomes unclear why God must include those laws in each complete concept. On the redundancy criterion proposed earlier, just as God does not add relational properties to complete concepts, so God does not write relational laws of intermonadic harmony into complete concepts – as something He must do in addition to creating the actual individual substances He does. It is worth emphasizing an important distinction in this context. Leibniz believes that the causal career of each individual substance is given by its ‘‘law of the series,’’ encoded in its complete concept and identified with that intrinsic primitive active force of a substance which Leibniz gives reason to think just is the form or primitive entelechy of an individual substance. (We shall take up these issues in chapter .) Clearly Leibniz intends the particular law-of-the-series of an individual substance to be essential to it, without which that substance could not exist. In his  March  letter to Arnauld he says of simple indivisible substances that ‘‘each substance contains in its nature a law of the continuation of the series of its own operations’’ (G ,: LA ); elsewhere he writes that ‘‘the essence of substances consists in . . . the law of the sequence of changes’’ (A .., our emphasis), and that ‘‘[t]his law of order . . . constitutes the individuality of each particular substance’’ (G ,: L ; cf. T §: H ). Now whether or not Leibniz’s claim that ‘‘nothing is permanent in things except the law itself which involves a continuous succession [of states] . . .’’ indicates that the law-of-the-series is the only law he recognizes as being included in an individual’s complete concept,²⁸ it is at least clear that an individual’s ²⁷ Ibid., pp. –. ²⁸ We interpret Leibniz’s claim to Arnauld that ‘‘one must admit that these predicates were laws contained in the subject or in the complete concept of me which makes what is called myself, which is the basis of the connection between all my different states’’ (G ,: LA ) to refer, with careless wording, to Leibniz’s law-of-the-series. The passage just quoted (‘‘nothing is permanent in things . . .’’) is to De Volder at G ,: L . Leibniz finishes this passage by adding that the law-of-the-series ‘‘corresponds, in individual things, to that law which determines the whole world.’’ Thus, while distinguishing individual laws from global laws, Leibniz acknowledges a close connection between them. It is a difficult matter getting clear on how strong Leibniz takes this connection to be. Leibniz seems to regard general laws of order for the world as exceptionless specifications of how global states are to unfold (Discourse §). But viewing ‘‘that law which

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Essentialism

law-of-the-series being essential to it does little to support the superessentialist reading. If the complete concept of x were co-instantiated with individual concepts other than those instantiated at the actual world, x would possess the same law-of-the-series in a world with different laws of nature. One diagnosis of what seems to us mistaken in claiming that individual substances cannot exist at a world in which the laws of nature are different would thus warn against the following conflation: ‘‘the laws of nature’’ are ‘‘what Leibniz refers to as ‘laws of the series’.’’²⁹ A bad argument would seem to lurk nearby: () For all x, x couldn’t exist with a different law-of-the-series. () For all x, if x couldn’t exist with different laws-of-nature, then x is world-bound. () Laws-of-the-series = Laws-of-nature. () Therefore, for all x, x is world-bound. Premise () is false. Laws-of-the-series pertain to successions of intramonadic states, while laws-of-nature pertain to inter-monadic correspondence. (Or, at best, laws-of-the-series form a subset of the laws of nature. Note that the argument above is not yet obviously valid either: even if an individual’s law-of-the-series is essential to it, this is consistent with that individual existing at a world where the set of laws-of-theseries instantiated does not share all the same members as the corresponding set at the actual world.) Strong essentialism cannot be rendered fully consistent with a literal reading of everything Leibniz says. He says too much, at times too carelessly. In sketching some account of how, according to strong essentialism, those properties not strictly contained in the complete concept can be ‘‘somehow deduced’’ from it, our latest effort has been away from thick individual concepts, in the direction of seeing the global determines the whole world’’ (above) in this way runs afoul of Leibniz’s insistence to De Volder and others that it is from the inner nature of a substance that its particular laws of the series is determined (or in what it consists): if the individual laws are connected so strongly to global ones as to be mere ‘‘variants’’ or ‘‘versions’’ of the ‘‘general law that rules the universe’’ (G ,–), it is unclear how we are to understand the supervenient laws of nature to be Leibniz’s ‘‘subordinate maxims,’’ explicitly viewed by him as capable of being superseded by miracles (Discourse §). We thus acknowledge the possibility of Leibnizian resources for arguing that certain global laws at a world may not supervene on the set of inner ones operative at a world; here and below we need only deny that (a) laws of nature are inner laws-of-the-series, and that (b) global laws of nature are so strongly connected with any particular law-of-the-series as to be contained in a complete concept in the way intrinsic monadic states are contained in it. We shall consider miracles in chapter . For extremely helpful discussions relevant to the issues gestured at in this note, see Sleigh, Leibniz and Arnauld, pp. –, –, –, ff, and Adams, Leibniz, pp. –, ff. ²⁹ Mondadori, ‘‘Leibniz and the Doctrine of Inter-World Identity,’’ p. .

Superessentialism vs. strong essentialism

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laws of nature at a world as supervening on the set thin complete concepts instantiated at that world. Robert Sleigh notes that there is a ‘‘plethora of nonequivalent characterizations of the content of a [complete individual] concept’’ to be found in Leibniz’s writings,’’³⁰ but is confident enough about the preferred thin reading of them to add that their equivocal nature ‘‘creates no serious problem of interpretation.’’ Perhaps so. Passages such as the following (in the long draft memorandum responding to Arnauld) nevertheless look to strain the strong essentialist view as we have conceived it: as there exist an infinite number of possible worlds, there exists also an infinite number of laws, some peculiar to one world, some to another, and each possible individual contains in the concept of him the laws of his world. (G ,: LA )

To opt for a thick or a thin construal of complete concepts is to opt (respectively) for a strict or a loose sense of ‘containment’ in respect to laws. Mondadori offers the following account of containment as it applies to laws: To say, then, that the laws of a given world are ‘‘contained’’ in the complete concepts which make up that world [qua possible], is to say that given those concepts the laws are thereby determined–and uniquely so.³¹

The idea here is that a set LN of laws of nature for world W are contained in the individual concept of x if and only if God can read off LN from the set of concepts exemplified at W. Although it departs from what Leibniz looks to imply on a literal reading of the passage above, that is indeed a plausible construal of the relevant sense of containment. Notice that it is consistent with TWI. Here is a second construal of containment as it applies to laws, more closely approaching the passage above to Arnauld. The laws of nature at the actual world supervene on the set of intrinsic monadic histories at the actual world. Each substance represents (expresses) the other monadic histories. Hence each individual substance represents the supervenience base for the natural laws. Thus the natural laws can be read off from the information represented by each actual individual substance, and it is in this sense that each actual substance contains in its concept the natural laws of this world. That is close, but it isn’t what Leibniz says: he says that each possible individual substance contains in ³⁰ Sleigh, Leibniz and Arnauld, p. . ³¹ Mondadori, ‘‘Leibniz and the Doctrine of Inter-World Identity,’’ p. .

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Essentialism

its concept the laws of its world. We have argued that it is a contingent fact that the inner monadic states of each individual substance count as perceptions or representations of what is in fact external to them, and that the separability (independence) requirement entails as much. Insofar as the texts we have examined recommend this view over the relational accounts of superessentialism, one can only doubt that Leibniz had the contingent character of inter-substantial representation sharply before his mind when writing that bit of the long memorandum. Both of these readings of containment as it applies to laws permit the transworld identity that we argue is consistent with the preponderance of texts. We do not wish to adjudicate between the first and second readings here.³²                      ,    ,              Leibnizian essentialism isn’t up for grabs: Leibniz accepted it. The scope or strength of his essentialism is more difficult to discern. If, in judging what Leibniz believed, the texts are suggestive of superessentialism, we have argued that Leibnizian essentialism itself is consistent with TWI, bringing with it no commitment to claiming that ‘‘if anything at all had gone differently from the way things go in the actual world, no actual individual would have existed.’’ Leibniz denied that there are irreducible inter-substantial relational truths or intrinsic relational properties as truth-makers needed to ground them; relevant here are bits of scholastic precedent on the nature of relations, Leibniz’s views about individual accidents and extrinsic denominations, and his own reductions of relational claims. Leibniz asserted a complete concept doctrine on which that account of relations positively invites strong essentialism. Relevant here are: the consistency of ‘x has the same complete concept ³² It may count somewhat in favor of the second proposal that it can be more comfortably wed to Sleigh’s distinction between ‘‘strict’’ and ‘‘flabby’’ individual concepts (Sleigh, Leibniz and Arnauld, pp. –). The strict concept of x, consisting as it does only of primitive properties, ‘‘contains’’ in no straightforward sense information entailing the existence and nature of x’s created colleagues; the flabby concept of x, resulting from some operation on the strict concept so as to suitably enlarge it, may serve the role of the second picture – of x’s concept qua representative of the whole supervenience base for laws. To the extent that Leibniz engaged in some thoroughgoing form of ‘‘concept packing’’ (Sleigh’s locution), an argument might be available for claiming that laws are contained in complete concepts. Sleigh denies that Leibniz engaged in premeditated concept packing. We concur. (But we should note there is much we say, in these pages, that Sleigh would not agree with: our respects of agreement and difference will be treated in § below, on moderate essentialism.)

Leibnizian essentialism, worlds, and counterpart theory

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at any world at which x exists’ with ‘x exists at more than one world’; texts recommending thin concepts; the failure of Leibniz’s relational idioms (‘‘perception,’’ ‘‘expression’’) to guarantee external relata; bits of scholastic, early modern, and Disputatio precedent for Leibniz’s mature commitment to the separability (independence) requirement; and the contingency of supervenient laws of nature. After all that, when the cumulative case is summed up, one might doubt whether it deserved all the fuss. But there remains unfinished business. We have been taking seriously the idea that Leibniz might allow TWI by motivating a strong essentialist reading with which TWI can sit happily. Yet one may wonder if the issue of TWI, as it pertains to Leibniz, might have been dealt with much differently than we have. Two diverging sentiments would tend in that direction. (A) First: ‘‘Your toil was ill-spent: the case against superessentialism is dead easy. Even if the texts are ambiguous or worse concerning strong essentialism, oughtn’t we to recognize that Leibniz’s thinking about God commits him to a denial of WBI? God is a substance, and Leibniz’s modal version of the ontological argument (cf. §§– of the Monadology) can scarcely be read as proving that individuals merely similar to but distinct from God inhabit other possible worlds. God exists at every world.’’ (B) Second: ‘‘Your toil was on the cheap: the discussion of the texts as they bear against superessentialism, in favor of strong essentialism, is unfairly selective. In particular, you ignore the most compelling case for superessentialism – namely, that Leibniz was a counterpart theorist and counterpart theory requires a metaphysic of world-bound individuals that only superessentialism can supply.’’ This latter sentiment has two components. It presumes that Leibniz did embrace a counterpart picture for certain modal purposes – a claim that we shall endorse. And, it presumes that this picture requires superessentialism and world-bound individuals – a claim we shall be concerned to argue against. Let us consider (A) and (B) in turn. . God and possible worlds If one takes the superessentialist line, how does one account for the fact that Leibniz refrains from saying of God that (for example) if He had willed differently, He would have been not God but someone else? Isn’t it clear that Leibniz believes that if God had acted differently, He would have still been the very same being? Doesn’t that then show that TWI holds for God? Doesn’t that then show that a superessentialist reading of

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Essentialism

Leibniz’s views on individual substances is indefensible? While endorsing no superessentialist reading of Leibniz ourselves, we do not wish to condone this easy method of dispensing with superessentialism. By way of defending our honest toil thus far, consider three things one might say against this particular line of objection. () Leibniz holds superessentialism to be true for created substances but not for God. On second glance this view is not altogether ad hoc. One might think that God has a more radical sort of freedom than individual creatures whereby divine actions are more loosely connected to the divine nature than are creatures’ actions to creaturely natures. In line with this, one might think that the connection between God’s nature and His actions is only necessary hypothetically upon God’s choosing a harmonious world, in the following way. For Leibniz, the typical connection between an individual’s nature and his/her actions is via some law: it is the nature of a substance together with some law about the best that explains a choice or action. In the particular case of God, now, when asking where the relevant law comes from, one might say that God (unlike creatures) chooses the law – this being a primordial sort of choice, atypical in being prior to law. Where creatures have some inner law that determines actions, God’s nature shouldn’t on this view be understood as having or being (so to speak) coeval with some law that strongly determines the will in choosing what it does. Another possible Leibnizian ground for having one style of modal theory for God and another for creatures is that only the latter, for Leibniz, inhabit worlds. Worlds figure in Leibniz’s thought primarily as internally consistent creation scenarios, possible in themselves, with God so to speak on the outside.³³ For Leibniz, a world is ‘‘a composite of created things’’ (c. –: LH  vii C ), an ‘‘aggregate of finite things’’ (: G ,: L ). () Margaret Wilson’s view is that Leibniz is a superessentialist³⁴ not only about created substances but also about God as well. But if () above is thus rejected, how is one to make sense of divine freedom on Leibniz’s behalf? On Wilson’s view, Leibniz can make sense of divine freedom using the very same resources underwriting his favorite attempt ³³ See Adams, Leibniz, pp. –. ³⁴ In ‘‘Possible Gods’’ Wilson writes: ‘‘I agree, by and large, with [the] ascription of superessentialism to Leibniz. That is, I agree . . . that for Leibniz no possible individual with properties different from those Caesar (for example) has in this world could be Caesar’’ (p. ). Wilson takes it as unproblematic that Leibniz’s views about substances unequivocally entail the extension of the complete concept doctrine to God, and her favored view, sketched below, has it that superessentialism applies to God (cf. p. ).

Leibnizian essentialism, worlds, and counterpart theory

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to make room for human freedom, namely by invoking the infinite analysis doctrine. According to that doctrine, the contingent features of a substance are those that, while contained in its complete concept, can only be proven at the limit. So it may only be provable at the limit that, say, God creates the best. Hence one can say that it is only a contingent truth that God creates the best, it being thus possible that He have done otherwise. () A third (and, it may emerge, best) response for the superessentialist to offer against the easy objection we are considering would suggest that Leibniz’s views on divine freedom and divine essence are rather less well-conceived than, and somewhat disconnected from, the bulk of his metaphysic of creatures. In short , it is a vain hope to suppose that his rather more scattered, less systematic claims about God’s essence can coherently call the tune for one’s interpretation of Leibniz’s considered and systematic account of complete concepts of substances and their relation to modal issues. Wilson is certainly right that the textual support for interpretation () is rather thin. But the same is true of her own interpretation (). Two brief points here: (a) First, Wilson’s interpretation relies upon a deployment of the infinite analysis doctrine in order to make sense of divine freedom. But to our knowledge Leibniz never seriously engages that doctrine to that end. (b) Second, Wilson’s interpretation, which stresses a parity between God and other individual substances on the score of freedom and contingency, would lead one to expect that Leibniz will carry over various aspects of his modal treatment of created substances to God. Yet they are not so carried over. In point of fact Leibniz never says such things as ‘‘If God had not done the best, then it would not have been God but another individual.’’ And while willing to talk of ‘‘possible Adams,’’ he is never willing to talk about ‘‘possible Gods.’’ But if Leibniz was self-consciously superessentialist about both divine and creaturely natures and aimed to provide similar treatments of freedom and contingency for both, why the disparity? Wilson offers a story about the disinclination to talk about ‘‘possible Gods’’: A plausible answer is the following: there is no conceptual inconsistency between certain salient features of our Sextus – say the outward circumstances of his birth – and a variety of different futures. There are then many different complete concepts that may be identified as concepts of ‘‘possible Sextuses.’’ On the other hand, the salient features of our God – notably His perfections – are not ultimately consistent (allowing infinite analysis) with a variety of different ‘‘futures’’: e.g., world decisions.³⁵ ³⁵ Wilson, Ibid., p. .

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Essentialism

This interpretation – which requires of God that His salient features alone entail His world-decisions (but only at the limit, since otherwise they would not be free) – seems to us a bit fanciful. Not only does Leibniz never seriously engage the infinite analysis doctrine as an account of divine freedom; at no point in any considered treatment of these issues does Leibniz lean on the distinction between salient and non-salient features. Moreover salience is rather a sticky business. The perfections of God are presumably only salient to one in an indistinct way; infinite analysis of God’s perfections would proceed from a distinct conception of those attributes such as lie well beyond one’s grasp. The suggestion that one has in their cognitive possession what would be the proper starting-point for an infinite deduction of decisions in the case of God but not of Sextus is at best misleading. One thing seems in any case clear: consciously or unconsciously, Leibniz is under considerable theological pressure. It just won’t sound very good to say, ‘‘If God had acted differently, He would have been a different being.’’ It will sound no better to say ‘‘When I talk about a possible way God might have been, I mean to talk about some being like God but different.’’ Nor will it much relieve theologians’ ears to hear him claim, ‘‘When I say God created the world freely, what I mean is that while the creation is essential to His nature, the strict deduction of his creative acts would only succeed at the limit.’’ While there are some philosophical pressures of a broadly systematic sort for Leibniz to be as essentialist about God as he is about creatures, and to treat divine and human freedom in the same way, there is theological pressure against developing his system in that direction. If Leibniz had been fully reflective about these tensions, how would he have reconciled them? Perhaps he would have acquiesced in () above, imposing a distinction between creaturely freedom and a more nuanced and radical divine freedom. Alternatively, he might have let systematic virtue trump theology and acquiesced in (), and, perhaps being unpersuaded by Wilson’s saliencetheoretic offerings, transferred his remarks about Sextus to those about God. Theological proprieties aside, there is no logical barrier to wedding God’s necessary existence with a Sextus-style counterpart story.³⁶ Finally, he might have opted for some alternative, more revisionist stance, according to which superessentialism (and, indeed, strong essentialism) is incorrect for both divine and human essences. The superessentialist is only in trouble if this latest, alternative view is ³⁶ Recalling note  and the method of rendering ‘essentially F’ true of some world-bound individual, one might after all do the same for ‘exists necessarily’.

Leibnizian essentialism, worlds, and counterpart theory

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Leibniz’s considered view. Yet it is very doubtful that one can secure that view from what Leibniz himself says on the basis of his less developed remarks about divine essence and divine freedom. Considerations about God do potentially put tension on Leibniz’s system. But it is unclear to us how wise would be a methodology of letting theologically driven remarks about God set the details of an agenda for relieving this tension when it comes to understanding what his system was in the first place. . Counterpart theory The superessentialist and strong essentialist readings agree on Leibniz’s commitment to the thesis that () an individual substance could not have a complete concept different from the one it actually has (Leibnizian essentialism). They disagree about Leibniz’s commitment to the claims that () every property of an individual is essential to it (superessentialism) and that therefore () substances are world-bound individuals (the denial of TWI). And what of the suggestion that Leibniz can avail himself of counterpart-theoretic resources in evaluating de re modal claims – that () talk of ways some actual individual x could have been F may be understood in terms of x’s having a complete concept one of whose counterparts is such that its complete concept contains (immediately or derivatively) F? There are two questions here. (C) Does Leibniz avail himself of counterpart-theoretic resources in evaluating de re modal claims? (D) Is Leibniz’s strong essentialism consistent with him doing so? As for question (C): here again, the texts are not at all conclusive, at best suggestive. Some (e.g. Wilson) have been prepared to go with suggestive texts in the case of superessentialism, opting away from suggestive texts in the case of counterpart theory because it appears inconsistent with other bits of his philosophy. Fair enough. But postponing this latter question (D) for a moment, it is worth reflecting on how suggestive the supposed counterpart texts are. Although Leibniz’s essentialism commits him – as he well saw – to de re modality, Leibniz to our knowledge had no developed, considered semantic theory of de re modality of the sort one confronts in contemporary discussions, counterpart-theoretic or otherwise. If one is looking for the something akin to the efforts of Lewis or Stalnaker, it surely isn’t there. But this should hardly deter one from looking for evidence that Leibniz thought about what grounds the truth of de re modal

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Essentialism

claims.³⁷ We said in § that although Leibniz was willing to deploy the idiom of worlds in modal contexts, he deployed the vehicle of possible worlds primarily for discussing theological issues associated with his accounts of creation and theodicy, tending rather more to the use of conditionals with contrary-to-fact antecedents when posing modal issues. That is true, as far as it goes. It went far enough in the context; but here the respect in which it paints with too wide a brush becomes relevant. Creation-theoretic, theodicean, and modal concerns will eventually intersect. Could God have created otherwise than He did? Must I have committed this sin? So the question before us, in seeking evidence that Leibniz thought about what grounds the truth of de re modal claims, is rather more precisely this; whether or not the idiom of possible worlds figures in the few – if few there be – places where Leibniz gives evidence of a concern about the truth-makers for (say) modal attributions of divine or creaturely freedom, and whether the counterpart picture is discernibly at work in them. Well, the texts are few and familiar but worth revisiting. Let’s revisit two, leaving a third for § to follow, where we shall have occasion to argue that the counterpart picture is of considerable interpretive help. The familiar, many-possible-Sextuses passage of Theodicy § uses the possible worlds idiom explicitly, but brings with it a somewhat less helpful context for our present purposes. Earlier in the Theodicy, Leibniz had struggled with the broadly Molinist account of divine foreknowledge as involving a kind of middle knowledge (scientia media), midway between God’s knowledge of what is actual (scientia visionis) and of what is purely possible (scientia simplicis intelligentiae). In the end, Leibniz saw middle knowledge as reducing to knowledge of the purely possible. Setting aside details of the dispute and Leibniz’s reasons for taking the position he does,³⁸ the question at issue earlier in §§– of the Theodicy, ³⁷ Do not confuse the contingency of true predications with the grounds of true de re counterfactuals. Concerning the former, Adams, Carriero, and others have treated hypothetical necessity and infinite analysis with care and at great length. See Adams, Leibniz, chapter , and John Carriero, ‘‘Leibniz on Infinite Resolution and Intra-mundane Contingency.’’ Parts of those accounts are relevant in ways we shan’t pursue systematically in our narrower discussion to follow. ³⁸ For a splendid treatment of the details see Robert Sleigh, ‘‘Leibniz on Divine Foreknowledge.’’ In setting aside Leibniz’s reasons for seeing God’s knowledge of the relevant counterfactuals as reducing to knowledge of the purely possible, we set aside the opportunity to emphasize Leibniz’s willingness – in many other passages besides the one considered here – to locate in possibles the ground of counterfactuals. However much the hypothetical necessity and infinite analysis doctrines figure in Leibniz’s thought, there is really no pretending that Leibniz saw the foundations of de re modality and possibilia (possible worlds, possible individuals) to be crucially connected with them. Leibniz’s hopes of combining these into a coherent package is, alas, another question (see Adams, Leibniz, p. ): in the end, it probably deserves little more than we give it below (four paragraphs down).

Leibnizian essentialism, worlds, and counterpart theory

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which concerns us here, is what to say about a certain counterfactual. In fact David did not hide in the city of Keilah when fleeing Saul: but what if he had? Would the inhabitants of Keilah have surrendered David to Saul upon Saul’s siege of the city? Leibniz’s approach to this counterfactual answers our central question above. For Leibniz to ask, as he does, ‘‘what foundation can God have for seeing what the people of Keilah would do?’’ (T §: H ) is for him to pose the truth-maker issue, of what grounds the truth of the counterfactual. And his response seems clear enough: I resort to my principle of an infinitude of possible worlds, represented in the eternal verities, that is, in the object of divine intelligence, where all conditional futurities must be comprised. For the case of the siege of Keilah forms part of a possible world, which differs from ours only in all that is connected with this hypothesis, and the idea of this possible world represents that which would happen in this case. (T §: H )

The truth value of our counterfactual is to be understood in terms of a world W* differing from ours only on the hypothesis of David’s having hidden in the city, and what W*-inhabitants of Keilah do in that world. That is more than suggestive. In a context where our central question above is explicitly posed by Leibniz, his operative schema is one of possible worlds, closest-similarity of worlds, and other-worldly inhabitants. The same account, though with less helpful context, is at work in Theodicy §. Other possible worlds? ‘‘[W]e shall see a whole world that [God] might have produced, wherein will be represented anything that can be asked of him; and in this way one may know also what would happen if any particular possibility should attain unto existence.’’ Similarity of worlds? ‘‘[I]f you put a case that differs from the actual world only in one single definite thing and in its results, a certain one of those determinate worlds will answer you.’’ Other-worldly inhabitants? ‘‘I will show you some, wherein shall be found . . . several Sextuses resembling him . . . You will find in one world a very happy and noble Sextus, in another a Sextus content with a mediocre state.’’ Consider again a familiar passage from the Arnauld correspondence cited earlier, in response to Arnauld’s worry that the complete concept doctrine threatened the freedom both of divine creation and of creaturely action (G ,: LA ): For by the individual concept of Adam I mean, to be sure, a perfect representation of a particular Adam who has particular individual conditions and who is thereby distinguished from an infinite number of other possible persons who are very similar yet distinct from him (as every ellipse is different from the circle,

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Essentialism

however much it approximates to it), and to whom God has preferred him, because it has pleased God to choose precisely this particular order of the universe; and all that follows from his decision is necessary only by a hypothetical necessity and does not at all destroy God’s liberty or that of created minds. There is a possible Adam whose posterity is thus, and an infinite number of other Adams whose posterity would be different . . . (G ,: LA –)

Leibniz’s strategy here, in response to Arnauld, is clear enough. The case before him concerns the strong essentialism of the complete concept doctrine, which looks to threaten the truth of de re modal claims to the effect that Adam could have been otherwise than he is. To rescue truths of that sort, Leibniz tells us what it is to assert truly that Adam could have been F or G. And as in the Theodicy, he does so by appealing to Adams at other worlds that are F or are G at those worlds (those other ‘‘orders’’ of creation). To account for the truth of de re modal claims about some actual individual x in terms of possibilia sufficiently similar to x at other worlds is to adopt a counterpart strategy. No other interpretation recommends itself. (As we shall see in §, there is more to recommend the counterpart reading.) None of this is new. Mondadori in particular has attended to these passages and others in considerable detail.³⁹ Mondadori is right to call them for what they are: these (and others) are texts where Leibniz is explicitly invited to give some account not simply of the contingency of various truths about creatures, but of the grounds for de re modal truths about how they could be otherwise; and in these contexts, Leibniz goes the way of counterparts. By our lights, the texts are more than suggestive. This is not yet to say that Leibniz developed a counterpart semantics. One can go the way of counterparts without doing that. When Leibniz has the grounds of de re counterfactuals in mind, a counterpart picture, we have argued, is at work. We haven’t argued that such a picture was always or even typically at work when simple questions of contingency and necessity were before him. In these latter contexts, famously, he became very much taken with his infinite analysis doctrine. Leibniz did little or nothing to connect the counterpart picture with the infinite analysis doctrine. For our part, there seems little point in trying to develop a systematic theory when there is no connecting theory at all to be found in the texts. ³⁹ See Mondadori’s ‘‘Reference, Essentialism, and Modality in Leibniz’s Metaphysics,’’ ‘‘Leibniz and the Doctrine of Inter-World Identity,’’ and especially his recent ‘‘On Some Disputed Questions in Leibniz’s Metaphysics.’’

Leibnizian essentialism, worlds, and counterpart theory



But systematic theory aside, how could the infinite analysis doctrine possibly be made to square with his counterpart picture of counterfactuals? It is not especially hard to see how, in the abstract, a reconciliation might be pulled off. The trick is to let infinite analysis select the counterparts. Thus: let a complete concept C* count as a counterpart of the complete concept of Adam – call it C – just in case the distinctness of C from C* is provable only by infinite analysis, where now anything finitely provable for C is also provable for C* and vice versa. Thus, whenever ‘C is F’ is contingently true by the lights of the infinite analysis doctrine, any individual concept C* lacking F but enjoying exactly the finitely provable features of C will count as a counterpart of C.⁴⁰ In this way, infinite analysis and Leibnizian counterpart theory can march in step. If ‘‘Possibly Adam does not do x’’ is true by the lights of the infinite analysis doctrine, then a possible Adam who does not do x will be admitted as a counterpart for the purposes of evaluating questions of the sort ‘‘What if Adam had . . .?’’ For our own part, then, we are disinclined to accept Margaret Wilson’s implicit suggestion that Leibniz’s infinite analysis approach to contingency debarred him from taking a counterpart approach seriously.⁴¹ There is, however (turning now to question (D) above), a more basic worry about the coherence of Leibniz’s approach on our strong essentialist reading of him. The question concerns Leibniz’s prospects for running strong essentialism and counterpart theory in a single harness. Suppose, as we have suggested that Mondadori, Ishiguro, and perhaps Mates⁴² are right to suppose, that there is evidence for Leibniz’s sympathy with the counterpart-theoretic approach. Let us set this alongside the strong essentialist reading of Leibniz that we prefer. Counterpart theory is typically understood as the conjunction of all of the following: (i) No object (except perhaps universals) exists at more than one world.⁴³ ⁴⁰ We are of course assuming that, if ‘C is F’ requires infinite analysis, and ‘C* is not-F’ requires infinite analysis, and C and C* differ only on the score of having or lacking F, then ‘C is not C*’ requires infinite analysis. For the proof of ‘C is not C*’ will proceed via ‘C is F and C* is not-F,’ which in turn will be proven via proofs of the conjuncts – these, ex hypothesi, requiring infinite analysis. ⁴¹ Wilson, ‘‘Possible Gods,’’ especially p. . ⁴² See note  above, final sentence. ⁴³ Strictly speaking this should read ‘‘no object exists in its entirety at more than one world,’’ so as to exclude five-dimensional objects (mereological sums of spatial, temporal, and modal [i.e. counter-] parts). Item (iii) below should also strictly be read as including ‘‘and that object is the, or one of the, most similar of all the W*-objects to the W-object.’’ Disregarding these refinements does not affect the discussion of the present section.



Essentialism

(ii) A modal claim at world W about an object that exists at W has its truth value in virtue of the properties which that object’s counterparts have at other worlds. (iii) An object at world W* is a counterpart of an object at W iff it is similar enough (in relevant respects) to the W-object. Ascribing to Leibniz both counterpart semantics and the (albeit quite restricted) TWI that strong essentialism permits may seem particularly odd, since the semantic elements (ii) and (iii) above are commonly thought to go hand-in-hand with the metaphysical claim (i). On our view, this reflects a misconception common to both Leibniz commentary and contemporary treatments of modality: it is mistaken to regard counterpart semantics (on the one hand) and strong Leibnizian essentialism with TWI (on the other) as ill-suited to one another. As a first step, consider what is clear enough – that many philosophers, inclined for whatever reasons to accept the metaphysical thesis of WBI, nevertheless want to allow many of our de re modal claims about individuals to come out true (in accordance with some principle of charity toward our modal intuitions). Counterpart semantics provides them with a means for doing so. Suppose that Adam is world-bound, and suppose that he is not F. It may nevertheless be true to say that Adam could have been F: it is true, not because in some non-actual world Adam is F, but rather because in some non-actual world a counterpart of Adam is F. Here is David Lewis on counterparts: Where some would say that you are in several worlds, in which you have somewhat different properties and somewhat different things happen to you, I prefer to say that you are in the actual world and no other, but you have counterparts in several other worlds. Your counterparts resemble you closely in content and context in important respects . . . They resemble you more closely than do the other things in their worlds. But they are not really you.⁴⁴

And here is Leibniz, sounding very like a counterpart theorist: by the individual concept of Adam I mean . . . a perfect representation of a particular Adam who has certain individual characteristics and is thus distinguished from an infinity of possible persons very similar to him yet for all that different from him. (To Arnauld: G ,: LA ) I will now show you some [worlds], wherein shall be found, not absolutely the same Sextus as you have seen . . . but several Sextuses resembling him, ⁴⁴ From pp. – of David Lewis, ‘‘Counterpart Theory and Quantified Modal Logic.’’

Leibnizian essentialism, worlds, and counterpart theory



possessing all that you know already of the true Sextus, but not all that is already in him imperceptibly . . . You will find in one world a very happy and noble Sextus, in another a Sextus content with a mediocre state . . . (T §: G ,: H )

While a commitment to WBI would motivate a counterpart semantics, it does not constitute the only motivation. Thus one cannot successfully argue from Leibniz’s sympathy with counterpart semantics to his endorsement of WBI: counterpart semantics is consistent with a metaphysic allowing TWI. It will be useful here, as a second step, to compare the views of Lewis and Leibniz. Both of them hold metaphysical opinions which preclude their taking work-a-day modal claims at face value (unless, that is, they shun principles of charity and claim that we are wrong about the truth value of much of our modal talk). In Lewis’s case, extreme modal realism raises a question about the truth value of ordinary counterfactual statements: on his view, the only tenable ontology of possible worlds is one which construes them as concrete objects, containing individuals that are numerically distinct from those at our world.⁴⁵ In Leibniz’s case, the question is raised by his strong essentialism, according to which an individual has all of its intrinsic properties essentially. Consider now some counterfactual with a false antecedent specifying some intrinsic property of an individual or some property deriving from its intrinsic properties. On both Lewis’s and Leibniz’s account, there is no possible world at which that very individual exists and satisfies the antecedent. Hence such statements, if taken at face value, will come out as all vacuously true, or all false, or all truthvalueless, depending upon how counterfactuals with impossible antecedents are to be handled. Thus our belief that many counterfactuals may be true and many others of them false cannot be sustained if they are taken at face value. Moreover, many possibility claims of the form ‘x could have been F’ which we intuitively take to be true will come as false. Accordingly, Lewis and Leibniz may be viewed as proposing a sort of rescue operation: modal claims are not to be taken at face value but are rather to be understood in terms of counterparts. Thus understood, many of our modal claims come out as true after all. (The infinite analysis doctrine is another sort of rescue operation, making ordinary claims of contingency for some property come out as true when the metaphysic reckons that property to be essential. As noted above, the ⁴⁵ See David Lewis, On the Plurality of Worlds.



Essentialism

two styles of rescue operations can be integrated, though we shall not pursue these issues in terms of any such integrated theory.) Now thus far we’ve been highlighting the similarities between these two philosophers. There are also important differences. In Lewis’s case, the metaphysic prompting a move to counterpart semantics is also one that entails WBI. If extreme modal realism is true, then it makes no sense to suppose that some individual at another possible world is identical with some individual at the actual world, since that individual will be a distinct hunk of matter.⁴⁶ Leibniz’s metaphysic, on the other hand, being weaker than superessentialism, does not entail WBI. Yet while his metaphysic is consistent with TWI, this alone will not salvage much of our modal talk. It is true that, taken at face value, the statement ‘‘I exist at another world’’ can be accommodated as true according to strong essentialism: for Leibniz, unlike Lewis, there are at least some modal claims that could be read at face value without doing violence to the modal intuitions a principle of charity seeks to preserve. But given strong essentialism, according to which all of an individual’s intrinsic properties are essential to it, one cannot go on to assign the truth values that we ordinarily assign to most of our interesting modal claims unless those claims are understood in some non-literal way. Suppose that Leibniz were to allow that Adam exists at some range of possible worlds, but that modal claims about Adam are to be understood in terms of (a) what counterparts are picked out in the context in which the modal claim is made and (b) what is true of those counterparts. Must Leibniz then concede that the way our very Adam is at possible worlds is irrelevant to the truth value of ordinary modal claims? No. Leibniz is perfectly free to allow that while the counterpart relation picks out individuals distinct from though similar to Adam, it may also pick out Adam himself at worlds where Adam exists. Note well: x has a particular individual y at another world as a counterpart if and only if that individual is similar enough to x and is more similar to x than anything else at that world. In some contexts, it may emerge that y = x. Indeed, Leibniz may even allow that relative to certain contexts of inquiry, the counterpart relation and the identity relation are one and ⁴⁶ This may be overstated. In particular, it might be suggested that even the extreme modal realist can countenance transworld identity for abstract objects. This is indeed a possible position. Lewis, in correspondence, has expressed some openness to combining TWI with his extreme modal realism, pointing out that (i) he inclines toward agnosticism about whether Armstrong-style universals exist and that (ii) if they do exist, then they are not world-bound. The Lewis that we describe in the text, one who unequivocally embraces WBI, is thus a simplified version of the actual Lewis.

Moderate essentialism



the same. The counterpart theorist will want to insist that gardenvariety modal talk about Adam ranges over certain individuals distinct from Adam; yet he may wish to concede that some uses of ‘how Adam might have been’, perhaps as they appear in specialized philosophical discussions of modality, are best interpreted as talk about how our very Adam is in other worlds – that is, as limiting cases wherein the relevant similarity relation is one of identity.            Strong essentialism is weaker than superessentialism. One might read Leibniz’s considered metaphysic of modality more weakly still. Of course all treatments allow that some intrinsic properties will count for Leibniz as contingent or accidental in the charity-driven sense suggested by Leibniz’s counterpart-theoretic (and infinite analysis theoretic) rescue operation. Our question here is which properties count for Leibniz as essential in the strict sense of ‘essential’ that govern discussions for and against superessentialist readings of him. As against superessentialism and our strong essentialism, one might agree that Leibniz allowed certain properties of an individual to be accidental to it, and locate among those accidental properties of a substance intrinsic, nonrelational ones as well.⁴⁷ Thus, one is invited to see Leibniz as drawing a traditional distinction between the essential (necessary) properties of an individual substance and its contingent (broadly construed, accidental) properties. Within the latter class and relative to individual substances of a given species, there is a further distinction between properties that are natural to substances of that species and properties that are not.

According to the moderate essentialist reading as Robert Sleigh thus envisions it, the complete concept of an individual includes all its monadic properties, accidental or essential. Relational properties are included in some derived sense, as the strong essentialist reading has it. Moreover, a complete concept determines a unique individual substance in that no two possible individuals could share the same complete concept. This is not yet to assert what is the core agreement between superessentialism and strong essentialism – that () an individual sub⁴⁷ The passage below is from Sleigh, Leibniz and Arnauld, p. . Although Sleigh never explicitly says that the natural properties of substances are primitive monadic properties, it seems clear that he takes at least many of them to be so, given his identification of natures with ‘‘primitive forces, hence real causes, in created substances’’ (p. ). We shall discuss primitive forces as real causes in chapter .



Essentialism

stance could not have a complete concept different from the one it actually has: the consequences of moderate essentialism for this first item of our four-part comparison package () – () will be considered below. Sleigh is however explicit in his rejection of () (and so we would argue (), i.e. WBI): in place of superessentialism he ascribes to Leibniz what is meant to be a weaker doctrine of ‘‘superintrinsicalness.’’ On this doctrine, for every property P had by a substance x, if a substance were to lack P, that substance wouldn’t be x. We shall return to this. . Counterparts and complete concepts What of item () in our comparison package? Sleigh does not discuss whether or not Leibniz should be construed as a counterpart theorist. One can scarcely blame him: however much Leibniz expresses sympathy for the counterpart approach, he does not develop it into any full-blooded semantic theory of modality. But perhaps Sleigh’s silence about counterparts is explained straightforwardly enough by the moderate essentialism itself, by his claim that according to Leibniz, a substance has many of its properties, monadic and non-monadic, accidentally.⁴⁸ If this moderate essentialist claim is correct, then Leibniz should be without any motive whatever for resorting to counterpart theory as a general strategy for making sense of talk of how individuals might have been different. And yet Leibniz does have such a general strategy in mind in those passages where he goes the way of counterparts. Set alongside those passages, the moderate essentialist reading will thus look to be a somewhat awkward one. If Leibniz allowed a large range of properties of a thing to be accidental to it, then the claim that there are many ways Adam might have been, both intrinsically and non-intrinsically, comes out as literally true. But it is clear in the many-Sextuses and many-Adams passages that Leibniz does not intend such talk to be read at face value – that is, they are not to be treated uniformly as descriptions of the way our actual Sextus or Adam is at other possible worlds. On the moderate essentialist reading, it becomes difficult to understand why they should not be read in that way. The strong essentialism that we take to be Leibniz’s actual view, while allowing for some accidental properties of individuals (the relational ones), also provides a clear ⁴⁸ Where ‘‘accidentally’’ – i.e., ‘‘contingently’’ – is to be taken at face value. Recall (cf. note ): ‘essential’ for the thorough-going counterpart theorist must strictly speaking be understood as those properties of an individual possessed by all of its counterparts. Again, except where explicitly stated, we are not using ‘essential’ and ‘accidental’ in this derived sense.

Moderate essentialism



motivation for Leibniz’s willingness to go the way of counterparts. In this respect strong essentialism emerges as preferable to moderate essentialism. Several other consequences follow from moderate essentialism that, on our view, recommend against it. The most significant of these is an apparent rejection of () – that is, a commitment to saying an individual could have fallen under a complete concept different from the one it actually falls under. This consequence follows from the moderate essentialist’s commitment to (a) and (b) below (in conjunction with the claim that if an individual x might have lacked some property F, then there is a possible world where x lacks F): (a) Some of the properties contained in x’s complete concept are properties that x might have lacked.⁴⁹ (b) If a property F is in the complete concept had by x at a world W, then x has F at W. While the claim that individuals could have had complete concepts different from the one they actually have sounds unintuitive, our misgiving is not primarily this (these are, as we shall see more clearly below, difficult matters). There are three ways in which that view fails to square with what Leibniz says, and with what he does not say. First, the denial of (), conjoined with Leibniz’s thesis that no two possible individuals share the same complete concept, entails that there are more complete concepts than there are possible individuals. If there were only as many complete concepts as possible individuals, and no two possible individuals shared the same concept, then each individual would have its complete concept essentially. Moderate essentialism is committed to denying the consequent and accepting the second conjunct of the antecedent; thus it is committed to rejecting the first conjunct. The notion that some possible individual has more than one complete concept associated with it at very least aligns poorly with Leibniz’s suggestion that God’s decision to instantiate a particular complete concept and his decision to create a particular individual are one and the same decision. Having decided to create Peter, God is not then faced with the further decision of which of Peter’s many possible complete concepts to instantiate. Rather, according to Leibniz, God’s decision to ⁴⁹ Thus Sleigh, Leibniz and Arnauld, p. : ‘‘[L]eibniz would reject the claim that whatever is included in an individual concept is included necessarily . . . Leibniz claimed that some components of a complete individual concept are included in it necessarily, some contingently.’’



Essentialism

create Peter is His decision to instantiate one complete concept in particular: In an exact sense [God] does not decree that Peter should sin or Judas be damned but only that, in preference to other possible individuals, Peter, who will sin – certainly, indeed, yet not necessarily but freely – and Judas, who will suffer damnation – under the same condition – shall come into existence, or that the possible concept shall become actual. (C : L –; our emphasis)

Second, one should bear in mind Leibniz’s willingness in Discourse § to refer to the complete concept of an individual as its haecceity. This terminology would be entirely misleading to his readers had Leibniz thought that a particular individual could have fallen under a different complete concept. For what is crucial to the traditional notion of an individual’s haecceity is precisely its role as a modal individuator – that its instantiation is necessary and sufficient for the existence of that individual. Third, if the moderate essentialist interpretation is correct, then it would seem that Leibniz had ready to hand a solution to the problem of freedom. If asked ‘‘How could it be that my life’s history is included in my complete concept and yet I be free?’’ he could have easily replied ‘‘Because your complete concept describes only what you actually do, not what you might have done. Since your complete concept could have been different, you might have acted differently than you in fact do, and this gives content to the thesis that you are free.’’ Were this easy solution available to him, surely he would have deployed it: as a response to the problem of freedom, it is too obvious for someone believing that many of the properties in one’s complete concept are contingent to have accepted it but never mentioned or pursued it. Now there are passages which prima facie count in favor of moderate essentialism and directly against our strong essentialism. These will be passages in which Leibniz seems committed to a distinction between essential and accidental properties within the class of properties making up a complete concept. For example, in De libertate, fato, gratia Dei we find Leibniz saying that: In this complete concept of possible Peter, which I concede is observed by God, are contained not only essential or necessary things, namely, those that flow from an incomplete or species concept . . . but also existential things, so to speak, or contingent items are included there, because it is of the nature of an individual substance that its concept is perfect or complete. (VE –: Grua )

Moderate essentialism



Here, one should think, Leibniz has ‘‘set out to explain in conceptual terms a dichotomy between essential and contingent properties of an individual’’⁵⁰ – one squarely at odds with the strong essentialist’s claim that according to Leibniz, () all properties of an individual concept are essential to it. But this passage, and others like it to be noted below, can be readily understood as consistent with strong essentialism. Leibniz, while no realist about species construed as mind-independent universals, was perfectly prepared to admit species construed as legitimate abstractions from individual concepts. The concept of the species of human being will, then, be a legitimate abstraction that filters out details of what defines particular humans, leaving in place only those defining features common to humans in general. Sometimes, Leibniz reserves the term ‘essence’ for the latter properties, which nevertheless form only a subset of the real definition of the individual to which that ‘‘essence’’ belongs. It is this notion of essence that is at work in the following passage to Arnauld: [T]here is nothing in me at all that can be conceived in general terms, that is in terms of essence, or of a specific or incomplete concept, from which one can infer that I shall necessarily take [the journey], whereas from the fact that I am a man one can conclude that I am capable of thought; and consequently, if I do not take this journey, that will not do violence to any eternal or necessary truth. (G ,: LA )

‘‘Essence’’ here, understood as an incomplete concept shared by a class of individuals conceived under some notion of generality (‘‘sub ratione generalitatis seu essentiae, seu notionis specificae sive incompletae,’’ as Leibniz had left the Latin in this July letter to Arnauld), is to be understood in the sense just explained. And again, when Leibniz says that his not taking the journey ‘‘does no violence to any eternal or necessary truth,’’ he clearly means that it is not essential to him in the refined sense that his being a man or capable of thought is speciesessential. Leibniz uses the ‘‘eternal or necessary’’ taxonomy to express specific essence elsewhere in the Arnauld correspondence, where Leibniz asserts that ‘‘specific concepts contain only necessary or eternal truths’’ (G ,: LA –). It appears elsewhere in De libertate creaturae et electione divina when making the distinction we’re recommending here: Of the essence of a [particular] thing is what pertains to it necessarily and perpetually; of the concept of an individual thing on the other hand is what ⁵⁰ Sleigh, ibid., p. .



Essentialism

pertains to it contingently or per accidens. (VE : Grua )

In saying, then, that the complete concept of an individual thing adds to the species-essential properties what is contingent or per accidens, Leibniz is not committing himself to any modal distinction within the complete concept at odds with the strong essentialist reading. That various properties are not species-essential to some individual substance s is perfectly consistent with the thesis that everything expressed by the complete concept of s is essential (in the contemporary sense) to the being of s. Put another way: that which is expressed by a complete concept adds to the real definition of a species enough to provide a real definition of particular individual member of that species in such a way that, strictly speaking, the individual could not have different intrinsic properties from the ones that it actually does.⁵¹ . Superintrinsicalness and superessentialism Let us turn to the doctrine of superintrinsicalness, attributed to Leibniz on Sleigh’s moderate essentialism. As initially presented⁵² it is the thesis that (SI) For every property P had by an individual x, if an individual lacked P, it wouldn’t be x. A subsequent discussion of superintrinsicalness presents two alternative formulations of the doctrine, the first as just given, and the second as follows: (SI) For any property P had by an individual x, if x lacked P, then x wouldn’t exist. According to Sleigh’s moderate essentialist reading, Leibniz was a superintrinsicalist but not a superessentialist (nor a strong essentialist). Is this a consistent position? Sleigh acknowledges that the position ‘‘generates problems of interpretation.’’ One problem is the unavoidable challenge of divining just what Leibniz intends in passages where this or that property is said by him to be intrinsic in the relevant sense at issue – in particular, of judging what Leibniz sees their modal implications to be. Or fails to see: ⁵¹ Following our ‘‘Leibniz on Superessentialism and World-Bound Individuals’’ (from which the present discussion is drawn), Mondadori has fairly noted in his recent ‘‘On Some Disputed Questions’’ that these points recently made – also by him, there – are just as well consistent with his own superessentialism. ⁵² Sleigh, Leibniz and Arnauld, p. . The ‘‘subsequent discussion’’ noted below, from which the alternate formulation (SI) is taken, comes at pp. –.

Moderate essentialism



one must be granted license to report what, on some fair-minded and good-willed interpretation of a historical figure, looks to be false or inconsistent. And here Leibniz’s intent may be sufficiently opaque as to leave one partly to one’s own devices, so long as those devices aren’t at odds with what of his intent is clear. To judge the consistency of the hypothesis that Leibniz accepts superintrinsicalism but denies superessentialism, one must take some accounting of the relevant subjunctive conditionals, and here one does one’s best. As recommended earlier, Leibniz is at least sympathetic with, and in places seems himself to deploy, a possible worlds approach to such conditionals. It is true in any case that this approach can – we know from contemporary work, does – shed light on what particular counterfactuals might amount to. In cases where Leibniz’s intent is less than clear and one is left partly to one’s own devices, one can fair-mindedly take up our question of consistency with that approach.⁵³ So let us consider the first formulation of superintrinsicalism (SI). This seems to us, as it seems to Sleigh, logically consistent with a rejection of superessentialism. Assume a standard Stalnaker/Lewis treatment of counterfactuals. On that semantics, superintrinsicalism can be true while superessentialism is false: for every property P that you have, at the worlds most similar to ours where an individual lacks P, that individual is not you; yet superessentialism remains false since there are distant worlds where you exist with different properties. However, it seems to us that the second formulation, (SI), entails superessentialism (and if restricted to intrinsic properties entails strong essentialism). On any semantics that we know of, the claim that (for any property P of yours) (E) If you were not P, then you wouldn’t exist is true only if the antecedent is necessarily false, that is, only if there are no possible worlds where you are not P. That, moreover, seems exactly right: (E) just does seem like another way of saying that you are essentially P.⁵⁴ Let us then distinguish two senses of intrinsicalness: ⁵³ Sleigh warns that ‘we must be wary of forcing the systems of Stalnaker or Lewis, for example, on Leibniz and Arnauld’ (Leibniz and Arnauld, p. ). Warning acknowledged. ⁵⁴ Gritting one’s teeth against the odd-sounding formulations: ‘If you were not P then you wouldn’t exist’ doesn’t mean ‘‘the closest worlds that do not contain you with P do not contain you at all’’ (if it did mean this, then SI, like SI, wouldn’t entail superessentialism – permitting remote worlds that do contain you with P). Rather, it means ‘‘the closest worlds that contain you with not-P do not contain you at all’’ – which is tantamount to ‘‘there is no world where you are not P’’ (since, if it is true that the closest worlds containing you with not-P don’t contain you, then it is vacuously true).



Essentialism

(I) If someone were to lack P, they wouldn’t be you. (I) If you were to lack P, you wouldn’t exist. We have contended that to claim that a substance x has a property P essentially is to claim that x has P intrinsically in sense (I). Superintrinsicalness (SI) thus entails superessentialism, and so it appears crucial to the consistency of Sleigh’s reading that Leibniz be committed to superintrinsicalness (SI) rather than (SI). We are now in a position to evaluate this reading on three points. First: since it is pivotal to this reading that Leibniz did not accept superessentialism, the view that (SI) is indeed a way ‘‘in which Leibniz seems to have construed’’ superintrinsicalism⁵⁵ gives up too much. It is too strong to be wed with a denial of superessentialism. Second, and equally important: When Leibniz is treating a property as intrinsic to its bearer (in the sense of ‘intrinsic’ at issue), it is frequently intrinsicalness (I) that is doing the work. Recall, for example, this: You will object that it is possible for you to ask why God did not give you more strength than he has. I answer: if he had done that, you would not exist, for he would have produced not you but another creature. (Grua )

And this: A falsity would therefore exist, if I did take [the journey], which would destroy the individual or complete concept of me, or what God conceives or conceived of me even before deciding to create me . . . (G ,: LA ; cf. G ,: L )

Not all of the relevant passages point in the direction we are gesturing at here: the texts are not conclusive. Nevertheless, insofar as many passages can only be read as another way of saying that the mentioned properties are essential, they count strongly against the moderate essentialist reading which would have such properties to be contingent. Third, and in light of the present chapter at large, we are aware of no convincing reason to suppose that Leibniz accepted superintrinsicalness in either of the senses given. It is one thing to say that certain properties of you are intrinsic, and yet another to say that all of your properties are intrinsic. By our lights, it would be strange for Leibniz to have believed that a certain monadic property of yours is intrinsic but that many other monadic properties are not. There is, for him, an important line between monadic and relational properties – between those derivative extrinsic denominations and their primitive intrinsic base. Given that ⁵⁵ Sleigh, Leibniz and Arnauld, p. , where (to be exact) Sleigh says this about the unquantified version I of intrinsicalness; its universal quantification comes at pp. –, passim.

Strong essentialism and compossibility



Leibniz’s own emphasis standardly has the intrinsic monadic base as its focus, we are on balance inclined to apply I only to our internal, monadic denominations, which is equivalent to the hypothesis of strong essentialism.                   . Some problems for strong essentialism Suppose, in line with our strong essentialism, that each possible individual substance is constituted by a primitive form or law-of-the-series that determines a sequence of intrinsic denominations. And suppose further – turning now to a distinguishing feature of strong essentialism – that those intrinsic denominations determine relational facts only when combined with laws of expression, where it is a contingent matter which laws of expression govern an individual substance (it being possible that the same individual substance and associated law-of-the-series⁵⁶ exist in a world with different laws of expression). It would then seem that every set of possible substances is compossible, including the set of all possible substances, since no intrinsic history is, considered in itself, incompatible with any other. Finally, suppose that a possible world is a maximal set of compossible substances: it follows that there is only one possible world. Thus looms the bugaboo of Spinozistic necessitarianism⁵⁷ – a consequence of the conception of substance we have attributed to Leibniz, together with an arguably Leibnizian conception of a possible world. This Spinozistic consequence is clearly one Leibniz wanted to avoid. But given a strong essentialist conception of substance, what resources did he have for avoiding it? And there is a still more basic worry: Leibniz says that not every group of possibles are compossible (G ,: L ). But given the strong essentialist conception of the nature of substance, what entitles him to say this? These concerns force us to engage with one of the central problems in making sense of the Leibnizian metaphysic. What is Leibniz’s considered view of compossibility? ⁵⁶ For more on the relation between laws-of-the-series and individual substances, see chapter , where we argue that the relation is identity. ⁵⁷ See Stuart Hampshire, Spinoza, p. ; Wallace Matson, ‘‘Steps Toward Spinozism’’; Jonathan Bennett, A Study of Spinoza’s ETHICS, pp. –; and especially Don Garrett, ‘‘Spinoza’s Necessitarianism.’’ Some have argued that Spinoza is not committed to necessitarianism: see Edwin Curley, Spinoza’s Metaphysics, esp. pp. –; and Edwin Curley and Gregory Walski, ‘‘Spinoza’s Necessitarianism Reconsidered.’’

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Essentialism

Margaret Wilson, following Fred D’Agostino,⁵⁸ distinguishes two approaches to articulating and explaining compossibility, which one may call ‘logical’ and ‘lawful.’ According to the logical approach, a group of substances are compossible if and only if there is no contradiction in supposing they (co-) exist. According to the lawful approach, compossibility is to be analyzed in terms of lawfulness: a group of substances are compossible if and only if there is (in the relevant sense) no unlawfulness in supposing that they (co-) exist. The lawful approach faces the following objection: By using ‘‘lawfulness’’ rather than ‘‘no contradiction’’ as the operative notion, one violates Leibniz’s own close association between all possibility claims and the idea of contradiction. As Leibniz says, ‘‘A compossible is that which with another does not imply a contradiction’’ (Grua ). It seems then that one should opt for the logical approach. But in the context of this approach, our reading of Leibniz’s considered view looks especially strained. For the logical approach can, it seems, be most intelligibly worked through by supposing that substances have relational properties directly build into God’s conception of them. Incompatibility of substances will then emerge from incompatible relational requirements. For example, part of Joe’s concept is ‘loves everyone,’ and part of Bill’s concept is ‘loved by no one except God.’ By contrast, if one thinks – as we do – that a fully adequate conception of each substance can be obtained by taking stock of its law-of-the-series, and, eo ipso, the sequence of monadic accidents emanating from the law, then it is not clear how God’s conception of any set of possible substances will entail a contradiction. . Wilson and Russell Wilson’s rich discussion of Leibniz on compossibility will provide useful background for our own view. Her positive story is framed in large part as an improvement on the story offered by Bertrand Russell. According to Russell, there are two versions of the Principle of Sufficient Reason (PSR), one that is absolutely necessary and one that is not. The less-thanabsolutely-necessary version requires that reality accord with the perfect ⁵⁸ See Margaret D. Wilson, ‘‘Compossibility and Law,’’ and Fred D’Agostino, ‘‘Compossibility and Relational Predicates.’’ In discussing the distinction we note just below (between ‘‘logical’’ and ‘‘lawful’’ approaches), Wilson follows the literature in the unhappy nomenclature of ‘‘analytic’’ and ‘‘synthetic,’’ so as to make references to other commentators easier to follow: she prefers ‘‘logical’’ and ‘‘lawful.’’ So do we, and borrow it from her here.

Strong essentialism and compossibility



laws of harmony. The absolutely-necessary version of PSR requires that there be lawfulness of some sort (though not that there be the laws guaranteeing maximal harmony).⁵⁹ Compossibility of substances is to be still cashed out in terms of freedom from contradiction. But compossibility requires not merely that there is no contradiction involved in considering the relevant substances as being co-instantiated: it requires also that there is no contradiction involved in considering the relevant substances instantiated at a lawful world. Throw in the axiom of lawfulness with certain complete conceptions of a set of substances, and a contradiction may result even if the conceptions of those substances alone do not entail a contradiction. In working through this account, one already senses well enough that there is a false dichotomy between the logical and lawful approaches. This indeed is one of the themes that Wilson emphasizes: the logical and lawful approaches can be happily reconciled so long as one recognizes that derivations of contradiction pertinent to compossibility will have axioms about laws figuring as crucial ingredients. So what is wrong with Russell’s approach? Wilson’s worry, reasonably enough, is that a mere requirement of lawfulness is too weak to render any bunch of possibles incompossible: ‘‘No matter how apparently chaotic the data one starts with may be – say, a scattering of dots on a page – it will always be possible to subsume them under some law of interrelation.’’⁶⁰ In short, if a conception of a set of substances doesn’t by itself yield contradiction, the addition of a maxim of lawfulness will have scarcely any additional logical bite. Wilson’s own suggestion is that facts about compossibility depend not merely on an abstract requirement of lawfulness but rather on a particular set of laws. Which laws? Her picture of substances – one with some textual support – is that they have the laws of their world written into them. If one is considering whether some bundle of substances are compossible, one not only considers the sequence of intrinsic denominations ⁵⁹ Bertrand Russell, A Critical Exposition of the Philosophy of Leibniz, p. : ‘‘What is called the ‘reign of law’ is, in Leibniz’s philosophy, metaphysically necessary, although the actual laws are contingent.’’ ⁶⁰ Margaret Wilson, ‘‘Compossibility and Law,’’ p. . Thus, Leibniz: ‘‘As concerns the universal order, everything is in conformity with it. So true is this that not only does nothing happen in the world which is absolutely irregular but one cannot even imagine such an event. For let us assume that someone puts down a number of points on paper entirely at random . . . I maintain that it is possible to find a geometric line whose law is constant and uniform and follows a certain rule which will pass through all these points and in the same order in which they were drawn’’ (Discourse §).

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Essentialism

yielded by their primitive active forces but also the laws that are written into them. Since some substance S may have written into it a law that contradicts the laws written into S, facts about incompossibility are readily forthcoming. (For example, suppose S and S both contain F, and both contain the law ‘If a thing is F, then nothing else is F’: one can deduce that S and S are incompossible.) Two features of Wilson’s account are worth distinguishing: () The relevant facts about laws that generate incompossibility results are much richer than the general requirement of lawfulness offered by Russell on behalf of Leibniz. () The facts about laws that figure in the generation of incompossibility results are, for Leibniz, written into the individual substances themselves. Now clearly, () is incompatible with our strong essentialism, presuming as it does that the laws of expression (and the consequent relational facts) are essential to the individual substances governed by those laws. A strong essentialist story about incompossibility, while perhaps making free use of () above, must refrain from assuming (). We take ourselves to have presented good grounds for resisting a picture according to which laws of expression get thrown into individual concepts. Recurring to our favored picture: the inner law-of-the-series of a substance prescribing an intra-monadic sequence of inner states does not fix the inter-monadic laws of expression for that substance. So certainly the law-of-the-series could be the same while laws of expression are different. If now the complete concept that ‘‘defines’’ an individual substance does not include merely its law-of-the-series (and attendant accidents) but superadded laws of expression as well, then identity of substance will not go with identity of law-of-the-series. But that identity thesis is absolutely fundamental to Leibniz’s conception of what an individual substance is. (If this is not plain already, it will become even plainer in subsequent chapters.) So we must resist (). But what, according to us, is Leibniz’s view of compossibility, given that Wilson’s account is unavailable to the strong essentialist reading? Recall again the problems presented earlier: how do we avoid the threat of Spinozistic necessitarianism? And, more basically, how do we propose to make sense of Leibniz’s insistence that not every set of possible concepts are compossible? We develop our own such story in what follows, beginning with some important groundclearing concerning the role of maximality.

Strong essentialism and compossibility



. Debugging the Spinozistic bugaboo The threat of Spinozistic necessitarian arises from an assumption that worlds are (or correspond to) maximal compossible sets of substances. But it is far from clear that this view is to be found in Leibniz. Let us consider a couple of passages that are prima facie most in line with the view that a world contains a maximal set of compossibles. When you say that ‘‘one world that is infinite (in every respect) must in a sense include all possible worlds’’, I agree – in the sense which I have given, taking possibles to be compossibles. (G ,: L ) Thus the universe is a collection of a certain order of compossibles only and the actual universe is a collection of all the possibles which exist, that is to say, those which form the richest composite. (G ,: L )

Benson Mates cites these passages in support of the view that ‘‘Leibniz does not consider that every collection of complete individual concepts constitutes a possible world; the concepts in question must be compossible and the collection must be maximal.’’⁶¹ Mates acknowledges in a note that in the very same letter to Bourguet from which these passages are drawn, Leibniz apparently contradicts his own maximality requirement: And since there are different combinations of possibilities, some of them better than others, there are many possible universes, each collection of compossibles making up one of them (our emphasis).

It would certainly be nice if one could avoid ascribing a contradiction to Leibniz here, especially when the alleged contradiction occurs not only within the same period of his philosophical maturation but, moreover, within five sentences of the same letter. The textual difficulty just noted is not the only strain on the maximality requirement. The maximality requirement also contradicts Leibniz’s separability requirement for really distinct substances. If each substance can, as Leibniz insists, exist as a world apart, independently of any others actual or possible, then each possible world is hardly maximal. Contrast, then, Mates’s assumption on Leibniz’s behalf that (owing to maximality) ‘‘each world contains infinitely many concepts [of individual substances]’’⁶² with the passage from Leibniz’s remarks on the Rorarius article, quoted earlier: ⁶¹ Mates, The Philosophy of Leibniz, p. . Talk of possible individual substances is, for Mates, talk of complete concepts: see p. . ⁶² Ibid. p. .

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Essentialism

It is true that if God were able to destroy all the things that are outside of the soul, and conserve the soul alone with its affections and modifications, they would bring it by its own dispositions to have the same sensations as before – as if the bodies remained – although in that case it would only be like a kind of dream. But since that is contrary to the designs of God, who has willed that the soul and the things outside of it are in agreement, it is clear that this pre-established harmony destroys such a fiction, which is a metaphysical possibility, but which does not accord with the facts and their reasons. (G ,, our emphases)

As it turns out, it seems to us not all that difficult to dissolve the apparently conflicting tendencies in Leibniz. We do know that Leibniz believed that the actual world enjoys a sort of maximality. This stems from the maximal goodness of God’s creative intentions – which, roughly, combines plenitude with lawful harmony. God would have done less than His best if He could have created more substances than He actually did without violating harmony in any way. The best world contains the best admixture of ‘‘variety and unity in variety’’ (Grua ) – a recipe that is ‘‘the most perfect way of multiplying beings to the greatest degree possible, and the best that is possible’’ (G ,). In short, the actual world is composed of the collection of finite substances that is maximally compossible with the laws of greatest harmony. However – returning now to the Bourget passages above cited by Mates in favor of maximality – while the ‘‘actual universe’’ (our emphasis) contains the ‘‘richest composite’’ (psst: consistent with the laws of harmony), we see no implication here at all for the maximality of every world. Similarly, while ‘‘one world that is infinite in every respect’’ (our emphasis) must be such that there are no possible substances compossible with it that are not actual, we see no implication that every world is infinite in every respect. On our view, then, maximality is at best morally necessary rather than a feature of every possible world. We can now see our way to allowing a possible world where some substance exists ‘‘a world apart.’’ Such a world is morally inferior and so, as he says in the Rorarius remarks, ‘‘contrary to the designs of God’’ but nevertheless ‘‘metaphysically possible,’’ since the designs of God determine moral necessity but not metaphysical necessity. . Hypothetical necessity and compossibility Take seriously the idea, associated with the separability requirement, that each monad is a world unto itself and it looks like any group of laws-of-the-series (and thus any individual substances), considered in

Strong essentialism and compossibility



themselves, are compossible. After all, if a law-of-the-series, considered in itself, fixes only an intrinsic monadic sequence and thus does not, considered in itself, determine any relational facts, how is it to exclude another given law-of-the-series from existing? We have arrived at the view that all possible substances are, considered in themselves, compatible with each other: all possible substance are per se compossible. But that can’t be right. Leibniz does not speak as if any set of substances are compossible. Some substances are incompossible with certain others. How then are we to make sense of this datum given the metaphysical picture we have ascribed to him? At a first pass: while substances may be compossible per se, they may not be compossible when certain axioms are thrown in. Recall Russell’s suggestion that incompossibility results are generated from individual concepts together with a very general axiom of lawfulness. Convinced by Wilson’s critique of that suggestion, we propose instead that incompossibility claims are only ever true in relation to a certain set of presumed particular lawful decrees. In most contexts, Leibniz is interested in what substances are compossible with God’s designs for the best. He is thus for the most part interested in questions of what things are hypothetically compossible, where the hypothesis involves certain – albeit morally necessary – decrees of harmony. Of course not every world enjoys the laws of harmony that actually prevail. There are other possible, morally inferior, sets of decrees. And for each set of decrees God can make, He knows which sets of substances are compossible with each other together with those laws. As a result, incompossibility claims are, in effect, claims of hypothetical impossibility – on the hypothesis of a certain set of lawful decrees (where typically the actual decrees are the ones in view) – rather than claims of impossibility per se. Recall the central features of Wilson’s approach: () The relevant facts about laws that generate incompossibility results are much richer than the general requirement of lawfulness offered by Russell on behalf of Leibniz; and () The facts about laws that figure in the generation of incompossibility results are, for Leibniz, written into the individual substances themselves. Unlike Wilson, we do not take it that those laws are written into each substance. We thus reject (). Like Wilson and unlike Russell, we endorse (). We take it that the relevant facts about laws that determine incompossibility results are fairly specific facts about which laws operate, rather than some general facts about lawfulness.

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Essentialism

All incompossibility, on our Leibnizian picture, is hypothetical incompossibility. We do not offer this reading as one on which Leibniz was altogether clear. Indeed, Leibniz for his own part professed himself somewhat confused about incompossibility: It is yet unknown to me what is the reason of the incompossibility of things, or how it is that different essences can be opposed to each other, seeing that all purely positive terms seem to be compatible. (G ,)

We offer our reading as the only sensible notion of incompossibility available to Leibniz given his considered metaphysic and, moreover, one that he nowhere clearly rejects. . Space, time and incompossibility Some readers may complain that we have ignored an important Leibnizian restriction on what can count as a genuinely possible world. There is at least some textual evidence that Leibniz wanted to say that every possible world enjoys a global order of spatio-temporal connectedness, and that this requires that at every world individual substances enjoy certain modes of connection, albeit not necessarily ones corresponding to the laws of harmony. Donald Rutherford has spotted this theme in Leibniz,⁶³ citing the following key text from early sections of the Theodicy:  . . . I call ‘World’ the whole succession and the whole agglomeration of all existent things, lest it be said that several worlds could have existed in different times and different places. . . . . For they must needs be reckoned all together as one world or, if you will, as one Universe. And even though one should fill all times and places, it still remains true that one might have filled them in innumerable ways, and that there is an infinitude of possible worlds among which God must needs have chosen the best . . . For it must be known that all things are connected in each one of the possible worlds: the universe, whatever it may be, is all of one piece, like an ocean: the least movement extends its effect there to any distance whatsoever, even though this effect become less perceptible in proportion to distance. (T §§,: H )

Thus we seem to have a requirement on all possible worlds that their contents be connected, and this appears to flow from a requirement on all possible worlds that their contents (modulo some level of description) fill a single space and time. And therein perhaps lies one way of filling out Russell’s original idea of a general requirement of lawfulness, so as ⁶³ Donald Rutherford, Leibniz and the Rational Order of Nature, pp. –. The Theodicy passage below is cited on p. .

Strong essentialism and compossibility

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to avoid the threat of vacuity that Wilson detects in it. Perhaps the general requirement of lawfulness is that monads be connected in such a way as to constitute a single spatio-temporal manifold. If that is correct, then there is a general requirement on compossibility that we have neglected: for a given set of individual concepts, they are compossible only if they could co-exist in a world where things are sufficiently connected in a way appropriate to there existing a spatio-temporal manifold embracing all the created substances. Consider now some offending (unconnected) set of substances. One may distinguish two views here: (i) God could create all the members of the set, but in that case, the existing things that He creates would not constitute a world. (ii) Since the set in question is incompatible with the connectedness requirement, God could not co-instantiate the members of the set. Rutherford seems to incline toward (i). He is aware, after all, that Leibniz affirms in his first reply to Bayle that: God could give to each substance its own phenomena independent of those of others, but in this way he would have made as many worlds without connection, so to speak, as there are substances . . . (G ,: L )

Noticing that Leibniz here seems to allow for the creation of disconnected monads, Rutherford uses this passage to ‘‘undermine the claim of these substances to form a single world.’’⁶⁴ Let us concede that Leibniz sometimes uses the notion of ‘a world’ to mean something like ‘bunch of monads connected in the right way to compose a unified spatio-temporal universe.’⁶⁵ With this sense of ‘world’ firmly in hand, one might now say, in light of the quoted Bayle reply above, that God could have created disconnected monads, and that in ⁶⁴ Ibid., p. . ⁶⁵ The concession itself may be a relatively weak one. Outside of the Theodicy passage (about which we shall complain presently), Leibniz says that ‘‘a single universe comprehends for us the totality of created things in all times and places; in this sense we use the term ‘world’’’(G ,: S ; our emphasis). But Leibniz’s concern in this passage, from a section of Causa Dei devoted to ‘‘contingent possibles,’’ is perhaps less one of laying down the condition of spatio-temporal connectedness as a requirement for all worlds, and more to reject the idea that there might be a plurality of actual worlds. ‘‘It is useless to invent a plurality of actual worlds, since a single universe comprehends for us the totality of created things . . .’’ If (speaking on some level of description at which the spatio-temporal idiom applies) something actual is within a spatio-temporal manifold, then (at that same level of description) everything else actual is within that same manifold as well. Thus: ‘‘there are no bodies that are not at some definite distance from us. For if there were, it would be impossible to say whether they exist at the present moment or not . . . From this it follows that not all possibles exist’’ (Grua ); ‘‘If there existed another series outside ours, it would not be possible to say whether something in it existed simultaneously with something in ours or not; thus it would be impossible to say whether it existed now or not, which is impossible’’ (LH  vi F, ; cited by Mates, The Philosophy of Leibniz, p. ).

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Essentialism

such a case they would not constitute a possible world. And one might take the point of the Theodicy passage to be that insofar as God was to make a universe or world, the monads must be connected. The point is all fine as far as it goes. The difficulty is that it is something of a wheel that turns idly without doing any work. The fundamental modal issues with which we have been engaged in this chapter are altogether unaffected. All monads are, for all this wheel-turning, compossible in that God could create any group of them. Each monad, for all this, is only accidentally connected to others, in that it is metaphysically possible that God creates the monad without its being connected with anything else. And in the broader sense of ‘world’, construed in Leibniz’s preferred way as a creation scenario for God, there is a scenario, a world where there are disconnected substances. The first position (i) forces no important revisions upon either the strong essentialist reading or the view of compossibility that we have defended in connection with it. Nor will the introduction of new restricted versions of the terms ‘compossible’, ‘essential’, and so on generate disputes that are more than terminological. Position (ii) above, by contrast, constitutes a direct challenge to the views we have been defending. It proposes a constraint on compossibility that we have ignored, and suggests a relational property – connectedness – as essential to substances. We have three concerns with this position. First, and most obviously, it fails to square with texts like that of the reply to Bayle which, emphasizing separability, manifest no concern whatever with spatio-temporal connectedness as a necessary feature of reality. Moreover, the Bayle reply itself is prefaced by the remark – omitted in Rutherford’s use of it – that the unhappy disconnectedness ‘‘could not arise in the natural order,’’ suggesting that it is not forbidden per se. If (ii) were to be defended, then all the texts emphasizing separability and the consequent ‘‘world apart’’ character of each monad would have to be judged as something of an aberration. Given the extent and tenor of those texts, we are strongly disinclined to make that judgment. But we are far from denying that aberrations, or anyway ill-fitting texts, are sometimes to be encountered in approaching Leibniz’s body of writings. Indeed, there may be some in the vicinity of our topic; for, second, it is not at all clear to us that the occasion where Leibniz comes closest to the position in question – Theodicy §§, – is an occasion where he is doing his most serious and careful metaphysics. At least one hopes not, since Leibniz goes on to gesture at a radically haecceitistic view of

Coda: miracles and essentialism

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worlds in the very next paragraph: ‘‘[given God’s plan to create the best] . . . nothing can be changed in the universe (any more than in a number) save its essence or, if you will, save its numerical individuality’’ (T §, H ). The extent to which that must be reckoned careless philosophy on Leibniz’s part will emerge very shortly, in chapter . Third, while we all –- Leibniz included – might sympathize with the Kantian idea that of necessity substances occupy a single spatio-temporal manifold, the plain fact is that Leibniz’s metaphysic does not have the resources to secure that necessity.⁶⁶ His deep and fundamental metaphysic is one of simple laws that yield internal patterns of unfolding. The spatio-temporal manifold, from the Leibnizian perspective, is a supervenient byproduct of God’s making a suitable bunch of substances. If now it is a necessary feature of the world that substances be connected, that must be reckoned a metaphysical dangler vis-a`-vis the main structural features of Leibniz’s metaphysical picture. Best then that we avoid ascribing commitment to the connectedness requirement if we can. And we can.  :                      In discussing the strength of Leibniz’s essentialism, we have studiously avoided the topic of miracles. But doesn’t the possibility of miracles make trouble for our strong essentialism? For example, couldn’t things have been such that I was miraculously annihilated a long time ago? And hasn’t Leibniz said that ‘‘God can exempt creatures from the laws he has prescribed for them, and produce in them what their nature does not bear, by performing a miracle’’ (T, ‘‘Preliminary Dissertation’’ §: H )? Doesn’t this show that my intrinsic accidents are not essential without qualification, their being absent from me in worlds where God miraculously intervenes? Leibniz does, in places, take seriously a kind of miracle that will make trouble for strong essentialism. None of the competing views discussed here are better off. If strong essentialism is in trouble on the score that my history could have been radically different in miracle worlds, then so a fortiori is superessentialism. Further, the possibility of miracles of this sort would also appear to make trouble for a superintrinsicalness reading. Have we been missing an obvious source of counterexample? ⁶⁶ Note that even if Leibniz were a superessentialist, he would lack the resources for supposing that every possible substance lives in a connected world. Superessentialism tells us only that if we do, then we must.

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Essentialism

With so many other interpretative issues at stake, we have factored out the threat of miracles in discussing the strength of Leibniz’s essentialism. Leibniz himself seemed to factor it out in that context. Certainly, Leibniz never does much by way of integrating his own serious thinking about modality with, say, the possibility of miraculous annihilation. Bracketing the noise generated by miracles is, therefore, a reasonable methodological strategy. But having been alerted to the issue of miracles, readers will still want to know: ‘‘Is some feature essential to me simpliciter, as opposed to being a feature I have in all non-miracle-worlds?’’ There is, we believe, a considered Leibnizian answer to this query: ‘‘Yes. While emanating accidents are only common to me in non-miracle-worlds, the law-ofseries/substantial form is essential simpliciter.’’ This refinement of the views expressed in this chapter can only be properly considered with a good deal of further scene-setting in place. Readers will find this and related issues explored in chapters  and .

 

Haecceitism and anti-haecceitism

Chapter  explored at some length the first of two problems of modal individuation, namely Leibniz’s essentialism. The central question there concerned what does and does not go into the complete concept that defines an individual in the required, modally robust way. In this chapter, we explore as promised a second and deeper problem of modal individuation. The question here is how a complete concept – thick or thin – could serve to ‘‘define’’ an individual at all. In order to present this problem with due clarity and focus, we begin with some careful scenesetting. There is little disagreement about this much of Leibniz’s metaphysics: it is a robust substance-accident realism, complete with individual substances underlying the attributes in which they are clothed, and a commitment to some version of essentialism. Nevertheless, there is a deep tension in Leibniz’s philosophy that seems to have gone unnoticed by commentators, and perhaps by Leibniz himself. The tension happens to bear on issues of contemporary philosophical relevance, and may be cast in now-familiar terms borrowed from Scotus by recent discussions of identity and modality. In ‘‘How to Russell a FregeChurch,’’ David Kaplan distinguishes two broad approaches to questions of transworld identity: The doctrine that holds that it does make sense to ask – without reference to common attributes and behavior – whether this is the same individual in another possible world . . . that a common ‘‘thisness’’ may underlie extreme dissimilarity or distinct thisnesses may underlie great resemblance, I call Haecceitism . . . The opposite view, Anti-Haecceitism, holds that for entities of distinct possible worlds there is no notion of transworld being. They may, of course, be linked by a common concept and distinguished by another concept – as Eisenhower and Nixon are linked across two moments of time by the concept the president of the 

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Haecceitism and anti-haecceitism

United States and distinguished, at the same pair of moments, by the concept the most respected member of his party – but there are, in general, many concepts linking any such pair and many distinguishing them. Each, in his own setting, may be clothed in attributes which cause them to resemble one another closely. But there is no metaphysical reality of sameness or difference which underlies the clothes. Our interests may cause us to identify individuals of distinct worlds, but we are then creating something . . . of a kind different from anything given by the metaphysics. Although the Anti-Haecceitist may seem to assert that no possible individual exists in more than one possible world, that view is properly reserved for the Haecceitist who holds to an unusually rigid brand of metaphysical determinism.¹

What we want from this is the philosophical taxonomy: the haecceitist is the philosopher whose theory allows for the face-value intelligibility of de re modal assertions generally, and of transworld identity claims in particular, however that theory might come down on the truth or falsity of such claims. According to Leibniz’s substance-accident realism, it is metaphysical reality and not our interests which underlies facts of sameness and difference of individual substances. On the superessentialist view of Leibniz, one should reckon him a haecceitist precisely of the sort noted in Kaplan’s last quoted line above – as a philosopher who can make perfect sense of de re modality and questions of transworld identity, who yet happens to believe that all assertions of transworld identity are strictly speaking false. We have argued in the preceding chapter that Leibniz should be understood as claiming only that all the intrinsic monadic properties of an individual substance are essential to it, allowing for the logical possibility that certain transworld identity claims might sneak through as true. We also confronted a third position – moderate essentialism – that differs from superessentialism and our own, strong essentialist reading. Both the moderate and strong essentialist departures from the superessentialist account nevertheless leave Leibniz a haecceitist. So it is agreed on all hands that Leibniz, being an essentialist of some sort, is committed to the intelligibility of de re modal ascriptions (taken at face value), that is, committed to haecceitism in Kaplan’s sense. The new and deeper theme examined in this chapter is that while Leibniz gives undeniable voice to a haecceitist position, various strands of his thought exert significant pressures toward an anti-haecceitist view. The main effort here, of a historical nature, is concerned to expose this ¹ From pp. – of David Kaplan, ‘‘How to Russell a Frege-Church.’’

Haecceitism and anti-haecceitism



tension, and to explain why it may have been important for Leibniz to resist – perhaps unconsciously, perhaps unsuccessfully – the pressures of anti-haecceitism. But our purpose is philosophical too: the tension we discuss, and the second glance at Leibnizian haecceitism it recommends, affords one a clearer view of how the principles of Sufficient Reason (PSR) and the Identity of Indiscernibles (PII), in their various guises, relate to the haecceitism/anti-haecceitism debate. In discovering what Leibniz has to contribute to a central debate in contemporary discussions of modal individuation, we shall uncover respects in which the place of PSR and PII in Leibniz’s own views about individuation, though much discussed, has not been well understood. Certain of those features will then be taken up in chapter . In the first and longest of the three sections to follow, we will argue that, despite the commonplace (if sometimes implicit) presumption of haecceitism underlying the work of Leibniz and his commentators, there is remarkably strong pressure in Leibniz’s mature philosophy toward anti-haecceitism. In § we address the importance of haecceitism to certain strands of Leibnizian doctrine, and recommend how best to interpret Leibniz’s haecceitist stance. § takes the first steps, to be continued in later chapters, toward combining the relevant threads of Leibnizian thought into a unified and coherent picture: there we ask how the notion of a complete concept might be understood as a means toward holding his distinctive brand of haecceitism together. We end that section with some reflections on the complete concept doctrine. In deploying the term ‘haecceitism’ and its cognates, we are not, of course, attributing to Leibniz the details of a theory of individuation espoused by Scotus himself. We have already seen in chapter  that the early Leibniz denies the formal distinction required to render Scotistic haecceities intelligible. Moreover, the mature Leibniz was never seriously tempted either by the Scotistic formal distinction generally or Scotistic haecceities (with their solo numero differences) in particular. We shall in what follows use ‘haecceitism’ to mean what Kaplan meant by that term.



Haecceitism and anti-haecceitism     -                  . General propositions and ‘de re’ modality

We need a working notion of singular propositions, to begin.² Following a now-familiar tradition associated most notably with Russell (in both the Principia Mathematica and Principles of Mathematics) and Kaplan, let a singular proposition be any proposition P involving as an immediate propositional constituent some individual or non-qualitative haecceity³ of an individual: intuitively, the constituent we have in mind is, or is uniquely determined by, that individual a corresponding to the directlyreferring singular term (individual constant) of a sentence used to express a proposition about a. (That particular individual a which P is about is determined directly by the propositional constituent, on the strictly Russellian view, because the constituent is the individual a itself.) A general proposition, then, is any proposition that is not singular, containing no individuals or haecceities: whatever determines the individual(s) that a general proposition is about, it does so ‘‘indirectly’’ via qualitative properties and relations the individual(s) happens to bear. General propositions can in a suitably rich language be expressed by sentences void of any directly referential devices such as proper names or indexicals; they correspond to sentences constructed solely from quantifiers, variables, qualitative predicates not expressing haecceities, and logical operators. (It is allowed that a modal operator at the front of a sentence S expressing a proposition P is a logical operator that yields a new sentence S' expressing a new proposition P'.) That there exists something that Socratizes is not – and ‘‘Something Socratizes’’ does not express – a general proposition, unless of course ‘Socratizes’ is elliptical for a definite description connoting only general properties. Here are some commonplace truths and truth-schemas. There are red things; necessarily all Fs are Gs; there is a round thing that is larger than some red thing; there is at least one G; there is a dog that is neither red nor larger than every blue thing; there is exactly one F that is G and H and . . . . Countless truths are much less commonplace, of considerably more complex logical form – truths about every molecule and atom of our world and their distinctive relations and configurations and charges and spins. Suppose that all the truths about any possible world ² The picture of propositions that follows is just that – a picture. We intend to rest as little metaphysical weight as possible on any particular concept of a proposition. ³ Or ‘‘thisness,’’ as Kaplan called it and as Robert M. Adams calls it in ‘‘Primitive Thisness and Primitive Identity.’’ A thisness is a property of being identical with a certain particular individual. What we characterize (below) as ‘‘qualitative predicates not expressing haecceities’’ correspond to what Adams calls ‘‘suchnesses.’’

Anti-haecceitist pressures

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could be captured by such general propositions. In supposing this, it may help to imagine a being – an omniscient Being, say⁴ – that surveys all logically possible states of affairs and conceives of each possible world in terms of a book or list of general propositions of quantificational form. And suppose now that one were to ask this being: is there anything that exists, or that could exist, which is essentially red, that is, red at each possible world where it exists? It seems clear enough that our imagined being would not only be unable to answer this question, but moreover would be unable to make much sense of it. Nothing within any list nor any comparison among them can serve to ground the truth or falsehood of the statement ‘There is something that is essentially red.’ For if the full truth at all worlds is general, there will be no determinate fact of the matter whether the thing that is F and G and H . . . in world W is, or isn’t, the thing that is F and G and H . . . in world W*. In short, purely general propositions look to contain no resources for tracking a particular object across lists or worlds: the concept of transworld identity, and with it the traditional de re modal notions of essence and accident, have been lost.⁵ (It must of course be granted that, if the question ‘Is there anything essentially red?’ were an elliptical way of asking whether anything was such that all its counterparts were red, where the counterpart relation amounts to a particular similarity relation determined by this or that philosophical interest, then the question would after all make good sense. The point remains, however, that one who thought that all ‘‘truthmakers’’ were general propositions or general facts would be unable to take questions about transworld identity, essence and accident at face value. She would have to regard them as either illegitimate or else elliptical for a question that is not strictly speaking about the identity relation at all.⁶) ⁴ It might be objected here (by a haecceitist) that our imagined Being cannot be omniscient, since He does not know whether you exist at the actual world or any other. By supposing that our Being is omniscient only with respect to general propositions, the objection presumes to be true what we have supposed for purposes of argument to be false, namely that there are singular propositions constituting different truths from any combination of general propositions. ⁵ In § below, we shall broach a philosophical thesis which, if intelligible, would render an assumption of this paragraph (but not its conclusion) questionable. The assumption is Kaplan’s haecceitist/anti-haecceitist dichotomy; the philosophical thesis which would render it a false dichotomy is that all general propositions taken together uniquely determine (all) the singular propositions. ⁶ It would be wrong to suppose, of course, that a counterpart theorist is unable to take questions of transworld-identity at face value. Insofar as the counterpart theorist provides an other-than-facevalue reading to ordinary talk that is apparently about transworld-identity, this is not because he is unable to take such statements at face value but because it is more charitable to accord them a looser interpretation. (See the discussion of Leibniz’s and David Lewis’s counterpart approaches, chapter ).



Haecceitism and anti-haecceitism

So much for the ‘‘generalist’’ picture, on the one hand. It is to singular propositions that one must turn if one is to take transworld identity claims at face value, as expressing truths.⁷ To complete the relevant contrast, then, imagine (on the other hand) the list of truths about any possible world to be embellished with singular propositions, atomic versions taking the logical form ‘a is F’, which either involve haecceitistic properties such as ‘Socratizes’ or else enjoy individuals as constituents. Questions of transworld identity and hence de re modal questions would now be perfectly intelligible. Suppose, for example, that one accepts haecceities: ‘Something is essentially red’ would be true just in case some haecceity was only possibly possessed by a red thing. Or suppose one accepts Russellian singular propositions of the form ‘x is F’; then ‘Something is essentially red’ would be true just in case, for some a, there is no possible world where ‘a is not red’ is true. The lesson to be learned is that in order to make sense of transworld identity claims, one needs to make room for singular propositions;⁸ if a correct and complete conception of the world involves only general propositions, then questions about transworld identity cannot be taken at face value. . Leibniz’s generalism It is now especially pertinent to inquire whether Leibniz made room for singular propositions. Restricting ourselves for the moment to the actual world,⁹ the question might be posed: when God conceives of the actual world, does He entertain any genuinely singular propositions? First, it is certainly true that Leibniz thinks sentences employing proper names (can) express truths. Even in texts where he is concerned ⁷ It is not enough here that singular propositions be true of the actual world. If one could fully and perspicuously describe any merely possible world in terms of only general propositions, the same problem will arise. Not only must claims like ‘a is F’ be literal and perspicuous descriptions of some state of affairs, but also ‘Possibly, a is F’ must likewise be a literal and perspicuous description of some modal truth or falsehood. A related point: one might believe in Russellian singular propositions but deny the intelligibility of transworld identity on the grounds that there is no fact of the matter about inter-world identity and diversity of singular propositions (determinate transworld identity of singular propositions requiring, after all, transworld identity of constituents). We are grateful to Timothy Williamson here. ⁸ The game changes somewhat if we allowed (as David Lewis does, and Leibniz does not) that non-actual individuals and worlds exist in the same way that the physical cosmos exists. This would provide another way of understanding transworld identity claims at face value (and of dismissing them all as false). A discussion of Lewis’s extreme modal realism would take us too far afield here: for a brief comparison of Leibniz and Lewis on this issue see p.  (n. ) of J. A. Cover, ‘‘Reference, Modality and Relational Time.’’ ⁹ The restriction will, for the moment, keep at arm’s length a certain distraction, namely worries about the possibility of singular propositions involving uncreated or non-existent objects.

Anti-haecceitist pressures

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to explain his views on the nature of truth, such familiar sentences as ‘Adam is the first man,’ ‘Caesar crossed the Rubicon,’ ‘Judas sinned,’ and ‘Alexander conquered Darius’ are among his favored examples. Second, Leibniz frequently makes claims that appear to be the hallmark of haecceitism combined with ‘‘metaphysical determinism’’ of the sort that Kaplan had in mind. Consider, for example, the following characteristic remarks familiar from chapter : (S) You will object that it is possible for you to ask why God did not give you more strength than he has. I answer: if he had done that, you would not exist, for he would have produced not you but another creature. (Grua ) (J) But someone will object, how does it come about that this man [Judas] will assuredly commit this sin? The reply is easy: it is that otherwise he would not be this man. (G ,: L )

Here Leibniz offers what look to be unequivocally de re modal judgments: he expresses denials of identity claims within modal contexts, on the basis of some essentialist scruples. In § we shall offer somewhat different evidence of Leibniz thinking like a haecceitist: it is enough here to recommend what many commentators already implicitly acknowledge – that one is not well placed to deny that Leibniz entertained a haecceitist metaphysical picture, and perhaps one that, if not fully super-essentialist, is at least strongly so, regarding all one’s intrinsic monadic properties as essential. Yet there is a view standardly ascribed to Leibniz that, while appearing to run in tandem with this metaphysical picture, begins to count against its very intelligibility. This is the view that subject terms of claims satisfied by a single individual can be unpacked into definite descriptions – descriptions which embrace, if not every property of an individual, then certainly a large cluster of intrinsic properties had by the individual. This semantic thesis bears sketching out, before setting it alongside Leibniz’s modal metaphysics. Recall again those familiar sentences deployed as examples in Leibniz’s discussions of truth. There is an obvious and innocent respect in which ‘Adam is the first man’ and ‘Alexander is a conqueror’ are ‘‘singular’’ claims, or better, express propositions having singular subjects: they are claims and propositions that are satisfied by, or assert something of, a single individual. But according to Leibniz, they are laden with generality in the sense earlier associated with ‘general proposition.’ This follows straight away from his predicate-in-subject doctrine of truth, according to which a proposition is true

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Haecceitism and anti-haecceitism

if its predicate is in its subject; thus, in every true affirmative proposition, necessary or contingent, universal or singular, the concept of the predicate is somehow contained in the concept of the subject, in such a way that anyone who understood the two concepts as God understands them would eo ipso perceive that the predicate is in the subject. (C –)

We shall return to this familiar passage shortly, in discussing the generality of concepts and the relation of propositions to the mind of God. For now, notice how closely this semantic thesis is connected with Leibniz’s doctrine of complete individual concepts: ‘‘In saying that the individual concept of Adam involves all that will ever happen to him, I mean nothing else than what all philosophers mean when they say that the predicate is in the subject of a true proposition’’ (G ,: LA ). Propositions expressed by ‘‘singular’’ claims (in the innocent sense) thus have complete individual concepts as their subject: on Leibniz’s standard formulation, such propositions take the form ‘A is B’ and express a relation between two concepts. Indeed, as Leibniz makes explicit in the Generales inquisitiones, ‘A is B’ should be understood as ‘Every A is B’ (C : PLP ), since A is B if the concepts every A and some B ‘‘coincide.’’ Leibniz will sometimes make this point abstractly in terms of the conditional ‘If something is A, then it is B’; elsewhere he follows a statement of the concept-containment doctrine of truth with a concrete example: Given that there is somebody who is Strong, Brash, Learned, a King, General of an army, Victor in the battle of Arbela, and the rest of what is ascribed in this way to Alexander the Great, then God . . . will see a complete concept in which all of these are contained virtually, or from which they all follow . . . King does not follow from Strong, nor Victor from General, but from the concept of Alexander follow King, Strong, Victor, and General; and that there is such a concept is manifest from the previously given definition of true proposition. For when we say ‘Alexander is strong’ we mean only that Strong is contained in this concept of Alexander. . . (SFL –; our emphasis)

Now at first glance, the semantic thesis that individual concepts associated with proper names (or individual referring terms generally) contain – in some sense of ‘‘contain’’ – filled-out descriptions seems to fit nicely with the metaphysical picture of individuals whose intrinsic monadic properties are essential to them. After all, the view just described entails that, for any such property F lacked by the individual satisfying ‘a’ at the actual world, sentences of the form ‘a is F’ are necessarily false. But in the light of our earlier discussion, it seems clear that this view of proper names does not rest easily with haecceitism. For

Anti-haecceitist pressures

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on this view, although one can assign truth and falsehood to modal claims involving proper names easily enough, it is unclear why such claims will enjoy anything more than a de dicto modal status. This is because the complete concept doctrine is most naturally interpreted as the view that all proper names are mere shorthand for definite descriptions.¹⁰ This natural interpretation (as we shall call it), together with the predicate-in-subject thesis, entails that a perspicuous description of what is expressed by items of the syntactic form ‘a is F’ would take the logical form ‘The thing that is F and G and H . . . is F’. All apparently singular claims express propositions that are general in the sense described earlier. If this is correct, then claims about transworld identity simply cannot be taken at face value. In short: while the existence of true de re modal claims is central to his haecceitism, Leibniz’s considered semantic view seems to entail that all necessary truths are de dicto necessary.¹¹ (And so it should be noted that, if the natural interpretation is the final and correct one, such that Leibniz is judged a straightforward antihaecceitist, the apparently unequivocal de re claims (S) and (J) quoted above must be reassessed as equivocal and de dicto. In the case of (J), for example, part of what it means to have ‘Judas’ or ‘this man’ [in this context] apply to a thing is for that thing to have ‘committed this sin’ apply to it. To what extent the natural interpretation can be fairly resisted will be broached in later sections.) The ‘‘generalist’’ strand of Leibniz’s thought is not isolated to his account of truth and proper names: his generalism makes its presence felt when Leibniz is offering a picture of how God conceives of possible ¹⁰ In ‘‘Reference, Essentialism and Modality in Leibniz’s Metaphysics,’’ Fabrizio Mondadori defends an interpretation of Leibniz’s theory of names as ‘‘anticipat[ing], in significant respects, what we might call (borrowing Donnellan’s terminology) the attributive view of proper names,’’ whereby ‘‘proper names name only by describing the objects they name’’ (p. ). ¹¹ Objection, on behalf of the natural interpretation: ‘‘The complete-concept doctrine, on the natural semantic reading of it, entails not only that If Adam sinned, then it is part of the meaning of ‘Adam’ that its bearer sinned, but also, more strongly, that If Adam sinned, then it is part of the meaning of any possible expression referring to Adam that its bearer sinned. That is a semantic thesis, de dicto (about language), but it generates an essence de re simply because it makes its claim not about this or that way of referring to the subject but about any possible way of referring to it’’ (our thanks to Jonathan Bennett for this way of posing the objection). Reply: The semantic thesis generates no such de re essence. An essence de re is a property had by the subject a at all worlds where a exists. This requires that one can evaluate claims of transworld identity for a. That the complete concept C of a is the only way of referring to a does not yet allow one to answer or even make sense of the question whether some individual x is identical with a. (One can consistently say both that C is the only way of referring to a and that de re modal questions make no sense at all when taken at face value; thus, the semantic thesis cannot provide an essence de re.) There is a bit more to say about the objection: on the relation of the complete concept doctrine to the exigencies of reference, see §. below.

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Haecceitism and anti-haecceitism

worlds. Return briefly to Leibnizian concepts, all of which are general but which (as the last quotation from Leibniz illustrates) can be more and less ‘‘complete.’’ It is the limiting-case fully complete individual concepts, understood by Leibniz to determine exactly one individual, which figure as subjects of simple propositions ‘A is B.’ A proposition thus has concepts as its constituent terms (G ,: L ; cf. G ,), and so Leibniz can say (above) that ‘‘anyone who understood the two concepts as God understands them would eo ipso perceive that the predicate is in the subject’’ (C –). The reference to God is not merely heuristic. All concepts, among which propositions themselves are numbered,¹² exist as ‘‘ideas’’ in the mind of God. This Leibnizian strain of Platonic realism underwrites his own rationalism about the ultimate intelligibility of everything actual and possible. (In a letter to Hansch of July  praising a certain ‘‘enthusiasmo Platonico,’’ Leibniz says that ‘‘many of the Platonic doctrines are most beautiful – [. . .] that there is an intelligible world in the divine mind, which I usually call the region of ideas . . .’’¹³) It is in terms of contents of the divine mind that Leibniz’s generalist notion of possible worlds is best understood. The actual world is only one of infinitely many possible worlds that God entertained and might have created or made actual: says Leibniz in his notes on Fardella (), ‘‘From an infinite number of possibilities God chose one worldseries, consisting of an infinite number of substances, each of which exhibits an infinite number of actions’’ (Stein : AG ). This formulation is characteristic in its reference to possible substances and (implicitly) their relation to God; elsewhere Leibniz says: God had knowledge of possible things, not only as separate, but as coordinated ¹² At C : PLP  Leibniz treats ‘A is B’ as a ‘‘term,’’ expressing A’s being B; cf. G , where ‘terms’ and ‘concepts’ are offered as synonyms. For a fine discussion of propositions and concepts, see ch.  of Benson Mates, The Philosophy of Leibniz. ¹³ E : L . It has been suggested to us that Leibniz retreats from this view in a  letter to M. Remond, addressing du Tertre’s attack on Malebranche: there, concerning ideas, Leibniz agrees that ‘‘there is no necessity . . . for taking them for something external to us; it is sufficient to regard ideas as notions . . . . as modifications of our soul.’’ But it seems to us that Leibniz rather defends Malebranche in this regard, when going on to say that ‘‘as God is the source of possibilities and consequently of ideas, the Father may be excused. . . in distinguishing [ideas] from notions and in taking them for perfections in God which we participate in by our knowledge . . . It even seems that Plato, speaking of ideas, and St. Augustine, speaking of truth, had kindred thoughts, which I find very remarkable; and this is the part of Malebranche’s system that I should like to have retained . . . And far from saying with the author of the Refutation that the system of St. Augustine is a little infected with the language and opinions of the Platonists, I would say that it is thereby enriched and set in relief.’’ See § of ‘‘Lettre a` Remond de Montmort contenant des remarques sur le livre du P. Tertre contre le P. Malebranche,’’ at E –.

Anti-haecceitist pressures

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in innumerable possible worlds, from which, by his most wise decision, he chose one. (G ,) There are many possible universes, each a collection of compossibles . . . (G ,) The wisdom of God, not content with embracing all the possibles, penetrates them, compares them, weighs them one against the other, to estimate their degrees of perfection or imperfection . . . [It] makes them an infinity of possible sequences of the universe, each of which contains an infinity of creatures. By this means the divine Wisdom distributes all the possibles it had already contemplated separately, into so many universal systems which it further compares with one another. (T §: H )

Leibniz is not considering here a super-collection of non-existent substances enjoying a shadowy sort of reality or Meinongian Aussersein or the like, upon which God looks to make manifold comparisons. Rather, the ‘‘possible substances’’ that are objects of God’s thought are simply the complete individual concepts already there in the divine intellect. Arnauld had reckoned purely possible substances as a kind of ‘‘figment of the imagination’’ (G ,), and this Leibniz provisionally allows, calling Arnauld’s ‘‘a view I do not oppose, if you understand by it . . . that they have no other reality than that which they have in the divine understanding’’ (G ,: LA ). Later in the same paragraph Leibniz says of possible substances that ‘‘In order to call something possible, it is enough for me that one can form a concept of it even though it should only exist in the divine understanding, which is, so to speak, the domain of possible realities’’ (G ,: LA ). So it is in terms of concepts that Leibniz is most plausibly understood to think of possible worlds and their inhabitants as being present to God’s mind. The generalist strand of thought which earlier looked to entail that all modal truths have at best de dicto status thus re-emerges on the present understanding of Leibnizian worlds. The exhaustive truth relative to (‘‘about’’) any world is represented in God’s mind as a list of propositions, together with whatever they imply via their constituent concepts. (Recalling chapters  and , Leibniz makes it clear that individual concepts do not immediately contain the whole truth about individuals, but rather the foundation of the whole truth.) Insofar as the concepts of propositions are general, and presuming that God has – so to speak – taken the trouble to see in them everything they imply, it becomes natural to think of the contents of God’s mind as a series or list of existential and universally quantified propositions, with one list

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Haecceitism and anti-haecceitism

flagged as actual. As before, one has here a picture that reckons all truths in the mind of God to have the form of general propositions. And as was argued earlier, if all the truths about worlds take the form of general propositions, then haecceitism seems unintelligible. The resources for (and expressions of ) any transworld comparison, and modal claims generally, will be de dicto. Leibniz’s generalism is the main feature of his philosophy that seems to require anti-haecceitism; but there are other elements of his thought that look to incline in the same direction. Perhaps the most pressing concern is that haecceitism is often felt to lend itself to a rejection of standard versions of the principle of the Identity of Indiscernibles (PII), which Leibniz is committed to accepting.¹⁴ Suppose it is granted that no two possible individuals share the same set of qualitative monadic and relational properties of the sort figuring in general propositions. (Again, haecceity properties and properties expressed by truth-functional constructions from them [such as is Socrates and is F ] won’t count as qualitative properties.) On this supposition, it would then seem difficult to maintain that properties such as is Socrates are irreducible to qualitative properties. The following reductio might be reckoned as sufficient to show this. Suppose one were to grant that PII is true, that is Socrates is a property had or lacked by every possible individual, and assume that this property is irreducible to qualitative properties. If no two possible individuals share the same set of qualitative properties, it would follow that some complex qualitative property (perhaps very long, perhaps disjunctive) was necessary and sufficient for having the property is Socrates. But then it would seem that the property is Socrates would be constructable out of qualitative properties. So it would be reducible after all, contrary to our assumption. One might thus be led to think that haecceitism can only be bought at the cost of relinquishing the relevant version of PII. Given the importance of the latter principle to Leibniz’s philosophy, one is encouraged to agree that Leibniz on reflection must admit that this cost is too high.                               ’         We began with a robust Leibnizian metaphysic of de re modality, with its familiar strong essentialist component; we seem left with an anti-haec¹⁴ This point is emphasized by Robert Adams in ‘‘Primitive Thisness and Primitive Identity.’’ The reductio offered below develops a line of thought implicit at pp. – of his essay.

The importance of haecceitism to Leibniz’s philosophy



ceitist Leibniz on our hands. What, if anything, is there to be salvaged and defended of the haecceitist undercurrent in standard readings of Leibniz – readings that explicitly or implicitly reckon him perfectly able to make sense of de re modal assertions and transworld identity claims? Is one to judge anti-haecceitism as closest to Leibniz’s heart, forgiving him and our short-sighted readings of him for the bits of haecceitism that seem to persist in his philosophy? . Haecceitism, PSR and PII One shortcoming of current discussions of Leibniz is that often little more than lipservice is paid to haecceitist strains in his work. Many commentators will say or imply that de re modal questions are there to be found in Leibniz – questions about whether this same individual could have failed to sin or cross the Rubicon or have some particular degree of strength – only to proceed with a treatment of Leibnizian modality in the purely de dicto terms of concept containment and proof-theoretical properties of propositions. Much of the fault must inevitably rest at Leibniz’s door: he said too little about modal connections between individuals themselves and their properties, and almost certainly did not have a clear vision of the full range of modal concepts at work in his own philosophy. But there is no profit in recognizing his haecceitist commitments only long enough to ignore them. We remain convinced that Leibniz does endorse the de re modality crucial to his essentialism and the intelligibility of transworld identity judgments. So let us dig in our heels, and ask what arguments might be brought to bear in justifying that view of Leibniz. Rather than rehearsing familiar territory (super-, strong, and moderate essentialism), in this section we want to think carefully about the relationship between haecceitism and two important Leibnizian principles: the Identity of Indiscernibles (PII) and the Principle of Sufficient Reason (PSR). One can begin to see how such principles bear on the haecceitism/anti-haecceitism issue by considering what might be said about PII and PSR were one to think that a full account of reality can be given in terms of general propositions (as understood above). It was noted earlier in § that one might be led to think that haecceitism can only be bought at the cost of relinquishing PII. Part of the task, then, of justifying the claim that Leibniz can and does endorse the de re modality crucial to his essentialism and his verdicts about transworld identity, is to see whether Leibniz’s endorsement of PII does in fact commit him to anti-haecceitism.



Haecceitism and anti-haecceitism

It is worth distinguishing intra- from inter-world versions of PII: Inter-PII: If two possible individuals are transworld indiscernible, then they are transworld identical. Intra-PII: No two individuals at a particular world are indiscernible. Inter-PII pretty obviously runs into trouble if there are no singular truths to underwrite de re modality. If one cannot take transworld identity claims at face value, then one cannot take the interworld principle at face value. It would have to be dismissed as unintelligible or as an elliptical way of saying something about transworld qualitative similarity, as the anti-haecceitist is wont to do. Consider next Intra-PII, which connects with haecceitism in less obvious but more interesting ways. Robert Adams has argued that one who thinks that the world can be fully described in terms of general propositions is committed to accepting that version of PII. His argument turns on the fact that such a view only admits qualitative properties into an account of the world.¹⁵ Adams’s line of thought is this: suppose one agreed that the infamous Max Black example (say, of a possible world containing only two qualitatively identical spheres) shows Intra-PII to be false.¹⁶ Then the property of being identical with one of those spheres in particular – the thisness of a sphere – cannot be constructed out of qualitative properties. So there are thisnesses that are not qualitative. Thus, not all properties are qualitative, hence not all propositions are general. It is important to see that this is not a successful argument. For mightn’t the anti-haecceitist, faced with the Black challenge, alternatively conclude that there are no such things as the thisnesses of individuals in that world? That is to say, perhaps there is no such property as being identical with one of those spheres in particular. He may insist that the ¹⁵ In his discussion of primitive thisnesses (Scotistic haecceities) versus qualitative (Leibnizian) thisnesses, Adams (ibid.) emphasizes what he sees as the ‘‘necessary connection between the Identity of Indiscernibles. . . and Leibniz’s conception of thisnesses as suchnesses’’ (p. ). Says Adams, ‘‘the purely qualitative conception of individuality stands or falls with the doctrine of Identity of Indiscernibles’’ (ibid.): and after claiming that one way of establishing the existence of (primitive) thisnesses distinct from suchnesses is to ‘‘exhibit possible cases in which two things would possess all the same suchnesses . . .’’ [i.e. find counterexamples to Intra-PII], he says that ‘‘a refutation of [PII] is precisely what is required for a defense of nonqualitative thisnesses’’ (ibid.). Later, Adams sets in opposition the view ‘‘on the one hand, that all thisnesses are purely qualitative’’ with the view that ‘‘on the other hand, we reject the Identity of Indiscernibles in favor of nonqualitative thisnesses’’ (ibid. pp. –). This implies that a Leibnizian cannot at once resist a commitment to non-qualitative thisnesses while allowing that Intra-PII be shown false. ¹⁶ Max Black, ‘‘The Identity of Indiscernibles.’’

The importance of haecceitism to Leibniz’s philosophy



full story about that world be captured by general propositions, of the sort ∃x(x is a sphere), ∃x∃y(x is a sphere and y is a sphere and x " y), and so on. If all the truths about that world can be fully captured in terms of such general propositions, then there doesn’t seem to be any such thing as a thisness, a property of being identical to one of the spheres in particular. It is a world of no thisnesses, no primitive or qualitative haecceities.¹⁷ While the preceding reflections suggest that the generalist needn’t be nearly so embarrassed to reject Intra-PII as some would have us believe, they serve also to highlight an interesting and important consequence of the view that all truths are general. There is a vast multiplication of worlds allowed by the typical haecceitist that is unintelligible for the generalist. Suppose one allowed the Black scenario. One might then be allowed to say, pointing to two actual qualitatively similar spheres (call them ‘Bill’ and ‘Ben’), that there is one Black world W where they are the sole occupants, and then, pointing to two other such spheres in our world (call them ‘Jill’ and ‘Jane’), that there is a distinct Black world W* where they are the sole occupants. (Of course neither pair exhibits exact similarity at the actual world. But, one shall say, the dissimilarity of the pairs is an accidental feature of the actual world.) In this way it emerges that, according to the haecceitist, there exists a vast multiplicity of Black worlds where each sphere in each world has precisely the same qualitative properties. There is one world where Bill and Ben exist, are  yard apart, are each  inches in diameter, are each homogeneous, and so on, another where Jill and Jane exist, are  yard apart, are each  inches in diameter, are each homogeneous, and so on. But this the generalist cannot allow. For if a Black world is completely described by such truths as ∃x(x is a sphere), ∃x∃y(x is a sphere and y is a sphere and x " y), and so on, then there is no way of conceptually multiplying them (as above) without changing the qualitative predicates in those world descriptions. If world W is identical with world W* just in the case that all and only the general propositions true at W are true at W*, then there is no such plurality of worlds as the typical haecceitist posits, and in ¹⁷ So Adams’s thought that generalism commits one to intra-world PII is wrong. That is not to deny that generalism, together with the thesis that all relational facts are reducible to non-relational ones, may commit one to intra-world PII. (After all, the generalist story about the Black world does trade on a primitive relation of difference.) So Leibniz may have a resource for defending intra-world PII even were he a generalist. But, as we shall see, a Leibnizian defense of PII could not then proceed in the manner that it normally does, namely, by switching considerations. In this connection, note that in chapter  we locate in Leibniz two styles of argument for PII – which we call Divine Preference (exemplified by switching arguments) and No Reason – recognizing that only the former relies on inter-world considerations.



Haecceitism and anti-haecceitism

particular no pair of distinct worlds differing only in the fact that Bill and Ben inhabit one world, Jill and Jane another. The thought that one can multiply worlds in the manner allowed by the typical haecceitist will be diagnosed by the generalist as proceeding from the confused assumption that one can without much ado take claims of transworld identity at face value. This will be important for what follows.¹⁸ Let us turn to the most familiar style of Leibnizian argument for the claim that there are not any two perfectly indistinguishable things – that is, Intra-PII, as applied to the actual world. The argument, which appears in the Clarke correspondence and elsewhere,¹⁹ appeals to PSR. If there were two such qualitatively indistinguishable individuals, God wouldn’t – so to speak – know ‘‘which way around’’ to put them in the world, and so would have no sufficient reason to create one world rather than the other where they are ‘‘switched.’’ Often this is read as supporting the necessary version of Intra-PII. But much of the time, Leibniz is only trying to show that Intra-PII, as applied to the actual world, is true. In § of Leibniz’s Fifth Letter to Clarke, he writes that ‘‘When I deny that there are two drops of water perfectly alike, or any two other bodies ¹⁸ It may also be important for the previous paragraph, if one wished to object that our argument against Adams succeeds only if we show that, in addition to primitive and qualitative thisnesses, no thisnesses is a genuine possibility. Presumably Adams’s argument would succeed, on this view of things, only if Adams shows that thisnesses are a genuine necessity. Setting this (properly) aside, suppose that our generalist does (i) allow for the possibility of Black worlds, and so denies PII for individuals, but also (ii) rejects the vast multiplicity of qualitatively identical worlds and so endorses PII for worlds. Such a generalist will not then want to permit non-supervenient haecceities, since this would violate (ii); but neither would such a generalist admit that each sphere in a Black world has its haecceity, constructible out of general properties, since this isn’t permitted by (i). Hence there are no thisnesses at Black worlds. One might object that if we allow for the Black world containing two spheres A and B, then we must allow for two other worlds where A and B, respectively, exist alone: (i) entails the denial of (ii). But surely (i) entails the denial of (ii) only if one adds the premise that A can exist without B, and B without A, where ‘A’ and ‘B’ pick out distinct spheres independently of a description. The generalist won’t allow that ‘A can exist without B’ expresses a genuinely singular proposition. What such a sentence means is that possibly there is a sphere that is F, G, H . . . and there is nothing else. And now we can see that just as our anti-haecceitist will not permit the multiplication of qualitatively identical Black worlds using numerically distinct spheres, so the anti-haecceitist will not permit this multiplication by conceptually removing one sphere and then putatively thinking of a distinct world by conceptually removing the other. Indeed, the latter maneuver requires the former, since in effect one is multiplying single-sphere worlds with these supposedly different counterfactual possibilities. ¹⁹ The connection between PSR and PII, to be taken up at length in chapter , is broached explicitly at C : L ; at G ,: L ; and implicitly at G ,: L . The style of argument discussed here – and which convincingly betrays Leibniz’s haecceitism (in Kaplan’s sense) – is what we call in chapter  the ‘‘Divine Preference’’ argument. It is less obvious that a distinct, much less-discussed style of Leibnizian argument for PII – what we call ‘‘No Reason’’ – requires de re modality (although a close cousin that we also discuss there, the No Reason argument for the numerical distinctness of transworld discernibles, obviously does import de re modality in a very direct way).

The importance of haecceitism to Leibniz’s philosophy



indiscernible from each other, I don’t say ’tis absolutely impossible to suppose them but that ’tis a thing contrary to the divine wisdom, and which consequently does not exist’’ (G , –: L ). The very next sentence (beginning § of the letter) is also modally timid: ‘‘I own that if two things perfectly indiscernible from each other did exist they would be two, but that supposition is false and contrary to the grand principle of reason.’’ Evidence for a modally timid PII will be taken up in chapter . For now, the crucial point to notice is that Leibniz’s argument presumes that if there were such a pair of indiscernibles, then there would also be a world where this pair is switched. But as we have already seen, this line of thought is intelligible only if one grants that there is more to a world than the general propositions true of it. Hence for PSR to work as an argument for the thesis that there are no actually indiscernible things, one must admit the intelligibility of some form of singular propositions. If Leibniz were to relinquish any version of haecceitism altogether – of the notion of transworld identity as a meaningful one – then not only would his recognition of de re modalities generally, and his strongly essentialist position more specifically, become senseless, but just as importantly the most familiar deployment of PSR to obtain conclusions about the lack of actual non-identical indiscernibles would break down.²⁰ One thus comes to see that some form of haecceitism is central to the Leibnizian metaphysic. For not only can the anti-haecceitist reject Intra-PII; but moreover, even granting PSR, there looks to be no good reason at all for the anti-haecceitist not to reject it. Given anti-haecceitism, one could score an easy victory for the enemy in this pivotal battle of the war with Clarke and the Newtonians.²¹ . Strong and weak haecceitism Leibniz’s views on PII not only show that he is committed to haecceitism. They also show what broad sort of haecceitism he must be ²⁰ It follows that the switching arguments Leibniz uses against the existence of points in space and moments in time then simply collapses, for that argument is merely a special case of the switching arguments for the intra-world PII thesis. Thanks to Brent Mundy here. (As noted, we shall consider in chapter  a much less familiar style of PSR argument for PII (the No Reason argument) not so obviously dependent upon haecceitism. But while recognizing the availability to Leibniz of a second style of PSR argument for PII, one should not lose sight of the fact that he is not merely willing to use, but indeed generally favors, the style of PSR-to-PII argument discussed here, and that this provides solid evidence of a serious commitment to haecceitism in Kaplan’s sense.) ²¹ So the importance of the previous paragraph save one is this: once one sees that – and how – the anti-haecceitist can allow Black worlds, one can see that the anti-haecceitist oughtn’t be tempted by switching arguments, even if she were fond of PSR.



Haecceitism and anti-haecceitism

committed to. Let us distinguish strong haecceitism from weak haecceitism. According to strong haecceitism, on the one hand, the singular propositions true at a world stand on their own: if there are transworld identities, they do not in any way supervene on the general propositions true at a world. Here are the sorts of things a strong haecceitist might then be prepared to say: ‘‘There is a possible world which enjoys exactly the same distribution of properties as our own world, but where Socrates does not exist. There is a pair of possible worlds sharing precisely the same distribution of properties, but where two individuals in one world are ‘switched’ in the other.’’ The weak haecceitist, on the other hand, does indeed admit singular propositions, but insists that they supervene on general propositions. Necessarily, for any singular proposition P, if P is true at a world, then there is some set of general propositions at that world whose truth is sufficient for P.²² (We do not intend any claim of logical asymmetry or explanatory direction to be built into ‘supervenience’ as we are using it here. To say family A supervenes on family B means that there can’t be an A-difference without a B-difference. But this does not entail that B fails to supervene on A (thus, for example, the weak haecceitist can consistently allow that the set of singular propositions at a world also uniquely fixes the general truths there). Nor does it entail that family A explains family B (thus the weak haecceitist’s supervenience thesis does not commit him to the view that general facts explain singular ones). This will all become important in due course.) Now it is clear that strong haecceitism would be anathema to Leibniz. One can fairly imagine him saying: ‘‘There can be no difference between two things solo numero; that is, no real difference is merely difference in thing alone. To conceive two worlds exactly alike save only that one contains a certain object (Socrates, say) where the other contains a numerically different but indistinguishable object (Schmocrates) is to conceive of mere fictions, between which God could have no sufficient reason for choosing.’’ One is forced to conclude that weak haecceitism is the view that best suits Leibniz’s metaphysical picture. While Leibniz’s views on PII are indeed pressures against strong haecceitism, a closer inspection of his ²² For those inclined to the quick response that weak haecceitism is crazy or unintelligible, consider that most of us are already weak haecceitists about numbers and other abstract objects: most of us reckon de re modal talk about numbers perfectly intelligible (‘The number five’ being a paradigm Kripkean rigid designator) while also tacitly acquiescing in some version of PII for abstract objects. See § of John O’Leary-Hawthorne and J. A. Cover, ‘‘Framing the Thisness Issue,’’ for more on this matter.

The importance of haecceitism to Leibniz’s philosophy



thinking does not brand him an anti-haecceitist, but rather a weak haecceitist. Happily, ascribing weak haecceitism to Leibniz does more than rescue the intelligibility of his arguments concerning PII and judgments of transworld identity and diversity. It supplies independent motivation for (and so, partial explanation of ) Leibniz’s commitment to strong essentialism. This is because it is extremely difficult to prevent weak haecceitism from collapsing into strong haecceitism without such a strongly essentialist picture. Let us explain this point. Suppose one accepted most commonplace modal assertions of the typical Kripkean sort – such claims as, ‘The spatio-temporal trajectory of a physical object is accidental to it,’ or ‘The exact size of an object is accidental to it.’ Suppose one now imagined a world W containing only two spheres in space, one slightly larger than the other. Suppose further that one allowed singular propositions about these spheres, as the haecceitist must. ‘Joe is larger than Bill,’ for example, might express one such true proposition. Now if the size and location of a sphere are accidental to it, it would seem to follow that Bill could have been where Joe is and a bit larger (indeed, as large as Joe actually is), and Joe where Bill is and a bit smaller (indeed, as small as Bill actually is). One is thus encouraged to conclude that there is a possible world W* where the distribution of properties is just the same as in W but where Joe and Bill are switched. One thus arrives at a view entailing strong haecceitism. The only way of blocking the view, it seems, is to insist that such properties as size and location and the like cannot all be accidental – a relatively strong essentialist result.²³ This is no mere stroke of good luck: one begins to see strong essentialism, PII, PSR, and weak haecceitism as intimately connected in such a way as to form inseparable aspects of a sweeping metaphysical vision. One might have expected as much from Leibniz. On the heels of our opening quotation from David Kaplan, we envisioned asking an omniscient being to survey all possible worlds, construed on the generalist picture, and to answer questions requiring the intelligibility of transworld identity. It seemed then that our imagined being would be unable to make much sense of such questions. On the present reading of Leibniz, one is invited to entertain the possibility of a view according to which the singular propositions at a world ²³ This is a philosophically significant point. Even those of us who don’t wish to endorse PSR and PII across the board may well balk at the multiplication of worlds that strong haecceitism allows. What many of us haven’t seen are the strongly essentialist consequences that such an attitude is likely to have.



Haecceitism and anti-haecceitism

supervene on the general ones. According to (this) Leibniz, Kaplan’s distinction is a false dichotomy: one could be neither a haecceitist of the sort that reckons facts about transworld identity as brute metaphysical facts, independent of the properties in which individuals are clothed, nor an anti-haecceitist that reckons transworld identity judgments unintelligible. For the weak haecceitist, transworld identity makes sense, but is a function of general truths at worlds. So the concept of transworld identity is not independent of similarity after all – but neither is it, for Leibniz, a function of our interests: there is one similarity relation, fixed by sameness of intrinsic monadic properties of individual substances. That is Leibniz’s strong essentialism (consistent with, but not entailing, superessentialism). (A crucial respect in which weak haecceitism differs from anti-haecceitism bears emphasis here. To say that one family of truths supervenes on another is not to say that the former are nothing over and above the latter: even if truths about mind supervene on truths of physics, it does not follow that truths of mind are truths of physics. While the antihaecceitist insists that modal judgments of sameness and difference are nothing over and above truths of qualitative similarity, the weak haecceitist, though acquiescing to deny the independence of the singular from the general, nevertheless denies that the former are nothing over and above the latter.)            ’                ? We have offered an interpretation of Leibniz that does justice to apparently diverging strands of his philosophy. Or anyway, we have offered the beginnings of an interpretation that attempts to do them justice: what remains unclear is the extent to which weak haecceitism can be rendered intelligible. Recall from § those aspects of Leibniz’s thought that looked to sort ill with haecceitism, strong or weak: his predicate-in-subject doctrine and his genuinely God’s eye view of truth. Given these, it must be asked whether Leibniz is entitled to his brand of haecceitism, and whether it is a genuinely possible position after all. This question is especially pressing in light of the following apparent difficulty, unique to Leibniz’s weak haecceitism. . Rationalism and singular propositions Consider what is right about calling Leibniz a ‘‘rationalist.’’ Meta-

How is Leibniz’s haecceitism possible?



physics is above all a science of the intelligible nature of being.²⁴ For Leibniz, this means in part that metaphysical inquiry and its aim of complete knowledge must answer to principles of reason, because the world itself answers to them in being above all intelligible: the nature of reality is in principle accessible to reason alone. The truths of metaphysics – truths about what there is and the nature of what there is – might then be reckoned the objects of a demonstrative, a priori rational science, quite on a par with geometry. This picture is reflected in Leibniz’s view that the intelligible world is both ‘‘in God and in some way also in us’’ (G ,: L ), though of course our finite minds can apprehend many existential truths only by help of the senses. God, on the other hand, has infallible, a priori knowledge of all worlds as abstractly possible and of truths at our own as actual.²⁵ In short, reality itself has a logical form, to which all true propositions and relations among them conform in accord with principles of reason. Where (for example) the sufficient reasons for our world being thus are to be found in some deeper, logically prior fact that it is so, truths expressing these facts cannot fail to stand in appropriate logical relations: to suppose otherwise is to abandon Leibniz’s rationalist vision of metaphysics as an a priori rational science. With these reflections before us, think again about weak haecceitism and singular propositions. It seems clear enough that Leibniz frowns on the notion of supervenient facts that are not in principle deducible a priori from its foundational, subvenient base.²⁶ Can the singular propositions true of a world be deduced a priori from the general propositions about that world? It is not obvious that they can. Suppose one is omniscient about the distribution of properties at a particular world, and suppose one then asks oneself whether Alexander exists at that world (where ‘Alexander exists’ expresses a singular proposition). Can one deduce that answer a priori? Apparently not. Even if singular truths supervene upon general truths, it remains the case that the statement ‘Alexander exists’ is not analytically implied by anything general. In order to deduce whether Alexander exists, one needs in ²⁴ See, for example, G , where metaphysics is characterized as ‘‘a science which has being for its object,’’ and C  where it is called the ‘‘science of intelligibles.’’ In connection with this theme we recommend Donald Rutherford’s discussion in chapter  of his Leibniz and the Rational Order of Nature. ²⁵ See, for example, § of Causa Dei (God’s knowledge ‘‘comprehends equally everything possible and everything actual’’) and G , (‘‘all things are understood by God a priori . . . for he does not need experience’’). ²⁶ This desideratum of Leibniz’s rationalism is implicit in the picture emerging from chapter  on inter-monadic relations.



Haecceitism and anti-haecceitism

addition to the general propositions about that world a further set of propositions giving the necessary and sufficient conditions for something’s being Alexander. By such brute introduction of auxiliary singular propositions, one would controvert Leibniz’s rationalistic view that all truths about the world are a priori deducible from the fundamental features of that world. In short, the challenge takes the form of a dilemma. Leibniz does of course believe that the truth of ‘Alexander exists’ is entailed by certain general truths: that is his weak haecceitism. But it is unclear how it can be entailed, except either by (a) the entailment being brute and hence not a priori accessible via the fundamental features of the world (threatening Leibniz’s rationalism), or else by (b) ‘Alexander exists’ being elliptical for various general propositions (threatening the collapse of Leibniz’s weak haecceitism into anti-haecceitism, according to which there are only general propositions). The details of this challenge will be addressed shortly. What it underscores here is a more general need for the weak haecceitist to explain how room can be made for singular propositions. In Leibniz’s own case, certain aspects of his work seem to make it difficult to give an intelligible semantic story about de re thoughts at all; in particular one must ask whether the common Russellian understanding of singular propositions conflicts with Leibniz’s view of God as the locus of truth. According to Leibniz, God has a full conception of what each world would be like were He to create it, and decides to make one of those conceptions actual. What He conceives with perfect distinctness (‘‘adequately’’), we can but think confusedly and obscurely. Though creatures grasp less perfectly the ‘‘ideas’’ (concepts and propositions) that are ‘‘in God himself’’ (G ,: L ), we express truths by expressing contents of the divine understanding.²⁷ Leibniz, as much as anyone, subscribes to a realism which is to be cashed out in terms of a God’s eye view of the world. One possible source of conflict between the Russellian view and Leibniz’s metaphysic concerns its contention (call it ‘‘Russellian actualism’’) that there are no singular propositions about non-actual individuals.²⁸ Of course, if those individuals had existed, there would have been singular propositions about them. But they don’t and there ²⁷ Says Leibniz in the New Essays .v.: ‘‘[W]hen God displays a truth to us, we come to possess the truth which is in his understanding, for although his ideas are infinitely more perfect and extensive than ours, they still have the same relationship that ours do’’ (RB ). See also NE .iv.: RB  together with NE .iv.: RB  for Leibniz’s claim that all our ideas have their archetype in the divine intellect. ²⁸ See, for example, Robert M. Adams, ‘‘Actualism and Thisness,’’ and Gregory W. Fitch, ‘‘The Nature of Singular Propositions.’’

How is Leibniz’s haecceitism possible?



aren’t. (Barring a Meinongian ontology of non-existent objects, this view is mandatory on the Russellian account.) Several Leibnizian challenges to Russellian propositions may be offered here. The first challenge, though probably illusory, is instructive. Imagine God before He has decreed which world, among infinitely many possible, is to be created; at this juncture all worlds are equal candidates (cf. § of Causa Dei). If, in entertaining these, God thinks de re truths about any worlds, He does so about all of them. Hence, on the actualist view, He must do so about none of them, including our own. What is likely mistaken about this challenge is that it represents God as deciding at a particular time to create. Presumably God knows from all eternity what to create, and so knows from all time which individuals are the actual ones.²⁹ But there is another, related challenge that is less easily written off. Consider worlds containing only non-actual individuals. If Russellian actualism is correct, then there are no singular propositions about those. But then it seems one cannot take questions about transworld identity and diversity between (say, our) Adam and individuals in those nonactual worlds at face value. Yet it is clear that Leibniz wants to take such questions at face value. Indeed this is especially so on the strong- or superessentialist readings of him, which entail that most or all individuals are world-bound. It would be inappropriate to take this argument (or the previous one) as showing that there are truths which God doesn’t know (or which He comes into as new items of knowledge at creation). But the argument does point to the fact that if one were to ground the intelligibility of assertions and denials of transworld identity in Russellian propositions, there would be lots of truths and falsehoods that many of us, including Leibniz, think exist that in fact do not.³⁰ ²⁹ God’s scientia visionis concerning this actual created world is, for Leibniz, a species of a priori scientia simplicis intelligentiae, differing from such eternal knowledge of all other abstractly possible worlds only in containing ‘‘the reflexive knowledge he has of his own decrees’’ (Causa Dei, §). ³⁰ Some philosophers have expressed a related concern about whether we can in principle think singular propositions about past and future individuals. Call this a ‘‘presentist’’ view of singular propositions. Others have claimed that some singular propositions can only be expressed by certain people with a privileged place in the world. This is especially encouraged by a consideration of demonstratives and indexicals. It is easy to think that singular propositions of the form ‘I am F’ or ‘It is F-ing now’ can only be expressed by me and by someone existing now (respectively). Call this an ‘‘indexical’’ view of singular propositions. The presentist and indexical views, if correct, clash in even more obvious ways with Leibniz’s claim that God is the locus of truth, knowing all truths from all eternity. To preserve the relevant bits of philosophical theology, a good Leibnizian would apparently have to insist that the presentist view is simply wrong, and that the indexical view mistakes cases where a single proposition is represented in different ways for cases where different propositions are being expressed (in different ways).

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Haecceitism and anti-haecceitism

A more obvious Leibnizian obstacle to the Russellian conception is this: since individual substances themselves are not in the mind of God, one cannot consistently hold that truths are entities in the divine understanding and also that individuals are constituents of some truths. The point is not a general one about how representing or entertaining certain propositions (by us or by God) is possible: it is consistent to think of concepts pertaining to individual substances as being in the mind of God (and dimly, for Leibniz, in us), but not the individual substances themselves. In what follows we’ll examine several ways in which one might respond to the uneasy position mapped out thus far. To the extent that Leibniz’s own view remains obscure, the proposals that follow will be unavoidably speculative: none of them is explicitly paraded by Leibniz himself. . Some false starts One salvage of Leibniz, presumably the most conservative, is just to insist that his supposedly unequivocal de re modal claims are not de re after all. On this proposal, the ‘‘natural interpretation’’ (of the complete concept doctrine, that all proper names express lists or conjunctions of general properties) is the correct interpretation, and Leibniz is a straight anti-haecceitist. The conservative proposal thus retains many of the prevailing treatments of Leibniz, of handling all modality in de dicto terms. When Leibniz offers modal sentences about you and your strength or Judas and his sin, he is in fact not expressing claims about you or Judas, but rather is expressing claims about other claims or about concepts – about the modal character of certain propositions or of relations among their concept-terms. Such a proposal indeed leaves many problems behind, but it does so rather more by turning one’s back on them than by seeking out resources Leibniz may have had for their solution. Moreover the conservative proposal does not reconcile crucial bits of what Leibniz says: in particular, Leibniz should not be saying what he does about indiscernibility and PSR. What exactly could the straight anti-haecceitist intelligibly mean by saying, for example, that God would have no reason on which to base his decision as to which way around to place the spheres?³¹ ³¹ Perhaps the anti-haecceitist – Leibniz on the conservative reading – will be said to mean something like this: ‘‘Once God has willed to create individuals meeting certain general descriptions, if there were some further decision to be made about ‘which individual is which’ or ‘which way

How is Leibniz’s haecceitism possible?



(Again, one might interpret Leibniz’s thought as running along the following lines: ‘‘If Intra-PII were incorrect, then there would be primitive thisnesses; but if there were primitive thisnesses then PSR would be violated; so by modus tollens, PII is correct.’’ On this interpretation, Leibniz thinks all truths are de dicto and sees an endorsement of Intra-PII as necessary to sustain this. This captures Adams’s interpretation of Leibniz. If it is the correct interpretation – and it may be – then the conclusion recommended by our earlier reflections is clear: Leibniz [with Adams] is philosophically mistaken. A denial of primitive thisnesses does not require that we endorse PII.) A considerably different salvage is suggested by the ‘‘possible-in-itsown-nature’’ strategy that Leibniz applied mostly to worlds,³² where (now) we apply to individuals certain modal predicates having no further basis in facts about alternative possible ways God might have created. That is, we might help ourselves to primitive modal predicates such as ‘possibly F’ (and such other modal predicates as are definable in terms of it), and locate these in individual complete concepts. In this manner one can preserve de re modality in such a way as to render intelligible talk of individuals existing or failing to exist at worlds.³³ But the advance this effort makes over the conservative approach, in preserving de re modality, is tempered by the shortcoming they share: we still cannot make good sense of Leibniz’s thought about PSR, PII, and switching. Suppose a Black world to be described along such lines as around to place them,’ then He could not possibly have any basis for making it; hence rationalist principles of reason show that there is no such decision to be made; hence it is simply the propositions about what general descriptions are instantiated that make up the whole truth.’’ But this proposal strips Leibniz’s switching arguments of any purchase whatever in their deployment against intra-world indiscernibles. For crucial to those arguments is God’s being confronted with an insoluble dilemma, a decision that can’t be made. Consistently with the proposed reading’s ‘‘If there were some further decision to be made about which is which . . .’’ there could for all that turn out to be intra-world indiscernibles, since on the generalist, anti-haecceitist position no further decision can intelligibly arise about ‘‘which is which.’’ By ignoring the possibility that the antecedent of the proposed reading might turn out always to be false, the conservative gloss turns Leibniz’s switching arguments into patently bad ones. (Of course, if one let ‘Bill’ be shorthand for the individual that’s F, G . . . and R-to-y, and ‘Bob’ be shorthand for the individual that’s F, G . . . and not R-to-y, then of course ‘‘which is which?’’ becomes intelligible; but no dilemma for divine decision-making can be generated out of this – having built in an answer to which is which. Again: Leibniz’s arguments need the decision dilemma. The conservative, anti-haecceitist Leibniz isn’t Leibniz.) ³² Leibniz speaks of worlds or states of affairs being intrinsically possible ‘‘in their own nature,’’ independently of God’s will (and so confronting Him as candidates for creation) in De libertate (see Grua –), the Confessio philosophi (see A ..–), and Discourse §. It seems also to be at work in the Theodicy. What we say below should not be taken to imply that Leibniz himself used ‘in its own nature’ to mean what we mean by ‘primitively’. ³³ The primitive de re modal locutions suffice to define existence at worlds (rather than defining de re notions in terms of worlds). See Roderick M. Chisholm, ‘‘Possibility without Haecceity.’’

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Haecceitism and anti-haecceitism

∃x∃y(x is a large sphere and y is a large sphere and x " y and x is possibly small and possibly a poached egg and y is possibly small and possibly a poached egg . . . [etc.]). Assuming – as seems obvious – that there is no property accidental to one sphere that is essential to another, this description does not allow the duplication of worlds by switching, since it doesn’t allow for the property of being identical with one of the spheres in particular. A distinct but related proposal may be extracted from a view of Leibnizian predicates noted by Benson Mates. On Mates’s account,³⁴ since Alexander has the attribute King in   but lacks that attribute in  , we must view a complete individual concept not as a set of properties, but as a series of such sets ordered by time. Now an alternative, if non-Leibnizian, way of handling the fact that a single individual Alexander exists at different times (thus at one, so at another) is to view properties themselves (or the predicates expressing them) as temporally indexed, as having a time-specification built into them. Such a trans-temporal account as this suggests the possibility of doing something similar for a transworld account: allow for a single individual to exist at different worlds by viewing properties as world-indexed. There is no good evidence that Leibniz in fact thought of this alternative, though it does go some distance toward reconciling Leibniz’s completeconcept and predicate-in-subject doctrines with de re modality. But it must be acknowledged that the deployment of primitive, unexplained world-names figuring in such a semantics looks distinctly unLeibnizian. Leibniz is most eager to explain worlds in terms of (compossible) concepts; by contrast, this strategy seems to individuate concepts by invoking a haecceitistic conception of worlds.³⁵ . Salvaging weak haecceitism So we return to haecceitism, and to those aspects of Leibniz’s thought (the predicate-in-subject doctrine, his God’s eye realism about truth, and his rationalism) that look most troublesome alongside it. The question yet on board is whether the distinctive brand of haecceitism emerging from earlier sections is coherent. As a step toward broaching a ³⁴ See Mates, The Philosophy of Leibniz, pp. – and –, and the related proposal by Robert Adams in Leibniz, pp. –. ³⁵ The relation of this strategy to Intra-PII and PSR is complicated. Indexing allows for the multiplication of worlds by multiplication of world-names. It allows for multiplication, but doesn’t entail it: one could argue that no two worlds are indiscernible, and that this constrains the number of world-names available for indexing. In this way, Intra-PII, PSR and indexing would be compatible.

How is Leibniz’s haecceitism possible?



final speculative salvage of Leibniz, consider his view that the essence of a thing is fundamentally the real possibility of that thing. If grasping the essence of a thing is being in a position to see the real possibility of that thing, then clearly here is one fact about what it would be to have in one’s cognitive possession (to understand) an individual concept: it is to be able to see a priori the possibility of a thing. This may be seen to reinforce the tension between Leibniz’s rationalism and contemporary views of singular propositions. The typical way of viewing singular propositions, as they figure in thought or language, is that one gets to think them via demonstrative acts;³⁶ on this view, one thinks them a posteriori. Now the standard account of singular terms as having denotation but no connotation poses no problem for one’s being able to think singular propositions, so long as the mechanism for our thinking them is understood in this a posteriori sort of way. Yet (as we have noted earlier) it is important to Leibniz that singular propositions be, first, graspable a priori, and second, done so in a way that allows one to see a priori the real possibility of the thing that singular proposition is about. But, crucially, singular terms as standardly conceived don’t look to satisfy this requirement. Grasping or understanding a ‘‘colorless’’ singular term does not seem like the sort of thing that can be done a priori. Moreover, if (per impossibile) one were to grasp it a priori, how is it that one would thereby be able to see that it possibly referred? Unless grasping a singular thought brought with it, eo ipso, a good deal of information about the relevant individual in question, grasping a singular thought a priori would not enable one to see the real possibility of the individual. In tandem with this line of thought, one can, in Leibniz’s stead, thus rule out any picture of singular propositions which reinforces the idea that singular terms have denotation but no connotation. Consider for example Scotistic haecceities – colorless entities with no a priori connection to properties. One may ask in Leibniz’s place: How is one to grasp such a haecceity a priori? And if one did grasp it, how is one to see a priori that it is possibly instantiated? This all serves as a prolegomenon to understanding what singular propositions would have to be like in order for Leibniz’s brand of weak haecceitism, coupled with his God’s eye realism about truth and his rationalism, to make sense. As we learned earlier, they cannot be Russellian, and as we have just seen, their subjects cannot have denotation without connotation. These constraints on a Leibnizian view of modality do not, it should be noted, conflict with the formal semantics of ³⁶ Note that this epistemology of singular propositions has a natural affinity with Russellian actualism.

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Haecceitism and anti-haecceitism

contemporary de re modality. The device used by most contemporary semantics of de re modality – assigning to each singular term a function that has the same value in every context of evaluation where it has a value – is in itself neutral on the epistemology of singular propositions (as well as on what metaphysical gloss we are going to give on singular propositions). What we shall do is offer a Leibnizian story that preserves the de re modal semantics and that, relatedly, allows talk of transworld identity and difference to be taken at face value,³⁷ but which departs significantly from a good deal of the epistemology and metaphysics nowadays accompanying that story. Let us then, on Leibniz’s behalf, try to re-construe the nature of Scotistic subjects of singular propositions, and their relation to the predicates of the proposition. Perhaps the singular haecceitistic subject (also) has or implies a connotation, some Leibnizian conceptual content, so that they do a priori imply certain characteristics of the individual; and perhaps this implication is not a formal, deductive matter at all. This last proposal, that the predicates be a priori contained in the subject without being formally deducible from them, points to what is wrong with the rationalist challenge to weak haecceitism posed earlier. It is no worry that singular propositions are not formally extractable from general ones, or the general from singular. For Leibniz, God sees a priori, though not via deductive means trading upon logical form, what is there to be seen in the contents of individual concepts. (Indeed, Leibniz thinks that God alone grasps individual concepts.) The formal deducibility picture – an artifact of the natural interpretation of names as disguised lists or conjunctions – is not what a rationalist’s a priorism of the Leibnizian stripe requires. This suggests a further re-construal of the relation of individual concepts to predicates. The predicate-in-subject doctrine is consistent with viewing the relation of predicate to subject as importantly analogous to the analytic truth, Whatever is red is colored. In bygone days philosophers puzzled over the fact that while this expression is analytic, it is nevertheless inappropriate to think of the concept Red as any articulated whole made up of semantic components: to do so is to invite the misguided question of what component or components must be added to coloredness to get redness. To be analytic, then, or for a predicate ³⁷ We remind the reader that this isn’t an automatic consequence of endorsing the contemporary formalism of de re modality; the counterpart theorist, for example, might use the formalism without taking de re modal talk at face value (just as the four-dimensionalist about physical objects might use diachronic identity talk but give ‘‘identity’’ an idiomatic reading).

How is Leibniz’s haecceitism possible?



to be contained in a subject, one needn’t suppose the subject to have a complexity of the sort that allows it to be represented as anything like a conjunction: analyticity needn’t be explained in terms of a predicate appearing as a conjunct of a perspicuously represented subject.³⁸ Given weak haecceitism, and given that all truths about an individual are contained in its individual concept, we have been forced to ask anew what individual concepts must be like if those Leibnizian commitments are in fact correct. The answer, in part, is that individual concepts must be acknowledged as having a dual aspect, of both singularity and generality. In particular, while an individual concept is such that it contains – in some sense of ‘contains’ – all the intrinsic general properties of an individual, one should not think of the individual concept as a mere list (or series of lists) of general properties. A complete individual concept, one might say, has some content over and above the general properties that can (at least by God) be extracted from it. To say what this extra content is would be to express something that corresponds to the roles played by individuals or bare haecceities in singular propositions as nowadays conceived: as with the propositions entertained by Russell, Kaplan, and others, individual concepts, unlike the predicates they contain, ground the intelligibility of de re modal thoughts, of transworld identity claims taken at face value and so on. By this account, the natural interpretation of singular terms must be judged wide of the mark: the complete concept doctrine is not the view that all proper names are mere shorthand for exhaustive definite descriptions. The difficulty with the view so far sketched comes in supplying details. Singular individual concepts cannot be universals; so they must in principle be singular, either ab alio or in se – either in virtue of the individual instantiating it, or in itself. If the former, individual concepts would be very like Aristotelian individual property instances (accidents), but which nevertheless contained general characteristics perhaps in the way Red contains Colored. This seems unlikely, if we are to make sense of God grasping uninstantiated individual concepts of so-called nonactual individuals. So individual concepts must be singular in them³⁸ The relation of singular subject to predicate might then be similar to the one implicit in a Kripkean treatment of (say) ‘HO’. Understanding this term requires understanding that it is a rigid designator; for this reason, the semantic role it plays is not equivalent to the description ‘‘is a stuff with hydrogen and oxygen atoms bonded together and (etc.) . . .’’ since understanding that description does not require one to know that if a stuff has this set of properties then it essentially has it. Yet ‘HO’, while a rigid referring term, nevertheless entails that description. So while ‘HO’ is a name, it nevertheless a priori yields information about what its bearer would have to be like. Similarly ‘The number five’ is a rigid referring term but one whose understanding provides us, a priori, with information about what it names.

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Haecceitism and anti-haecceitism

selves. They must in this respect be like Scotistic thisnesses, but unlike them in necessarily containing a particular set of qualitative properties. The singular component determines the relevant set of general concepts. And conversely, it seems: the relevant set of general properties must be instantiated in only one possible individual, precisely like the singular component. That is the Identity of Indiscernibles, PII. So the general properties determine the singular one as well. (As noted earlier, there is no logical impropriety in saying that the general facts supervene on the singular and also the singular on the general.) This dual aspect of individual concepts – their singularity as well as the generality of what they contain – is required by the haecceitist strain of Leibniz’s thought. It is also invited by his choice of words when discussing complete individual concepts in Discourse §: it is the nature of an individual substance or complete being to have a concept so complete that it is sufficient to make us understand and deduce from it all the predicates of the subject to which the concept is attributed . . . Thus the quality of king which belonged to Alexander the Great, if we abstract it from its subject, is not determined enough to define an individual, for it does not include the other qualities of the same subject or everything which the concept of this prince includes. God, on the other hand, in seeing the individual notion or haecceitas of Alexander, sees in it at the same time the basis and the reason for all the predicates which can truly be affirmed of him . . . (G ,: L –)

Several items in this familiar passage bear special note. The first, of course, is (i) Leibniz’s deliberate use of Scotistic terminology – scarcely a candidate for being misunderstood by anyone so familiar with the scholastic heritage as Leibniz’s readers. Complete concepts formally express modal individuators, that is, are materially adequate to the metaphysical principle of individuation of a substance. Second, (ii) Leibniz has not said, nor do his words imply, that the complete individual concept straightaway contains the intrinsic predicates of an individual in the way a list or conjunction is naturally understood to contain its members. Elsewhere (during this same time period) Leibniz’s words are similarly measured: in his  July  letter to Arnauld, for example, Leibniz says that the predicate concept ‘‘is in a sense included in that of the subject’’ (G ,: LA ; our emphasis). And his claim to Hessen-Rheinfels () that an individual concept ‘‘involves or embraces’’ the predicates of an individual (G ,) suggests a relation rather less straightforward than the natural interpretation has it. This leads to a third point, namely that (iii) Leibniz understands individual concepts as standing in an explanatory relation to the predicates of an

How is Leibniz’s haecceitism possible?



individual, as presumably no list or conjunction stands to its members. In the Discourse § passage above, Leibniz does not tell us that God’s seeing the individual concept simply is his seeing the predicates; rather, when seeing the individual notion or haecceitas of Alexander, God sees in it at the same time the basis and the reason for all the predicates which can be truly affirmed of him. This reinforces the suspicion that an individual concept is not related to the predicates contained in it in any straightforwardly formal or deductive way, but furthermore tells us something about how Leibniz conceived of that relation: an individual concept contains the predicates of an individual in such a way that to understand the concept is to understand why the individual falling under it is the way it is. Leibniz repeats the explanatory theme later in the Discourse (§) when saying that the dictatorship of Caesar ‘‘is based in his concept or nature’’ and that ‘‘there is a reason in that concept why he has resolved to cross the Rubicon’’ (G ,: L ; our emphases). Whatever is singular in the content of an individual concept, whatever goes beyond the generality of the predicates it somehow contains, must figure in this distinctly explanatory aspect of individual concepts. This point leads indirectly to a fourth. The passage quoted above is in fact a semantic pause, punctuating what is otherwise largely metaphysical territory (see §. below). The metaphysics of Discourse § detours into semantics precisely because, as Leibniz makes explicit, (iv) an individual concept is intended to express God’s understanding of the form or nature or essence of an individual substance. This form or essence is for him quasi-Aristotelian, a simple and fundamental inner principle of immanent causal change that accounts for (explains) the properties a thing has. Just prior to the quoted passage, Leibniz had offered the Aristotelian actiones sunt suppositorum doctrine, followed by the claim that ‘‘every true predication has some basis in the nature of things.’’ So the individual concept and the predicates it ‘‘contains’’ corresponds to the individual substance’s form or essence and the properties it specifies.³⁹ Just as substances are determinate simples of the Leibnizian metaphysic, possessing an inner law-of-the-series (or ³⁹ In De libertate, Leibniz does not dispute that part of a critic’s summary that ‘‘In his intellect, God has a perfect concept or idea of possible Peter containing all truths about Peter, of which the objective reality constitutes the full nature or essence of Peter’’ (Grua ). A similar reaction occurs later in Discourse §, to the claim that ‘‘[Caesar’s] nature or form corresponds to [his individual] concept . . .’’ (‘Corresponds’ is just right: concepts are too closely associated with forms or natures themselves in the draft for a letter of  December  to Arnauld, where Leibniz speaks of an individual substance’s ‘‘concept, idea, essence or nature . . . ’’ [G ,–: LA ].)

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Haecceitism and anti-haecceitism

primitive active force) that in some sense contains and explains all the states of the substance, so an individual concept is a determinate, singular item of the Leibnizian semantics that contains and explains all the predicates true of a subject. Just as a mathematical function for some equation is not to be identified with the points making up the curve, so an individual’s law-of-the-series is not to be identified with the ordered succession it uniquely specifies; and neither is the individual concept to be identified with the predicates it determines. The function, the law, and the individual concept contain in them the points and states and predicates, but in a way quite unlike the curve, succession, and list contain them as components. Clearly, there are important issues raised by this compact discussion of Leibnizian natures. We shall undertake in chapter  to unpack and expand upon the Leibnizian notion of the law-of-the-series, as it relates to an individual substance. In that context, Leibniz’s conception of inner laws and their relation to form, active force, essence, and accident will, we hope, be thrown into much sharper relief. For now, two observations are in order concerning the singular concepts that express God’s understanding of substantial forms, actual and possible. First, on the present understanding of singular concepts, the singular is more basic than the general both in the mind of God and in the created world. God’s understanding flows from singular concepts and propositions (neither of which are properly understood in terms of mere lists of general concepts); likewise, the accidents manifest in the world are to be explained by reference to the substances in which they inhere. On our account, then, the priority of the singular is vital to Leibniz’s metaphysical vision. (If one is inclined to think that this priority thesis conflicts with weak haecceitism, we need only recall again a point made earlier – that the supervenience of one family upon another does not entail any particular direction of explanation. On our view, the situation as regards the general and the singular is symmetrical with respect to supervenience, yet asymmetrical with regard to the direction of explanation.) Second, it is worth noting that our current reading helps to rescue Leibniz from an apparent confusion. Notoriously, Leibniz wants to connect his predicate-in-subject doctrine with a deterministic metaphysics, according to which the nature of a thing at a time in some sense contains a trace of its past and marks of its future. Yet some quite natural ways of construing the predicate-insubject doctrine make this appear to be simply a philosophical mistake on Leibniz’s part. For example, suppose one said this: a name or

How is Leibniz’s haecceitism possible?



singular referring term is shorthand for a list of temporally indexed properties. So construed, one is in no position to infer a metaphysics of determinism from the semantic doctrine. If, by contrast, one follows our current recommendation – of seeing the singular concept as mirroring a simple inner principle of change – then the connection will be warranted. This interpretation takes seriously the picture of the contents of the divine mind as in part expressing or mirroring the world, taking seriously as it does the relation of singular concepts to general ones as corresponding to the relation of quasi-Aristotelian essence to properties. In closing this part of our discussion, let us return to Robert Adams’s query about weak haecceitism, posed now as a question for the singular nature of Leibnizian thisnesses – of individual concepts: if every thisness is necessarily equivalent to a unique (albeit very complex) suchness, it is abundantly difficult to see how one could argue that thisnesses, as items distinct from suchnesses, cannot be scrapped from the picture altogether. That is, if every singular proposition is transworld extensionally equivalent to a (‘‘long’’) general proposition, why not make do without singular propositions? We offer the following answer on Leibniz’s behalf: without singular propositions, one cannot understand claims about Aristotelian essentialism and transworld identity at face value. But one can understand them at face value. They are perfectly intelligible so understood. Isn’t that reason enough to give singular propositions the status they deserve? Isn’t that reason enough for denying the notion that ‘‘singular propositions ought to be eliminated because each one of them stands or falls with a certain general proposition’’? . Whence the complete concept doctrine? Metaphysics and reference Stepping back from the fray, and pretending as best one can to approach the complete concept doctrine for the first time, it must be confessed that motivations for the doctrine are something of a mystery. Why did Leibniz believe it? There is a good deal to be said for believing the truth. The complete concept doctrine, in concert with the predicate-in-subject account, can of course be read so that Leibniz’s story comes away with a clear shot at being true. The chore in that case is to avoid triviality, which has rather less to be said for it. Take the complete concept of a thing to be ‘‘a concept expressing the whole truth about a thing,’’ and take the logical subject as ‘‘the whole truth about a thing,’’ and the supposedly import-

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Haecceitism and anti-haecceitism

ant doctrines offer us something like this: ‘‘The whole truth about a thing includes any particular truth about that thing.’’ To read Leibniz in this way is to read him as (a) altogether misguided in attaching any importance to these doctrines, and (b) altogether misguided in thinking that any metaphysical theses of consequence are connected to them (as when, for example, he associates the doctrine of marks and traces with the predicate-in-subject account, or speaks of everything that happens to a substance as being a consequence of its complete idea or concept alone). So what exactly is the point of this package of Leibniz’s – of the complete concept doctrine and the predicate-in-subject account? Jonathan Bennett has complained to us that too few Leibniz scholars tackle this important question head-on, and has pled with us to do better. Tackling it head-on would require, on the one hand, providing Leibniz’s package with a non-trivial reading, and on the other providing some account of Leibniz’s motivation for it as a substantive thesis with genuine philosophical bite. The chore in spelling out a non-trivial reading of Leibniz’s package is to account for what looks to be a gross extravagance, a bit of overkill: the logical subject of propositions is to be a concept expressing no less than a thing’s essence, and this is to contain nothing less that the whole truth about the thing. Bennett has his own account of what is going on there,⁴⁰ rooted in considerations about the exigencies of reference. Begin with the question of how you and I refer to a thing. Here is a natural answer: by possessing a descriptive profile of the thing. But the natural answer won’t do, if left at that. For our deployment of a descriptive profile may well fall short of determining unique reference, by falling short of expressing properties that just a single individual possesses. The solution is therefore that we wield linguistic devices expressing a description sufficiently rich to guarantee our success in picking out just a single individual. The Leibnizian Moral: the only way for a proper name in our mouths to secure unique reference is for it to have a super-rich profile contained within the concept it expresses.⁴¹ ‘‘But mightn’t a partial profile luckily secure reference? No doubt many purely possible ⁴⁰ We’ve gotten the story from brief discussions with Bennett, and aim to represent it faithfully if not in full detail. Bennett’s account bears some affinities to the picture emerging from Fabrizio Mondadori, ‘‘Reference, Essentialism and Modality in Leibniz’s Metaphysics,’’ and Benson Mates’s The Philosophy of Leibniz (esp. chapters  and  passim). ⁴¹ As we have noted earlier, such containment needn’t, and arguably doesn’t for Leibniz, take the form of a conjunctive list.

How is Leibniz’s haecceitism possible?



essences will enjoy some partial description; but for all that there may be only one actual individual which in fact enjoys it, and that’s enough.’’ First Leibnizian Reply: the actual odds are much worse than this. Since ‘‘leaps are prohibited not only in the case of motion, but also in the whole order of things and truths’’ ( to Remond, at G ,: L ), the Law of Continuity operates at the actual world, so that ‘‘nature leaves no gaps in the orderings she follows’’ (NE .vi.: RB ). The qualitative spread in nature is more tightly packed than one might think. Second Leibnizian Reply: the sense of a genuine proper name, if it is to determine a unique referent, must be of the kind that would enable God to succeed in singling out a determinate possible individual (let us say) prior to creation. So the meaning of a proper name must be something that, once perspicuously grasped, enables one to distinguish an individual from not merely all actual ones, but rather all other possible ones. In short, then, the sense of a proper name must express a superrich profile that can be met by at most one individual: insofar as a proper name is capable of referring at all, its sense must embrace each and every truth about a thing. (If – speaking now in the formal not the material mode – things are individuated by intrinsic histories, as strong essentialism would have it, then this proposal is to be amended to require only the intrinsic history to be contained in the subject-concept, the ‘‘relational history’’ being contained in that concept only in the attenuated sense that the concept of the subject provides a basis, in conjunction with the laws, for inferring all the relational truths [cf. chapters  and ].) Here now are two ways of thinking about this interpretation. (i) Leibniz is thinking of qualitative descriptions as the only way that we creatures can refer to a thing. But the view itself is mistaken. Leibniz is overlooking the availability to us of the devices of indexicals and demonstratives, and in particular the exploitation of one’s location in a spatio-temporal nexus whereby those devices serve as a means of referring. So Leibniz does have a motivation for his complete-concept/ predicate-in-subject package, as a semantics for proper names as used by us; but it rests upon a mistake. One might well doubt if the mature Leibniz was guilty of any such oversight. After all, the not-so-mature Leibniz of the Confessio had (recalling § of chapter ) already stressed the availability of demonstrative means of reference when considering how we might succeed in designating just one of a number of similar eggs whose qualitative



Haecceitism and anti-haecceitism

differences are very thin indeed. In considering the possibility of uniquely latching on to just one among many indiscernible eggs, he writes: What is this? What is it to determine something? . . . [I]n order to be able to distinguish the eggs continuously – which is what a designation or perpetual determination consists in (supposing that one has permitted nothing to spread on them, no mark attached to them, no sign printed on them, by which they cease to be similar) – it is necessary either that you keep these eggs in some container that is immobile, where they remain unchanged; or that you bring it about that their site or container, if it is mobile, nevertheless is not breakable, and that they are fixed in it, so that they retain the same relationship always to certain previously determined marks imprinted on parts of the container; or finally, if you are going to allow them complete freedom from restraint, it will be necessary that at each moment of time during which they move you continuously follow the motion of each through each place either with your eyes or hands or some other kind of contact. (A ..)

This, in effect, provides a nice summary of how one can exploit one’s relationship to a thing within the spatio-temporal nexus as a means of singling it out even in tightly cramped qualitative quarters. Arguably the mature Leibniz – writing now in a context not of indiscernible things but of a world where qualitative continuity threatens us with ‘‘tiny differences we could not take in’’ – makes a similar point in the New Essays: it seems, he says, ‘‘impossible for us to know individuals or to find any way of precisely determining the individuality of any thing except by keeping hold of the thing itself’’ (NE .iii.: RB ). We can interpret ‘‘keeping hold of the thing itself ’’ as an abbreviation for some or all of the tracking tricks mentioned in the Confessio passage. (Note that an alternative translation offered by Remnant and Bennett of the all-crucial ‘a` moins de la garder elle meˆme’ – viz. ‘‘except by keeping it unchanged’’ – ties in even more closely with the wording of the Confessio passage.) Now this mature remark is located in a context where Leibniz is clearly concerned to stress that no descriptive profile less than a super-rich one can serve in singling out a thing, and thus (his emphasis to Locke) that no abstraction will succeed in providing unique singular reference. But Leibniz’s point here is not that we do in fact secure reference by possessing the super-rich complete concept. Indeed he stresses here that ‘‘only someone who is capable of grasping the infinite could know the principle of individuation of a given thing,’’ implying that we cannot know any such principle and so cannot ourselves grasp the associated complete concept. (God is another matter.) His point is rather that we

How is Leibniz’s haecceitism possible?



cannot secure reference by cognizing a profile – only an infinite description being sufficient on that score – and that we instead must know individuals by somehow ‘‘keeping hold of them’’ in the ways suggested by the Confessio passage.⁴² As noted, there is to be sure an important difference between the Confessio passage and the New Essays passage: in the former but not the latter Leibniz takes seriously the possibility of genuine indiscernibles. But there is a crucial similarity very nearby: lacking as creatures the resources to fully grasp the infinite qualitative detail of the world, one is left with the problem of there being things that are indiscernible-to-us as far as qualitative profile goes. And clearly, the designatory resources that Leibniz offers to compensate for indiscernibility-in-re have ready application to the problem of indiscernibility-by-us. In sum, one can fairly resist the suggestion that Leibniz’s complete concept doctrine is motivated by a conviction that concepts containing super-rich descriptions are the only means by which we can achieve reference. On the contrary, it would seem that Leibniz believed that we achieve reference by other means since we – failing in our grasp upon the infinite – lack proper access to the concepts in question. That is one way of evaluating the Bennett interpretation. An alternative would be this. (ii) Leibniz’s complete-concept/predicate-in-subject package is concerned with the exigencies of reference. But while that package seems too burdensome for the likes of creatures, as the New Essays passage suggests, its real motivation concerns reference by God, as it were, and not by us. Think again of God ‘‘prior to creation.’’ Demonstratives and indexicals, ostension and spatio-temporal connection – none of this can be of any help in God’s cognitive access of possible creaturely essences. (Here one must of course ignore artificially concocted exceptions, e.g. ‘‘The first essence that I will instantiate shall ⁴² There is another interpretation of the New Essays passage. Read ‘keeping hold of the thing itself ’ not as expressing ‘‘Confessio-style tracking’’ but as ‘‘know a thing in all its detail.’’ So read, the point is then that since we creatures cannot know a thing in all its detail, we cannot ‘‘know individuals’’ and so can’t ‘‘precisely determine the individuality of any thing.’’ If one inclines toward reading Leibniz in this way, then (it seems to us) one had better charitably allot to Leibniz a distinction between ‘‘knowing a thing’’ and ‘‘referring to a thing’’: without that bit of charity, the point of Leibniz’s passage would be that, lacking full knowledge of anything’s detail, we cannot refer to anything. Not only is it implausible in its own right that Leibniz thought we cannot refer to any single thing, but as the Confessio passage makes clear, Leibniz was surely aware that unique designation does not require a full descriptive profile – even though such a profile might well be required for one to know what is materially adequate for the principle of individuation. On this reading, the point of the New Essays passage is that we cannot know the principle of individuation for things, and is not about reference at all.



Haecceitism and anti-haecceitism

be called ‘Adam’.’’) Hence the divine mind must get its cognitive grip on creaturely individual essences via concepts that contain some qualitative profile. But as before, that won’t do as it stands. For any thin profile will not uniquely latch onto a possible individual essence. Thus for God to get cognitive hold upon a possible essence, He requires a concept so rich as to determine a whole intrinsic history. Abstract away from any aspect of that history and one will not have determinate reference any longer. In short, divine reference can only be secured (leaving aside the concocted exceptions) via a formal or conceptual item that is materially adequate to the principle of individuation of a thing. Since the principle is ultra-rich, God’s means of cognitive access to a possible individual essence must inevitably involve an ultra-rich conception too. The general thesis operative in the first alternative (i) above – that to refer to x is to have in one’s cognitive possession the principle of individuation of x – is, so to say, only true prior to creation. So then: ‘‘everything has a complete notion according to which it is conceived by God, who conceives everything perfectly’’ (G ,). Suppose now the meaning of a proper name to be given by the concept that God associates with its reference. Needless to say, we do not conceive everything perfectly: we have a more confused, less distinct grasp of that concept than does God. Thus questions remain. How does a proper name in our mouth get to refer, and relatedly how does it get to express a particular concept in God’s mind? Perhaps this: it gets to refer to x by the name’s being associated with a confused perception C of x (surely Leibniz can refer to Leibniz, and we to him); it gets to express God’s concept C* via the facts that C* is the concept of x in God’s mind and it is x that one is referring to. What of these alternatives, (i) and (ii)? The second is better. How creatures succeed in referring is surely not at the heart of Leibniz’s complete-concept/predicate-in-subject package. Leibniz knows that we can refer, and that we must do this despite and indeed ultimately via perceiving confusedly. But alternative (ii), as a story about reference, still leaves Leibniz guilty of serious confusions. Where, in (ii), is any source for the substantive philosophical theses with genuine metaphysical bite? So construed, for example, it offers no way of connecting Leibniz’s package with a doctrine of marks and traces. Let us begin instead with the metaphysics. What is foundational and distinctively Leibnizian here is that according to his metaphysic, there must be in each individual substance an inner principle of change that explains all of its accidents. So one begins in a way with why Leibniz

How is Leibniz’s haecceitism possible?



believes the metaphysics. And here one has at least something to go on, some motivations for Leibniz’s own strain of the basic story we described at the outset as ‘‘a robust substance-accident realism, complete with individual substances underlying the accidents in which they are clothed.’’ (a) Substances do have accidents: but substances are simple and windowless, and accidents can’t migrate (for if they did, says Leibniz, we should have no grounds for distinguishing separable substances from what would thereby be separable accidents). So individual substances don’t causally interact, and hence the explanation of an intrinsic property enjoyed by a substance must come from the inside. There are alternatives to this, in logical space, but Leibniz has reasons for denying them. Thus, (b) the idea that the intrinsic properties of a substance come out of nowhere offends any commitment to serious rationalism, according to which nature is fully intelligible. God, at least, has reasons for the inherence of particular accidents in the world. But (c) Leibniz rejects the notion that God is the causal-explanatory source of all accidents, simply implanting them in creatures. That is the way of Occasionalism, and from there the step is but a short one to Spinozism. And in any case, (d) no metaphysician of Leibniz’s stripe, enamored with a broadly Aristotelian causal realism of persisting substances-cumaccidents, will say that inherence – the inherence of an accident in a substance – is a primitive: God’s implanting accidents in substances isn’t their inhering in them. (e) So the accidents must arise within the created order: a fully rationalist conception of the substance-accident metaphysic has it that, in a deep way, substances themselves are the causalexplanatory source of the accidents inhering in them. On such a metaphysic, substances are to be understood as enjoying a lawful primitive force of action whereby accidents emanate from the substance, from within. That is genuine inherence, genuine causal realism, a story answering to the demands of a causal-explanatory rationalism by which the accidents of creatures can be properly said to be their accidents. Indeed, as we shall see in chapter , Leibniz is prepared to say that what constitutes an enduring substantial creature is a causally active law-ofthe series itself, a singular nature or form having built into it the full history of changes the substance undergoes. So there is the metaphysics. Moving on now, one can distinguish two issues: (A) Why does a substantial law-of-the-series contain its history? This is answered by the metaphysics. (B) Why does the concept expressing a substantial law/form contain a priori each and every aspect of the history? That is to ask why it is that, when God conceives of some



Haecceitism and anti-haecceitism

possible substance, His understanding of it is a conception embracing every aspect of its history. Here, recurring to an earlier theme (§. above) that is Leibniz’s own, one is invited think about what it would be to understand a substantial law-of-the-series or active form by analogy with the question ‘‘What is it to understand a mathematical function?’’ A proper understanding of a function requires that one sees how by its very nature that function operates on arguments to deliver values. This does not straightforwardly mean that to conceive of the function is to merely conceive of a list, an ordered series of arguments and values itself. To repeat: just as a mathematical function for some equation is not to be identified with the sequence of Cartesian pairs (points) making up the curve, so an individual law-of-the-series is not to be identified with the ordered succession it uniquely specifies; and neither is the individual concept to be identified with the predicates it determines. (The function, the law, and the individual concept contain in them the points and states and predicates, but in a way quite unlike a sequence of points, a succession, and a list contain them as components.) And here at last considerations about reference begin to show themselves. For given Leibniz’s substantial-law-theoretic account of individual natures, it is easy to see that God refers to (secures a cognitive latch onto) some substantial law/form only via an understanding sufficient to conceive a priori a complete sequence or history – one corresponding to the history which that substantial law, if instantiated, would yield as immanent causal output. While we can allow with Aristotle that the order of understanding in us needn’t mirror the order of being, we arrive at the happy conclusion that in the case of God, the order of understanding mirrors the order of being. That is how things should be. Thus one begins (like the real Leibniz, if not the Russell–Couturat Leibniz) with the metaphysics. One adds to it a well-motivated picture of what it is for God to enjoy cognitive hold of a possible essence. The main pieces of Leibniz’s story are all there, and look to suffer no serious confusion. In particular, for example, the doctrine of marks and traces is a correlate of the complete-concept/predicate-in-subject package, since the entire sequence of a history flows from a substantial law of which God’s understanding is a singular conception of the thing. The latter is what Leibniz calls the complete concept, by which he means – as he so often says – the concept God has when conceiving perfectly of possible singular natures or individuals. To recapitulate. Here are three doctrines:

How is Leibniz’s haecceitism possible?



() The inner principle of change is the immanent causal source of an entire history. () That inner principle constitutes the individuality of a thing. () In order to think an inner principle of change (and thus the individuality of a thing) one must have a conception of it rich enough to enable a priori understanding of an entire history. Exigencies of reference enter at (), and Leibniz’s focus there is God. But the complete-concept/predicate-in-subject package is properly understood only as part of a larger metaphysical story that includes (), (), and ().

 

Sufficient reason and the identity of indiscernibles

From early on in Leibniz’s philosophical career until his very last letter to Clarke, Leibniz was keen to emphasize the importance of what he called his ‘‘two great principles.’’ In the familiar words of the Monadology, ‘‘all our reasonings are based on two great principles, that of contradiction . . . and that of sufficient reason.’’¹ If the first of these is presupposed by his logic generally and (as he implies in the Monadology and the Clarke Correspondence) by all reasoning about logical possibility and necessity in particular, it is undoubtedly the second of the two – the Principle of Sufficient Reason (PSR) – that figures most prominently in Leibniz’s metaphysical theorizing. Indeed one can think of scarcely any central doctrine in Leibniz’s metaphysics that is not beholden in some fairly direct way to the Principle of Sufficient Reason. Leibniz explicitly reckons PSR a necessary condition for his concept-containment account of truth (C –: L –), and thereby (in Leibniz’s hands, for good or ill) in the doctrines of spontaneity and marks and traces (G ,: L –); PSR is a crucial premise in several of Leibniz’s arguments for the existence of God, in his account of volitional actions by creatures and by God, in his argument that ours is the best possible world, and in his relationalist arguments against absolute space and time. Leibniz’s appropriation of PSR in this latter context – in his polemic against the Newtonians – is in fact an instance of a quite general deployment of the Principle, namely, in answering the question ‘‘How many?’’ By Leibniz’s reckoning, the absolutist about space gives the wrong answer when considering how many possible worlds are just like this one with regard to objects and their relations. From the scholastics ¹ Monadology §§– at G ,: L . See also Theodicy (Appendix: ‘‘Observations of the Book Concerning ‘The Origin of Evil’. . .’’ at G ,–: H –) and elsewhere (VE ; G ,–: L ). The Principle of Contradiction arises already in the s (cf. G ,: L ); The Principle of Sufficient Reason arises as early as  (A...: see also the Confessio of ca.  at A ..–).



Two styles of argument for PII



on down, the question ‘‘How many?’’ is one among several chief questions that any so-called theory of individuation must provide the conceptual resources for answering. And here another of Leibniz’s principles, the Identity of Indiscernibles (PII), plays a central role. Indeed, Leibniz’s chief use of PII is in just this context. As noted in chapter , PII expresses for Leibniz one part of the intension of ‘individual substance’ deeply important to him: numerical distinction is accompanied by qualitative difference, exact qualitative similarity by numerical sameness. But unlike the Principle of Contradiction and PSR, which assume rather the place of (unargued) axioms in Leibniz’s system, PII is a principle for which Leibniz is prepared to argue.² Although his reasons for endorsing PII are themselves rarely transparent, it is well known that PSR figures in Leibniz’s willingness to deploy PII in its most crucial contexts. Our purpose in this chapter is to examine the connection between PSR and PII, attending in particular to a mode of connection that has been either under-appreciated or misunderstood. First, we shall suggest that the most natural account of Leibniz’s argument for PII, and the most familiar, is but one of two quite different lines of defense running from PSR to PII. In § we shall explain the second, less familiar argument – an argument that, as it arose and was postponed in our discussion of transworld identity in chapter , looks on the surface to be a particularly bad one. Section  is devoted to examining more carefully how the two styles of argument are related, and indirectly to assessing which of the arguments looks to be the better. Finally, in § we pose a puzzle – anticipated already in chapter  – about the modal strength of the key elements in Leibniz’s two arguments.                P II Leibniz’s expressions of PII are well known. ‘‘There cannot be two individual things in nature which differ in number alone’’ (C : L );³ ‘‘Things that differ must differ in some way, that is, must have an internal difference that can be designated’’ (G ,: L ); ‘‘There are never two beings in nature that are perfectly alike, in which it is impossible to discover an internal difference, that is, one founded on an intrinsic denomination’’ (G ,: L ); ‘‘There is no such thing as two individuals indiscernible from each other . . . To suppose two things ² Though on occasion Leibniz will call PII ‘‘an axiom’’ (cf. G ,: L ). ³ That is in First Truths; the same formulation occurs in Discourse § (G ,: L ) and in the Preface to the New Essays (RB ).



Sufficient reason and the identity of indiscernibles

indiscernible is to suppose the same thing under two names’’ (G ,: L ). PII can be stated as follows: PII ∀x∀y (If x and y are intrinsically indiscernible, then x is identical with y).⁴ . The familiar PSR defense of PII We noted above that one of Leibniz’s chief deployments of PII is against (Newtonian) absolutism. It is typically in just such contexts, where the Principle is not simply given as one among several of Leibniz’s favored beliefs but is put to explicit argumentative work, that Leibniz offers what might be viewed as a PSR defense of PII. A characteristic example, from the letters to Clarke: [I]f space were an absolute being, something would happen for which it would be impossible that there should be a sufficient reason–which is against my axiom. And I can prove it thus. Space is something absolutely uniform, and, without things placed in it, one point of space does not absolutely differ in any respect from another point of space. Now from hence it follows (supposing space to be something in itself, besides the order of bodies among themselves) that ‘tis impossible there should be a reason why God, preserving the same situations of bodies among themselves, should have placed them in space after one certain particular manner and not otherwise; why everything was not placed the quite contrary way, for instance, by changing east into west. . . [T]hose two states, the one such as it is now, the other supposed to be the quite contrary way, would not at all differ from one another . . . the one would be exactly the same thing as the other, they being absolutely indiscernible, and consequently there is no room to inquire after a reason for the preference of the one to the other. (Third Letter to Clarke; G ,: L )

The suggestion here is that if there were such things as indiscernible points understood independently of events otherwise said to occur ‘‘at’’ them, then God should have been confronted with a decision between alternatives for which there could be no sufficient reason to choose one over the other. Since PSR requires that no such case can (and hence, no such case does) arise, there are no indiscernible points of space as the absolutist supposes. Call this line of argument from PSR to PII the ‘‘Divine Preference’’ ⁴ We assume that ‘intrinsic denomination’, as Leibniz uses it, excludes properties that are in their very nature relational. Not every commentator agrees with us: see chapter  for a discussion of the matter. ‘Intrinsically indiscernible’, as it occurs in our formulation, means ‘‘have the same intrinsic properties.’’ We treat ‘intrinsic property’ as conceptually primitive here. (See David Lewis, ‘‘Extrinsic Properties,’’ for the dangers of some natural explications.)

Two styles of argument for PII



argument. As we shall understand it, Leibniz concludes that there are no indiscernibles on the following grounds: if ours were a world W in which there are indiscernibles, then there would be some distinct possible world W* such that God could have no sufficient reason for preferring W over W*; but since by PSR God in fact has a reason for every decision – here, for preferring ours to any non-actual world – it follows that there are no indiscernible objects. (One obvious way of constructing arguments of this sort against putative actual indiscernibles a and b, as Leibniz suggests and as deployed in chapter , is to envision a morally equivalent non-actual world⁵ in which a and b are, so to speak, ‘‘switched.’’ If in our world Bill is next to the Tower of Pisa and there is an intrinsic duplicate Bob next to the Eiffel Tower, then there is a qualitatively indiscernible world, enjoying the exact same distribution of properties as ours, in which it is Bob near the Tower of Pisa and Bill near the Eiffel Tower. Or, given a world W with just three qualitatively identical homogeneous spheres in a row with even spaces between the center sphere B and the outside spheres A and C, there is a distinct world W* having precisely the same distribution of properties in which C is in the middle and A and B occupy the end positions.) . An alternative PSR defense of PII But there is another way that Leibniz might be seen to reason from PSR to PII. The possibility of an alternative argument arises in connection with what is – by Leibniz’s reckoning – a close connection between PSR and his predicate-in-subject doctrine of truth. Let’s rehearse this connection briefly, by way of background. According to the predicate-in-subject doctrine, the truth of any proposition ‘A is B’ consists in the predicate concept’s containment in the subject concept. Leibniz holds that as a consequence, every true proposition admits of an a priori proof,⁶ whereby the reason for any predicate true of an individual substance can be discovered in the ⁵ Two worlds are morally equivalent if and only if one is just as good as the other relative to divine standards of value. ‘Morally’ thus has its broadest Leibnizian use here (and hereafter), of the ‘‘final-ends’’ sort that figures in Leibniz’s language of moral necessity, by which God chooses the best world. (The general, value-theoretic parameter of goodness itself, along which God judges worlds and aims to maximize in creation, is itself of three narrower species: metaphysical [harmony], physical [pleasure], and ‘‘moral’’ in the finer sense of virtue applicable only to intelligent creatures.) ⁶ ‘‘A priori proof’’ in whatever Leibniz’s pre-Kantian sense of that term might amount to. In proof-theoretic contexts relevant to the connection between PSR and his predicate-in-subject doctrine, Leibniz doesn’t expand on exactly what that sense is. For more on the issue, see Robert M. Adams, Leibniz: Determinist, Theist, Idealist, pp.  and –.



Sufficient reason and the identity of indiscernibles

subject concept. Thus in speaking of such a demonstration in Discourse § he says that if one were to carry out the complete demonstration by virtue of which one could prove this connection between the subject, who is Caesar, and the predicate, which is his successful undertaking, he would actually show that the future dictatorship of Caesar is based in his concept or nature and that there is a reason in that concept why he has resolved to cross the Rubicon . . . (G ,–: L )

Leibniz’s view that PSR ‘‘is contained in the definition of truth and falsity’’ (G ,) is reflected in the following passages: To say that the predicate is in the subject is to say that there is always something to be conceived in the subject which serves to explain why the predicate pertains to it . . . (G ,: LA ) The principle that a reason must be given is this: that every true proposition not known per se has an a priori proof, or that a reason can be given for every truth . . . (G ,) It is evident, therefore, that all truths – even the most contingent – have an a priori proof, or some reason why they are truths rather than not. And this is just what is meant when it is commonly said that nothing happens without a cause or that there is nothing without a reason. (G ,)

So it is no surprise that in Primary Truths, after offering his predicatein-subject doctrine of truth and its consequences for a priori provability, Leibniz claims that ‘‘the accepted axiom, that there is nothing without a reason . . . follows from these considerations . . . otherwise there would be a truth which could not be proved a priori’’ (C : L ). And it is here that Leibniz indicates a connection between PSR and what we might call (broadly speaking) conclusions about sameness. The notion of sameness he has at first in mind is sameness of ‘‘consequences’’ or predicates applied to subjects in a case of perfectly similar subjects or ‘‘givens’’ – say, equal weights placed on a balance, as in Archimedes’ postulate: ‘‘given equal weights on both sides of a balance with equal arms, everything is in equilibrium.’’ This, he says, is an example of a general result licensed by PSR: for ‘‘when in the givens everything on the one side is the same as it is on the other side, then everything will be the same in the unknowns, that is, the consequents.’’⁷ We are justified in drawing the conclusion of sameness (in the behavior of the balance ⁷ First Truths (C : L ). Thus, from the Generales Inquisitiones: ‘‘If all things are alike on each side in our hypotheses, there can be no difference in the conclusions’’ (C ).

Explaining the no-reason argument for PII



arms, in the example) because of PSR – that is, ‘‘because no reason can be given for any difference, a reason that certainly must be derived from the givens.’’ The same line of thought arises in Leibniz’s Second Letter to Clarke, where he cites Archimedes’ implicit use of PSR in De aequilibrio: ‘‘if there be a balance in which everything is exactly alike on both sides and equal weights are hung on the two ends of the balance, the whole will be at rest. This is because no reason can be given why one side should weigh down rather than the other.’’⁸ Now this is not exactly a deployment of PSR toward conclusions of numerical sameness or identity. But the implied inference schema – ‘‘if no reason for a difference, then the same’’ – is immediately extended in the very next paragraph of First Truths to support instances of PII: ‘‘From these considerations it also follows that, in nature, there cannot be two individual things that differ in number alone.’’ Leibniz’s defense: ‘‘For it certainly must be possible to explain why they are different, and that explanation must derive from some difference they contain.’’ Let us call the relevant instance of this sort of defense of PII, applied to particular substances a and b, simply the ‘‘No Reason’’ argument: If a and b are indiscernible, then there is no reason for saying that they are two rather than one. But there must be a reason for the distinctness claim. Therefore a and b are one.                -          P II To the extent that such texts manifest Leibniz’s willingness to deploy a form of argument distinct from the more familiar and well-understood Divine Preference argument, one is invited to ask what more might be said to clarify and evaluate the No Reason route from PSR to PII. . Two objections As it stands, the No Reason argument seems to face two immediate and related objections. The argument is of the following sort: supposing that a and b are indiscernible, NR There is no reason for saying that a and b are two; therefore a and b are one. ⁸ G ,: L . In that letter, Leibniz alludes to his use of PSR in the Theodicy, where he had deployed it (now taking the balance example from Bayle, at T §: H –) against the possibility of ‘‘perfect equipoise’’ in cases of creaturely free action: we are never in the position of Buridan’s ass (T §§–: H –).



Sufficient reason and the identity of indiscernibles

First, () even granting that in such a case one has no reason for saying that a and b are two, it is not at all obvious why the argument shouldn’t cut in both directions. That is, in such a case of indiscernible a and b, there would seem to be no less a reason for denying that they are two than for denying that they are one. Why, then, prefer the above argument over the following argument? NR* There is no reason for denying that a and b are two; therefore they are two. The proponent of this first objection – echoing remarks by Margaret Wilson and Robert Adams in a related context (below, §.) – wonders why the burden of proof should be put where it is. Why is the burden of proof being placed upon one who says that a and b could be indiscernible and yet distinct, rather than on one who says that any case in which a and b are indiscernible is a case in which a and b are the same? A defender of the No Reason argument might reply: ‘‘Yet there is a sufficient reason for denying a and b are two; it consists in the fact that there is no sufficient reason for saying a and b are two; hence the premise for the flip-side argument is false.’’ But again, why not say instead ‘‘There is a sufficient reason for affirming that a and b are two; it consists in the fact that there is no sufficient reason for denying that they are two?’’ Here is a mathematical analogue. Suppose I discover that there is no direct proof for P and also no direct proof for not-P. Shall one say that I have discovered that there is no proof for P, which (indirectly) proves not-P; or shall one say that I have discovered that there is no proof for not-P, which (indirectly) proves P? One is hard-pressed to see why I should prefer one mode of argument over the other unless some further data can be brought to bear. Why not say in this case that one simply doesn’t know which, or – if one doesn’t like evidence-transcendence – why not say that there is no fact of the matter? The latter disjunct of this last rejoinder leads immediately into a second objection against the No Reason argument. It is this. () Leibniz seems to have presumed in these contexts that the issue is more than one of mere talk – that in cases of indiscernibility there is a fact of the matter in the world concerning identity and difference. But why not say instead that there is no fact of the matter concerning identity and difference in such cases? That Leibniz does not seriously consider this option may seem particularly puzzling, given prima facie evidence of his willingness to entertain conventionalist proposals in other contexts. In a letter of 

Explaining the no-reason argument for PII



January  to De Volder, immediately prior to claiming that there is nothing permanent in an individual substance except its persisting law-of-the-series which ‘‘constitutes its individuality,’’ Leibniz says that if it is claimed that substances do not remain the same but that different substances which follow upon prior ones are always produced by God, this would be to quarrel about a word, for there is no further principle in things, by which such a controversy can be decided. (G ,: L )

Robert Sleigh notes of this passage that ‘‘Leibniz appears to suggest that whether we adopt an ontology of transitory individuals or an ontology of persisting substances is a matter of convention – a decision not grounded in the nature of things.’’⁹ If that is correct, why shouldn’t Leibniz be willing to consider a similar attitude with respect to the identity and diversity of indiscernibles? One might think that there is no conventionalist option available to Leibniz, because he takes the bivalence of propositions to be a priori axiomatic. In the context of discussing his predicate-in-subject account of truth, Leibniz replies to a scenario reminiscent of the mathematical analogy noted above: is everything true which cannot be proved false, or everything false which cannot be proved true? What, then, of the cases of which neither of these holds? It must be said that both truth and falsity can always be proved . . .¹⁰

By ‘‘truth and falsity can always be proved’’ we take Leibniz to mean that every proposition is such that there is a proof of its truth or else a proof of its falsity (its denial). Bivalence is implicit in Leibniz’s formulations of the first of his ‘‘two great principles’’ – the Principle of Contradiction. ‘‘I assume,’’ says Leibniz, ‘‘that every judgment (that is, affirmation or negation) is either true or false, and that if the affirmation is true the negation is false’’ (G ,: L ), echoing elsewhere that ‘‘A proposition is either true or false’’ and that ‘‘it cannot happen that a proposition is neither true nor false’’ (NE .ii.: RB –). Thus if one replied to the No Reason argument by saying ‘‘You have seen there is no reason for the proposition P and concluded not-P, but perhaps neither is true,’’ Leibniz might well respond: ‘‘Bivalence tells me that P is either true or else it is false; PSR tells me that if P is true, then P has a sufficient reason; and so in the absence of reasons for P, I can deduce not-P.’’ ⁹ Robert C. Sleigh, Jr., Leibniz and Arnauld: A Commentary on Their Correspondence, p. . In the end Sleigh thinks that appearances are deceiving here: see pp. ff. ¹⁰ This is part of a marginal note that Leibniz added to his Generales Inquisitiones (C : PLP ).



Sufficient reason and the identity of indiscernibles

None of this shows, however, that conventionalism is unavailable to Leibniz. Conventionalism is compatible with a view that every possible state of affairs determinately obtains or does not obtain at every possible world. In cases where one wants to go conventionalist, one can insist that certain ways of speaking do not even express any genuine possibility – that they are just talk. And it is pretty clear that Leibniz on occasion wants to go conventionalist in that sort of way – as when he asserts of blocks of marble no less than of a heap of stones that ‘‘it can therefore be said of these composites and similar things what Democritus said very well of them, namely, they exist by opinion, or by custom’’ (G ,: LA ). If some linguistic community says of a flock of sheep that ‘‘it is an object,’’ there is no genuine property being ascribed or else no state of affairs genuinely at issue. Thus, faced with the observation that there is no sufficient reason for the truth of a sentence ‘P’, one can have recourse to the view that ‘P’ does not succeed in expressing some state of affairs that may or may not obtain, and so is not forced by any No Reason line of thinking to conclude that ‘Not-P’ expresses a true proposition, even when put under dialectical duress from Bivalence and PSR. Bivalence plus PSR does not tell against conventionalism. The second objection is still in place. . Another Leibnizian principle Let us return for now to the first ‘‘flip-side’’ objection to Leibniz’s No Reason defense of PII. One might discern in neighboring quarters an invitation to pose it against Leibniz. Recall (chapter ) that Leibniz clearly endorsed the intra-world version of PII. That is to say, he believed that if a and b are in the same world and are indiscernible, then a is identical with b. It is plausible to think that he also believed the inter-world version of PII – that is to say, if a in W is indiscernible from b in W, then a and b are identical. Whether Leibniz in fact endorsed inter-world PII is not uncontroversial, given the controversial idea that he believed in world-bound individuals: add that to the idea that some object in another possible world is an intrinsic duplicate of some actual thing, and inter-world PII is untenable. But while it is controversial to ascribe both intra- and inter-world versions of PII (even when restricted to intrinsic properties) to Leibniz, there is no doubt he affirmed the non-identity of intrinsic discernibles in both the intra- and inter-world forms. That is to say, he believes both that (i) if a and b are in the same world and are intrinsically different, then they are numerically distinct,

Explaining the no-reason argument for PII



and also that (ii) if a in one world is intrinsically different from b in another, then a and b are numerically distinct. Now one of Leibniz’s arguments for the non-identity of transworld discernibles (TWD) is very much the flip side of the No Reason argument. The No Reason argument for PII, recall, has the following form: given indiscernibles a and b, NR There is no reason for saying that a and b are two; therefore a and b are one. The argument for TWD runs as follows: TWD There is no reason for saying that a and b are one; therefore they are two. Thus we encountered in chapter  the following to Arnauld: It follows, also, that if he had had other circumstances this would not have been our Adam, but another, because nothing prevents us from saying that this would be another. He is, therefore, another. (G ,: LA ) If, in the life of any person, and even in the whole universe, anything went differently from what it has, nothing would prevent us from saying that it was another person or another possible universe which God had chosen. It would then indeed be another individual. (G ,: LA –)

Clearly the two objections raised in connection with the No Reason Argument (for intra-world PII) can readily be transformed into objections to the no reason argument for TWD. (') First, one should wonder why the above no reason argument for TWD is to be preferred to the following one: TWD* There is no reason for denying that a and b are one; therefore they are one. Robert Adams’s recent diagnosis of the TWD-passages to Arnauld follows Margaret Wilson’s earlier appraisal: This looks like an appeal to the Principle of Sufficient Reason: there is no compelling reason to say it would be the same individual if different events happened to him; therefore, it would not be the same individual. This is a weak argument. . . One wonders . . . whether the argument does not cut both ways. As Wilson says, ‘‘The question presents itself insistently: what prevents us from denying it would be a different Adam if circumstances had been different . . .?’’ Would it be any easier to find a sufficient reason for denying counterfactual identity than for affirming it? Leibniz seems to assume here that presumption



Sufficient reason and the identity of indiscernibles

favors nonidentity – that identity needs to be explained in a way that distinctness does not, and hence that there is more need of reasons for affirming than for denying identity.¹¹

That is to say, if we are to prefer the former argument (TWD) to the latter flip-side argument (TWD*), it must arise from a prima facie epistemic obligation to give non-identity preference over identity. But surely, when seen alongside the No Reason argument (NR) for Intra-PII, this assessment quickly comes to seem like an odd diagnosis. For in that context, the prima facie obligation, if there is one, favors a preference for identity over non-identity. (') Second, one might again wonder why Leibniz does not take seriously a conventionalist option in the context of TWD. In his provisional diagnosis of the TWD-passages to Arnauld, Sleigh writes: ‘‘This sounds like the principle of sufficient reason run amok. Generalizing the reasoning apparently involved, one dreads the case where nothing prevents saying p and nothing prevents saying not p.’’¹² Fair enough, it seems: why not assert that there is no fact of the matter whether or not a and b are identical in a case where a and b are transworld discernible? By eschewing any facts of diversity/identity requiring explanation, one runs no risk of violating PSR. Indeed, the risk of violating PSR is all the more vanishing given that, on the conventionalist proposal as construed above, there simply are no facts of transworld non-identity needing a positive explanation. If asked for a reason for asserting that there are two things rather than one in a case of transworld comparison between indiscernibles, the conventionalist will insist that only words are at stake, and hence that there is no genuine distinction in reality at issue. In short, it seems at first glance that both versions of ‘‘no reason’’ thinking in Leibniz are deeply flawed. Both versions are deployed in ignorance of the fact that equally good flip-side arguments cut the other way. And both arguments ignore the availability of conventionalism: this despite Leibniz’s apparent willingness to countenance the possibility ¹¹ Adams, Leibniz, p. . The quotation from Margaret Wilson is taken from p.  of her ‘‘Possible Gods.’’ ¹² Sleigh, Leibniz and Arnauld, p. . Sleigh’s provisional diagnosis is not his final one: he continues, ‘‘But the culprit – the principle ‘For all p, if nothing prevents saying p, then p’ – is not involved here.’’ Leibniz’s purpose in these passages, by Sleigh’s lights, is simply to insist that there are metaphysical conditions for identity that ‘‘must be rigorous, objective, and independent of convention.’’ We concur that this is Leibniz’s purpose in both intra- and inter-world contexts: it will be clear in the sequel, however, that we think the spirit of this objective, non-conventionalist reading needn’t be divorced from the letter of a PSR-reading.

Explaining the no-reason argument for PII



of conventionalism in other contexts. In what follows, we attempt to rescue the ‘‘No Reason’’ approach from the ignominy it appears to face. . Answering the objections Let us first take up the no-fact-of-the-matter, conventionalist reply to the No Reason argument. It is easy to over-play the conventionalist flavor noted by Sleigh in the  De Volder passage. Here is the relevant passage in full: But if it is claimed that substances do not remain the same but that different substances which follow upon prior ones are always produced by God, this would be to quarrel about a word, for there is no further principle in things, by which such a controversy can be decided. The succeeding substance will be considered the same as the preceding as long as the same law of the series, or of simple continuous transition persists, which makes us believe in the same subject of change, or the monad. The fact that a certain law persists, which involves all of the future states of that which we conceive to be the same – this is the very fact, I say, which constitutes the enduring substance. (G ,: L )

Note well that Leibniz’s attenuated conventionalism here is conducted against the backdrop of a full-blooded realism concerning facts of identity and difference with regard to laws-of-the-series. Leibniz takes off from a deep fact of identity – namely between a certain law-of-theseries at one time and at a later time. He then asserts, crucially, that there is no further fact that would justify a claim of diversity. So one is left with the fact of identity between the law-of-the-series at one time and at another. If one insists on calling the law-of-the-series in its later life Smith and the very same law-of-the-series in an earlier epoch Jones, that is just talk: what there is in reality is one and the same law-of-theseries, with no deeper principle of diversity that would lend metaphysical basis to the diversity of names.¹³ Permit us to run with this objectivist, realist picture. The dialectic is clear. There are deep facts concerning identity and diversity of law-of¹³ To the extent that one does find Leibniz endorsing a less attenuated conventionalism, it is to our knowledge always in the context of eschewing a deep principle of unity for aggregates – as in the claim to Arnauld that we can say of composites (e.g., flocks, blocks of marble) what Democritus said of them. Leibniz’s point there is continuous with the point we shall be urging in what follows – that the deep principles of unity and diversity go with identity and diversity of laws-of-the-series (form), and that any other superimposed claims of identity and diversity must have their basis in talk rather than in the world.



Sufficient reason and the identity of indiscernibles

the-series (relatedly, substantial form). Insofar as one is to say that a and b are one in a case where a and b enjoy differing substantial forms, one is in need of a principle of unity/identity that underlies difference with regard to law/substantial form which will entitle one to posit a single entity, despite a plurality of laws/substantial forms. Insofar as one is to say that a and b are two in cases where the substantial form is the same, one is in need of a principle of plurality/difference that underlies unity which will entitle one to posit many, despite a single substantial form/law. (Here and in what follows we use ‘law-of-the-series’ and ‘substantial form’ interchangeably, based on our conviction – defended in the following chapter – that laws-of-series are, for Leibniz, identical with substantial forms.) So there are two jobs that would need performing if one were to make the relevant posits. What resources are available for performing these tasks? It is quite clear that for Leibniz, sameness and difference of accidents will not perform either of these jobs. If substantial form/law-of-theseries is the same for both a and b, then a and b will not differ with regard to kinds of accidents: for on Leibniz’s picture, qualitative differences arise from a difference of law/form. (For more on this, see chapter .) Nor can Leibniz allow that mere numerical difference in qualitatively similar accidents provides the basis for diversity of substantial form/law; for on his account – and here Leibniz is in fine scholastic company – the individuation of accidents is parasitic on the logically prior individuation of substances to which they belong (cf. chapter , §.). A different option, perhaps, is to let relation operate as a principle of diversity. Suppose that a has a primitive relation of difference to b. That can operate as a principle of diversity despite coincidence of substantial form. Similarly, one might deploy spatio-temporal relations as a principle of diversity in a case of agreement of substantial form. In such ways, one might use relation as a principle of difference. But this option is unavailable to the mature Leibniz: as argued in chapter  he will not treat relations as metaphysically fundamental. (The topic of relations and individuation will be discussed further and at greater length in chapter , §..) Yet another option is to follow Aquinas. While substantial form alone is the ultimate ground of identity and difference of angels, it is matter that provides a principle of diversity in the case of corporeal substances. In principle, this strategy could be used as a ground of unity as well – so long as one supposed that the unity enjoyed by a material substance can

Explaining the no-reason argument for PII



be beholden to plurality of forms. (This supposition was an important topic of debate for the medievals, pitting Aquinas over against the majority opinion.¹⁴) But matter too is an option the mature Leibniz rejects as a possible foundation of unity and plurality of individual substances. (The topic of matter and individuation is considered at greater length in chapter , §..) A final option is to resort to Scotistic haecceities – to primitive individuating entities – as a principle of identity and diversity of substances. But here too it is clear that Leibniz would have no truck with non-quidditative haecceities of this sort. (Chapter , §.D; chapter , §; the topic of haecceitistic individuation is considered again in chapter , §..) In short, there is no ground in reality available for unifying diverse substantial forms or for diversifying a unified substantial form. What one is left with, then, as Leibniz has conceived the dialectic, are the facts of diversity and identity of substantial form as the only basis in reality for talk of identity and diversity. Seen in this light, Leibniz’s No Reason argument looks to emerge as a bit of sober metaphysics, not the wayward thinking attributed to him by Wilson and Adams. The proposed line of argument may be cast in the following way. Confronted with an exemplification of some substantial form, one can argue: (i) There is at least one instance of a substantial form. (ii) Nothing in the world can ground more than one instance of that substantial form. (iii) But there is more than one instance only if something in the world grounds more than one instance. (iv) So there is one and only one instance of that substantial form. After all, for any F, there is one F if and only if there is at least one F and there is not more than one F. Where F is the form under consideration, that there is at least one will be guaranteed by the initial hypothesis, that there is at least one instance of the substantial form. That there is not more than one is guaranteed by the lack of any principle for diversification of ¹⁴ More carefully, it was a particular instance of this supposition in its most general form – that the existence of more than one form in a substance S might be a necessary condition for the unity S – that was at issue in the debate between Aquinas and the majority. Arguments against the Thomistic account in favor of the rival many-forms account, drawn from theology (e.g., transubstantiation, the Incarnation) and philosophy (death, the notion of inherence), were typically in support of diverse sorts of forms – sensory and intellectual, say – in unified material substances. See chapter , §. (note ) and §..



Sufficient reason and the identity of indiscernibles

that substantial form. Lacking such a principle, there is not more than one: since there is at least one and not more than one, there is (just) one. Leibniz’s operative insight may be cast in slightly more scholastic terms. Insofar as a substantial form is in any way to be associated with more than one substance, it has somehow – as the scholastics say – to be ‘‘divided from itself’’ (here, there; present in this thing, present in that). Prima facie, there are three models for how a substantial form can be divided from itself. One is relation (paradigmatically spatio-temporal, but also possibly primitive). A second model posits some more ultimate subject of predication. A third posits some mode of combination of substantial forms with other components in such a way that one can make sense of numerically different composites sharing a substantial form. Relation is disallowed as a fundamental principle of self-division, as we read Leibniz. And no more ultimate subject of predication than form/law-of-theseries is available at the groundfloor of Leibniz’s metaphysic. What about combination? Clearly differing accidents cannot combine with the same substantial form, since accidents have their ground in form. Nor are bits of passive unsignated matter available. Perhaps Leibniz’s distinction between active form/law and primitive passive power invites the combination construal. But passive power, at most an aspect of an individual substance, is not something really distinct from form in combination with which form may be divided from itself.¹⁵ A somewhat different effort in this direction might suggest that a form can be ‘‘divided from itself,’’ if not in the typical way by combination with another, then perhaps by the corporeal substances to which they belong. But form itself must be the ground of expression which in turn, for Leibniz, is the ground of corporeal difference. And if substantial form plus laws of harmony ground the facts about what a thing expresses, then one cannot intelligibly conceive a and b to enjoy different properties of expression in the same world (supposing a and b are alike with regard to substantial form), since laws of harmony are fixed relative to a world and form is numerically the same. Nothing, in such a case, would explain the postulated difference in expression. (And, given that the ¹⁵ That is, nothing ‘‘really distinct’’ in anything like the scholastic sense (the formal distinction having no place in Leibniz’s account). In the context of considering corporeal substance, one does better – as recommended perhaps by the  June  letter to De Volder – to reckon both the active form or soul and the passive primary matter as abstractions, neither of which is strictly speaking part of a simple substance ‘‘completed’’ by these. Passivity in any case figures at best in an artificial construal of ‘‘combination,’’ projected onto the organic whole either by virtue of a distinction between passive and active aspects of a simple substance’s relation to an aggregate body, or else as an aspect of the degree to which a monad tends to imperfection or confused perception (cf. G ,: L ). For more on this see chapter , §..

Comparing the two styles of PSR argument



driving metaphysical picture is one refusing to make relations primitive, one cannot suppose that belonging to a corporeal substance could be a primitive relation in the world. See chapter  §. and the argument of chapter .) A similar strategy can justify Leibniz’s No Reason approach to TWD. Where a and b have different accidents, one can infer that a and b enjoy different laws-of-the-series/substantial forms. It is, after all, central to Leibniz’s view of the world that insofar as there is a difference in accidents, that difference is to be grounded in a difference in the laws-of-the-series from which such accidents emanate. Supposing, then, that a and b are transworld dissimilar with regard to accidents, one may conclude that a and b enjoy different substantial forms. In the earlier case, we required a principle of diversity in order to justify positing many where we have only one law-of-the-series. In the present case we require a principle of unity in order to justify positing one where there are many laws-of-the series. Lacking fair recourse to relation/matter/Scotistic haecceities/I-know-not-whats, one is left with many, with plurality. In the No Reason argument for PII, there is a principled metaphysical ground for taking identity as the default position: we have identity of law-of-the-series/form. In the no reason argument for TWD, there is a principled metaphysical ground for taking diversity as the default position: we have diversity of law-of-the-series/form. In the absence of any grounds in reality for finding unity underlying different laws or diversity underlying the same law, one is left only with the facts of diversity and unity of law/form. Insofar as one’s methods of counting reflect such facts, they will have a grounding in the world. Insofar as one’s method of counting does not reflect such facts, the ‘‘diversity’’ will have solely a nominal basis. It is, as it were, mere talk.                 P SR      Having recommended that the less familiar, prima facie implausible, No Reason argument from PSR to PII is no aberrant strain of momentarily bad thinking on Leibniz’s part, we should like to move now to examine more carefully how the two styles of argument for PII – Divine Preference and No Reason – are related, indirectly assessing which of the arguments looks to be the better. Our reflections here will be of a relatively general and exploratory kind, aimed at seeing just how Leibniz’s two arguments intersect other threads of this metaphysic.

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Sufficient reason and the identity of indiscernibles . Switching and interpenetration

Consider, for purposes of argument, a possible world with two indiscernibles at different places. The No Reason argument and the Divine Preference argument can be seen to operate in importantly different ways. As we have sought to show, the No Reason argument relies, inter alia, on Leibniz’s doctrine that external denominations require an internal grounding. Again, suppose they did not require such grounding. Then it would seem, in our present context, that one could appeal to either a primitive relation of difference or (granting a scholastic scenario of corporeal substance) a relation of distance as the grounds for multiplying substantial forms/laws-of-the-series. Acquiescing in such relations would require of an opponent of indiscernibles a retreat to the moral considerations implicit in the Divine Preference argument,¹⁶ as opposed to the logical-ontological considerations of the No Reason approach. (And here, perhaps, one might judge the presence of No Reason arguments in Leibniz as strong indirect support of our chapter  account of Leibniz on relations.) So the No Reason strategy cannot permit ungrounded relations in the fundamental metaphysics. The Divine Preference argument, by contrast, needn’t deny the possibility of primitive relations. For suppose that numerical difference or spatial distance could be primitive relations. Still, the Divine Preference argument would proceed as usual: even conceding that there are primitive relations of numerical difference or spatial distance, it seems clear that there is no moral difference between a world where the indiscernibles are switched (i.e. where they preserve the same difference/spatial relations to each other but diverging difference/spatial relations to everything else). Divine Preference can thus have dialectical force even against those who are not willing to agree with Leibniz that all external denominations of difference, space, and time have a grounding in the internal denominations of the things viewed as occupying the logical space of numerical difference or occupying space (recall, notably, the exchange with Clarke). In short, while the No Reason argument relies on intra-world considerations – specifically having to do with the ontological structures available for grounding truths about one and many – the Divine ¹⁶ ‘Moral’ considerations in the sense that Leibniz’s operative notion of ‘reasons’ in the Divine Preference argument concern judgments of value in deciding among competing worlds or states of affairs. See note .

Comparing the two styles of PSR argument

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Preference argument relies on inter-world considerations – specifically having to do with morally better and worse. In some cases, the conceptual addition of certain putative structures to the actual world may help to ground extra truths at those envisioned worlds, without doing anything to our intuitive judgments of moral superiority/inferiority as between those worlds and ours. This difference in strategies is an important and revealing one, worth pursuing further. The relevant contrast between Leibniz’s two arguments can be brought out with particular sharpness by considering what might be said about the metaphysical possibility of interpenetrating things. What is impossible about a world with interpenetrating indiscernibles? Bertrand Russell is one commentator who is aware that while Leibniz ‘‘no doubt relied, as a rule, on his readers admitting that two things could not coexist in one spatio-temporal point,’’¹⁷ the Leibnizian metaphysic nevertheless oughtn’t to be understood as bottoming out on any assumption of this nature. Indeed, it is arguable that Leibniz only makes this assumption in certain dialectical contexts and has no systematic reasons against interpenetrators from the point of view of high theory.¹⁸ That is not yet to say that he had no argument against indiscernible interpenetrators. So let us consider what a Leibnizian argument against indiscernible interpenetrators might look like, from both the Divine Preference and No Reason perspectives.

A. Divine preference Imagine (or try to imagine) a world containing a sewing pin, with two fully interpenetrating (i.e. spatio-temporally coincident) and indiscernible things dancing in step on the head of the pin. And consider first the following attempt to apply the Divine Preference argument: ‘‘But God would have no reason to prefer that world over one in which those dancers are switched around.’’ That is clearly no good. ‘‘Switching around’’ presupposes actual spatial or temporal separation. Assume actual interpenetration, and there is no switching to be considered. Is there still a version of the Divine Preference argument available here? If one assumed that there are not only primitive relations of difference available (as entertained above) but also Scotistic haecceities, there ¹⁷ See Bertrand Russell, The Philosophy of Leibniz, p. . ¹⁸ For a defense of this see §. of chapter , where interpenetration is taken up at considerable length.

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Sufficient reason and the identity of indiscernibles

arises a clear threat to the PSR requirements of Divine Preference. For while it makes no sense to suppose that the actual penetrators are switched around at some non-actual world, one can, having Scotistic haecceities at one’s disposal, imagine a world where one or both of the actual interpenetrators is replaced with a non-actual duplicate. Suppose it is Jim and Helen actually marching in step on the head of the pin. Unless – implausibly – being Jim and being Helen are the only haecceities that can enjoy the company of the indiscernible clothing of Jim and Helen, we might well suppose that there is another possible world where Jim and Harriet march in step. Here the concern of moral indistinguishability comes to the fore, and we have a version of the Divine Preference argument available. The difficulty, of course, is that were there Scotistic haecceities, Divine Preference arguments would tell against almost any possible world God might create, with or without interpenetrating duplicates. If He just created Helen, He could have created the indiscernible Harriet instead, with no moral cost. Perhaps there is another way of trying to run a Divine Preference argument against interpenetrating duplicates. If there could be two interpenetrating indiscernibles, then there is presumably a world where there are three interpenetrators of the same sort, and another world where there is only one and hence no interpenetration. Thus one might reasonably raise the concern whether God would have any reason to prefer the two over the three over the one. (Note that our ‘‘three rather than two’’ version of the Divine Preference argument relies solely on facts of numerical difference, whereas the Scotistic version relies on facts about which is which, who is who.) Here the difficulty is that if these alternatives really are a matter of moral indifference, then the argument will show too much. For the line of argument suggests that there is no moral difference between a world with just one dancer and a world with two interpenetrating dancers. But that would prohibit God from creating a world with just one dancer. For (the argument must go) why not create the interpenetrating-dancer world instead? In brief: if we take the Divine Preference argument to be of the form, ‘‘God wouldn’t make that world, because if He did, there would be another, morally equivalent world,’’ then it is hard to see how in the present context a Divine Preference argument is supposed to go. This result should not be surprising, since the basic strategy of Divine Preference arguments is to exploit inter-world switching, a tactic unavailable for interpenetrators. None of this is to deny that in a broader sense, moral considerations

Comparing the two styles of PSR argument

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concerning divine preference might, for a Leibnizian, tell against interpenetrating duplicates. If moral goodness involves, inter alia, a maximal ratio of number to variety, that might tell in favor of a world with one dancer over one with qualitatively redundant duplicates.¹⁹ B. No reason Now consider the No Reason argument. Moral indistinguishability is not the point at all there. Recall that when applying the No Reason argument to the imagined case of two intrinsically indiscernible and spatially separated things, there arose two pressing concerns: What is the ground of the relation of spatial separation? What is the ground of numerical difference? The need to find a grounding for spatial separation disappears in the case of interpenetrability. Of course, there is a need to ground spatial colocation. But that can be given easily enough in terms of each having the same spatial relation to everything else. The requirement of grounding the external in the internal cuts against the idea of there being duplicates having different spatial relations; but it hardly cuts against the idea of there being duplicates having the same spatial relations. Compare this with Russell’s observations concerning how Leibniz’s thesis that reality contains a continuum (of substancescum-qualitative-accidents) relates to PII. A thing’s place in the continuum supervenes on its intrinsic nature – a consequence of the requirement that the external be grounded in the internal. This entails that there couldn’t be two things that were intrinsic duplicates but at different places in continuum; but it hardly cuts against the idea that there could be duplicates at the same place in the continuum. As Russell notes, then, the continuum thesis ‘‘must be taken only as showing how the world can be explained consistently with the Identity of Indiscernibles. For continuity asserts that every place in the series is filled, whereas the Identity of Indiscernibles asserts that no place is filled twice over.’’²⁰ While the No Reason argument cannot exploit spatial separation in the case of interpenetrating duplicates, it can, however, exploit the relation of numerical difference implicit in such a case. The concern here is as before: there could be no ground in the world for numerical duplication of substantial form as required by the story. In the case of ¹⁹ Or not: there are tricky issues concerning judgments of harmony here. One might argue that infinitely many interpenetrators at each place would not disrupt harmony and would add to the plurality, and hence there is reason to think the actual world contains infinitely many duplicate interpenetrators at each location. ²⁰ Russell, The Philosophy of Leibniz, p. .

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Sufficient reason and the identity of indiscernibles

Divine Preference, one looks with a moral eye to other worlds in order to raise problems for interpenetrators. But in the case of the No Reason argument, there is no reliance on interworld comparisons of this sort. The No Reason argument requires that we consider only the lack of intraworld ground for substantial diversity. . The modal strength of PII What modal status does Leibniz attach to the claim that ‘‘There are no indiscernible but numerically distinct things’’? While it may seem rather natural to ascribe to him the view that it is impossible that there be indiscernible things, we have encountered already in chapter  textual reasons for thinking that Leibniz is sometimes modally cautious here.²¹ Since PII is seen by Leibniz as being deducible from PSR, we seem by implication to be faced with the contention that PSR is itself modally weak.²² In the first paragraph of his Fourth Reply, Clarke objects to the Divine Preference argument from PSR to PII on the grounds that it threatens divine freedom, leading as it seems to ‘‘universal necessity and fate’’. In replying, Leibniz notes, inter alia, that Clarke has failed to distinguish between two notions of necessity, one which ‘‘takes place because the opposite implies a contradiction (which necessity is called logical, metaphysical, or mathematical),’’ the other being ‘‘a necessity which is moral, whereby a wise being chooses the best’’ (G ,: L ). Exploiting this distinction, he goes on to remind Clarke that ‘‘to say that God can only choose what is best, and to infer thence that what he does not choose is impossible, this, I say, is confounding of terms; ‘tis blending . . . metaphysical necessity and moral necessity’’ (G ,: L ). So PII and PSR are both represented as being metaphysically ²¹ Chapter , §.. The lack of absolute or metaphysical necessity for PII is evident, for example, in §§– of the Fifth Letter to Clarke; but see also earlier in the letter, at Leibniz’s § response: ‘‘This supposition of two indiscernibles, such as two pieces of matter perfectly alike, seems indeed to be possible in abstract terms, but it is not consistent with the order of things, nor with the divine wisdom by which nothing is admitted without a reason’’ (G ,: L ). Also, in the Fourth Letter: ‘‘to admit a vacuum in nature is ascribing to God a very imperfect work’’ (G ,: L ). Note also that in his early Mediatio de principio individui (), Leibniz holds back from admitting necessity for PII: ‘‘And indeed, unless we admit that it is impossible that there should be two things which are perfectly similar . . . ’’ (A ..: DSR ). ²² As will be clear in what follows, Leibniz does embrace the ‘‘seeming implication.’’ But one should be cautious about assuming that all the relevant notions of modal strength are preserved by entailment. In particular, necessity per se, as it was conceived by Leibniz and others before him, was not automatically preserved by entailment. P can be necessary per se and entail Q, but it nevertheless be true that Q is not necessary considered in itself. See John Carriero, ‘‘Leibniz on Infinite Resolution and Intra-mundane Contingency,’’ pp. –.

Comparing the two styles of PSR argument

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contingent. This feature of the Leibnizian metaphysic is worth examining from the perspective of both the Divine Preference argument and the No Reason argument. Notice, at the outset, that while both styles of argument for PII – No Reason and Divine Preference – deploy what Leibniz calls his Principle of Sufficient Reason, the operative notion of reason is somewhat different as between the two arguments. The Divine Preference argument deploys a requirement of reasons construed broadly as final causes – that is, reasons construed as divine ends that justify the manner of God’s creation. The No Reason argument deploys a requirement of reasons construed broadly as truthmakers – that is, a requirement that for every truth there is something in the structure of reality, mirrored in the logical structure of concepts, that provides a ground for that truth.²³ Let us consider the modal weakness of PII on each construal. The modal weakness of the Divine Preference argument is relatively easy to render intelligible. Suppose we gloss this defense of PII as an argument to the effect that the best world will not contain numerically distinct indiscernible individuals. The demand to explain the contingency of PII from the Divine Preference perspective is parasitic, then, on the requirement to explain the contingency of God creating the best. There is of course a notorious prima facie obstacle to explaining the contingency of this world’s being actual ‘‘supposing it is the best.’’ God is necessarily perfect. But it seems that the necessarily perfect being necessarily wills the best. And being necessarily omnipotent, His will always succeeds. So He necessarily creates this world. The strategies that Leibniz offers at various points in his career to rebut this natural line of thought are well known. First he questions the move from perfect nature to perfect will by insisting that the divine nature does not necessitate the inclinations of the divine will. Second, he says that various worlds considered in themselves are ‘‘possible in their own nature, even if they are not possible in respect to the divine will’’ (Grua : AG ; cf. G ,: L ). Third, he marshals infinite proof considerations, according to which only at the limit of inter-world comparisons will it turn out that our world is the best. If only finitely provable truths are necessary, then it is contingent that this world is the best even while it is provably so at the limit. Note here that while the first ²³ Arguably each construal of ‘reason’ can be rendered univocally intelligible ultimately in terms of a further sense – that of efficient cause. Reasons construed as final require an efficient cause in the divine will; reasons construed as truthmakers require an efficient cause in the potentialities of the divine nature.

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Sufficient reason and the identity of indiscernibles

and second strategies rely – if in slightly different ways – on the thought that it is divine will, in contrast to divine nature, that is the source of contingency, the last (third) strategy does not obviously depend upon any such presumption. After all, there is infinite complexity at the level both of the divine will and of the divine nature, which may by the lights of infinite analysis allow one to locate contingency in each. This is a point to which we shall return. When one turns to the No Reason argument, there are rather fewer resources available that might allow one to make sense of the contingency of PII. As we have noted, the No Reason argument does not in any obvious way rely on inter-world moral considerations. It thus does not, in any obvious way, involve an implicit appeal to the machinations of the divine will. So even granting the contingency of which world is best, it remains unclear how to make out the contingency of PII from a Leibnizian perspective. Moreover, as we noted earlier in §., the No Reason argument is intimately connected to Leibniz’s predicate-insubject conception of truth, according to which every truth is to enjoy some sort of a priori grounding in the concept of the subject. If the PII flows from the very nature of truth, how can it be contingent? Now it is of course arguable that in those contexts where Leibniz expresses a willingness to entertain the contingency of PII, he has the Divine Preference argument in mind, and/or is in a dialectical context where, forgoing appeal to his deepest metaphysics, he is willing to grant for purposes of debate that indiscernibles are possible.²⁴ One might nevertheless wonder how Leibniz might have made sense of the contingency of PII from a No Reason perspective. One conceivable line of argument is this: God’s potentialities do in fact include such metaphysical paraphernalia as Scotistic haecceities, absolute space, primitive relations of difference and so on; nevertheless on moral grounds He simply does not actualize any such potentialities. This approach makes the No Reason ²⁴ In §. of chapter , in the context of recommending that one needn’t and perhaps oughtn’t ascribe a spatio-temporal connectedness requirement to Leibnizian possible worlds, we doubted that Leibniz was appealing to his deepest metaphysics in the early parts of the Theodicy. Our concern there was Leibniz’s concession to a strongly haecceitist permissiveness of indiscernible worlds: ‘‘[Given God’s plan to create the best] . . . nothing can be changed in the universe (any more than in a number) save its essence or, if you will, save its numerical individuality’’ (T §: H ). It is perhaps worth noting that one will encounter modally timid expressions of PII early in the Theodicy, such as the following: ‘‘[T]he case of Buridan’s ass between two meadows, impelled equally towards both of them, is a fiction that cannot occur in the universe, in the order of Nature. . . It is true that, if the case were possible, one must say that the ass would starve himself to death: but fundamentally the question deals in the impossible, unless it be that God bring the thing about expressly’’ (T §: H , our emphases on the modally timid bits).

Comparing the two styles of PSR argument

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argument parasitic on Divine Preference considerations. For on this approach it is in no sense part of the essential nature of every possible thing that it lacks a duplicate. Rather it is merely in the nature of the kinds of things God has actually created. (How can this be made to rest easily with the idea that the No Reason perspective is wrapped up with a view about truth? Well, by reading the predicate-in-subject account as the claim that every truth about the things God has actually created is such as to have a basis in the subject, and one endows the doctrine with the requisite modal weakness. This is not to say that there is no modal robustness left. The things that God actually created may still be necessarily such as to provide a metaphysical foundation for the predicates true of them. That is consistent with God’s nature allowing for the possibility of other things for which the law of contradiction but not the predicate-in-subject doctrine is satisfied.) This perspective will no doubt strike the reader as very un-Leibnizian. We shall consider just how un-Leibnizian it is in § below. A rather different strategy for trying to secure the contingency of PII from a No Reason perspective is to invoke infinite analysis. Only at the limit can one prove the truth of the statement Caesar is Caesar, since only at the limit of analysis will we have fully analyzed the right and left subject terms and recognized no basis for a distinction. Generalizing, the proof of the identity of a and b where a and b are indiscernibles will require infinite analysis, and so the statement of identity of a and b will have, by the standards of contingency implicit in the infinite analysis doctrine, the status of contingent truth. Now there is of course a sense in which Leibniz’s No Reason account, as we have interpreted it, offers a finite proof for PII: . Nothing could ground the multiplication of substantial forms. . For there to be a possible plurality of indiscernible substances, it must be possible that something in reality ground the multiplication of substantial forms. . Therefore, there is no possible plurality of indiscernible substances. True enough: that is a sound argument given Leibniz’s metaphysical views. But it is not a sound argument counting as a proof in the strict sense Leibniz intended for the infinite analysis doctrine. Thus, if one thought of the proof that Caesar has no distinct duplicate as proceeding via the infinite analysis of Caesar’s complete concept, one can make

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Sufficient reason and the identity of indiscernibles

some sense of the claim that PII is contingent, even from a ‘‘No Reason’’ perspective. We hesitate, however, to parade this way of rendering intelligible the contingency-overtones of certain PII texts. For it does, after all, require our playing up ‘Caesar is Caesar’ as contingent – hardly one of the results of the infinite analysis doctrine about which Leibniz should be most proud. Leibniz’s hope for infinite analysis, when applied to the creaturely essences in the divine mind considered as possible rather than to the actual/non-actual distinction, is meant to offer an account of how one can salvage in particular the contingency of free-action predicates contained in concepts of possible agents. If it turns out that the strategy lends contingency to both ‘Caesar sinned’ and ‘Caesar is Caesar’ – as we fear it does²⁵ – then it presumably can’t do the crucial job of salvaging the contingency needed for freedom. Perhaps considerations having to do with miracles provide a better way of accounting for the modal weakness of PII. Assume that an individual substance gives rise to the accidents dictated by its law-of-theseries only barring miracles (see chapter ). (And correlatively, assume that the reason for the truth of a predication can be found within a subject only supposing that God declines to miraculously interfere: when God does so interfere, the truth is grounded in God’s miraculous will and not the subject.) Then one can make sense of numerically distinct substantial forms/laws-of-the-series with the same accidents – where the reason for the accidents of the one thing is to be found in its law, and the reason for the accidents of the other thing is to be found in part in the vicissitudes of divine tinkering. This view leaves a core doctrine as necessary – namely that two things cannot have the same form/law-of-the-series – and drives a miraculous wedge between law and accident. On this account, one’s pessimism about discovering perfectly indiscernible leaves in the garden²⁶ will be based in part on the deliverances of revelation or on one’s moral sensibility concerning the extent to which a good God would interfere with the laws of development that He prescribed for things at creation. Whether this is a bona fide way of making sense of the contingency of PII depends on what one makes of Leibniz’s view on miracles. On one interpretation, the sort of tinkering that this story requires is not one that Leibniz’s metaphysic ²⁵ See John O’Leary-Hawthorne and J. A. Cover, ‘‘Infinite Analysis and Possible Concepts.’’ ²⁶ And (permit us license) one’s optimism about discovering indiscernible wafers in the orthodox mystery of the Eucharist – where the relation among the wafers is not only qualitative similarity but identity. That sort of discovery would scarcely be relevant to PII in the present context.

Divine will, divine nature, and metaphysics

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permits, even when God is said to work in miraculous ways (chapter , §.). Once again, we are hesitant to parade this account of the concession that PII is contingent from a No Reason perspective. In sum, then: the task of making sense of the contingency of PII is relatively unproblematic from a Divine Preference perspective. When one turns to the No Reason approach, however, matters are far more difficult. Although we have offered some speculative reconstructions of the contingency of PII from within the framework of that approach, none of those attempts can be firmly rooted in what Leibniz himself actually offered.           ,         ,        There is an approach to metaphysics one can associate with allowing matters to bottom out with divine preference. In order to provide a flavor for such an approach, let us begin by imagining that all sorts of weird and wonderful metaphysical structures are possible, on account of the fact that one is guilty of no logical contradiction in entertaining them. Since, for example, there is no straightforward contradiction in the notion of a Scotistic substance, such substances are possible even if they are not actual. They are not actual for the simple reason that God chose not to create substances like that. Against the background of scholastic and contemporary concerns to get at the bottom of issues about individuals as such, one is inevitably left a little disappointed. But if possibility is sheer logical possibility, then perhaps there is very little that is useful to say about individuals as such. What ought to be of interest to the metaphysician, according to this approach, is the metaphysical structure of the things that belong to the natural order that God sees fit to create. This in turn is to be cashed out – presuming of course that one sticks with theism – in connection with considerations of final causes, grounded ultimately in the divine will. Not surprisingly, in contexts when Leibniz feels the need to recognize the limitless power of God, he is ready to speak of God’s potentialities extending in all sorts of strange and wonderful directions. In those contexts, it appears that the question ‘‘What order is suitable to divine wisdom?’’ is the key to all the interesting metaphysics, and not, say, the question ‘‘What principles of individuation govern all the possible things that it is within God’s absolute power to create?’’ An excellent case in point is provided by Leibniz’s discussion of personal identity in the New Essays (.xxvii). When considering bizarre possibilities – an exchange of

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Sufficient reason and the identity of indiscernibles

conscious states between two souls; the creation of vacuums; the existence of two indiscernible souls that duplicate each others’ history; my consciousness extending backwards to a different soul so that I remember its states; my being deceived about my own inner conscious life; and others still – Leibniz repeatedly wants to say that God has it within His power to make the world in that way, but that their actuality is contrary to the natural order which God’s wisdom in fact dictates. Thus (note well the relevant provisos): I have already said that there can be an intelligible reason for the element of error in perceptions which are mediate and outer, but with regard to immediate ones such a reason could not be found except by having recourse to God’s omnipotence. (RB ) I admit that if God brought it about that consciousness were transferred to other souls, the latter would have to be treated according to moral notions as though they were the same. But this would disrupt the order of things for no reason . . . (RB ) I acknowledge that if all the appearances of one mind were transferred to another . . . [then this would require] a miracle – like supposing God to create a vacuum. For I have already explained why this is not in conformity with the natural order. (RB –) if we are speaking of what can naturally occur . . . the two similar souls could remain similar only for a time. Since they would be numerically different, there would have to be a difference at least in their insensible constitutions, and the latter must unfold in the fullness of time. (RB –)

But (to our minds) it is best to resist thinking that Leibniz fully endorsed any such approach to metaphysics. That approach relies on the idea that, in effect, talk about what is metaphysically possible is rather a free-for-all, constrained only by the principle of contradiction.²⁷ Yet in the context of Leibniz’s considered views about the nature of divine ideas and their modal implications, one can see that possibility space has a rather more disciplined structure than the picture painted above would lead one to think: recall the discussions of complete concepts and possibility, for example, in chapters  and . True enough, Leibniz believed that the Principle of Contradiction is the ‘‘great prin²⁷ We note in passing that the free-for-all approach to possibility lacks currency on the contemporary scene. No one argues: ‘‘There is a possible world with numbers and a possible world without numbers. After all, there is no contradiction in affirming the existence of numbers, and no contradiction in denying the existence of numbers, logic itself being neutral on questions of existence.’’

Divine will, divine nature, and metaphysics

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ciple of reason’’ relevant to arguments about possibility. But for an idea to be possible, it must be decomposable into simple ideas in God’s mind (simple divine potentialities). The Principle of Contradiction operates practically as a test for possibility only when one knows what the genuine simple concepts are. If, as seems plausible given Leibniz’s mind-set, there are no combinations of simple potentialities corresponding to, say, Scotistic extravagances, then such talk will not express genuine possibilities. From the point of view of his logico-semantics, it appears that at least a good deal of interesting metaphysics will flow from a consideration of divine potentialities. Thus, all possibilities are given by combinations of simple substances constituted by a law-of-theseries/substantial form that at once individuates them, and at the same time provides the ground for the accidents inhering in them; extrinsic denominations will have no fundamental role in depicting any possible world, and they will, for every world, flow from the combination of lawsof-series that constitute each world; at no world will any accident have its feet in two substances; at no world will an accident migrate from one substance to another; at every world, accidents will emanate from laws-of-the-series created by God. So at no world will there be homogeneous matter, absolute time and space, vacuums, free-floating accidents, exchange of conscious experiences between souls . . . and so on. Allied to Leibniz’s favorite logico-semantics, metaphysics will be not so much an investigation of divine preference as an investigation of the structure of divine potentialities. And so we have a contrast. Emphasize the absolute nature of omnipotence, and little metaphysics of interest will emerge from a study of the structure of divine potentialities. Emphasize the structured character of divine potentialities, as dictated by the simple forms that await combination, and modal metaphysics has plenty to say. As it plays itself out in the Leibnizian corpus, this contrast merits further investigation. It is a research project that we leave to others. What is the ultimate locus of justification for the Principle of the Identity of Indiscernibles? On the one hand, the Divine Preference approach connects PII with the divine will. On the other hand, the No Reason approach connects PII at least primarily with the divine nature. Insofar as one connects any central principles of Leibnizian metaphysics with the divine will and leaves it at that, one opens the door to the contingency of PII. Here then are three pictures implicit in our discussion: () The ultimate locus of all basic principles about number, individuals,



Sufficient reason and the identity of indiscernibles

form, and accidents is the divine nature. Here, deploy the No Reason argument for PII. () Distinguish the thesis that no two things have the same substantial form/law-of-the-series from the thesis that no two things share the same accidents/intrinsic history. The former is grounded by the divine nature, the latter by the divine will. Here, deploy the No Reason argument to get the former, and use the Divine Preference argument to get from the former to the latter. () The ultimate locus of all basic principles about number, individuals, form and accidents is the divine will. Here, deploy the Divine Preference argument for PII. The exegetical task of sifting out a considered Leibnizian view is made difficult by a confluence of tensions and by several loose ends, noted here. Consider that at least one of Leibniz’s guiding conceptions of distinctions between possibility, necessity, and actuality connects the triad above with the distinction between God’s nature and God’s will. Put bluntly: God’s nature determines possibility space, God’s will determines what within possibility space is to be actualized. Against the background of this conception, the Divine Preference argument tends toward the thesis that PII is actually true though contingently so, while the No Reason approach tends towards the thesis that PII²⁸ is necessarily true, it being common to all God’s conceptions of possible creation. Viewed in this way, it is not surprising that Leibniz vacillates between more and less modally committal ways of speaking in connection with PII. When the issue is that of motivating a certain style of divine decision-making, he claims ‘‘I don’t say ’tis absolutely impossible to suppose [two drops of water perfectly alike] but that ’tis a thing contrary to the divine wisdom’’ (G ,–: L ); when concerned with the ontological ground of truths about one and many, he says ‘‘If two individuals were perfectly similar and equal and, in short, indistinguishable in themselves, there would be no principle of individuation. I would even venture to say that in such a case there would be no individual distinctness, no separate individuals’’ (NE .xxvii.: RB ) Alongside the explication of necessity, contingency and actuality in terms of nature and will, however, there is another, prima facie orthogonal distinction – between that which can only be proved at the ²⁸ At least it tends that way in the form-indiscernible version, setting miraculous fiddling with accidents aside.

Divine will, divine nature, and metaphysics

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limit by infinite analysis and that which can be proved by finite means. When played out in this way, the contingency of PII can prevail even when, at the limit, the Identity of Indiscernibles is mandated by the divine nature. We doubt that the nature/will conception was very properly reconciled with the infinite analysis conception in the Leibnizian scheme.

 

Law-of-the-series, identity, and change

As noted at the end of chapter , a theme of the mature Leibniz’s metaphysic conspicuously absent from the Disputatio is the identity of persisting individual substances over time. We develop that theme in the current chapter, indicating how its treatment in the hands of Leibniz is distinctive in comparison with both scholastic and contemporary approaches. In this context we can deliver on some promissory notes of previous chapters about the nature of individual substances themselves. Scholastic philosophers gave no privileged place in their accounts of individuation to what contemporary metaphysicians have invented as something of a pastime – the topic of diachronic identity.¹ This is not to deny that at some level the scholastics had views about the diachronic aspects of substances: in particular, substances endure through time despite a change of accidents. Accounts of what constitutes a substance’s persisting over time, meanwhile, were wrung from a much broader range of considerations than one finds in contemporary approaches to diachronic concerns about substances. Of special import for the scholastic turn of mind were kinds of change in addition to change of accident. In particular, two other sorts of change, very much at the metaphysical groundfloor, demanded attention: (i) Aristotelian generation and corruption, whereby substances arise and dissipate in the natural world, and (ii) ex nihilo creation and annihilation. In investigating (i) and (ii) scholastic metaphysicians found pressure towards a component ontology of individual substance – to what we called in chapter  a ‘‘blueprint approach’’ to individuation. While workaday survival ¹ Or anyway, so the topic – the familiar cluster of issues associated with this nomenclature – has unfortunately come to be called: the quiet implication that there is a kind of identity called ‘‘diachronic’’ is, of course, silly. That adjective applies not to identity (the relation that everything stands in to itself and nothing else), but to questions or problems arising in connection with enduring things. Our topic in this chapter is diachronic aspects of Leibniz’s individual persisting substances.

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Law-of-the-series, identity, and change

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through change forces a distinction of substance from accident, (i) and (ii) appear prima facie to require, on the one hand, a distinction of matter from substantial form, and on the other a distinction of essence from existence. In brief, matter provides the before and after in substantial generation and corruption, while the essence (accounting for the potentiality of a thing’s coming into existence at all) provides the before and after in creation ex nihilo and annihilation. The different sorts of coming-to-be provided only one kind of pressure towards a component metaphysic. The apparent existence of natures/kinds/species in common to all humans or all horses (say) also provided decompositional pressure – in this case in favor of decomposing a substance into common nature plus certain further ingredients. Armed with a component-style scholastic metaphysic, one might well imagine the kind of account of diachronic identity that resulted: one analyzes a given substance into certain essential components, and provides conditions for its survival in terms of them. (And what if one now asks after the persistence conditions for the components themselves? Were a component ontologist pushed in this way, at some point along the decompositional road he will have to admit that either the diachronic identity of some component is incapable of analysis, or else offer an analysis that is other than component-style.²) As one turns to contemporary trends in philosophy, one finds in place a style of analysis that is very much other than component-style. The contemporary strategy in large measure tends to proceed in terms of relations between individuals and their later selves, where such relations typically include relations of continuity – causal, spatio-temporal, psychological, and so on – but may include other sorts of relations as well (recall the role of origins in Kripke). We thus have before us two sorts of models for approaching questions about the persistence of individual substances over time: component models and relational models. Insofar as any philosopher adopts a metaphysic of enduring things, he will invite deep questions of substantial persistence. Leibniz is no exception. What is of special interest in connection with Leibniz is that neither the component nor relational models of identity through change align especially well with his picture of the world. As we shall argue, and as one might on reflection expect from the writer of the Disputatio, Leibniz is not especially sympathetic to a com² Assuming the things don’t have components all the way down, i.e. that it is not the case that every component has components.

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Law-of-the-series, identity, and change

ponent metaphysic of individual substances. Against the background of scholastic motivations for a component metaphysic, it is hardly surprising that Leibniz himself does not opt for that style of account. The nominalism of the Disputatio which precluded his reifying common natures is never rescinded. Nor does Leibniz ever go back on the conviction that essence is not really separable from existence (the urargument of Disputatio §§– being that if essence were left over after the putative separation, it would exist). Finally, the mature Leibniz will find no motivation for a component ontology from Aristotelian generation and corruption in nature, since there is no place in his scheme for the generation and corruption of individual substances – this by his lights precisely owing to their simplicity. The orientation of the mature Leibniz thus appears to cry out against a component ontology. There are, however, tendencies in the other direction. Leibniz does, after all, speak of individual substances as each containing their own law-of-the-series, and appears to take such laws with ontological seriousness. Moreover he distinguishes the primitive active and primitive passive force in substances. Aren’t these signs of commitment to a component ontology? What is needed here is an account of Leibniz’s metaphysic of laws-of-the-series, active forms and forces, and their relation to individual substance themselves. We shall undertake to recommend such an account, resisting pressures to read Leibniz as a component ontologist. Reflecting now on the contemporary, relational-style approach, it seems equally clear that such an approach stands at some distance from the Leibnizian way of doing things. As we have urged, Leibniz does not wish to put relations to serious metaphysical work.³ Any account of diachronic identity that bottoms out with relational facts will thus have no place in the Leibnizian scheme. But what is Leibniz to put in place of this? Given his views on relations, we know that diachronic facts relevant to identity over time will be grounded on how things are internally with the relata. But how, if at all, can any meat be put on these schematic bones? We do our best on Leibniz’s behalf in the body of this chapter.

³ See chapter . Of course, it might be argued that Leibniz’s concern was with inter-monadic relations and that he would have no problem with deploying intra-monadic relations as the ground of diachronic identity. We suggested in chapter  that trans-temporal but intra-monadic relations demand analysis for Leibniz every bit as much as inter-monadic relations. The positive picture of diachronic identity developed in this chapter on Leibniz’s behalf is very much in keeping with that suggestion.

The metaphysics of individual substance

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                                 .. Complete concept and haecceity Central to the mature Leibniz’s account of individual substance are two categories of notions. First is a set of general defining features of substance, familiar from the Aristotelian tradition and firmly fixed by the intension of ‘substance’ as then conceived: (a) that which is independent of other things; (b) that which is the subject of predication, but is not predicated of another; (c) that which contains within it a principle of activity; and (d) that which persists through change.⁴ Second is a set of core notions deployed with their distinctive Leibnizian glosses: complete individual concept, law-of-the-series, active force, form, and soul or entelechy. As we now turn to seeing how these threads are woven together in the Leibnizian scheme, the notion of a complete concept provides the easiest point of entry. The complete concept doctrine as Leibniz understands it entails that there is some strong connection between all the predicates true of a substance S (alternatively, all the intrinsic properties/accidents it enjoys), on the one hand, and the metaphysical guts – the nature – of the substance S itself on the other. However strong it may be, that connection isn’t identity: first, a substance is a genuine unity, one and not many; second, as noted in (b) above, substances fall under concepts, have predicates true of them, and are the bearers of properties/accidents, and so are not themselves concepts or predicates or properties; and third, substances are created, contingent, causally active individuals while concepts are eternal, necessary, passive items in the mind of God. Distinguishing then between the complete concept of S and the inner nature of S by virtue of which all the predicates contained in or specified by its complete concept are true of S, Leibniz says, familiarly: [W]e can say it is the nature of an individual substance or complete being to have a concept so complete that it is sufficient to make us understand and deduce from it all the properties of the subject to which the concept is attributed. God . . . in seeing the individual notion or haecceity of Alexander, sees in it at the same time the basis and the reason for all the predicates which can be truly affirmed of him . . . There are at all times in the soul of Alexander traces of all that has happened to him and marks of all that will happen to him.⁵ ⁴ See chapter , note . ⁵ Discourse §: G ,: L,. A discussion of marks and traces will be taken up in the sequel: see §. below.

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Law-of-the-series, identity, and change

Following our discussion in §. of chapter  on Leibniz’s haecceitism,⁶ suppose we borrow from the letter of the second passage above – where Leibniz looks to identify the haecceity of Alexander with his complete concept – and call the Haecceity (capital ‘H’) of a substance that metaphysically basic foundation of or in the individual substance, corresponding to the complete concept, by virtue of which Leibniz here claims the substance has the properties/accidents it does.⁷ We learned in chapter  that neither the complete concept nor its metaphysical counterpart Haecceity can be construed, as the ‘natural interpretation’ would have it, on the model of a mere list or conjunction: crucial here is Leibniz’s insistence that what God sees in the complete concept – what is furnished by S’s Haecceity – are genuinely explanatory resources for the properties/accidents of S.⁸ If, as should by now be relatively apparent, Leibniz believes that the complete concept of an individual substance S serves as a materially adequate expression of the metaphysical principle of individuation for S, then it is no less clear that the Haecceity of a substance, being the metaphysical foundation for all predicates expressed by its complete concept, suffices for marking off that individual from all other individuals. But taking seriously now the scholastic inclination to treat the individuation of substances in terms of the role played by various elements or entities said (modulo some distinction) to be ‘‘in’’ an individual, we may ask: is there more to S than the Haecceity of S? Put otherwise: does Leibniz’s mature metaphysic of individual substances include more than we have described as ‘‘that in the nature of a substance by virtue of which it has the properties it does’’? Still otherwise: granting his commitment to the general defining features of substance (of the sort noted in our first category above) and the core notions operative in Leibniz’s account of substance (as in our second category above), is the mature Leibniz forced to admit any kind of compositional picture of individual substances? The question could be ⁶ And following the usage of Paul Bartha at p.  of his ‘‘Substantial Form and the Nature of Individual Substance.’’ ⁷ Recall from chapter  that in Discourse §, to the objection ‘‘But someone might insist that [Caesar’s] nature or form corresponds to this notion, and since God has imposed this personality on him, it is henceforth necessary for him to satisfy it,’’ Leibniz replies not by denying that the nature of a substance corresponds to the complete notion, but by denying that this (with premises) entails the absence of freedom. We’re calling this metaphysical item that Leibniz thinks corresponds to the complete concept of S the nature or Haecceity of S. ⁸ And so Leibniz must resist the Russellian picture according to which ‘‘Predicates do not inhere in the substance in any other sense than that in which letters inhere in the alphabet’’ (Bertrand Russell, A Critical Exposition of the Philosophy of Leibniz, p. ).

The metaphysics of individual substance

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viewed as one that might be put to the mature Leibniz himself, in reflecting on the core position of the early Disputatio: if Haecceity, construed in the scholastic spirit as among the res of the created world, individuates a substance, is substance individuated by whole entity? . Haecceity and the law-of-the-series If the nature or Haecceity of an individual suffices to ground all its predicates (in a sense of ‘grounding’ undoubtedly yet needing to be filled out), then Leibniz has secured by it individuation of the robust sort he sought both early and late – of the sort entailing what in item (a) of our first category we called ‘‘independence’’ or separability: given the Haecceity alone we are guaranteed that all the predicates true of an individual will indeed belong to it as a consequence of its nature, no assistance from the outside needed (divine concurrence aside, of which more later). The predicates or accidents of S do not belong to it haphazard-like, of course: the career of a substance is an ordered, lawful unfolding of its properties/accidents, in accordance with its nature. There are clear Aristotelian overtones here, tracing ultimately from Aristotle’s view (of book  of the Physics and elsewhere) that the distinguishing mark of what exists by nature (as opposed to artifice) is its possessing an innate impulse for regular, explainable change – fire upward, earth downward, acorns-to-oaks, and so on. In part, too, Leibniz doubtless saw that his aim to give metaphysical underpinning to a lawful mechanical physics demanded natures having an intelligible lawlike structure. In his most outspoken mature discourse on the idea of the Haecceity or nature of individual substances (De Ipsa Natura, ), Leibniz begins by insisting that ‘‘the origin of mechanism itself has come . . . from a higher and so to speak, a metaphysical source.’’ The ultimate source is of course some original divine decree together with the perfections of God; but Leibniz is at pains to argue – against certain occasionalist sentiments – that such a decree, far from acting directly though at a temporal distance on creatures themselves, has instead left behind in them an ‘‘internal law (legem insitam) from which their actions and passions follow’’ (G ,: L ). ‘‘The law set up by God does in fact leave some vestige of him expressed in things’’ – what, he says, ‘‘we usually designate by the name nature, from which the series of phenomena follows according to the prescription of the first command’’ (G ,: L ). Earlier, in a letter to Arnauld of , Leibniz had claimed that ‘‘each substance contains in its nature a law



Law-of-the-series, identity, and change

of the continuation of the series of its own operations’’ (G ,: LA ). Nowhere does Leibniz give one good reason to think that such language of ‘‘containment in the nature of a thing’’ implies composition of the scholastic sort. Quite the contrary implication was explicit in the early Leibniz, where already a familiar theme of the mature years – that the Haecceity or nature of each individual substance embodies a ‘‘law of the series’’ – is expressed by his claim of  that ‘‘the essence of substances consists in . . . the law of the sequence of changes, as in the nature of the series in numbers’’ (A .., our emphasis). There is nothing unwitting or shortlived about this expression of a strong connection between the law-of-the-series and a substance’s Haecceity or nature. In his  reply to Bayle’s criticism of the New System, Leibniz writes that ‘‘This law of order . . . constitutes the individuality of each particular substance’’ (G ,: L ). So far as we can discover, the texts give no good reason to be hesitant about identifying the Haecceity or nature of S with S’s law-of-the-series, no reason thus far for seeing any compositional overtones in Leibniz’s mature doctrine of individual substance. Recall again our earlier query: is there more to S than the Haecceity of S? Does Leibniz’s metaphysic of individual substances require of or in them more than we have described as ‘‘that in the nature of a substance by virtue of which it has the properties it does’’? There is little reason to deny a negative response on this question. In the Theodicy Leibniz reminds us ‘‘that by nature every simple substance has perception, and that its individuality consists in the perpetual law which brings about the sequence of perceptions’’(T §: H ). Here the theme of ‘whole entity’ looks to remain: the place of individual laws-of-the-series in Leibniz’s mature account of substances is the place of substances themselves. Were that incorrect, it would be altogether surprising that Leibniz should treat laws-of-the-series themselves as securing item (d) in our first category above – that substances are enduring, persisting things. In a letter of  to De Volder Leibniz writes: For me nothing is permanent in things except the law itself, which involves a continuous succession and which corresponds, in individual things, to that [law] which is of the whole universe . . . The fact that a certain law persists, which involves the future states of what we conceive to be the same – this is the very fact, I say, that constitutes the same substance (G ,–: L –).

The Haecceity of S, then, is the law-of-the-series of S – that is, S itself.

The metaphysics of individual substance

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. Laws-of-the-series and form as active If on broadly textual grounds one invited to grant that what Leibniz alternatively calls the nature, the law-of-the-series, of S is the substance S itself, there may yet be other pronouncements of Leibniz on the metaphysic of individual substance compromising the view that substances do not ‘‘decompose’’ in the scholastic sense. Are there such pronouncements requiring us to recognize distinct metaphysical elements in substances not yet identified, playing distinct roles not yet broached? If so, does Leibniz succeed in incorporating them into a unified and complete account of individual substance? One might be tempted with the following line. No doubt Leibniz saw Haecceity and law-of-the-series as fundamental to a proper account of individual substance; and indeed he may well have taken these to be alternative expressions of one and the same metaphysical component in his story of what an individual substance is. But Leibniz thought there was more to an individual substance than this, as evidenced by his emphasis on the concepts of activity and form. Following an analogy of R. S. Woolhouse, one might think of the Haecceity or law as being ‘‘like the scripts for a play,’’ similar to Leibniz’s own metaphor of a musical score or a mathematical formula.⁹ However much there may be of both content (what we earlier viewed as the metaphysical counterpart to the complete concept) and order (as prescribed the law-of-the-series) in our sketch of individual substance offered thus far, there is nothing yet of activity in it, nothing that secures item (c) in our first category above – that substance is that which contains within it a principle of activity. Scripts and formulae are one thing, actors and point-plotters quite another. Hence there must be, in the Leibnizian individual substance, some distinct component playing a distinct role – what he calls the substantial form or soul. And thus is Leibniz’s mature metaphysic of individual substance very closely akin to the traditional ‘‘compositional’’ accounts of the scholastics. Paul Bartha defends just this line, arguing further that while ‘‘Leibniz held something like Scotus’ theory of a two-component nature of substance,’’¹⁰ his account is void of any theoretical apparatus like that of the scholastics via which to unify these components of substance. Indeed, perhaps Leibniz ‘‘simply could not reconcile himself to any sort of ⁹ See p.  of R. S. Woolhouse, ‘‘The Nature of an Individual Substance.’’ ¹⁰ Bartha, ‘‘Substantial Form and the Nature of Individual Substance,’’ p. . The two quoted items to follow are from p. : the two following that are from p. .

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Law-of-the-series, identity, and change

composition within a monad’’ despite the distinct elements he was avowedly committed to. On Bartha’s account, ‘‘There is no way for Leibniz to accommodate the two elements of substance which are demanded by his philosophy.’’ Hence, ‘‘it is mistaken to think that Leibniz had a fully developed conception of substance’’; at best he offers ‘‘only a partial characterization of the nature of individual substance.’’ There is no doubting that Leibniz departed in crucial respects from Scotus’s project, at least this far: for Scotus, the haecceity of an individual was a positive non-quidditative entity which, together with a common nature from which it was formally distinct, played the role of the ultimate differentia, thus individuating the substance. Leibnizian Haecceity too serves to individuate the substance, but (chapter ) is nevertheless quidditative – that is, has content corresponding to the complete concept. The crucial question is whether Leibniz agrees with Scotus to the extent of endorsing a further component in the individual substance distinct from its Haecceity, distinct from its law-of-the-series. And the proposal is that he does, in his commitment to form or a principle of active force. There seems to us to be little direct evidence for this view, and sufficient textual evidence against it as correctly representing Leibniz’s account of individual substance, early or late. The evidence for it, to Bartha’s reckoning, is the absence of texts indicating any willingness on Leibniz’s part to see Haecceity or the law-of-the-series as accounting for the activity of substance, and the wealth of texts in which Leibniz has form itself to play this role. But already in  Leibniz appears willing to identify the law-of-the-series with primitive force of action: in his notes on Foucher’s reply to his critique of the Recherche de la veritate, Leibniz insisted that ‘‘the essence of substances consists in the primitive force of action, or in the law of the sequence of changes’’ (G ,: L,). This theme is a constant of Leibniz’s thought well into his mature years. Indeed, its frequency throughout the mature texts manifests the extent to which his thought during the so-called middle years is relatively continuous with his later monadological account. It is true that the thread in Discourse §§– runs pretty quickly from the complete concept to what Leibniz says ‘‘ancient and scholastic philosophers had some knowledge of when they spoke of substantial form,’’ without specific attention there being given to active force. But there is little doubt even here that this latter element in Leibniz’s account of substance, found in the notion of form, entelechy, or soul, is what Leibniz is explicitly prepared to identify with the law-of-the-series. In De Ipsa Natura of 

The metaphysics of individual substance

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Leibniz speaks of ‘‘a soul or form analogous to the soul – a first entelechy, that is, or a kind of nisus or primitive force of action which is itself that inherent law impressed upon it by the divine command’’ (G ,: L ). The next year he writes to De Volder that I recognize, in the active force which exerts itself in various ways through motion, the primitive entelechy or in a word, something analogous to the soul, whose nature consists in a certain perpetual law of the same series of changes through which it runs unhindered. (G ,: L )

In the next letter (skipping a draft not sent) to De Volder, Leibniz identifies this ‘‘primitive entelechy’’ with the monad (G ,–: L –). If the direct textual evidence recommends heavily against reading Leibniz as endorsing a compositional account on which the Haecceity or law-of-the-series is to be distinguished from (as Leibniz often puts it) the ‘‘form or force,’’ one might add as indirect evidence the very feature Bartha finds puzzling – that Leibniz’s theory of individual substance is void of any theoretical apparatus like that of the scholastics via which such putatively distinct elements would be united. From the Disputatio on through to the New Essays, Leibniz is unwilling to accept the virtual (formal) distinctions many of his predecessors had pressed in this service. Scotus (and more immediately familiar to Leibniz, Fonseca, Pererius, and Bassolis) had insisted that the haecceity and the form of a substance were only formally, not really distinct. Such virtual (not real) distinctions are on Leibniz’s mind when – now leaving well behind complaints about ‘‘common nature’’ – he writes, in the New Essays: I was surprised one day to find in the Summa of Theology of Father Honore Fabri . . . that he denied the validity in divine matters of the great principle that things that are the same as a third thing are the same as each other . . . In his Philosophy the same author rejects the ‘‘virtual distinctions’’ which the Scotists apply to created things, because, he says, they would violate the principle of contradiction; and when it is brought against him that we must acknowledge such distinctions in God, he replies that it is ordained by faith. But how can faith ordain anything that violates a principle in whose absence all belief, and affirmation and negation, would be pointless? (NE .xvii: RB )

Surely Leibniz saw well enough the threat to the transitivity of identity should he (i) identify the Haecceity or nature of substance with the law-of-the-series, and (ii) identify the nature of substance with ‘‘form or force,’’ but (iii) deny the relevant identities as a compositional analysis of individual substance would require. That Leibniz’s theory of individual



Law-of-the-series, identity, and change

substance is void of sufficiently rich theoretical apparatus via which distinct elements of a compositional account would be unified counts less in favor of the judgment that ‘‘it is mistaken to think that Leibniz had a fully developed conception of substance,’’¹¹ and rather more in favor of the judgment that Leibniz had no compositional account at all. What the early Leibniz of the Disputatio would have insisted upon as his ‘‘whole entity’’ answer to the problem of individuation is manifest in precisely this: the Haecceity of S is the law-of-the-series, is the form or force, the primitive entelechy, the monad, the substance S. In § and § below we shall presuppose this picture of active substance as being (and not merely containing as an aspect or an element) a law-of-the-series. But risking distraction from that theme as the backdrop to issues about persistence over time, we pause briefly to acknowledge what – at this distance from chapter  – may seem a distraction all its own, namely our apparent oversight of Leibniz’s willingness to speak of corporeal substance. As discussed in chapter , there are two central lines of interpretation concerning corporeal substance. On one account, Leibniz is said to distinguish the corporeal substance from its dominant monad, the latter combining with the organic machine of secondary matter to constitute the former. If that is Leibniz’s view in the corporeal substance texts, then it immediately follows that Leibniz needs a component-style metaphysic for some substances, namely corporeal substances (cf. G ,; G ,; C ). On a second ‘‘one-substance’’ account, a corporeal substance is identical with a monad insofar as it has an organic body. (Analogy: A king is a person insofar as he has a kingdom.) Our orientation to the issue of corporeal substance was announced in chapter : we grant that there are texts suggesting a commitment to compound-substance in that period, but would argue that any such commitment sorts ill with the guiding threads of his considered metaphysic. Here, as there, we shall not be exploring the compound-substance view, and in particular we shall not be examining which threads of the early Leibniz’s thoughts on individual substances (including his whole entity doctrine, his denial of formal distinctions, his requirement of the real separability of distinct existences and so on) are preserved by the details of a compoundsubstance reading. The second of the two pictures, toward which we strongly incline, is beyond the scope of our efforts here to defend any further. That picture entails that there are only simple non-composite ¹¹ Ibid., p. .

The metaphysics of individual substance



individual substances – a theme which in any case is dominant in the mature Leibniz, and which will continue to be our focus in later sections. But even if, as we should prefer, Leibniz’s most considered account will view a ‘‘corporeal substance’’ as a monad qua possessor of an organic-machine body (cf. G ,; G ,: MP ), one does not thereby escape all suspicions of composition. Sure enough, from the perspective of this one-substance approach to corporeal substance, there is no serious suspicion of composition within a substance arising from the presence of secondary matter in accounts of corporeal substance. The secondary matter of a dominant monad is not a constituent of it, nor a substance in its own right, but rather an aggregate that is intimately expressed by the dominant monad’s perceptual states (G ,). But Leibniz also speaks of the primary matter of a corporeal substance. Rather as Bartha seeks to find an active form distinct from the nature or Haecceity of an individual substance, so one might construe Leibniz’s willingness to speak of a monad as ‘‘completed’’ (G ,: L ) by primitive entelechy together with primary matter as endorsing a compositional account of corporeal substance, even on the one-substance approach to corporeal substance.¹² But Leibniz is clear, even in this period of difficult texts, that what is variously called ‘matter’, ‘primitive passive power’, or ‘primary matter’ is a feature, an aspect, a modification of active substance – telling De Volder, for example, that ‘‘there is a primary active or substantial being that is modified by a disposition of matter or of passivity’’ (G ,: L ). From the earliest scholastics on down, the passivity in creatures was commonly understood in terms of matter as mere potentiality – this over against the Creator as purely active, actual. This is a necessary feature of creatures on the traditional picture, a point Leibniz expresses when telling Arnauld that matter is ‘‘something that is always essential to the same substance’’ – and going on to explicitly associate the ‘‘primitive passive power’’ of substance with the scholastic tradition (G ,: LA ). So there is a basis in substances for what the mind must recognize as a feature or aspect of created substances (passivity), and to this extent Leibniz would be willing to call primary matter, the passive element of any created substance S, rationally distinct from S in the Suarezian mode ¹² Leibniz sometimes uses ‘entelechy’ as broadly synonymous with the ‘‘primitive active’’ aspect of a substantial monad (as here to De Volder) instead of the monad itself (as customary in Principles of Nature and Grace and the Monadology). Our comments about primary matter to follow apply equally to ‘entelechy’ on this usage.



Law-of-the-series, identity, and change

of the reasoned reason (distinctio rationis ratiocinantis). At best, then, primary matter or the passive element, when abstracted by the mind apart from the substance of which it is an essential modification, is an ens rationis, unfit for any role in the compositional schemes with which Leibniz would have been familiar. (It is perhaps worth noting that the compositional picture seems to be explicitly resisted in the December portion of the  exchange with Bernoulli – issuing in part from Leibniz’s having called ‘‘matter in itself . . . not a substance, but something incomplete’’ [GM ,: AG ]. Leibniz met Bernoulli’s request to clarify ‘incomplete’ with this: ‘‘I respond: it is the passive without the active, the active without the passive.’’ Bernoulli worried that this answer, looking as it does to imply that God and angels are incomplete, might give ‘‘the malevolent and envious grounds for twisting your words’’ – suggesting to Leibniz that he hadn’t been sufficiently clear in meaning ‘‘incomplete with respect to composition, not to perfection’’ [GM ,, our emphasis]. Leibniz resists that diagnosis, insisting that only God is a ‘‘purely separate Intelligence’’ and ‘‘pure act,’’ and that angels, being imperfect like all creatures, must [as ‘‘most of the Fathers are wont to say’’] have bodies in some sense [GM ,]. This latter is a reference to passivity as a kind of imperfection inherent in all creatures, and it is the passive aspect of a substance that Leibniz has identified as primary matter, not any proper constituent of a substance.)                   Let us return then to our picture of active individual substances, according to which a substance neither contains as an element (component), nor possesses as an aspect or feature, but is what Leibniz calls a law-of-the-series. This will doubtless ring off-key in the contemporary, post-Humean ear. But anyone possessed of sufficient metaphysical bearings to find it implausible that laws are mere descriptive summaries of one happenstance after another – that is, anyone recognizing in the descriptive nothing sufficiently rich to account for what is prescriptive about the genuinely nomological – will locate causal powers in the objects themselves. Leibniz himself, shrinking from the sour note of unanswered why-questions, found the resources for (immanent) causal explanation in Aristotelian form. Laws don’t simply hover over the contingent mosaic of qualities in the world, but get a grip on the objects

Substantial laws on the model of immanent functions



themselves, constraining the unfolding of accidents from within.¹³ That picture, of a modally robust causal efficacy ‘‘in the objects’’ is perhaps what most attracted Leibniz to the notion of a form, whose ‘‘nature consists in force’’ (G ,: L ). Again, to De Volder, he says that ‘‘I recognize in the active force . . . the primitive entelechy or, in a word, something analogous to the soul, whose nature consists in a certain perpetual law’’ (G ,: L ). What is law-enforcing is causally active: the substantial form is the law-of-the-series, the substance itself. One can hardly resist the suggestion that, when Leibniz claimed of a substance that ‘‘its individuality consists in the perpetual law’’ (T §: H ), or that ‘‘the essence of substances consists in . . . the law of the sequences of changes’’ (A ..), he was simply giving mature content to the whole entity view of the Disputatio. Reverting to the scholastic idiom, the strong language of ‘‘consists in’’ can scarcely be glossed so as to render the law-of-the-series in any way really or formally distinct from the substance. It is the substance, its own Haecceity. . Immanent functions How might this picture we are ascribing to Leibniz – of individual substance as a law-of-the-series, alternatively described as ‘substantial form’, ‘monad’, ‘entelechy’, sometimes ‘primitive active force’ – be filled out in a way that helps us reflect on diachronic aspects of persisting substances? In chapter  on Leibniz’s haecceitism, we sketched in a preliminary but suggestive fashion one way of thinking about the law-ofthe-series, explicit in the analogies Leibniz himself offers, according to which laws are understood on the model of functions. In this section, we shall take seriously that way of thinking, attempting to put some flesh on what is admittedly only a skeleton in the texts. Here more than elsewhere one is invited to the luxury of rational reconstruction thus far avoided. Leibniz (we think) would have applauded the effort, particularly if it serves to render perspicuous certain of his less well-developed pronouncements on topics immediately relevant to the persistence of individual substances. First, let us be clear that insofar as one proceeds in thinking of Leibnizian laws-of-the-series on the model of functions, one should ¹³ The Humean tenor of pre-established harmony among monadic perceptions is dampened by recognizing that global causal laws are ultimately made true by God’s creating causally efficacious substantial forms/laws-of-series on which those laws supervene.



Law-of-the-series, identity, and change

think of the functions as immanent, that is, as very much in the created world. While to some readers this may look to destroy Leibniz’s suggested analogy between laws and functions – given that mathematical functions are standardly conceived as Platonic objects – the idea of an immanent function does not seem to us particularly elusive. After all, the notion of a universal does not altogether evaporate when universals are considered immanent. Nor is the view that universals are immanent a mere possible position in logical space, for not only was it orthodoxy within scholastic ontology (insofar as universals were admitted at all), but various contemporary philosophers – including, notably, D.M. Armstrong – think of universals as immanent.¹⁴ On the immanent view, then, one is not to understand, say, redness (pretending it is a universal) as existing in Platonic Heaven and instantiated by various objects, but rather as in the world, wholly present in red objects. We shan’t attempt a philosophical defense of immanentism here. It suffices for our purposes that it be a familiar enough and respectable philosophical position about universals. For, against the background of the intelligibility of immanent universals, it seems to us that there is no special reason that functions cannot also be conceived as immanent, that is, in the world. What would it be for a function/universal to be in the created world rather than in Platonic Heaven? To fix our ideas, suppose to begin one regarded spatio-temporal relations as fundamental, giving this sort of gloss: things that are in the world stand in spatio-temporal relationships to themselves and to other things. As a first pass, then, one is to think of the groundfloor metaphysic as involving immanent functions that actually enjoy spatio-temporal relationships to themselves and other things. A more distinctively Leibnizian story will then mark off the abstract, ideal entities from the actual created entities by way of distinguishing between those things that are not, and those things that are, the right sorts of entities to exercise causal powers. And on our story that is what forms as immanent functions are. They do not merely describe the pattern of causal powers exercised by things in the world, but on the contrary are those things possessed of causal powers. This conception of laws, while unfamiliar to the post-Humean ear, strikes us as both intriguing and defensible. One corollary of the immanent conception is the contingency of all immanent things. This point is a familiar one from the immanent/ transcendent debate. Those who are transcendentalists will tend to ¹⁴ See, for example, Armstrong’s Universals and Scientific Realism. Volume I: Nominalism and Realism, pp. –.

Substantial laws on the model of immanent functions



think of our individual functions as necessary beings, explaining contingency in terms of contingent relational facts about their instances. Those who are immanentists agree that contingency arises in part from where and when the immanent function is present; but the immanentist will insist that were some individual function F not present anywhere in the world, that function would not exist. Accordingly, it is natural for them to say that there are possible functions that do not actually exist.¹⁵ Let us suppose, then, that an individual substance, a law-of-the-series, is an immanent, contingent function having (total temporary) states as arguments and as values. The exercise of primitive active force consists in that immanent function’s yielding a state as value. Such states, meanwhile, being arguments and values of the function, are not the function itself, nor (recalling the sketch in later sections of chapter ) is the substantial function identical with the list of arguments and values. One might extend the picture slightly by connecting certain Leibnizian terms of art with some natural questions. Under what conditions can a state serve as an argument for the function? When and only when it belongs to the function. When does it belong? When and only when it emanates from the individual function itself. Under what conditions does it do that? When and only when the state serves as value (output) to that function. As a corollary, then: whenever a state is the value of the immanent function, it eo ipso serves as an argument to the immanent function. Having picked up the Leibnizian theme of an individual substance as a function, the view of substantial form as law-of-the-series sketched thus far makes vivid certain issues of divine creation. Suppose that God actualizes some substantial law-functions. As causally efficacious immanent laws, there are constraints on how such functions are able to commence from the outset into their causal careers. Given the lawful nature of the immanent causal origin of states of a substance, there must, at minimum, be a first argument in order to begin the unfolding of subsequent states; once a first argument is given, the law can then deliver (emanate) a state as value that serves as the next argument (in accordance with which the law then delivers . . . etc.). And here we are faced with something of a puzzle, if our sketch of the preceding paragraph is taken seriously. For supposing that the only way for a state to belong to a function is for the state to emanate from it, how is God to ¹⁵ Whether the perspicuous logical form of this commitment is one that quantifies over possible individual functions or one that puts the possibility operator (de dicto) on the outside is a question that needn’t concern us here.



Law-of-the-series, identity, and change

succeed in giving the function a first state? One option here, in replying to this ‘‘puzzle of the first state,’’ is to qualify our initial story: a state belongs to an immanent law-of-the-series either by emanating from the function or by God’s ordaining that the state so belong to it. That has the flavor perhaps of being contrived, but it constitutes one kind of solution to the puzzle, consistent with most accounts of miracles and with the natural gloss of Leibniz’s in particular – of some state of a substance arising from what is beyond the natural causal powers of that substance to bring about.¹⁶ (We shall return to miracles in §. below.) Nevertheless there remains a notable disanalogy between the picture we have sketched and (what seems to us to be) the actual Leibniz. For it would appear that on the function model, there could well be two exactly similar functions enjoying overlapping but different histories due to the fact that God blesses each function with different initial states. That is: if the initial states are not causally or otherwise constrained by the law-of-the-series itself, but instead by way of a miraculous act of creation, then apparently facts about the initial state have nothing much to do with the nature of the function itself. In such a case, one could coherently envision the following: some substance (some individual law-function) S starts off with state F and then enjoys states G and H and I . . . but neverthelesss might instead have started off with G, then emanating H, I . . . with no appearance of F. Indeed the option here under consideration suggests even the possibility of no overlap. For suppose S would deliver H* as output given G* as argument and I* as output given H* as argument, and so on. Consistently with this, one may imagine that S actually enjoys none of these states owing to the fact that it is given F to begin with, and that no stepwise transitions from argument to value – beginning with F – deliver any one of the series G*, H*, I*, etc. Now it seems to us that Leibniz never entertains these ‘‘same-law/ different-series’’ scenarios. In particular Leibniz never talks about the same individual law-of-the-series possibly yielding a different sequence of states owing to a different initial state. In telling De Volder that ‘‘the entire progression is sufficiently contained in the beginning’’ (G ,: L ), and more generally that for any present moment t, ‘‘everything ¹⁶ Echoing the spirit of Discourse § (‘‘that which surpasses the natures of all created substances is supernatural’’), Leibniz speaks in the Theodicy of God’s ‘‘produc[ing] in them that which their nature does not bear, by performing a miracle’’ (Preliminary Dissertation §: H ). There are deep interpretive puzzles beneath the surface of these and other miracles-texts, with which we shall not fully engage here. They are engaged most fully by Robert M. Adams, Leibniz: Determinist, Theist, Idealist, § of chapter .

Substantial laws on the model of immanent functions



future is predetermined in the present state of the substance’’ (G ,: L ) – nowhere in these texts or others does Leibniz give evidence that he might comfortably go on to say ‘‘though, given different beginnings, the same law will yield different progressions.’’ Some readers will disagree with us. Leibniz, they will say, held that the law-of-the-series and the initial state are distinct contributors to the nature of an individual: thus a different individual might have had the same law, being different because of the different initial state. True enough (one might continue): Leibniz says nothing about all this. But he has no need to. The operative framework in Leibniz’s thought is not exactly one according to which God considers different ways of combining laws and initial states to get complete individual histories (sequences). Rather, Leibniz’s framework is one according to which God has in mind all the possible complete individual histories, and considers what law-and-initial-state is needed for this history, for that history, and for each other. In this framework, Leibniz simply has no need to mention the idle fact that the raw materials – laws-of-the-series and initial states – for individual histories could be re-assembled to give histories God does not want. Yet there remains pressure, from quarters other than his silence, against reading Leibniz in this way. Certain bits of his philosophy would evidently come under fairly serious strain. Recalling lessons from chapter  about Leibniz’s No Reason style argumentation, for example, suppose the above reading were granted for the sake of argument as expressing Leibniz’s position. It will no longer be true, when considering (under the supposition) some actual individual and a possible individual with a different history of accidents, that there is no reason for denying that they are two. To our mind, that x and y have the same law would be an excellent reason for denying that they are two. After all, in the diachronic case broached to De Volder in the  passage, Leibniz is keen to insist on law-of-the-series as the ground of numerical identity (G ,: L ). This being so, PII will emerge as very shaky if history doesn’t march in lock-step with law. Certainly the whole picture of substantial form/law as individuator will rest easily alongside interworld PII only if initial states cannot vary while laws remain the same. But leaving broader philosophical issues aside, what Leibniz does say scarcely counts against our preference to read Leibniz as we do. In the De Volder letter, Leibniz says that the law ‘‘involves all of the future states’’ of the enduring substance – as if the law itself, not the law plus a state at a time, determines the history. Moreover, in his  March 



Law-of-the-series, identity, and change

letter to Arnauld, Leibniz says of each substance that ‘‘except for dependence on God, all of its actions come from its own depths’’ (G ,: LA ), leaving it unclear how a first action provided by God could be said to arise from its depths. Indeed, Leibniz insists in the preceding sentence that the law ‘‘contained in its nature’’ is not only the law of the continuous series of its operations, but of ‘‘all that has happened and will happen to it.’’ Now one might choose to wield the ‘‘same-law/different-series’’ worry as a criticism: Leibniz should have noticed the possibility of different series being associated with a single law. Leibniz does in any case speak of ‘‘the order in which its terms will proceed when its beginning and the law of its progression are given’’ (G ,: L ), encouraging us perhaps to believe that subsequent states will co-vary with both the law and the initial state, where the same law with different beginning will yield a different series of states. So perhaps the same-law/ different-history scenarios are ones that he was committed to without his ever really noticing that he was. (And if that is right, then Leibniz will have to reconsider his commitment to the distinctness of transworld discernibles [see chapter , §.]. For if that is right, there may indeed be something that prevents us from saying that a possible being with a different history is distinct from our Adam: perhaps the possible being has the same law-of-the-series and merely a different initial state. We shall not open the floodgates too wide here.) In a more generous spirit, it seems worth trying to construct a metaphysical framework respecting the intuition that somehow the nature of the law itself constrains what states it can properly have, and so what initial state it can have. Suppose that Leibniz’s view is properly described as one according to which God supplies the first state when creating the individual law-function – implied in various texts already noted, and in De Ipsa Natura when speaking of the individual nature or law from which the series of changes follows ‘‘according to the prescription of the first command’’ (G ,: L ). One might gloss this general position as half intimating that God could create the individual law-function but then (unkindly) leave it hanging without any first state, and half intimating that God could create it and then supply it with a different first state than He in fact supplied. But Leibniz’s considered view seems to us rather to be that in His very creation of an immanent law, God thereby supplies a particular initial argument for that individual function. If this is his considered view, it is easy enough to flesh out a metaphysic of immanent individual functions lining up with it.

Substantial laws on the model of immanent functions



Our initial picture of the range of arguments was this: anything that belongs to the function may serve as an argument. Permit now, as a limiting case, that the function as well as the states emanating from it belong to the individual function. The law-function itself might then in effect serve as initial argument at the moment of creation: in creating the substance (law-of-the-series), God thereby creates the first argument and – assuming the first value is an emanated state – we are off and running. One advantage of letting one’s reconstruction associate this feature with the objects of divine creation, aside from alignment with Leibniz’s sympathies, is that this picture preserves in purer form the intuition that the only way for a state to belong to a substance is by emanating from it: no exception here for the first state, no need for any contrived stipulation in saying what it is for a state to belong to a thing. Proceeding now with the picture sketched thus far, we can articulate more clearly how an individual function uniquely determines a series of states. The substance-function yields by real causal emanation a particular first state simply by being in existence at all. And it yields its future states in the way Leibniz clearly intends, in accordance with the nature of the function that constitutes its very being. What is it for a state to be a possible state of that function? Given that (as now presented) it is inconceivable that the substance-function have a different sequence emanating from it, a possible state of that individual function is a state appearing in the sequence uniquely determined by it. It is thus either the state that is yielded as first value when the function figures as argument, or else a state that can be arrived at stepwise by repeated use of value as argument. Insofar as we are looking for a sufficiently detailed, perspicuous reconstruction doing justice to the thrust of Leibniz’s metaphysic of active enduring substances, the immanent function model seems to us a resourceful candidate. In what follows, we develop it in connection with two difficult topics that, while central and important to Leibniz, receive rather less of his energy and attention – namely miracles and the doctrine of marks and traces. . Miracles There is no unambiguous account of miracles, ready for the picking, in Leibniz’s discussions of the subject. Here are three pictures, cast in the model we are pursuing, that might be extracted from the corpus by variously emphasizing certain texts and underplaying others.



Law-of-the-series, identity, and change

() Occasionalism is false. Were there no causally active creatures but instead all events arose as the direct result of divine action, we should be threatened with the false notion that ours is a world of only perpetual miracles (G ,: L ). There are miracles, of course. Under this category are unquestionably those ‘‘of the first rank’’ – those occurrences ‘‘surpass[ing] all the force of creatures’’ (T §: H ; cf. G ,: L ). Here are numbered the (actual) creation and (possible) annihilation of substances, and presumably the Incarnation – events that are in no way the upshot of the causal activity of creatures. But there are other kinds of events we call miracles that, while departing from the globally supervening laws that describe the normal, largely regular course of creaturely events, are nevertheless occurrences prefigured in the substantial law-functions. That is, those miraculous states occur straightforwardly as particular values of those individual functions. Suppose then that one distinguishes regular from irregular functions. Regular functions define a sequence that falls into a certain standard pattern that one may fairly call ‘‘the ordinary course of nature.’’ Were all created law-functions of this sort, the global laws of nature supervening on the mosaic of intrinsic monadic states might be viewed as defining a smooth curve, on which all states of all functions firmly lie. But there are in fact (at our world) other functions, irregular ones, from which emerge sequences some of whose states would not fall exactly on that curve. The mosaic of law-states at our world, including among them those of certain irregular functions, may still be viewed as defining a ‘‘best line,’’ on which the preponderance of all states of all substancefunctions lie, and from which those irregular states are atypical departures. Since ‘‘irregularity’’ likely presupposes a backdrop of regularity,¹⁷ there may well be a limit to how much irregularity it makes sense to imagine. But, certainly, irregular functions are conceivable, and it is these from which such lower, inferior miracles may be seen to arise. Meanwhile, once God has performed the first-rank miracle of creating a world of regular and irregular law-functions, He leaves them to their own causally active devices to unfold the states written into them – unless of course He wills to positively intervene and annihilate them. () According to the second picture, there are two things wrong with this initial account just sketched. First, in making annihilation and ¹⁷ Though, perhaps, we can make sense of God overriding his subordinate maxims on a regular basis without their losing the status of subordinate maxims. In that case, God’s subordinate maxims wouldn’t correspond to any regularities in the world, and thus would not correspond to anything like Humean laws of nature.

Substantial laws on the model of immanent functions



creation (and the incarnation) the only events in the created world that cannot be fully explained by the substantial laws-of-the-series themselves, the first picture risks our thinking that the survival of a substancelaw requires only that God refrain from annihilating it. But if the occasionalist thesis is out of bounds, so too is the deist sentiment implicit above: there is a positive contribution that God must make to the created world in order for an immanent law to survive. The persisting law needs not merely to be left alone, but to be conserved; and at the very least, conservation is of the same (unnatural) kind as creation – namely divine input to the created realm as opposed to something achieved by the causal resources within the created realm alone. Second, the earlier picture implies that, assuming the immanent function exists at all, it is metaphysically impossible that it have different states than those prescribed by its nature as a law. Traditional Christian orthodoxy will presumably judge that result off the mark: God could – miraculously, without threatening the persistence of the substance – endow a function with states different than the ones prescribed by its nature as a law. The emphasis on ‘could’ is of course important. Perhaps it would be a slightly odd Creator who chose to prefigure one series in an individual lawfunction and then install another rather than (permit us to say) making His mind up once and for all at the outset, prefiguring what He wanted. On the second picture, however, the suggested possibility is to be left open: it is left open due to it being final-cause, harmony-theoretical reasons that ground the otherwise uniform conformity of sequence with law, and not principles of the metaphysical structure of substantial law-functions themselves. () The third picture takes an intermediate position between the first two. Like the second picture (unlike the first), it maintains the view that preservation of substance demands a positive contribution by God, rather than simply a divine propensity to leave the substance well alone. Like the first picture (unlike the second), it does not concede that God could preserve the enduring substance while miraculously giving it different states than those prefigured in the law. The prefiguring does not fully determine the future – but this only because the law could be annihilated, and not because the law could have persisted with different states. Insofar as we call a state of a substance miraculous, one will account for this along the lines of the first story. As briefly laid out, these three pictures define themselves in terms of where they stand on two bones of contention: (i) the mode of divine conservation, and (ii) the strength of divine input whereby law gives rise



Law-of-the-series, identity, and change

to state. In respect of (i), there is little disputing that the first picture – according to which, following creation, the persistence of a substance is guaranteed simply by the absence of divine intervention (annihilation) – does not accord with the balance of texts. Leibniz is clear that ‘‘things are not simply produced by God when they begin existing, but moreover they would not continue existing unless a certain continuous action of God terminated in them, on the cessation of which they would cease’’ (De libertate, fato, gratia Dei: Grua ). From the Theodicy: What can be said for certain on the present subject is that the creature depends continually upon divine operation, and that it depends upon that no less after the time of its beginning than when it first begins. This dependence implies that it would not continue to exist if God did not continue to act. (T §: H ; cf. T §: H ).

Moreover, as the final bit of that passage suggests, insofar as it consists in the direct causal activity of God, the conservation required by creaturely dependence is of the same (non-natural) kind as creation: says Leibniz, ‘this dependence . . . is a continued creation’’ (T§: H cf. Grua ). Preserving the need for active conservation by God, the second and third pictures remain fully on board. In respect of (ii) – the degree of divine input into miraculous states of substances – Robert Adams inclines strongly towards the third, at least as the predominant tendency of Leibniz’s thought.¹⁸ His case is a strong one, though we find the textual resources rather too thin to yield a very determinate judgment. The framework of functions, adopted as a regimentation of the Leibnizian metaphysic, can itself offer no recommendation one way or another, unless perhaps the effort to spell out () or () in more detail encounters a logical obstacle or proves to reveal explanatory advantages (over its rival) alongside miracles texts. It will in any case be helpful, as a way both of developing the function model and as a way of sharpening the relevant contrasts, to spell out the model for each of the three positions described above. (') The first picture, textually defective but helpful for comparative purposes, is straightforward enough and can be treated with dispatch. One is invited to think of an array of immanent individual functions which move from arguments to values, which values serve as arguments for emanating values, which . . . and so on. Whether a particular value counts as a miracle depends upon whether its place in the sequence is anomalous, not with respect to the function itself, but rather with ¹⁸ Adams, Leibniz, pp. –.

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

respect to the normal (though not exceptionless) global regularities that characterize the order of created things. Thus it might be an almost exceptionless regularity that whenever a (total temporary) state contains an accident of kind F, the total-state value emanated on that argument contains G, while nevertheless – in the case of a particular (irregular) function – one element in the sequence of total states contains F but the next element in the order of values of the function fails to contain G. Of course if an immanent function isn’t created/actualized, then it is properly understood as only specifying states in abstracto in the mind of God, emanating no actual states. Similarly, if an immanent function is annihilated at the point of producing some value V, that value V will not then serve as argument for emanating a subsequent value V' (God having intervened to annihilate the substance), though it determines V' in abstracto. (In the spirit of this most simple picture, might one describe a model in which the annihilation of a simple substance is prefigured within it – i.e. as deducible stepwise from the first argument via the function itself? Presumably so. (a) Altering our earlier picture, one might conceive of a function as not automatically capable of taking any [all] values as arguments, but instead only capable of taking as arguments those values enjoying a certain character. Some possible functions are then such that F does not fall within the domain of its arguments, F lacking that particular character. Imagine now that F can indeed be deduced stepwise from the first argument as a later value via the law-function. That function will fizzle out having produced F; state F will lie at the end of the sequence. Alternatively, (b) some possible functions are such that when it takes a value F as subsequent argument, it delivers F as value. Assume that intra-monadic time requires intra-monadic change, and the substance-function will have come to the end of its sequence. Yet again, (c) assume a continuous time. A substance can then fail to exist at t and all moments thereafter without there being some instant which is the last instant of its existence. There are possible functions that deliver a value for each argument ad infinitum but which are such that all of its values occur before t.¹⁹ None of (a) – (c) offers a plausible regimentation of Leibniz’s own picture of annihilation, insofar as he conceives annihilation as a miracle of the first rank.) (') The second picture requires considerable fiddling with the first, ¹⁹ This is, in effect, the picture that Moses Mendelssohn had rejected in his Pha¨don (), taken up more favorably by Kant when discussing the permanence of the soul in the Paralogisms of the Transcendental Dialectic (B ff).



Law-of-the-series, identity, and change

reasonably straightforward picture. What is needed is a model according to which there is causal contribution not only on the creaturely side of the individual function itself, but also on the side of God. After claiming in a letter to Bourguet that ‘‘when I speak of the force and action in creatures, I intend that each creature is at present full of its future, and that it follows a certain natural course if nothing prevents it,’’ Leibniz quickly goes on to add that ‘‘I don’t say, on this account, that the future of the creature follows its present state without the concourse of God, and am of the view that conservation is a continued creation’’ (G ,).²⁰ Wedding now our two components above – (i) the mode of conservation and (ii) the strength of divine input whereby an individual function itself gives rise to a state of the individual – what is thus needed for an account of miracles is divine input of a special sort: the input must be necessary to preserve existence while nevertheless installing states other than those that are prefigured in the law-function alone, all the while allowing for Leibniz’s insistence on creaturely contribution. Here is one such model. Let suitable arguments for immanent functions in the created order be two-place. One place is occupied by a state belonging to a substance – where a state belongs to a substance if and only if it emanates from the substance, and it emanates from the substance if and only if it is a value. The other place is occupied by a divine decree. Divine decrees of the sort relevant as input to functions fall into two categories. One sort of divine decree consists of a relatively bland endorsement – an endorsement so to speak for the striving of the law itself. One may suppose it to be of the form ‘Let nature take its course in law-function S when state s is part of the argument.’ Supposing s is an emanating value, then one of the arguments for the individual function will be the pair:

²⁰ Hasn’t Leibniz worked himself into a contradiction here? The first ‘‘P will happen if nothing prevents it,’’ looks to contradict the second ‘‘P will not happen unless God continuously creates.’’ For prima facie, the first says ‘‘Non-interference is sufficient for P happening,’’ while the second says ‘‘Non-interference isn’t sufficient, since continuous creation is necessary.’’ Our salvage: No, there is no contradiction. Leibniz says that ‘‘it follows a certain natural course if nothing prevents it.’’ So there is a particular course determined by nature. But the course of nature itself requires a conserving concourse of God. That is what, inter alia, the course of nature is. Thus, the first ‘P will happen if nothing prevents it’ means ‘‘P will happen so long as nature takes its course,’’ and the second ‘P will not happen unless God continuously creates’ means ‘‘Conservation is required for nature to take its course.’’ Hence, Leibniz’s claims to Bourguet are these: the first says ‘‘Non-interference from factors external to the course of nature is sufficient for P happening,’’ and the second says ‘‘Divine conservation is internal to the course of nature.’’ That is no contradiction. (Our thanks to Jonathan Bennett for posing the problem.)

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

:s, ‘Let nature take its course in S when state s is part of the argument’9.

Here, for state s to serve as part of the argument, there needs to be a divine endorsement, as desired; but the details of the transition from the above argument to emanating subsequent value are not encoded in the content of the divine decree but rather in the nature of the individual substance (function) itself. Imagine then that our individual function delivers s as value when given the above pair as argument. In addition to the relatively bland endorsement, there is another sort of possible divine decree – the miraculous decree. One may suppose a decree of this sort to be of the form ‘When s is part of an argument, s* will be the value for S’. When s is combined with this miraculous decree, we have the argument :s, ‘When s is part of the argument, s* will be the value’9.

One can fairly suppose that a fundamental feature of the created order of individual substance-functions is a propensity to obey divine instructions. Thus whenever there is a miraculous decree, individual functions are such that they generate as value what is specified by the content of the decree, taken as part of the argument; in the present case, our law-function S will take the value s*. Notice here that values still emanate from law-functions even in the case of miraculous decrees, on this model. This is a desirable feature – not simply in its preserving an account of substance and emanating accidents in terms of function and value, but in (A) according with various Leibnizian themes that are relevant to miracles, and in (B) aligning with certain elements of miracles-texts that one might have thought required the third picture. In connection with (A) for example: if God simply ‘‘bypassed’’ the function and created an accident in my vicinity, so to speak – say, some particular thought – what would make it my accident? Indeed, what exactly would it be for God to give it to me? For a thought to be mine is for it to issue from ‘‘my law,’’ from me. The law is nine-tenths of ownership. Relatedly, our model secures a picture of annihilation as what happens when the very active nature of a substance is thwarted by the absence of conservation, capturing Leibniz’s view that a creature ‘‘would not continue to exist if God did not continue to act’’ (T §: H ; cf. Grua ). With respect to any emanated value God can do three things: () issue a bland endorsement of the natural order with respect to that function and that occurrent state; () issue a miraculous decree; () issue no decree. Since the domain of arguments



Law-of-the-series, identity, and change

include only pairs, if a value has no accompanying decree, it will not serve as part of any argument. In the case of (), then, God in effect renders activity on the part of substance impossible, guaranteeing the end of any functional sequence argument-to-value-to-argument . . . Absent divine input of some sort, the function cannot maintain its integrity: that is annihilation. In contrast to the first, defective model, conservation requires God’s positively doing something, and God’s doing nothing (with respect to that substance) achieves annihilation. This latter point is relevant in connection with (B), with certain of the miracles texts. God’s active concurrence (bland conservation) is required in any case; and on the second picture only a certain species of required conserving-decrees counts as miraculous. That renders natural a way of speaking that Leibniz himself and his predecessors found natural, of describing miracles as – what might otherwise sound odd – God’s ‘‘miraculous concurrence.’’ Indeed the second picture aligns nicely with the stated aim of Discourse § to explain ‘‘how it is possible for God sometimes to influence human beings or other substances by an extraordinary or miraculous concurrence, since it seems that nothing extraordinary or supernatural can happen to them, given that all their events are only consequences of their nature.’’ Likewise for the comparison of miraculous decree with bland endorsement, as alongside Leibniz’s claim to Arnauld that ‘‘extraordinary concourse excepted, [God’s] ordinary concurrence consists only in preserving the substance itself in conformity with its previous state and the changes that it bears’’ (G ,–: LA ). What the second picture offers, then, is a way of reconciling certain strands of the miracles texts that one might have thought (with Adams) required the third picture.²¹ With the first picture aside, it is agreed on all hands that God makes a crucial contribution all along the way; so the existence of some counterfactual dependence upon divine input can’t itself be viewed by Leibniz as a threat to his view that all states emanate from the law-function itself. By viewing divine contribution in the way our second picture recommends, we can see that to claim (as no doubt the orthodox picture would most naturally have us claim) that the ²¹ The relevant strands are those texts suggesting – rather contrary to the view expressed to Arnauld above, which Adams must call disingenuous on Leibniz’s part (Adams, Leibniz, pp. –) – that all states, including miraculous ones, are prefigured in and issue internally from the substancefunction itself. The reconciliation is of a sort that shows some promise in helping (modulo certain fussing with superintrinsicalism) to address Sleigh’s ‘‘alleged problem’’ of miracles, at pp. – of his Leibniz and Arnauld. We shan’t pursue that here.

Substantial laws on the model of immanent functions



miraculous states of substances require divine input, or that such substances wouldn’t undergo those miraculous states unless God ‘‘intervened’’ in some way departing from the common order of things, is not yet to deny that miraculous states emanate from the law-function itself. Crucially, then, to this extent our second picture looks to preserve the notion that the persistence of individual substances consists in the states of substance x at t and states of y at t' being immanently caused by the same law-function, despite miraculous decrees from the outside by God. But it must be granted that the second picture is scarcely congenial to the Leibnizian modal lay of the land. Suppose the law-function S in fact emanates s as value for the pair :s, bland endorsement9 as argument. The second picture has it that nevertheless miracles are possible, this being construed (in application to S) as the claim that, were S to be given the argument pair :s, miraculous decree9 it would emanate s* as value instead. If that is a possibility, then clearly s is not essential to S, even though it is an intrinsic non-relational state emanating by real causality from the law-function. This would then compromise the strong essentialism we have attributed to Leibniz (as it would likewise compromise superessentialism). If this was his considered view on miracles, then we must conclude that it was never properly reconciled with the rest of Leibniz’s metaphysic.²² (') One may now fill out the third picture, to complete the contrast. It is an intermediate account, according to which (like the second) conservation requires positive contribution by God, while (like the first) miracles are departures from the regular order fully prefigured in the individual substance-function. This requires a functional model rather less complicated than the second, rather more complicated than the first. The conservation details are already in place, borrowed over from the second picture. For the miraculous states, we need only simplify the second picture in the following way: require as arguments a pair consisting of a state (value) and a decree, but think of God as having now only two options: (a) bland endorsement, and (b) no endorsement. When ²² See chapter , ‘‘Coda.’’ Recall issues concerning the relation of first state to law, above (§.), which prima facie also threaten to compromise Leibniz’s strong essentialism by allowing same-law/different-history scenarios.



Law-of-the-series, identity, and change

there is a transition from argument to value, the details of the transition are encoded in the nature of the law itself rather than in the details of the decree. But endorsement is required at each step. Absent the endorsement, we have annihilation. . Marks and traces A substance, Leibniz tells us, contains marks of its past and traces of its future, a thesis that gets put to use in deducing various metaphysical theorems. In one particularly elegant passage, for example, Leibniz informs us that a homogeneous square chunk of passive matter cannot contain marks and traces of its past, since its current state is neutral on its mode of origin: [W]hether two parallelograms or two triangles are put together in the appropriate way . . . the same square will, as is clear, always be produced. Neither of these can be distinguished from the other in any way, not even by the wisest being. So given a square of this kind, it will be in the power of no one – not even the wisest being – to discover its cause, since the problem is not determinate. The effect, therefore, seems not to involve its cause. So if we are certain, from some other source, that the effect does involve its cause, then it is necessary that the method of production must always be discernible in the squares that have been produced. And so it is impossible that two squares of this kind should be perfectly similar; for they will consist of matter, but that matter will have a mind, and the mind will retain the effect of its former state . . . This argument is very fine, and proves that matter is not homogenous . . . (A ..–: DSR )

How might one locate the marks and traces metaphysic of enduring individual substances within the immanent function model? Let us define a consistent sequence C for a law-of-the-series L as a sequence such that it is consistent with the function which is L that C be the total history of states emanating from L. (By ‘state’ we mean – borrowing from Grice – the ‘‘total temporary state’’ of a thing, that is, the whole way that a substance is with regard to its intrinsic character at a time under some complete general description. So we cannot stipulatively exclude the possibility that a state ‘‘repeat’’ itself at a later time, as Leibniz himself seems to have allowed (G ,) in granting individual accidents solo numero difference.) Consistency with the function requires that (i) it be possible that the first element of C be the first state that L enjoys,²³ and (ii) for each adjacent pair in C, the first element is a ²³ Suppose, for example, that a Law defines its own first state by taking itself as argument and delivering a state s as value. Then a consistent sequence must take s as its first element. Suppose a Law instead generates a state either by taking a prior state of its own as argument or a divine decree as argument. Then a consistent sequence must have as a first state a value which the Law

Substantial laws on the model of immanent functions



possible argument of L which delivers the second element as value, and (iii) if C has a last member s, L permits s to end its history.²⁴ Define the ancestral history of a state in a sequence as the ordered n-tuple of preceding members of the sequence. Define the future history of a state in a sequence as the ordered n-tuple of subsequent members of the sequence. One may now formulate in the following way the thesis that a state of a substance at a time traces its history: : A state s of law-of-the-series L traces its whole past iff every appearance of s in a consistent sequence for L has the same ancestral history. Along these same lines, one can define what it is for a particular intrinsic quality in a state to trace a particular bit of intrinsic history: an intrinsic quality q forming part of state s of law-of-the-series L traces the appearance of intrinsic quality q iff every appearance of q in a consistent sequence for L has an ancestral history in which q forms part of some state or other.²⁵ Turning now to marking, as opposing to tracing, the same strategy can obviously apply: : A total state s of law-of-the-series L marks its whole future iff every appearance of s in a consistent sequence for L has the same future history. One can along these lines also define what it is for a particular intrinsic quality in a total state to mark a particular bit of intrinsic future: an intrinsic quality q forming part of total state s of law-of-the-series L marks the appearance of intrinsic quality q iff every appearance of q in a consistent sequence for L has a future history in which q forms part of some state or other. (Notice that if arguments for laws are two-place – involving, for permits as value for some divine decree. ²⁴ Recalling earlier discussion, perhaps this is because s is a value which is absent from the domain of arguments. ²⁵ For the purposes of this quasi-formalized theory one may consider an accident as an ordered triple :L,q,n9 of law, quality, and number, where the number n corresponds to the quality’s enjoying an nth place in the sequence or else forms part of some state that enjoys an nth place in the sequence. An accident-triple holds of a sequence iff (i) the sequence is a possible sequence of the law that is the first member of the triple, (ii) the quality appears somewhere in the sequence either as the whole or part of some state in the sequence, and (iii) the quality appears in the nth place of the sequence (as whole or part) where n corresponds to the third member of the triple. An accident-triple a traces an accident-triple a iff (a) every sequence for which the first triple holds is such that the second triple holds for that sequence and (b) the third element of a is larger than the third element of a.



Law-of-the-series, identity, and change

example, a non-miraculous endorsement of the natural order – then one will need further refinements. Relatedly, one may, if one wishes to allow for the possibility of miraculous tinkering by God, restrict the marks and traces doctrine to possible sequences that are non-miraculous. For the sake of simplicity, we will not attempt to incorporate refinements having to do with miracles here.) Leaving miracles to one side, then, does the existence of a law that marks its future at each time entail that it traces its past? Such a claim is by no means straightforwardly defensible. Suppose, for example, that a law L had the following functional character: from L as argument, it delivers F as value. From F as argument, it delivers G as value. From G as argument, it delivers H as value. From H as argument it delivers G as value. This law will deliver the series FGHGHGH . . . Suppose now that one encounters the individual when it is G. Given this law, one can determine easily enough where the thing is headed – next H then G then H . . . But one cannot determine the most recent state of the thing. For, consistently with the law, one can say that either F or H is the most recent state. Of course if there are additional constraints on any law of the series (ones that, for example, preclude repetition), one would have to look at those constraints and re-evaluate whether marking one’s future entails tracing one’s past. One is inclined to say that Leibniz has nothing like as strong reasons for  as he has for . And one might diagnose his full-blown commitment to both in the following way. He needs the forwardlooking  for his deterministic, immanent-causation account of substances, which is fundamental to his entire metaphysical scheme. Yet in fact nothing else – or anyway nothing else so weighty as his commitment to determinism – requires the backward-looking . Leibniz, not seeing the lesson of the previous paragraph, combined with  his false belief that it entails , and committed himself equally to both. However there are, arguably, legitimate Leibnizian motivations for  that do not rely on any such philosophically dubious enthymeme. These include the following related ideas: () Given any substance at any time, the complete active law-of-the-series on the one hand is fully present at those times, and on the other fully determines a complete intrinsic history in such a way that, one who is cognitively acquainted with that active form or law in a perspicuous way would see a complete history – from start to finish – contained in it. () In line with a theme of chapter , according to which the individuality of a substance

Substantial laws on the model of immanent functions



is fully internal to it, one should require that at each time a substance is possessed of something intrinsic to it by virtue of which it bears its individuality on its sleeve. Since a substance’s past is constitutively relevant to its individuality (given strong essentialism), this entails that the substance must bear its past on its sleeve in the form of  at each moment of its existence. We aren’t proposing, in this, to offer any final word on the hypothesis that Leibniz carelessly ran  and  in harness; we merely note that it is not yet perfectly clear that he did. There is, in passing, a different mistake that Leibniz might have made – one not so gross as thinking that  entails . Suppose that a possible substance/law expresses a sequence of the form FGHGH . . . as entertained above. It would thus arise that a substance can, in a sense, bear its whole history and thus its individuality on its sleeve at a time, without at that time expressing where it is in its history. Perhaps Leibniz did not see this. Suppose that at time t, God can discern that there exists a law yielding FGHGH . . . as a history. God may now know exactly which substance exists at that time. Further, He can know exactly what sequence that substance will enjoy as its history. But He may not yet be in a position to discern exactly where in its history the substance is. Supposing it is G at t, was its previous state F or H? Consistently with knowing which substance and intrinsic life is at play, the previous state may not yet be determinable. This story does, admittedly, require the conceptual possibility of repetition of total temporary states within substances. To put  on its firmest footing – to avoid the skimpy tracing here envisaged – Leibniz would need recourse to some way of blocking this conceptual possibility. We shall not inquire further here as to whether he had the resources for ruling out any such repetition. As before, we don’t propose to offer any final word on whether Leibniz ran  and  together, that is, conflated the theses that (i) a substance at each time expresses its entire history and that (ii) a substance at each time expresses where it is in its entire history. Call a state for which  holds a ‘weak mark’ and a state for which  holds a ‘weak trace.’ We introduce this language to account for the fact that being a state for which  and  holds does not entail that the state, considered in itself, has a very strong connection with the past and future. A substance/function L can enjoy weak marks and traces of its past and future and, for all that, it remain prima facie coherent that another function L* enjoys a state exactly resembling some state of L but have (non-miraculously) a different past and future.  and

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Law-of-the-series, identity, and change

 only require that the function together with the state at a time entail how things are going to go and how things went. Vary the function, keep the state the same, and  and  may still be satisfied even if the future and history is now different. This picture of the relationship of current states to past and future mimics, in effect, the relationship between the states of a thing and the rest of the world that we suggested earlier on Leibniz’s behalf. The reader may recall that in chapter  we suggested that the thesis that a monad expresses everything about the world does not prohibit a monadic duplicate’s existing in a different world. Expression requires only that the states of the monad, when coupled with the laws of this world, entail what’s going on elsewhere. Vary the laws of intermonadic harmony and one varies the facts concerning which of your monadic states express what, even if your monadic states remain unchanged. Well motivated as the foregoing remarks may be as a statement of Leibniz’s views about the relationship of one monad’s states to the states of other monads, the weak marks and traces view for intra-monadic unfolding seems less plausible as an exercise in rational reconstruction. For Leibniz nowhere appears to take seriously the idea that two substances be wholly alike at a time with regard to accidents while differing at that time with regard to law, and hence with regard to what is marked and what is traced by each group of exactly resembling accidents.²⁶ Suppose Leibniz does not want to allow that a state might mark and trace varying futures and pasts according to the law it is coupled with. This requires a metaphysic prohibiting laws to co-vary while states stay qualitatively the same. (Perhaps the states would not remain numerically the same, supposing accidents are numerically individuated by the law to which they belong. But Leibniz nowhere trades on mere solo numero differences between accidents as something that could have significance vis-a`-vis either discerning things or else the causal powers of things.) So on the current picture we have a requirement that (miracles aside) there cannot be different laws at a time with exactly resembling states at that ²⁶ Some readers may at this point balk at our whole discussion. They may insist that, assuming the functions are different, it is simply trivial that the accidents at any time are different: after all, different dispositional predicates are true of each substance (one law may be such that the predicate ‘When taking F as argument, deliver G as value’ is true of it, another law not). This is too quick. Leibniz, in line with many contemporary metaphysicians, does not accept as a trivial matter, that for each predicate true of the thing, there is a corresponding accident. He does accept that for each predicate true of a thing, there is a foundation in the thing for its being true of the thing. But one cannot assume that, trivially, there is a one–one correspondence between predicates and accidents. (After all, two-place relational predicates don’t, we have argued, have corresponding accidents.)

Substantial laws on the model of immanent functions



time. One can construct a model of marks and traces respecting this fact:  : , and there is no possible law-of-the-series to which a total state exactly resembling s belongs that dictates a different future for s. More perspicuously: A total state s of law-of-theseries L strongly marks its whole future iff every appearance of s in a consistent sequence for any possible law has the same future history.  : , and there is no possible law-of-the-series to which a total state exactly resembling s belongs that dictates a different past for s. More perspicuously: a total state s of law-of-theseries L strongly traces its whole past iff every appearance of s in a consistent sequence for any possible law has the same ancestral history.

Notice that the conjunction of      does not require that there be only one consistent sequence for each function. It requires instead that, inter alia, each sequence consistent with a given function be unique to that function. Leibniz, as we have interpreted him, held that each function has one consistent sequence.²⁷ But his reason shouldn’t have been that any state of a substance contains strong marks and traces of its future and past. His reason should have been – and, it seems to us, was, insofar as he clearly distinguished this from the last – that the primitive active power of an individual substance is a sufficient ground for the particular sequence that is enjoyed by that substance. We have the core of a quasi-formal model for the marks and traces doctrine which precludes there being possible substances that are indiscernible at a time but which mark and trace different pasts or futures owing to their enjoying different laws. But what conception can one have of the state of a substance which renders it intelligible that the state not be enjoyable by a different law-of-the-series? The states of a given substance are of course numerically unsharable, since their individuation is parasitic on their bearer: if you and I have exactly resembling headaches, they are not numerically one, since accidents are individuated by their bearers. The question is, rather: ‘‘Why can’t two substances have exactly resembling total temporary states?’’ What is it about the ²⁷ Again, leaving miracles to one side. The other main exegetical issue relevant here is whether Leibniz would have allowed a different initial state for a given law of the series, a topic discussed above.



Law-of-the-series, identity, and change

nature of laws and the nature of states with their ingredient accidents which precludes different laws from sharing duplicate total temporary states? One of Leibniz’s favorite analogies – that of a mathematical equation or law that determines a unique curve – is certainly of no help here. For a pair of curves can surely intersect before going their own ways again. An appeal to the prohibition of divine arbitrariness seems to help very little. For why should the choice between laws that intersect (so to speak) at a time be arbitrary? Nor can a requirement that past and future truths have a present truthmaker suffice as an argument for strong marks and traces, since weak marks and traces suffice just as well to provide present truthmakers for past and future truths (so long as we allow the law-ofthe-series itself to be part of the truthmaker). And what of the Identity of Indiscernibles doctrine? Can PII be used to preclude the possibility of two substances having qualitatively duplicate states at a time? The difficulty here is that the considerations typically used to motivate PII fail in the present case. Recall from chapter  the two main threads of argument, Divine Preference and No Reason. As just noted, Divine Preference looks to get little if any purchase here, since it seems that God might very well have a reason for preferring one law over another even were the laws to temporarily intersect in their intrinsic trajectories. The No Reason perspective fares no better. One cannot say here, ‘‘There is no reason for saying they are two.’’ There is a reason. Indeed, there is a very Leibnizian reason: there are two different substantial forms. The best we can do by way of motivating   and   on Leibniz’s behalf is as follows. If one thinks that for each dispositional aspect of a law there corresponds a dispositional accident at each time, then one can secure the desired strong account. Now it is hard to think that Leibniz inclined toward the view that substances might differ only with respect to purely dispositional accidents. Perhaps, then, accidents have a dual nature – an intrinsic character and also that of marking a disposition. For consider: intentions have an intrinsic character but also a future directedness, while memories have an intrinsic character but also a past directedness. Leibniz was, after all, operating with a model of monads as equal or lesser versions of minds. An intention to day-dream encodes the disposition to go from that intention (as argument) to day-dreaming. A memory of day-dreaming encodes a disposition to move from day-dreaming as argument to that memory. Suppose now that each disposition of a thing is encoded by an accident

Substantial form, communicability, and time



that also enjoys an intrinsic character, and that each intrinsic accident encodes some disposition or other. One might now be quite reluctant to suppose that two substantial forms have qualitatively duplicate states but different dispositions on account of their being different laws. The picture is not fully satisfying. We continue to suspect that from the point of view of pure metaphysics, there are no very compelling Leibnizian grounds against a weak marks and traces conception, according to which the law itself is the partial truthmaker for truths about the past and future of a substance.             ,              ,        From a scholastic perspective there is, prima facie, a deep problem besetting the idea that substances are individuated by form. Forms are general – they can be common to diverse substances, common to disparate places, common to disparate times. In short they are communicable. Supposing that individual substances are incommunicable, it follows that individual substances cannot be individuated by substantial form. Now it may appear that Leibniz has a ready solution to this prima facie problem. His substantial forms, after all, include all the properties of a thing. But so stated, Leibniz’s view seems susceptible to Aquinas’s critique of Avicenna, namely: ‘‘However many universal forms you pile up, you can never make them add up to anything singular’’ (De veritate .). This concern was echoed by Scotus: ‘‘no matter what common things are simultaneously conjoined, it is never incompatible with the whole aggregate of itself that it should exist in something other than that in which it exists.’’²⁸ A fully Leibnizian solution to our scholastic inquiry can be approached, in the spirit of earlier discussion in chapter , by thinking about the grounds for communicability. Insofar as a form is to be somehow divided from itself, there seem to be three obvious candidates for how this can be done: (I) There are more ultimate subjects of predication than substantial form, whereby one and the same substantial form is predicated now of this more ultimate subject, now of that. (II) Substantial forms can enter into combination with another sort of metaphysical item, such that one and the same form can enter into ²⁸ From the Quaestiones subtilissimae super libros Metaphysicorum Aristotelis , q., as cited and translated by Marilyn McCord Adams, William Ockham, .



Law-of-the-series, identity, and change

combination with numerically different items. For example one form combines one this parcel of signed matter and also with that parcel. (III) The forms divide from themselves thanks to a spatio-temporal manifold.²⁹ Regarding these possible sources of communicability, Leibniz will take much the same line as Aquinas did for angels (an analogy that Leibniz may have anticipated already in the Disputatio, and explicitly notes at Discourse §; at G ,: LA –; and elsewhere). After all, despite his critique of Avicenna, Aquinas did want to hold that substantial form individuates angels. Why was he not worried in that context that form is still inherently general and thus incapable of individuating angels, which are individuals? The reason is that Thomas saw nothing available to serve as a basis for communicability of species in the case of the intelligences: no more ultimate subjects; no components like matter to combine with form to yield a substantial unity; no spatio-temporal manifold. Much the same approach can be deployed by Leibniz. Matter, having no place in the fundamental metaphysics, cannot provide for communicability of substantial forms. Likewise in the case of the spatiotemporal manifold. Nor can we intelligibly suppose any more fundamental subjects of predication. So we are left with forms that are somehow quidditative but nevertheless incommunicable and singular. The most serious potential threat here, for Leibniz, is time. There is, of course, a sense in which the communicability of individual substances in time is fully to be expected. After all, we do think of ourselves (unless we are four-dimensionalists) as fully present at many different times. However, ‘‘communicability’’ of this attenuated sort is by no means a ground for numerical diversity; and so it is not a basis for thinking that form can be common to many things. So what considerations involving time might figure as a basis for ²⁹ Of course, if either the more ultimate subjects of () or the ingredients of () are individuated in part by reference to any such spatio-temporal manifold – as is plausible, for example, with parcels of matter – then those stories are at least partially parasitic on () also. Alternatively, if one thought of spatio-temporal regions as objects in their own right, then this could collapse into a version of (), so that the most ultimate subjects of predication are regions, forms being modifications of regions. Communicability will now, on this picture, amount to one and the same form’s modifying two different regions. Or, eschewing an ontology of points, regions, instants, and periods, one might instead develop the story by using relation as the principle of communicability. Now communicability amounts to one and the same form’s being at either a temporal or spatial distance from itself.

Substantial form, communicability, and time



thinking that forms or laws have communicability of the sort depriving them of the capacity to individuate substances? Once one thinks of immanent individual functions as being in time, it seems that one can perfectly well allow their annihilation and then re-creation. Thus one can well imagine an immanent law-of-the-series being created at t, running a sequence of thirty states, whereupon God annihilates it;³⁰ then, after a while, God re-creates the immanent function, lets the sequence run again for thirty states (maybe less, maybe more), and annihilates it. Imagine that function is the one associated with you, and that you are going through its first epoch, so to speak. It seems very odd to think that you will be re-created. Perhaps your functional nature will, but you won’t. And so it seems that your functional nature is not identical to you. Surely you are not communicable in a discontinuous way across time, but just as surely your functional nature is. Given this fundamental difference, one is led to conclude that you must have some further individuating component or characteristic. So would run a scholastic critique of Leibniz grounded on considerations of communicability and time. What will Leibniz have to say here? If one thinks of time as an independent underlying manifold within which substantial change occurs, then Leibniz has nothing whatever to say. For against that background, the re-creation story is perfectly intelligible. Now one might say that the re-creation story doesn’t yet show that two numerically distinct things can share the same law. Confronted with the scenario told in regard to oneself, for example, one might instead say: ‘‘Surprisingly, I can enjoy a gappy existence. I can enjoy the same life history all over again.’’ But that conception of the story is at least a strained one. Moreover, it would in any case align poorly with the doctrine of marks and traces, since it is not at all clear how to render intelligible the idea that some state of a substance at a time prefigures such a repetition as the story envisages. Arguably, Leibniz did not think of time as an independent underlying ³⁰ There are some puzzles here. What does annihilation mean for a form? Consider an immanent universal. To annihilate it means, one might have thought, to ensure that it isn’t present at any time in the future. Given that, it might be odd to describe what is going on as annihilation. Suppose it isn’t. Suppose God merely ensures that your function isn’t around for  minutes and that it is inappropriate to describe this as annihilation. The function then gets instantiated  minutes later. Does it pick up where it left off, or does it begin again? In what sense are the facts of time causally efficacious here? As we shall be understanding Leibniz below, these tricky issues do not arise. But if one understands time to be a real manifold that provides the backdrop for causal goings-on in substances, the issues do certainly arise and have no readily available solution so far as we see.



Law-of-the-series, identity, and change

manifold, offering definitions of temporal relations in non-temporal terms (see GM ,: L ; VE –; VE ). As a number of commentators have suggested, Leibniz endorses all the resources for a causal theory of time, whereby the intra-monadic causal order supervenes on the order of reasons, and the inter-monadic temporal order supervenes on the similarity and difference of intra-monadic sequences.³¹ Assume the causal theory of time. It would seem that the risk of communicability can be then avoided, since, from the perspective of a Leibnizian causal theory of time, it is extremely hard to make sense of the scenario of a form being communicable across time. Suppose for reductio that there is a form x and a form y, such that x has ABC, y has ABC, and y’s first state is later than x’s last state. According to the causal theory emerging from the Metaphysical Foundations of Mathematics, for y’s A to be later than x’s C, either (i) x’s C is the reason for y’s A or (ii) there is some perceptual state P in some substance z that reflects/expresses x’s C and some later perceptual state P in z that reflects/expresses y’s A. But this latter, from the Leibnizian perspective, would allow expression relations that have no basis in the things themselves: for unless we allow primitive extrinsic denominations into the picture, we shall have no resources for explaining what it is about P that makes it an expression of x’s C rather than y’s C. One is left with no grounds for distinguishing x and y on the score of time. But given they are functional duplicates, one is now in no position to say that ‘they’ are (numerically) two rather than one. Clearly it’s no good to distinguish x and y on the grounds that the first A-accident is numerically different from the second-A accident: again, Leibniz would deny the presumption that accidents are per se individuals whose individuation is not parasitic on the substance in which they inhere. In conclusion, then, the communicability-based critique of form or law as the principle of individuation seems no more serious for Leibniz’s simple monads than it is for Aquinas’s angels. Viewed in the light of some other central threads of his metaphysics, Leibniz’s claim that every substance is individuated by its whole entity – the law-of-the-series or form which it is – emerges in our thinking as defensible. ³¹ A defense of reading Leibnizian time as having a secondary, derived status, and an account of Leibniz as a causal theorist of time, can be found in J. A. Cover, ‘‘Non-Basic Time and Reductive Strategies: Leibniz’s Theory of Time.’’ See also Part  of H. Mehlberg, ‘‘Essai sur la the´orie causale du temps’’; John A. Winnie, ‘‘The Causal Theory of Time,’’ pp. –; and Bas van Fraassen, An Introduction to the Philosophy of Time and Space, pp. –.

 

The threat of one substance

There are two ways in which the Spinozistic world-view threatens to consume Leibniz’s metaphysic. The first is necessitarianism, familiar both in tempting the early Leibniz and giving rise to an extended and difficult program of resistance from the late s onward. The second threat, from Spinoza’s one-substance doctrine, has received comparatively little attention.¹ In chapter  of his A Critical Exposition of the Philosophy of Leibniz, Bertrand Russell makes the following, rather striking remark: on the principles of Leibniz’s logic, the Identity of Indiscernibles does not go far enough. He should, like Spinoza, have admitted only one substance.²

Russell’s motivations for this remark are universally either ignored or under-appreciated. We propose to make a case for the Russellian verdict, and to offer an interpretive gloss on some rather cryptic Russellian remarks in the light of that case. In doing so, our overarching aim is to make manifest one of the deepest challenges facing the Leibnizian metaphysic, and moreover to bring into clearer relief a pressing concern for any metaphysics of individuals.            -        Famously, Leibniz declared that ‘‘Spinoza would be right, if there were no monads.’’³ In the previous chapter we developed as best we could a ¹ That is, little attention as a threat (but see Robert Adams, Leibniz: Determinist, Theist, Idealist, pp. –). Ludwig Stein argues for a ‘‘Spinoza friendly’’ period in Leibniz’s early years of – in Leibniz und Spinoza, esp. pp. –. That issue has received attention from G. H. R. Parkinson in his ‘‘Leibniz’s Paris Writings in Relation to Spinoza,’’ and from Mark Kulstad in ‘‘Did Leibniz Incline toward Monistic Pantheism in ?’’ ² Bertrand Russell, A Critical Exposition of the Philosophy of Leibniz, p. . ³ G ,: L . Our thanks to Gregory Brown and Glenn Hartz for getting us to see the need for this paragraph and the next. They will doubtless wish the need had been more fully met.





The threat of one substance

picture of what monads are for Leibniz, namely, immanent active forms/laws from which accidents emanate. Leibniz’s monadology tells us that there are many such immanent laws. A Spinozistic monadology would tell us that there is only one. Now that ontology is not exactly the threat we are concerned with here. Leibniz aims explicitly to avoid that threat with a metaphysic according to which things distinct from God are not ‘‘of a passing nature, vanishing into simple accidents or modifications’’ (G ,). And as Leibniz well sees, such a metaphysic requires in creatures something answering to the familiar and traditional concept of substance – in particular to the notions of persistence and force: ‘‘the substance of things consists in the force of acting . . .’’ from which it follows, Leibniz says, that ‘‘no enduring thing can be produced [by God] if there is no force that long endures in them’’ (G ,: L ). Absent such an internal force by which creatures causally contribute to their accidents, it would follow that no created substance, no identical soul, would be permanent, and hence that nothing would be conserved by God, but everything would reduce to certain evanescent and flowing modifications or phantasms, so to speak, of the one permanent divine substance . . . God would be the nature and substance of all things – a doctrine of most evil repute, which a writer who was subtle indeed but irreligious, in recent years imposed upon the world . . . (De Ipsa Natura: G ,–)

As Leibniz says in a letter of  to Lelong: By the force I give to substances, I understand nothing other than a state from which another state follows, if nothing prevents it . . . [Were] it destroyed, there would remain almost none of them – or rather, none of them at all. And I dare say that without force, there would be no substance, and one will, in spite of oneself, fall into the opinion of Spinoza according to which creatures are merely passing modifications.⁴

Leibniz was more careful in the first passage: it is not that without form or force in creatures, there would be ‘‘no substances at all’’ (to Lelong) but rather ‘‘no created substances’’ at all (De Ipsa Natura). Now, in asking what is at the foundations of Leibniz’s philosophy that prohibits a ‘‘Spinozistic’’ one-substance metaphysics, two sorts of question arise. First: on what grounds does Leibniz distinguish God from the substantial immanent laws of the natural world, whether they be one or many? Second: on what grounds does Leibniz secure a metaphysic of many substantial immanent laws rather than one? The first issue con⁴ Andre´ Robinet, ed., Malebranche et Leibniz: Relationes personelles, p. .

Motivating the one-substance threat



cerns the basis for claiming that there are creaturely substances distinct from God. The second issue concerns the basis for a metaphysic of many creaturely substances. Fascinating and important as it is, we shall not be addressing the first of these issues here. That is, we shall not be pursuing the question of God’s relation to the world generally, nor in particular of how well Leibniz’s familiar remarks above – expressing his considered means of avoiding Spinozism proper – can adequately be wed to his view that whatever there is of perfection (‘‘positive reality’’) in the created order must arise from God (cf. Causa dei at G ,), who ‘‘produces creatures continually by a kind of emanation as we produce our thoughts’’ (Discourse §).⁵ Rather, we shall restrict our focus to the second issue, to the question of ‘‘how many?’’ as it applies to creatures, supposing that Leibniz can defend his claim that the created order is (let us say) substantial rather than merely modal. Even with this focus, we can readily enough – indeed we suspect more readily – unpack the concerns motivating Russell’s earlier remarks, and survey the resources available to Leibniz or anyone else in addressing those concerns. But our inquiries to follow are not irrelevant to the first issue, the first question. As we encounter pressures on Leibniz toward collapsing a metaphysic of many created substances into a ‘‘spinozistic’’ (small ‘s’) metaphysic of just one, the reader will see analogous pressures toward collapsing the distinction between God and the created world.⁶ Our main focus of concern can be rendered vivid in the following terms. Abstract away for the moment the substantial ground from which qualities (accidents) arise, and consider the distribution of all qualities at ⁵ See also Monadology §. One should have supposed that if we stand to God in the relation our thoughts stand to us, then we are rather more like modes of the divine mind than enduring substances. It might be suggested that creatures cannot be ‘‘in God’’ as modes are in the divine mind because what there is of reality in creatures is limited, and there is nothing of limitation in God. Perhaps. But it is unclear why this should mark out anything deeper than a basis for distinguishing what is uncaused in the divine nature from what is caused by and so distinct from Him and His attributes – that distinction bringing no relevant information about the ontological status of the causal offspring. Moreover positive perfections can be limited (this in degree) without somehow possessing negation intrinsically (here of kind). (We shall return to this briefly in §. below.) And the traditional doctrine of eminent containment, which recommends that the resources contained in God differ from their creaturely correlates by being ‘‘of a higher form,’’ traces to a scholastic provenance emphasizing degree rather than kind. No doubt big enough differences in degree suffice for differences of kind, but again, that difference may mark the distinction between Creator and creature, not (yet) substance and mode. As for the mature Leibniz’s view of God’s continued contribution, there are questions of whether one should distinguish conservation from concurrence, and more crucially how either of these is to be satisfactorily wed to the metaphysic of causally active individual substances. See chapter , and § of Robert C. Sleigh’s ‘‘Leibniz on Malebranche on Causality.’’ ⁶ See, for example, note .



The threat of one substance

a world – the totality of accidents making up the manifold that is (under the abstraction) our world. If a Leibnizian rationalism about reality is to provide compelling grounds for a metaphysic of many created substances rather than one, then some compelling reason must be provided why we oughtn’t to think that one substantial active principle or law-of-theseries, rather than many, makes up the world. There is nothing about the nature of accidents per se, as manifest qualities in the world, requiring many laws rather than one. Nor is there any compelling reason, a priori, to suppose that a single law could not provide a massive and rich diversity of accidents – this particularly so in light of the fact that even the commonplace workaday laws of Leibniz’s received metaphysic have a near unfathomable richness to them. The Leibnizian might at the very outset appeal to considerations of divine preference: ‘‘It is possible in itself that God make a world just like ours in qualitative nature, variety and richness which contains only one substance, but found a world exhibiting the same mosaic of accidents with many substances morally preferable.’’ Not only is bottoming out in final causes dissatisfying as an ultimate metaphysical theory about the nature of things (cf. chapter ), but the implicit moral reasoning seems, at least prima facie, to deploy the very kind of solo numero distinctions that Leibniz eschews when considerations of moral weight are at the fore. Why not, then, endorse a metaphysic of the created order with one law and – adopting now Spinoza’s preferred taxonomy – many modes? It may seem from the Leibnizian perspective that such a threat arises only upon ignoring the law of identity that has come to be known as Leibniz’s Law, according to which if x = y, then x and y are indiscernible. Suppose that a tomato exists (i.e. that there is a substance underlying the tomato’s accidents) and suppose that a grain of sand exists (i.e. that there is a substance underlying the accidents of the grain of sand). Does Leibniz’s Law entail that the substance underlying the accidents of the tomato is not the substance underlying the accidents of the grain of sand? Not obviously. For it is difficult to see how Leibniz’s Law itself can cut much ice against assuming that one law gives rise to them all: from that law emanates redness here, yellow ochre there, softness here and hardness there, and so on.⁷ If one helped oneself at the outset to the ⁷ One is invited in a Leibnizian setting to bring on board some version of ‘‘phenomenalism,’’ where the fundamental predicates will be mentalistic and will ultimately provide the analytic foundation for such predicates as ‘redness here.’ The existence of a single law hardly prohibits any such phenomenalist strategy. (The invitation will apply later in this chapter as well, when discussing bodies.)

Two Leibnizian theses



supposition that the grain has qualities that the tomato lacks, then Leibniz’s Law might weakly confirm a claim of numerical distinctness; but here the claim that the grain has qualities that the tomato lacks would tacitly rely on a presumption of numerical distinctness between the grain and the tomato; and that is precisely what is at issue in the context of these rarefied metaphysical disputes. Concerning a single face one might say that the scowl has properties that the blush lacks. In supposing a single law could give rise to our actual mosaic of accidents, no special problem is presented by Leibniz’s Law. So much for the preliminary case for a one-substance ‘‘spinozistic’’ threat. In what follows we wish to develop the threat in connection with some salient details of the Leibnizian metaphysic.                  .. Relations cannot individuate substances There is no doubting that the most familiar and intuitive basis for workaday attributions of numerical distinctness between individuals is spatial separation. The grain is distinct from the tomato because (i) substance can’t be in two places at the same time and (ii) the tomato and the grain stand in a relation of spatial distance to one another. While the Leibniz of the Confessio was prepared to lean on spatial relations as the basis for numerical distinction (cf. chapter  §), such a tack was anathema to the mature Leibniz. Consider first the possibility of interpenetration, to which (recall from chapter ) Leibniz was open. In the Essay (.ii.) Locke had claimed that, among the propositions of natural philosophy demanding assent immediately upon our understanding them, is the proposition ‘‘That two Bodies cannot be in the same place.’’ Leibniz replies that this proposition needs proof. Indeed, it is rejected by all those who believe in condensation and rarefaction, strictly and properly so-called . . . ; not to mention Christians, most of whom think that the opposite – namely the penetration of dimensions – is possible for God (NE .i.: RB )

On the ‘‘strict and properly so-called’’ picture of condensation, when some (rarefied) bit of matter becomes more dense, some of its parts which had been at a spatial distance from one another come to be at the same place. The possibility of condensation thus construed – and so of interpenetration – was commonly granted by the earlier Peripatetics. Among the most outspoken of medievals to espouse the account was



The threat of one substance

perhaps Ockham, who – en route to concluding that since bodies can be of greater or lesser extension they needn’t be extended at all – claimed that ‘‘when something dense is made from something rarefied, those parts of the rarefied thing first coexisted with many parts in many places, and now those same parts coexist in one place . . .’’⁸ Descartes would later reject the possibility of what Leibniz refers to (above) as condensation properly so-called,⁹ believing that if extension is the whole essence of material body and there is only a conceptual, not a real, distinction between body and space, numerically distinct bodies could not occupy the same place (Principles .,: AT A,, –: CSM ., ). But Descartes’s account still invites the second of Leibniz’s complaints to Locke: theological orthodoxy seems to require the ‘‘penetration of dimensions’’ in the Sacrament of the Eucharist, according to which the Christ’s body enjoys a real presence in the body of the host.¹⁰ If, given the possibility of condensation and real presence, substances can interpenetrate, then spatial relations cannot be the fundamental principle of sameness and difference. Later in the New Essays .xxvii. when criticizing spatial location as a ‘‘principle of individuation,’’ Leibniz writes that this principle is founded on the assumption that interpenetration is contrary to nature. This is a reasonable assumption; but experience itself shows that we are not bound to it when it comes to distinguishing things. For instance, we find that two shadows or two rays of light interpenetrate, and we could devise an imaginary world where bodies did the same . . . (RB )

That is the old Leibniz of the New Essays, speaking of an imaginary world. The earlier Leibniz of the Paris period spoke of the actual world when he argued, from the context of his conatus physics, that Descartes was right to think of bodies as wholes whose parts move with a common ⁸ Reportatio , q . ⁹ Supposing, with Descartes, that interpenetration is impossible, need we accept the claim – accepted pretty much on all hands – that condensation entails interpenetration (colocation)? No. Here are two arguments, the second preferable to the first. () A batch M of continuous matter in spherical region R of continuous space must all come to be in smaller spherical sub-region R'. But R' is full – that is, all concentric sub-regions of R’ are full. In order to make room for all of M in R’, think of the concentric subregions as rooms in a Zeno-designed Hilbert’s Hotel, and vacate some outermost region in R' by moving all occupants closer toward the center. () Suppose that a continuous region R of space is completely filled by a continuous batch M of point-masses of matter. That all of M can fill some sub-region R’ of R is clear from the fact that any infinite set S of elements can be put into one-to-one correspondence with a proper infinite subset of S. ¹⁰ That Leibniz has in mind the doctrine of real presence (the substance of Christ’s body is present in the sacramental bread) is suggested both by (i) his reference to ‘‘most Christians,’’ this doctrine being common to Protestants (Lutherans) and Catholics alike, and by (ii) the fact that transubstantiation denies what Leibniz in this context needs – namely that the substance of the bread remains in the sacrament. Or so it seems to us.

Two Leibnizian theses



motion. Common motion, for Leibniz by way of Aristotle, entailed common spatial location of (let us say) some parts of parts of the whole – namely the parts’ adjoining physical boundaries. Common spatial position of the extrema or boundaries of adjoining parts was a necessary condition for cohesion within a continuous whole, unlike an aggregate whose parts are discontinuous or discreet and whose boundaries are merely contiguous: ‘‘For by the very fact that the parts are discontinuous, each will have its own separate boundaries [terminos] (for Aristotle defines continuous things as hon ta eschata hen [those whose boundaries are one])’’ (A ..). In the case of merely contiguous boundaries, all bets are off as to common motion. But ‘‘things whose boundaries are one, hon ta eschata hen, are continuous or cohering, by Aristotle’s definition as well as mine, since if two things are in one place, one cannot be impelled without the other’’ (A ..).¹¹ Leibniz’s intentions in ‘‘two things in one place’’ are clear when he writes that ‘‘I should think that the endeavor [conatus] of the parts toward each other, or the motion through which they press on each other, would itself suffice to explain the cohesion of bodies. For bodies which press on each other endeavor to penetrate each other. The endeavor is the beginning; the union is the penetration’’ (G ,). Leibniz then is far from claiming that interpenetration or co-location is impossible. Returning now to the New Essays, by denying the impossibility of interpenetration, Leibniz denies what has entailed it – that spatial relations are the grounds for individuation.¹² From the passage immediately preceding the one quoted above: ¹¹ Our thanks to Sam Levey for drawing this bit of Leibniz’s physics to our attention. One might doubt whether Leibniz’s conditional argument here is much good, and whether Aristotle’s actual position (as opposed to Leibniz’s gloss) might have been better. In Physics . Aristotle does says that in continuous, as opposed to contiguous, bodies, the boundaries ‘‘are contained in each other’’ (a), which may recommend Leibniz’s gloss. But that gloss is scarcely suggested by what precedes it: ‘‘things are called continuous when the touching limits of each become one and the same.’’ We incline toward reading Aristotle here to mean one boundary, shared by the joined parts, not two co-located boundaries. If that is right, his view is at least prima facie well taken: sharing a numerically identical boundary would guarantee common motion better than co-located distinct boundaries (which, having in the recent past been spatially separated, might just as readily be so in the near future, compromising cohesion). We leave to others the details of Aristotle’s view, noting however that (i) in On Generation and Corruption, at least, Aristotle departs from Anaxagoras before him (and the Stoics after) by denying that the basic ingredient bodies of the natural world are ever in the same place, and that (ii) Aristotle isn’t beyond arguing against opponents by proving that their views entail the co-location of distinct bodies in the same place (see Physics ..b–; De Anima ..b). ¹² Caution: strictly speaking, for Leibniz to argue that being in the same place does not suffice for being numerically the same individual is not yet to argue that being in different places won’t suffice for being numerically distinct individuals. That’s relevant to the passage to follow, and to the final paragraph of this section.



The threat of one substance

In addition to the difference of time or of place there must always be an internal principle of distinction . . . Thus, although time and place (i.e. the relations to what lies outside) do distinguish for us things which we could not easily tell apart by reference to themselves alone, things are nevertheless distinguishable in themselves. So time and place do not constitute the core of identity and diversity, despite the fact that diversity in time or place brings with it differences in the states that are impressed upon a thing, and thus goes hand in hand with diversity of things. To which it must be added that it is by means of things that we must distinguish one time or place from another, rather than vice versa . . . (NE .xxvii.: RB )

The New Essays passage is, of course, all of a piece with Leibniz’s thesis about relations generally – with the familiar Leibnizian theme that extrinsic denominations supervene on (have their foundation in) intrinsic monadic facts/denominations of individual substances.¹³ In the end, relations don’t serve for Leibniz as a basis of numerical distinctness. This excludes spatial separation as a ground of numerical distinction; but it also excludes other relational candidates – including, most obviously, what Leibniz might reckon PSR to exclude in any case, namely a primitive relation of numerical difference. Primitive difference among created substances is no more inviting to Leibniz than was the rejected way of Negation in the Disputatio: in Aristotelian terms, to regard a negative fact of ‘x not being y’ as a primary determination is to turn our backs on the fundamental commitment to an intrinsic positive determination as the ground of numerical distinctness. Finally, in connection with the issue of spatial relations themselves, we should note in passing that the doctrine of real presence works against any account of body endorsing a spatio-temporal principle of individuation – whether the account emerges from Cartesian physics or otherwise, whether it invites Protestant (Lutheran) theology or otherwise. For the possibility of real presence entails the possibility of multipresence. Thus in De Transubstatione the early Leibniz is willing explicitly to speak of ‘‘the substance of Christ’s body being present in all places where the appearance of consecrated bread and wine exists’’ (A...: L ).¹⁴ There is a genuine theological concern here, one that despite ¹³ And so Leibniz goes on in the New Essays to affirm PII by insisting that, were there indiscernible substances, they would be ‘‘indistinguishable in themselves and discernible only by means of external denominations with no internal foundation; which is contrary to the greatest principles of reason’’ (NE .xxvii.: RB ). ¹⁴ In the Fourth Objections, Arnauld had worried that ‘‘according to [Descartes’s] doctrines it seems that the Church’s teaching concerning the sacred mysteries of the Eucharist cannot remain completely intact’’ (AT ,: CSM .–): the doctrine of transubstantiation requires that the substance of the host is taken away from the bread and only the accidents remain, while

Two Leibnizian theses



his changing views on real accidents Leibniz was prepared to countenance with more than a passing gesture in mature years: if the reality of the Eucharistic presence – conjoined with the doctrine of transubstantiation or not – shows that the form of a substance can be fully present at many places at the same time, then spatial separation between substantial form a and b is not sufficient grounds for the numerical distinctness of substance a and substance b. . The basic properties are simple, positive and compatible The first Leibnizian thesis, then, is that relations cannot individuate individual substances. A second thesis – sketched here and deployed below – emerges from Leibniz’s views about the nature of basic properties of substances. As we read him, Leibniz’s picture is this: at the metaphysical groundfloor there are individual active substantial forms with their properties, and all fundamental, monadic properties of substances are simple, positive and compatible. That is not to deny of course that there are complex predicates, negative predicates and incompatible predicates: but truths deploying such predicates will be grounded in the metaphysical landscape of substance and basic monadic properties. Turning first to simplicity, recall Leibniz’s belief that any predicate F will, at least at the limit, bottom out under decompositional analysis into simple predicates corresponding to simple ideas or perfections in God. Simple predicates correspond to the ‘‘first terms’’ of the early De Arte Combinatoria (), at which time Leibniz still conceived the task of carrying out analyses of concepts ‘‘down to simple parts, i.e. indefinable terms’’ (A ..–) as belonging to the logic of discovery. Sometime before the Generales Inquisitiones (), Leibniz had given up the youthful dream that humans could in fact complete such analyses down to their primitive simple concepts: since ‘‘we do not understand distinctly enough the way in which the natures of things flow from God, nor the Descartes denies that there are any such real species or accidents (only extension, shape, and motion). In noting the exchange between Arnauld and Descartes, Leibniz argues that this effort to avoid conflict with transubstantiation scarcely gets to the bottom of things: ‘‘Once when [Descartes] had to discuss the Holy Eucharist, he substituted for real species only apparent ones, and thus revived a doctrine rejected by a universal consensus of theologians. But this would mean little, if his philosophy could allow bodies to exist in several places at once. For if a body and space are one and the same, how can we avoid the consequence that in different spaces or places there must be different bodies?’’ (c. ; A ..: W ). Leibniz’s point is that we must avoid this consequence – that is, must ‘‘allow a body to exist in several places at once’’ – to preserve the multiple-location of Christ’s body required by orthodox Eucharistic theology.



The threat of one substance

ideas of things from the idea of God’’ – an understanding ‘‘in which ultimate analysis would consist’’ – we must acknowledge that simple concepts remain in the possession of the divine intellect and that ‘‘[a]n analysis of concepts such that we can reach primitive concepts . . . does not seem to be within human power.’’¹⁵ But Leibniz never retreats from the view that there are such primitive simple predicates or concepts, to which all others are analyzable in the limit. They figure centrally in his efforts to supply ontological arguments for the existence of God with their missing premise that God is a possible being. That effort, arising already in his discussions with Spinoza (where Leibniz understands the simple concepts to express the perfections of God)¹⁶ and taken for granted in the Monadology (§), comprises one of two solutions to the general task of showing that some concept is possible: either empirically or a priori. The a priori method would consist of an analysis into primitive simple concepts – an analysis that, midway between the ‘‘Two Notations’’ for Spinoza and the Monadology, Leibniz is again cautious of claiming we can in fact perform: I won’t now venture to determine whether people can ever produce a perfect analysis of their notions or whether they can reduce their thoughts to primitive possibilities or to irresolvable notions or (what comes to the same thing) to the absolute attributes of God, indeed to the first causes and the ultimate reason of things.¹⁷

This latest reference to ‘‘the absolute attributes of God’’ and ‘‘the first causes of things’’ highlights a second, closely related aspect of Leibniz’s picture from which the simplicity of all basic monadic predicates of substances is apparent. On the Thomistic account of divine creation, it is required that God be an ‘‘exemplary cause’’ in the production of creatures in order for individual substances to receive some determinate ‘‘forms’’ or ‘‘species’’ (cf. ST a, q., ). During the Paris period Leibniz had extended the Thomistic conception of such forms or ideas in the divine mind being ‘‘multiplied’’ (Aquinas’s term) in relation to creatures, claiming that ‘‘the origin of things from God is of the same kind as the origin of properties from an essence’’ (A ..: DSR ). As in the earlier ‘‘Notations’’ for his exchange with Spinoza, the essence of God is said again to ‘‘consist in the fact that he is the subject of all compatible attributes,’’ where as before ‘‘an attribute of God is any simple form’’ (A ¹⁵ From the Introductio ad Encyclopaediam Arcanum, at C –, written probably after  and before  (see PLP xxvii). ¹⁶ See his ‘‘Two Notations for Discussion with Spinoza’’ () at G ,–: L –. ¹⁷ Meditationes de cognitione, veritate et ideis (): G ,: AG .

Two Leibnizian theses



..: DSR ). So the suggestion here, on which Leibniz elaborates relatively little in this period or later, is a kind of causing as giving account whereby God – ‘‘the subject of all absolute simple forms’’ (A ..: DSR ) – in some way shares those simple perfections in creating finite substances. It is precisely this account that Leibniz of the Discourse period had in mind when referring (above, from the Introductio) to ‘‘the way in which the natures of things flow from God.’’¹⁸ Turning now to compatibility,¹⁹ Leibniz’s early attempts at providing a mathematical representation of truth and validity show that he was, early on in his career, thinking of simple properties as compatible. Consider, for example, his Elementa calculi (). There, each simple concept is given by a prime number, its ‘‘symbolic number.’’ The complex concept composed of any two simple concepts is given by multiplying the symbolic numbers of the simple concepts. Note that in this system, every combination of simple concepts will be coherent: that claim is secured by the mathematical fact that any pair of primes yield a determinate number when they are multiplied with each other. Any finite list of simple concepts will, indeed, determine a possible concept about which various affirmative claims will be true, since any list of primes multiply to yield a particular number. Leibniz is in any case explicit about simple primitive concepts being mutually compatible: writing to Sophie (c. ) he says that ‘‘In the elements of symbolic logic are simple thoughts, and simple forms are the source of things. I maintain that all these simple forms are mutually compatible’’ (G ,). And the earlier creation picture – according to which the basic elements of any decompositional analysis have their source in the divine perfections – recommends this same positive, compatible status for all basic monadic predicates/properties. ‘‘God is the subject of all absolute simple forms – absolute, that is, affirmative’’ (A...: DSR ). All such positive properties, exemplaries of the simple primitive properties in creatures, are, Leibniz argues, ‘‘com¹⁸ There is no doubt a (partly philological) story to be told by way of connecting Leibniz’s ‘‘per Dei influxum’’ here, echoed in the taxonomy of the Discourse (§, ‘‘produced by a kind of emanation’’) and the Monadology (§, ‘‘all the created or derivative Monads are productions and are born, so to speak, by continual Fulgurations of the Divinity’’), to a mixed provenance in neo-Platonic and Aristotelian thought. We leave the story to others, save to caution against reading too much of Plotinian (or Spinozistic) overtones into the language itself. By the thirteenth century, the Platonic and Aristotelian mixture was well enough in place to permit Thomas’s de modo emanationis rerum a primo principio of ST a, q. as a pretty unexceptional way of speaking about creation: ‘‘. . . et hanc quidem emanationem deignamus nomine creationis’’ (a). ¹⁹ Reserving ‘compossibility’ for the relation between possible substances, discussed in chapter , §.



The threat of one substance

patible with each other or can be in the same subject’’ (G ,). Now it might be said (not implausibly) that this compatibility of all perfections in the same divine subject cannot be applied to their simple primitive offspring in creatures, since the latter must be somehow ‘‘limited’’ versions of their exemplaries, involving a negation of them. Postponing for §§. and . below a more detailed philosophical assessment of negation itself, the following reflection is apposite. The data at least make clear what is agreed on all hands, that the basic, groundfloor monadic properties of individuals, at which all decompositional analyses bottom out, are, as Leibniz says, primitive, simple properties. Now, lacking any good evidence from Leibniz to the contrary, it is safe to reckon his intention behind ‘simple’ as expressing this feature of any primitive concept A – that it is not built up of other concepts, whether as a conjunction of simpler ones (say, B and C ) or as involving the negation of some other concept (say, not-B ): a ‘‘simple and primitive’’ concept, is ‘‘a concept from which nothing can be removed’’ (G ,: L ). On this proposal, whatever the respect of limitation in creaturely ‘simple forms’ relative to their divine exemplaries, they cannot be intrinsically privative simple properties involving negation and some other property. Indeed (reverting here to the logic), Leibniz seems to indicate in the  Generales Inquisitiones that the privative is better understood as the lack of a property, not the possession of some (permit us) ‘‘negative property’’ at all. Thus, ‘‘ . . . ‘non-entity’ is that which is purely privative’’ (C ), where ‘entity’ expresses something possible (C ): one scarcely expresses a possible entity with ‘Not-B,’ nor even with some well filled-out ‘Not-B, Not-C, . . . ,’ as if saying what isn’t amounts to saying what is. (And how does one express something possible, some possible entity? Says Leibniz, ‘‘A positive term is the same as ‘an entity.’’’) A glance through his best approximations of ‘‘simple primitive terms’’ for the Inquiry (under the proviso granted a few years earlier concerning our inability to find those concepts that are absolute primae) will turn up nothing overtly or implicitly negative. . Spinozistic trouble Recall again the two threats to the Leibnizian metaphysic noted at the outset of this chapter: Spinozistic necessitarianism, and a one-substance doctrine. Our two recent Leibnizian theses – that relations cannot individuate substances and that all basic monadic predicates of substances are simple, positive, and compatible – make prima facie trouble for

Two Leibnizian theses



Leibniz’s resistance to the first of these threats. Keen on resisting Spinoza’s necessitarianism following their meeting in November , Leibniz had insisted that not all possible substances exist, for (as he would later put it to Bourguet) not all possibles are compossible, and ‘‘thus the universe is a collection of a certain order of compossibles only’’ (G ,: L ). Suppose then (with Mates²⁰) that one construes possible worlds as maximal sets of compossible substances, or alternatively of compossible complete concepts. If all predicates of any possible individual substance are (or reduce decompositionally to predicates that are) compatible with those of any other, then each possible substance is compossible with every other. It emerges that there is only one possible world after all. Leibniz may well have the resources for solving this problem. We have argued in chapter  (§.) that a presupposition of maximality for possible worlds is best withheld from Leibniz’s considered view. One might of course wonder whether God could have ordained less than the best – but here we return to familiar territory, and away from any special necessitarian threat that might loom from the apparent compatibility of all monadic predicates of individual substances. Our two Leibnizian theses make for much deeper trouble, however, in connection with the second threat of a one-substance doctrine. For prior to worrying about how individual substances can be fairly clustered into possible worlds, one must take stock of concerns about the ontological ground of numerical difference between substances in the first place – a ground presupposed by necessitarian concerns about modal mixing and matching of individual substances. Are there individuals (plural) to cluster at all? Suppose one believed that one was confronted with two substances, Jim and John. Jim is taken to have three simple positive properties F, G, and H and John to have three simple positive properties I, J, and K. Once one admits the compatibility of all simple positive predicates, one shall have to admit a possible world where there is one substance – call it Bob – that has F, G, H, I, J, and K. This admission immediately raises worries of divine preference. Why should God prefer the world with Jim and John rather than the world with Bob? Isn’t this a difference solo numero? But the problem runs even more deeply than this. For by Leibniz’s own lights, external denominations require a foundation in internal denominations. What then is to ground the relation of dif²⁰ See pp. – of Benson Mates, The Philosophy of Leibniz, and his chapter , esp. pp. –.



The threat of one substance

ference between the bearer of F, G, and H and the bearer of I, J, and K? Note here that the following set of truths do not entail that there is more than one thing in the world: ‘‘Any combination of F, G, H, I, J, K could be had by a single subject. Something is F. Something is G. Something is H. Something is I. Something is J. Something is K.’’ And one is no closer to deducing the desired Leibnizian result – of two numerically distinct substances – if one adds: ‘‘Something is F, G, H. Something is I, J, K.’’ Now of course the desired Leibnizian result is entailed once one throws in ‘‘and the something that is I, J, K is numerically distinct from the something that is F, G, and H.’’ But this is theft over honest toil, helping oneself to the result one should like to earn from the nature of things: it is to make the relation of numerical difference basic in order of explanation as opposed to something explainable by intrinsic denominations. It seems, then, that in positing a metaphysical groundfloor of a plurality of individuals enjoying positive simple monadic accidents, Leibniz succeeds only in violating his own proposal that all relations be grounded in intrinsic denominations. One might well wonder if the relation of identity (difference) is an exception here. That is, perhaps one is to let facts of identity and difference be primitive facts alongside facts about monadic predicates, these former facts enjoying no deeper explanation. But let us not forget that this still risks the permission of solo numero differences between this and other possible worlds. If the mosaic of accidents is in itself neutral as between one law-of-the-series and many, then there will be many worlds differing only in the primitive relations of identity and difference – including one world with a single created active form/law from which emanates the whole qualitative mosaic of our world of many substances.²¹           Let us now return to the discussion of Russell’s that led him to the remarks with which we began this chapter. The relevant segment of discussion begins with a presentation of what Russell takes to be Leibniz’s defense of PII: Every extrinsic denomination – i.e. every relation – has an intrinsic foundation, i.e. a corresponding predicate (G ,). The substance is, therefore, wholly ²¹ Would the single-law world be one in which God knew what He succeeded in creating? Perhaps He set out to create – and then, having done so, couldn’t know if He had succeeded or not.

Returning to Russell



defined when all its predicates are enumerated so that no way remains in which the substances could fail to be unique. For suppose A and B were two indiscernible substances. Then A would differ from B exactly as B would differ from A. They would, as Leibniz once remarks regarding atoms, be different though without a difference (G ,). Or we may put the argument thus: A differs from B, in the sense that they are different substances; but to be thus different is to have a relation to B. This relation must have a corresponding predicate of A. But since B does not differ from itself, B cannot have the same predicate. Hence A and B will differ as to predicates, contrary to the hypothesis.²²

The idea is clear enough. If every extrinsic denomination requires an intrinsic basis, then the predicate ‘being different from B’ requires an intrinsic basis in A. But A, by hypothesis, is intrinsically qualitatively identical with B. And so the predicate ‘being different from B’ – clearly lacked by B – can’t have an intrinsic basis in A. Given the requirement of an intrinsic basis, then, A is not numerically distinct from B. Now the details of Russell’s argument can be questioned here. One might, for example, urge that the argument illicitly deploys a sort of strong haecceitism (cf. chapter ). For if one describes the world in purely general terms (without singular names) as the anti-haecceitist recommends – ‘∃x∃y(Fx & Fy & . . . & x " y)’ – then it is open to question whether there really is any property expressed by ‘being numerically different from B’ in need of explanation. Still, the gist of the argument can be preserved even on anti-haecceitism, for there is still a relation of difference to be explained. Each thing has the property of ‘being numerically distinct from something that is F’²³ supposing two duplicate F things. Yet it is hard to see how any of the intrinsic properties of either substance (of either substitution instance rendering our general description true) can provide the internal denomination by which the external denomination ‘being numerically distinct from an F-thing’ can get its grounding. Russell’s argument goes through, at least in this slightly amended form. So far so good. Let us now proceed to what follows in Russell’s discussion: This argument is valid, I think, to the extent of proving that, if subject and predicate be the canonical form of propositions, there cannot be two indiscernible substances. The difficulty is, to prevent its proving that there cannot be two substances at all. For the numerical diversity of the substances is logically ²² Russell, The Philosophy of Leibniz, p. . ²³ Or, if one denies that every open sentence expresses a property, there remains to be explained the state of affairs something’s being distinct from some F.



The threat of one substance

prior to their diversity as to predicates: there can be no question of their differing in respect of predicates unless they first differ numerically. But the bare judgment of numerical diversity itself is open to all the objections which Leibniz can urge against indiscernibles. Until predicates have been assigned, the two substances remain indiscernible; but they cannot have predicates by which they cease to be indiscernible, unless they are first distinguished as numerically different.²⁴

Russell’s idea is that the line of thought telling against indiscernible substances tells also against discernible substances. Why? The argument against indiscernibles was premised on the idea that external denominations require internal denominations, there being no internal denominations sufficient to ground numerical distinctness in the case of indiscernibles. But the idea tells equally against putatively discernible substances. For suppose that ∃x∃y(Fx & Gy & . . . & x " y). Something has the property of being different from something that is F. What internal denomination grounds this? Having available only simple positive and compatible properties at the metaphysical groundfloor, there is no more hope of grounding numerical difference between discernibles in intrinsic denominations than there is hope of grounding in intrinsic denominations the numerical difference between indiscernibles.²⁵ As far as we can see, Russell is exactly right. The task yet confronting the Leibnizian metaphysician is to ground the claim of plurality. Russell’s own diagnosis, it turns out, extends even further to the doctrine of substance itself. As Russell is thinking, one who wants to resist the idea that there are ‘‘bare judgments of numerical diversity’’ with no deeper grounding will ultimately wish to abandon even a one-substance doctrine. After all, even a one-substance doctrine presupposes determinate facts of the matter with regard to questions of the form. ‘‘Is the bearer of this accident identical with the bearer of that accident?’’ Russell’s preferred orientation is towards a no-substance doctrine, wherein the world collapses into the sum of its accidents. (That orientation would apply just as well against a one-created-substance world.) ‘‘Predicates do not inhere in the substance in any other sense than that in which letters inhere in the alphabet.’’ That is, so to say, you’ve just got the letters. In effect, then, Russell is arguing as follows. Leibniz’s requirement ²⁴ Russell, The Philosophy of Leibniz, p. . ²⁵ See Russell, ibid., pp. –, for his recognition and discussion of Leibniz’s claim that all ‘‘simple ideas’’ are mutually compatible.

Returning to Russell

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that numerical sameness and difference in substances be intelligible in terms of the predicates of substances ultimately forces us to abandon – in addition to the plurality of substances – yet another central strand of Leibnizian metaphysic: that accidents are grounded in simple active forms/substances from which they emanate and in which they thereby inhere. There is available in logical space a reconciliation that Leibniz and Russell never (to our knowledge) considered. The reconciliation may be accomplished by thinking of ‘substance’ on the model of a mass noun rather than a count noun. ‘Mass’ has the unfortunate overtones of ‘matter’ here, but that is mere background noise. The point is, that in statements such as ‘Accidents emanate from substance’ and ‘Accidents are grounded by primitive force,’ one can avoid awkward questions of identity and numerical diversity by forgoing the count-noun mode of description of ultimate reality (in just the way ‘ultimate reality’ does) while preserving a metaphysic in which accidents do have a deeper grounding in ultimate reality.²⁶ So there are three alternatives to the preferred many-substance metaphysic: one substance, no substance, substance. Russell, naturally enough, has in mind only the former two alternatives, and judging that a many-substance metaphysic cannot be reconciled with the view that the world is intelligible through its simple monadic predicates, prescribes a no-substance metaphysic for Leibniz. While the mass-term account preserves more of Leibniz’s metaphysic than Russell’s own recommendation, it would no doubt still be anathema to Leibniz. (‘‘No doubt it would’’ – without intending to express any similar confidence in saying just why it would. As a start, the mass ontology does not seem to be easily wedded to a metaphysic of mind or spiritual substance. Nor is it clear how the fundamental concepts of law-of-the-series and inner-principleof-change are to be cashed out in mass terms. Leibniz may in any case have simply not understood what a fundamental metaphysic without any count nouns would look like. [He would not have been alone here.] Indeed, to the extent one tried to deploy the mass idiom, many of his worries about the need for metaphysical foundations, of a sort he reckoned Descartes unable to supply, would look to remain on board, un-answered. Suppose one aimed to think in terms of masses when approaching the question of matter. It would remain true – wouldn’t it? – that every quantity of matter is composed of smaller quantities of ²⁶ We note in this connection that Spinoza might be read as using ‘substance’ as a mass noun: see Jonathan Bennett, A Study of Spinoza’s ETHICS, p. .

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The threat of one substance

matter [assuming all matter is extended]. Here one still seems to be left with the sense of there being no groundfloor if there is just matter. Has one cheated in appropriating ‘quantity of matter,’ which may be said to be a count noun? Without that taxonomic resource, it is far from clear what a perspicuous metaphysic of matter that is mass-theoretic would even look like.) For the remainder of our discussion, we leave the mass-noun metaphysics to the side. Disregarding it, the threat we have been discussing in this section may thus be expressed as the proposal that (i) – (iii) below form an inconsistent triad: (i) Reality is constituted out of a plurality of substances in which accidents inhere. (ii) All basic properties/accidents are monadic, simple, and compatible. (iii) Facts of numerical sameness and difference between substances are intelligible through their properties/accidents.²⁷ Item (i) is a broad-brush version of Leibniz’s basic metaphysical picture. Item (ii) is required by his eschewal of primitive inter-monadic relations, coupled with his account of analysis as bottoming out in simple, compatible concepts in the divine mind. Item (iii) is prima facie the driving force behind PII. We shall consider presently whether more can be done by way of rescuing Leibniz from this triad.                                      The problem of giving a metaphysic of numerical diversity is not just a problem for Leibniz. It is a problem for us all. Leibniz of the Disputatio saw fit – in the fashion of good scholastic methodology – to investigate in turn the options one might pursue in developing a theory of individuation. Confronting a challenge to Leibniz’s own metaphysic, we are invited to pause long enough to consider in turn what conceptual resources might be brought to bear in meeting it, and to understand reasons from within traditional approaches to individuation for registering concern about those resources. (The reader will recall brief encounters with some of the ideas that follow, in chapter .) We leave for ²⁷ Note that the argument against Leibniz, from this inconsistent triad, can in principle be deployed not just against a metaphysic of many created substances, but even ultimately against a metaphysic of one created substance, assuming as the latter does the numerical diversity of God and created substance.

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others to render a final diagnosis of what, if anything, is wrong with these reasons. . Relation As we have seen, Leibniz disavows intersubstantial relations as the ground of numerical diversity. Many would judge this as a crucial mistake. Those of us who were nursed on the idea that the spatiotemporal manifold provides the criteria for identity and difference, or that the origins of a thing provide the key to identity and difference, will naturally incline towards the belief that relation is not only necessary but perhaps also sufficient for facts concerning numerical identity and diversity. Much of the scholastic tradition was rather less eager to make relations do such work. Was this just prejudice? Probably not. To focus our thoughts, we shall direct our attention to the resources of spatiotemporal relations, noting along the way how various analogous problems arise for other implementations of the relations-approach to individuation. Consider the following arguably good reasons for concern about making spatio-temporal relations hold the key to individuation (say, by using spatial separation as a sufficient condition of difference at a time and spatio-temporal continuity as a necessary condition for sameness over time): () Spatio-temporal relations won’t work for immaterial minds that do not occupy space, for the Heavenly multitude, and so on. Insofar as one thinks there is, waiting to be discovered, a unified account of individuation for all substances, this concern may be reckoned not simply a piecemeal objection to using spatio-temporal relations in individuating certain substances, but a reason to look elsewhere for the general, most fundamental story about individuation (whatever the substance in question). Leibniz himself showed his cards in the Disputatio about that preference, leaving the divided Thomistic approach (one story for material creatures, a different story for angels) right out of his survey. It is worth noting that a great many candidate relations work prima facie in only some cases, and not all. For example, a necessity-of-origins approach cannot work to distinguish things that come into being genuinely ex nihilo, and cannot work to distinguish things sharing a single origin – the former being perhaps a limiting case of the latter. Returning to the case of spatio-temporal relations, we noted in an earlier chapter its relevance to material substances on a broadly Thomistic account,

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The threat of one substance

matter serving to individuate only together with dimensive quantity (that is, spatio-temporal determinations). It is relevant too for Thomistic cousins of a Leibnizian bent who would number corporeal substances among the individuals that exist (recalling now the ‘‘two substance’’ view of corporeal substance discussed in chapter ). Suppose a corporeal substance consists in a simple soul (with its primitive active and passive aspects) united with an enduring organic body (secondary matter); and suppose the relation of monadic domination cannot stand between a single entelechy and many organic bodies. The spatio-temporal features operative in the phenomenal story of that body as citizen of the physical world will not find their way into an account of individuation told at the metaphysical groundfoor. However true it may be that the order of knowing is often the reverse of the order of being, so that the phenomena may arise as epistemically prior, to individuate substances in terms of the phenomena is to reverse the order of being with the order of knowing. () The criterion of spatio-temporal relation presumes the impossibility of full spatio-temporal interpenetration (whereby A and B take up the same space for the whole of their careers). This presumed impossibility must be based either on the idea that complete overlap, even at a time, is never possible, or that while overlap for part of a pair’s career is possible, full overlap isn’t. Suppose our earlier, text-based challenges of mere overlap-for-a-time were permitted by the proponent of a spatio-temporal criterion, allowing nevertheless for individuation of a thing in terms of full careers. It is unclear how the stated impossibility – the second, remaining impossibility above – can be intelligibly made out. Having allowed for a world in which two spheres overlap for a part of their careers between . p.m and two seconds later, there would seem to be also another, short-lived world lasting only two seconds, where the state of affairs internal to the pair from .oo p.m. to . p.m. +  seconds is exactly similar – that is, a world where there is total career overlap. The interpenetration point is especially relevant, of course, to contemporary coincidentalists, descended from Locke, who would have it that (say) this lump of clay and the statue it constitutes are, while sharing the same boundaries, numerically distinct. The concerns of () and () are straight out of Leibniz. His fundamental realities are more like angels than rocks, and so space – and arguably time as well, on the causal construal sketched briefly in chapter  – can only be emergent and not individuating. Meanwhile Leibniz is explicit,

A philosophical examination of our main problem

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when operating at the emergent level of body, that interpenetration is not to be ruled out by fiat. That same attitude is representative of current debates about co-location.²⁸ () In deploying spatio-temporal separation as a criterion for individuation, one presumes that the things so individuated cannot be at a distance from themselves, cannot be ‘communicable‘ (in scholastic lingo) by being fully present in many places or in different further subjects of predication. There are several points here. (i) Perhaps some would be happy to take it as axiomatic that nothing can be in two places at once. Scholastic and rationalistic minds alike were rather less ready to acquiesce in primitive necessary truths when encountering intellectual resistance. On reflection, one can scarcely frown on their patience. (ii) Furthermore the typical run of the scholastic mind had good reason to suppose that a doctrine of incommunicability is false if it is predicated of all things. For suppose there are immanent universals – universals that are fully present in many places (as opposed to occupants of Platonic or Fregean Heaven that are related by exemplification or instantiation to things in the spatial world without themselves ever existing in the spatial world). The intelligibility of immanent universals makes immediate trouble for an un-argued assumption that nothing can be at a distance from itself.²⁹ (iii) And there is, as noted, theological motivation for allowing multipresence: the substantial form of the body of Christ is communicable (in the Eucharist). If substantial form is sometimes communicable, it is not axiomatically true but simply false that no substance can be at a distance from itself. (And here, too, preference for a unified account of individuation would join the fray.) () Some versions of the relational account can serve only as a very partial, stop-gap story of individuation. This can arise in the spatiotemporal case in the following way. Suppose one endorses a sort of absolutism about space and place, insisting: ‘‘Two corporeal things are different if and only if they occupy different places.’’ One is then left with the further question, ‘‘When are place a and place b two places rather than one?’’ A structurally similar concern arises in the context of a different species of the same genus of relational approaches. Suppose one goes for a necessity-of-origins view. A and B are different if the origin of A is different from the origin of B. Again one is left with the further question, ‘‘When is the origin of A distinct from the origin of B?’’ ²⁸ And not just because coincidentalism is taken seriously. Few today would be willing to wager that, as a matter of de re necessity, no two particles of matter could ever interpenetrate. ²⁹ See, for example, John O’Leary-Hawthorne and J. A. Cover, ‘‘A World of Universals.’’

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The threat of one substance

Common causes are commonplace, and recourse to (say) numerically distinct intentions in the mind of God is little more than recourse to a non-relational account of individuation. () In concerning itself with the threat of a one-substance doctrine, this chapter is directed primarily at candidates for a satisfactory criterion of numerical difference. As we have seen in chapter , many scholastics were concerned to distinguish criteria of numerical difference from questions of individuation proper. After all, numerical difference is a symmetrical notion. If there is anything distinctive about each of the things that are numerically many, accounts of difference deploying symmetrical notions in explaining their plurality will leave us in the dark concerning what those distinctive features are. As a result, they will leave us in the dark about what is perhaps the most central concern within the context of individuation, namely, ‘‘What makes things the particular things that they are?’’ (Alternatively, ‘‘What makes this thing distinct from every other possible thing?’’) Consequently, it was traditionally important in giving a fully general account of individuation that one offer answers to both the numerical difference question and the question of individuation proper. The failure of relation to supply this second feature of a full account of individuation can be put in particularly sharp relief in connection with spatial separation. Suppose one accepted the following principle for material beings: For any world W and any material being x and any material being y in W: x is distinct from y iff x is spatio-temporally separated from y.

And suppose one now fastened on a particular world containing a rock and a stick that are spatially separated. By the above criterion one knows that the rock and stick and not the same thing (that is, one knows that it is not the case that there exists one thing that is present as a stick here and present as a rock there). But one doesn’t know what makes the rock the very thing that it is. There may, after all, very well be a world where the rock exists without the stick, even a world where the rock exists alone. What makes the rock the very individual that it is has nothing at all to do with spatial separation from the stick, or indeed from anything at all, since that spatial separation is very much a contingent feature of the rock. The point can be made another way by contrasting intra- from inter-world numerical diversity. Spatial separation works as a prima facie plausible principle of intra-world diversity. But it does not serve as an account of inter-world identity and diversity. After all, things can certainly interpenetrate – so to speak – across worlds. That is to say, the

A philosophical examination of our main problem

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space fully occupied by one thing in W may be the space fully occupied by a numerically distinct thing in W. In asking what individuates this rock, one wishes to know, inter alia, what is unique and common to the rock (call it Joe) at every world at which it exists – what makes it the case, or what explains the fact, that it is Joe that is the object of God’s creation at those worlds (rather than Smith). In deciding to create Joe at those worlds, what precautions did God have to take? Spatial separation from Fred the stick is pretty much neither here nor there in this context of inquiry. The point generalizes to many other relational accounts of individuation. Suppose, for example, one wanted a primitive relation of numerical diversity to ground our judgments of diversity and identity. That may be good enough, as far as it goes: but again, it goes only so far as supplying a criterion of difference, and scarcely serves to ground further facts of individuation – of what makes a thing the thing it is. To know that x isn’t y is not yet to know what thing x is. Of course, if one went the modally tenuous route of full-blooded anti-haecceitism, what we have treated here as questions of individuation proper may well turn out to be mere pseudo-questions. In that situation, questions of intra-world numerical diversity may be the only intelligible residue left to bother over. In that case one is likely betterdisposed to letting the spatio-temporal relations do the whole work – though, alas, worries () – () above remain pressing. . Accidents According to one important strand of scholastic thinking, some things are individuals per se, others per accidens. What this means is that some things have their individuality within themselves, others have their individuality parasitic on other things. Standardly, accidents were put into the latter category. That is, insofar as one answers questions of sameness and difference for accidents, it must be parasitic on answers about sameness and difference for things in which the accidents inhere. This approach is far from foreign to contemporary discussion. Consider for example the account of events (or, for some, states of affairs) made popular by Jaegwon Kim.³⁰ In understanding events as triples of things, properties, and times – roughly, as the instantiation of P by S at T – Kim ³⁰ See Kim’s ‘‘Causation, Nomic Subsumption, and the Concept of an Event,’’ and his ‘‘Events as Property Exemplifications.’’ For a recent defense of this general metaphysic of events (divorced from Kim’s semantics) and of its connection to Leibniz’s individual accidents, see Jonathan Bennett, Events and Their Names, esp. chapter .

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The threat of one substance

inter alia makes the individuation of events parasitic on the individuation of things that the events happen to. Against this background, it must seem very odd to answer questions of individuation for substances by trading on answers to questions of individuation for accidents. Suppose, for example, one claimed that what makes you distinct from me is that your trope/accident of humanity is different from mine, and further – moving now from questions of difference to questions of individuation proper – that what makes me me is the very accident of humanity I enjoy. On the scholastic picture, this answer gets things just exactly backwards: what makes your trope of humanity the very trope it is has everything to do with the fact that it belongs to you. One gets the view back to front to suggest that what makes you you is that you possess this very trope of humanity. There are further concerns. Perhaps the trope of humanity I have now is numerically distinct from the one I have later. If so, one can’t rely on the idea that a thing cannot have two exactly qualitatively similar accidents in giving an account of individuation. Indeed the Disputatio Leibniz was even willing to entertain simultaneous accidents belonging to a single subject that differ solo numero (cf. Disputatio §).³¹ We note in passing that insofar as accidents are individuated parasitically on substances, Russell’s suggestion that we dispense with substance altogether will of course be rendered hopelessly problematic. If God can – or rather, as Russell (having no substances available) must express it, if from a ‘‘God’s eye view, one can’’ – only keep track of individual accidents by keeping track of ‘‘their’’ individual substances, then there is no sense to be made of a world containing only accidents. Accidents, failing to be individuals per se, are not well suited for making up the fabric of the world. . Matter The Thomist tradition, while allowing that substantial forms do all the individuating work for angels, requires the addition of signated matter ³¹ G ,: MLI . Laurence B. McCullough, in his Leibniz on Individuals and Individuation, assimilates Leibniz’s approach to accidents to Suarez’s (p. ). On the present point at least, Suarez is more conservative, allowing for simultaneous and similar accidents that differ in number only, in cases where those accidents somehow differ in end, relation, or function. And so there can be two similar images at a time, one of Peter, one of Paul, but not two whitenesses of the same shade belonging to a subject at the same time. See Disputationes metaphysicae , §: ‘‘Whether it is inconsistent that two accidents differing only in number can be simultaneously in the same subject by virtue of their individuality’’ (Berton, vol. , pp. ff).

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to form in individuating corporeal substances. As various scholastic commentators were aware, this approach, inter alia, has the drawback of pushing the question back to a more difficult one – namely, of what individuates a particular quantity of matter. And here a circularity threat arises. For, as in the case of accidents, one might wish to individuate (say) a quantity of flesh in terms of the substance whose flesh it is rather than the other way around. Alternatively, one might use spatiotemporal determinations as the individuator of quantities of matter (if one was prepared to discount the possibility of interpenetration and condensation). As anticipated earlier, such an account would then appear to be trading on spatio-temporal relations after all, making one wonder whether the detour via parcels of matter is at all worthwhile. Needless to say, this whole approach is unavailable to one who, like Leibniz, has no parcels of matter available at the metaphysical groundfloor. The contemporary mind is unlikely to find that metaphysic worth taking seriously – having perhaps been unable to progress far enough beyond the deliverances of common sense to distinguish appearance from reality, or having learned that idealism (non-linguistic phenomenalism) is long dead. The former obstacle, unless applied across the board to the pronouncements of (say) modern physics as well, is sheer bias. Common sense only tells us to look both ways before crossing against a red; and while the appearances tell us for all the world that material objects have colors and are really solid (genuinely ‘‘filled up’’ with dense matter), the contemporary mind is willing to defer to high theory when coming to believe otherwise. Meanwhile, those who learned that phenomenalist-idealism is dead learned about difficulties confronting a project grounded almost entirely on the deliverances of perception. Leibniz’s project isn’t of that sort, but is grounded instead on the challenges of accounting for activity in passive matter and for the required unity of wholes with parts. The latter challenge looms large – or by our lights, should loom large – for any serious metaphysician. The skeptical reader is invited to give sober attention to the argument of Leibniz’s  April  letter to Arnauld (G ,–: LA –), and to reflect while doing so on reasons they might have for supposing that there exists a non-arbitrary principle governing the composition of extended wholes out of parts.³² ³² There are remarkable similarities between Leibniz’s arguments in that letter and Peter van Inwagen’s struggle to find a good answer to the ‘‘special composition question’’ in chapters – of his Material Beings. Leibniz would – perhaps does – absolutely applaud those chapters.

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The threat of one substance . Haecceities

Scotistic haecceities constitute another, prima facie, attractive option. What makes the thing that is you you and the thing that is me me is that there is a haecceity of you-ness that is instantiated by or a component of you and a haecceity of me-ness that is instantiated by or a component of me.³³ It is important to recognize that haecceitism here requires not merely that there be a thing deserving the name, being genuinely unique to you, but that it explain your individuality. Suppose one opts for the contemporary, property construal of haecceities, and consider the standard set-theoretic (extensional) treatment of properties. According to most set-theories, there is a singleton set for each thing. This set would have many of the traits that haecceities are intended to have – after all, only you participate in (that is to say, belong to) your haecceity and so on. But one couldn’t very well explain what it is to be you in terms of your haecceity thus construed. Haecceities on the Scotistic construal are primitive, ‘colorless’ thisnesses which, unlike the singleton-set haecceities, are aimed to do some explanatory work. Unlike the singleton set, the being of a haecceity is not intended to be merely parasitic on the being of the substance that instantiates or has it. So what’s wrong then with a Scotistic account of individuation? (i) One difficulty might be theological. If bare colorless haecceities are inaccessible to mind qua mind (except derivatively, via their possessors), it is hard to see how God could recognize possibility space – the space of singular essences – from all eternity. The Scotistic doctrine of intuition, according to which God can somehow comprehend you-ness and me-ness directly, was designed to fix this, but renders the story a good deal more obscure than one should have liked. (ii) But a more basic and difficult problem is to explain the connection between the haecceity and other essential properties. Having no internal structure able to constrain such connections, the explanatory task looks insurmountable: supposing I am essentially a man, what is there to be said about the internal relation between my me-ness and my manhood? (iii) A final problem concerns haecceities themselves. What individuates a haecceity? Does the haecceity have a second-order haecceity which in turn has a thirdorder haecceity and so on? If one doesn’t like this ungrounded hierarchy, one might want instead to say the haecceity is its own haecceity. ³³ The disjunctive formulation is intended to be neutral as between haecceities as nowadays typically discussed, according to which they are properties, and the Scotistic view of them as of an ontological category distinct from properties (which to Scotus’ mind are unfit for the role because properties are, by their very nature, able to be shared).

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But then it would seem that the haecceity of me is possessed by two things – it and me (cf. chapter , §.). The natural recourse here is to say that I am my own haecceity – and so we return to something like the whole entity doctrine of Leibniz.

. Negation An absurdly obvious way of trying to launch an analysis of intra-world numerical sameness and difference of substance is by deploying negation. Leibniz’s law would recommend as much: (SD) It is a sufficient condition for x’s being distinct from y that for some F, Fx and not Fy. As Fred D’Agostino notes in discussing the incompossibility problem itself as it relates to a plurality of worlds,³⁴ if one has only simple positive predicates of substances to combinatorily mix and match with, it is unclear that adding negation can help to explain why any actualized complete concept is incompossible with any distinct possible but nonactualized complete concept. The point is relatively simple. Given simple positive predicates F, G, etc. and any negative predicates not-F, not-G, etc., we can tell a priori – by looking at any predicative expression of the form ‘x is F,’ ‘x is F & G,’ etc. – whether it is possibly true. But given such possible predications, there is no a priori way of showing that any of them – say, ‘x is F & G’ and ‘y is F & not-G’ are not compossibly true. And supposing that our world, like all worlds, is a maximal compossible set of substances (complete concepts), it would then seem that our world contains all possible substances. On the assumption of maximal compossibility as defining a world,³⁵ then, negation does not help to avoid all possible worlds collapsing into one (Spinozistic necessitarianism). But negation can, it would seem, help to avoid all actual substances collapsing into one, via the sufficient condition for diversity (SD) above: if x is F and y is not-F, then surely x is numerically distinct from y. One can hardly quibble with the sufficient condition (SD). But not all sufficient conditions are on equal explanatory footing; the scholastic quibble with this approach will concern explanatory issues rather than ³⁴ See D’Agostino, ‘‘Leibniz on Compossibility and Relational Predicates.’’ ³⁵ An assumption that, recall, we do not follow most commentators in attributing to Leibniz. See chapter , §..

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The threat of one substance

the truth of the sufficient condition itself. Let us distinguish two modes of explanatory organization here: (A) x is distinct from y because x is F and y is not-F; (B) y is not-F because y is distinct from all the F things. Both of those modes of explanatory organization are perfectly consistent with (SD). But the order of explanation varies. Approach (A) seeks to explain numerical difference in terms of negation. Approach (B) seeks to explain facts of negation in terms of numerical difference. And virtually every scholastic would find the second approach more intuitive: their inclination would be to ask, ‘‘Can the basic facts of numerical difference between substances really be explained by a mere privation of accidents?’’³⁶ Those persuaded that there are no negative universals/ accidents in the world would find such a query particularly persuasive. We have, of course, represented Leibniz himself as embracing the view that there are no irreducibly basic privations at the metaphysical groundfloor: while there are negative truths, there are no accidents in the world of simple substances corresponding to negations of positive predicates. And if that is right, then one cannot be satisfied on Leibniz’s behalf with an invocation of negation to explain numerical difference. For that very reason we presume that Leibniz the metaphysician – along with all of the scholastics – would not be very happy with the explanation of numerical difference implicit in certain of his early attempts to provide a mathematical analysis of truth. Consider his Rules from which a decision can be made, by means of numbers, about the validity of inferences and about the forms and moods of categorial syllogisms (April : C ff: PLP ff). Here, each complex concept is represented by a pair of numbers, one positive, one negative.³⁷ The positive number corresponds to the product of the numbers corresponding to the basic concepts that are required for the complex concept to apply. And the negative number ³⁶ In the Disputatio, Leibniz is explicit in doubting – as he put it – that anything positive like the individuality of a thing could be grounded wholly on something negative (Disputatio §). ³⁷ Contrast his April  Elements of a Calculus, where each concept is represented by a single number corresponding to the product of the number assigned to each of the constituent concepts. A notable problem for that account is that it seems all too easy for ‘Some F is G’ to be true, and near impossible for ‘No F is G’ to be true, given the truth conditions for ‘Some F is G’ – viz., that there merely needs to be some concept that, when multiplied by the number corresponding to F, produces a number into which G divides. Thus, ‘‘in a particular affirmative proposition, it is enough that the inclusion should hold with some addition’’ (C : PLP ). How, now, can any claim of the form ‘Some F is G’ fail to be true, since for any pair of numbers, there are myriad additions that, when multiplied with the first, produce a number into which the second can be divided?

A philosophical examination of our main problem



corresponds to the product of the numbers corresponding to the basic concepts whose absence is required for the complex concept to apply. Something of the form ‘Every F is G’ is true when all of the concepts required for the predicate are required for the subject, and when all of the concepts whose absence is required for the predicate figure among the concepts whose absence is required for the subject. Given numerical assignments to constituent concepts, the mathematical story will be both that the positive number associated with the predicate divides into the positive number of the subject, and that the negative number associated with the predicate divides into the negative number associated with the subject (cf. C : PLP –). Meanwhile, ‘No F is G’ will be true just in the case that one of the concepts required by the subject is prohibited by the predicate (or vice versa). The associated mathematical story is that ‘No F is G’ is true just in the case that the ‘‘two numbers of different signs and different terms have a common divisor’’ (C : PLP ). This can carry over into an account of, say, the non-identity of Caesar and Brutus: something positively required by Caesar is negatively required by Brutus. Suppose (waiving the fact that individual concepts are supposed to be infinite, a fact that helped vitiate the generality of the mathematical story) that Caesar is A, B, C, and not-D, and Brutus is A, B, D, and not-C. We can prove the non-identity of Caesar and Brutus by adverting to the fact that C is required by Caesar’s concept and prohibited by Brutus’ concept. On such a story, the fact that Brutus is not-C is the ultimate explanation of the fact that Brutus is not Caesar. Numerical assignments merely provide a mathematical model for such explanations. Whatever number is assigned to ‘C,’ the mathematical representation will have it that the negative number of Brutus divides into the positive number of Caesar (since that is the product of C and another number); and so, quite obviously, the mathematical story for ‘No Caesar is Brutus’ will accordingly go through. Now anyone convinced that there are no negative accidents in the world will certainly be dissatisfied with this as the fundamental explanation of non-identity. Continuing with the story just sketched, let Caesar be A, B, C, not-D, let Brutus be A, B, D, not-C, and Cutus A, B, C, D. At the level of intension, we can, in the manner just described, prove quite readily that Caesar is not Brutus. But suppose we are confronted with a world that, as far as positive accidents go, contains A, B, C, and D. What is it in the world that makes it true that Caesar and Brutus have been instantiated rather than just Cutus? If there were negative accidents, then we could advert to the presence of not-C-ness



The threat of one substance

and not-D-ness in our explanation.³⁸ But if there are no negative accidents then that cannot be the fundamental story. What we need is to find something in the world that makes it true that nothing has all of A, B, C, D. And if there are no negative accidents, then it isn’t the not-C-ness of something and the not-D-ness of something that is going to provide the fundamental metaphysical story concerning this state of affairs of numerical difference. . All Suppose one sticks to simple positive properties, aiming yet to account for the numerical diversity of x and y without appeal to intersubstantial relations or matter or haecceity or negation. Perhaps a fact of the sort ‘‘and that’s all’’ is key to our concerns about individuation. A sufficient condition for x being distinct from y might be of the form, x is F and G and y is G and H and that’s all. How might the ‘‘that’s all’’ strategy be rendered intelligible within the context of serious ontology? One contemporary approach would construe the operative concept as a variably polyadic relation: in the scenario described, G and H bear the relation of alling to y.³⁹ Particular ontological strategies such as this are bound to be somewhat controversial, but it is not our aim to dismiss them, either on our behalf or on behalf of imaginary scholastic interlocutors. The central issue, once again, is one of explanatory order. Is the fact that y is G and H and that’s all to be partially explained in terms of y’s being numerically distinct from every F thing? If so, it is unclear how one would fairly utilize the ‘‘that’s all’’ fact to explain the fact that y is numerically different from x. Here (and above) there are deep and difficult questions nearby: do such ³⁸ Though, even here, there are difficulties. Let Brute be A, B, not-C, not-D. Even granting the presence of not-C-ness and not-D-ness in the world, we haven’t secured the material as yet to explain what makes it true that we have Caesar and Brutus rather than Cutus and Brute. If we help ourselves to the fact that the thing which is not-C is distinct from the thing that is not-D, then we can rule out Brute. But that is to help ourselves to the very facts of numerical identity and difference for which we were aiming to provide a metaphysical foundation. By themselves, the negative accidents only guarantee that there are at least two things in the world, not exactly how many or which is which. ³⁹ For an approach in this spirit, see the treatment of totality in D. M. Armstrong’s A Combinatorial Theory of Possibility, pp. –. A variably-polyadic relation would be expressed by an n-place predicate where – so to speak – the value of n (greater than one) is left open: ‘are shipmates’ is variably polyadic, in which Bill and Ted might stand, or Bill and Ted and Rod if room in the boat permits it. See Richard Grandy, ‘‘Anadic Logic and English’’ and Adam Morton, ‘‘Complex Individuals and Multigrade Relations.’’

A partial rescue



questions of explanatory order ultimately make sense? And if they do make sense, what is the correct order of formal cause? We invite the reader to be sensitive to such questions. It is clear enough, in any case, that alling facts won’t help much with questions of individuation proper, involving inter-world judgments of sameness and difference, unless one allows world-indexed or modal properties into the relation of alling. (The fact that some actual x is alled by F and G and some possible y is alled by G hardly seems adequate to constitute the ground of numerical difference of the actual thing from the possible thing.) But suppose we restrict ourselves to questions of intra-world sameness and difference. It is important to distinguish the following questions. What are the grounds for numerical diversity at the actual world? Could there be a world where the distribution of accidents was just the same as in ours but where there was a different number of substances (perhaps just one)? Even if one were persuaded that the alling approach helped with the former question of numerical diversity, it may not by itself do much to help with the latter question, crucial to our threat of spinozism. For this question concerns whether there exists some world at which just one thing alls the properties had by distinct things at the actual world. Without recourse to negation or internal exclusion relations between properties, alling facts will not be of much help. In what follows, it will be useful to bear in mind not only the panoply of approaches to numerical difference, but also the distinction between ‘‘Is the actual world a one-substance world?’’ and ‘‘Is there a possible world just like the actual one which is a one-substance world?’’             Let us return to the inconsistent triad posed at the end of § above: (i) Reality is constituted out of a plurality of substances in which accidents inhere. (ii) All basic properties/accidents are monadic, simple, and compatible. (iii) Facts of numerical sameness and difference between substances are intelligible through their properties/accidents. Readers will not be surprised to learn that we incline towards a denial of (iii) on Leibniz’s behalf. Russell of course would say that a denial of (iii) undercuts Leibniz’s motivation for the Identity of Indiscernibles. For as



The threat of one substance

Russell sees it, PII is motivated in large measure by a picture according to which substances are – as he puts it – defined by their predicates/ accidents. If we are to begin to rescue a Leibnizian metaphysic from a spinozistic threat of one (created) substance doctrine, and from a Russellian collapse into a non-substantial mosaic of accidents, we need to distance Leibniz from the view that a substance is defined by its accidents, while retaining some rationale for the view that substances are never wholly alike in respect of them. That is, PII must turn out to be materially adequate – in the sense of admitting no counterexample – to the facts of individuality without providing the ‘‘principle’’ of individuation in the scholastic sense of providing the foundation or source (the Aristotelian arche´) of the individuality of the substance.⁴⁰ We have recommended (chapter ) a function-theoretic model as a fair and helpful approximation to Leibniz’s picture of the law-of-theseries. With that model before us, we may first note that Russell’s compulsion to collapse a substance into a series of predicates has been imitated in the contemporary metaphysics of functions. Consider the set of ordered pairs describing a function. On one very natural way of thinking, that set, while specifying a value for each argument, is hardly the function itself. But according to another, rather more common approach, the set of ordered pairs is identical with the function itself. The latter approach approximates, in the realm of the ontology of mathematics, the Russellian approach to the metaphysics of substances. An element in an ordered sequence, on the latter approach, belongs to the function as a letter belongs in the alphabet. On the former approach, the relation between an element in an ordered sequence and a function is hardly like that of part to whole (or member to set). The analogy goes a little further. Note that a set of ordered pairs, considered in itself, may be understood both as a description of all the arguments and values of a particular function, and as the real addition of partial descriptions of all the arguments and values of two distinct functions. (So one and the same set of ordered pairs +:,9, :,9, :,9, . . . , is both the complete description of the squaring function and also the addition of two partial descriptions of [i] the function that squares evens and delivers the identical argument as value for odds and ⁴⁰ See chapter , §.. And so we would (while acknowledging its spirit) reject the letter of Donald Rutherford’s claim that ‘‘Leibniz holds that substances are individuated . . . through the sum of their predicates’’ (Donald Rutherford, Leibniz and the Rational Order of Nature, p. ). ‘‘The sum of its predicates’’ is, as we have been saying it, materially adequate to a metaphysical principle of individuation for the substance.

A partial rescue



[ii] the function that squares odds and delivers the identical argument as value for evens. The set of ordered pairs does, after all, describe the argument/value pairs for the former function with regard to evens and describe the argument/value pairs for the latter function with regard to odds. This same scenario can be run for partial functions, where our set of ordered pairs is both the complete description of the squaring function and the composition of two partial functions – one defined over the evens and the other defined over the odds.) Now just as a series of predicates can be understood, prima facie, both as the product of a single law and as the product of a number of discrete laws, so an infinite set of ordered pairs can be viewed as corresponding to one or to many functions. Now of course in the case of functions, construed as abstract entities, there is no metaphysical puzzle here. All of the functions exist. The set of ordered pairs is both a description of the arguments and values of one function as well as a combination of partial descriptions of arguments and values of a pair of functions (and so on). By contrast: if one thinks of functions as corresponding to possible laws, and, crucially for the Leibnizian, of laws-of-the-series as the genuine reification of some of them in the created order, then there will be real questions about which are actualized – to which the answer ‘‘All of them’’ is one, albeit rather controversial, answer. The function model does provide a clue, however, to how a rescue of Leibniz might begin. For notice that even if one inclines toward giving functions an ontological reality distinct from ordered pairs, one might well yet insist that no two functions are wholly alike with respect to argument and value. There is nothing strained or implausible about claiming that two functions cannot genuinely be distinct if they are functionally exactly alike, even while claiming that functions are more than mere lists of ordered pairs. Once one knows what a function is, one will understand that functional similarity suffices for total similarity; but this in no way suggests that in describing a set of ordered pairs one thereby comes to know what a function is. These considerations transfer, mutatis mutandis, to laws. Consider the possible sequences of events conforming to some causal law L. A metaphysically timid (read: Humean) way of thinking might lead one to identify L with those sequences. But a perfectly respectable, metaphysically robust way of thinking would have it that the governance of a law isn’t to be understood on a Humean model, while nevertheless maintaining that two laws cannot be alike with respect to patterns of conformity of all possible sequences. The sense in which the



The threat of one substance

predicates of a thing ‘‘define’’ the thing is the sense in which sequences define a law: they uniquely determine it. But in supplying you with the sequences I do not tell you (so to speak) what it is to be that law. Nor do I, in providing you with a list of sequences, let you know eo ipso that I am supplying you with a list of the patterns associated with one law rather than the result of adding the patterns associated with two laws respectively. The only sense in which the patterns define a law is the sense in which two laws cannot be wholly alike with respect to patterns of conformity. It is this latter intuition that recommends an Identity of Indiscernibles in respect of substantial active laws-of-series. Earlier we distinguished two important questions: ‘‘Is the actual world a one-substance world?’’ and ‘‘Is there a possible world just like the actual one which is a one-substance world?’’ Let us first consider the former. As we are now fleshing out the Leibnizian story, the substantial laws-of-the-series making up the actual world cannot be determinately recovered simply from the facts about accidents, if one supposes that those facts are not identity- and difference-laden. Suppose one is given facts of the form ‘‘something is F; something is G.’’ Our Leibniz will not pretend that one can recover the facts of numerical diversity from them. Recalling the discussion of chapter , Leibniz is a sort of haecceitist – not one who posits the bare colorless haecceities of Scotus, but one who takes laws-ofthe-series to play a haecceitistic role. The Identity of Indiscernibles is materially adequate for the conception of Haecceity (read: principle of individuation) as law, which can give PII a grounding without threatening any collapse of the world into a Russellian mosaic. So the laws themselves constitute the facts about number, numerical differences emerging in pretty much the same way they were guaranteed to emerge from Scotistic haecceities. We have mentioned one way that the laws differ from Scotistic haecceities. They are, as it were, colorful rather than colorless. There is another difference: unlike Scotistic haecceities, the immanent laws are numerically identical with the substances themselves. It is in this latter fact that the continued viability of Leibniz’s whole-entity doctrine consists. Now this story does not address why God would have made the world He did, one with many laws-of-the-series. Rather it addresses so to speak what He would be up to in making it. Put another way: it renders perspicuous the truth-makers for claims of identity and difference. And crucially, it does so in a way that prima facie retains a motivation for PII. Russell’s deep conviction that the motivation for PII is one requiring no substance is held well at bay.

A partial rescue



But there are other strands of the Leibnizian metaphysic that are not so readily rescued by this picture. First, recall again the way in which we introduced the one-substance threat – via the Leibnizian thesis that every extrinsic denomination has its basis in the intrinsic denominations of individual substances. If one thinks of every intrinsic denomination as an accident, then one is in no position to rescue that Leibnizian thesis – no position to do so, at least, if one has on board a perfectly general view of extrinsic denominations as including such abstract logical relations as numerical difference. How damaging it is to Leibniz to concede that such abstract logical relations are an exception, or else to concede that the limiting case of intrinsic denomination is the law-of-the-series itself (it being the Haecceity of the individual), we shall leave to the reader’s judgment. And then there remains the deep and puzzling issue raised by our second question: ‘‘Is there a possible world just like the actual one that is a one-substance world?’’ Even supposing that God did make many substances, couldn’t He have made a world exactly like the actual one with regard to the mosaic of accidents containing just one substance? One might, of course, retreat immediately to common sense here: ‘‘Of course a single substance couldn’t enjoy both my and your conscious lives.’’ But retreating to such Mooreian appeals and calling it a day is simply not playing the rationalist game. There really is pressure on Leibniz towards allowing the one-substance world that we are envisaging. Given simple compatible monadic predicates at the metaphysical groundfloor, it is hard to see decompositional analysis as revealing any incoherence in our putative super-law (super-concept). But were Leibniz to allow the spinozistic story as even possible, there would be embarrassing questions to confront of a broadly ‘‘final cause’’ sort. Isn’t God being arbitrary in creating this many-substance world as opposed to the spinozistic quasi-duplicate? And isn’t this the very sort of solo numero difference that Leibniz is apt to inveigh against? A quick-and-easy escape would invoke the strong criteria for the identity of accidents: if the identity of accidents is derivative on the identity of substantial laws-of-the-series, then none of the accidents in the actual world exist in the spinozistic world. But the worry facing Leibniz trades on exact similarity, not identity of accidents. Replacement of accidents by numerically distinct qualitative duplicates is once again merely a difference solo numero, of no concern to an omni-benevolent Creator acting on reasons. If there is a rescue here, it requires some finessing of the concept of ‘solo numero.’ Contrast the following:



The threat of one substance

(a) A pair of worlds W and W that differ only in that two duplicates are switched; (b) A pair of worlds W and W that differ only in that Sam exists in W and a qualitative duplicate but numerically distinct being, Bill, exists in W; (c) A pair of worlds W and W that differ only in that while Sam exists in W, Sam and a perfect interpenetrating duplicate Bill exists at W. It may be that Leibniz’s notion of ‘solo numero’ is intended to reckon only (a) and (b) as involving morally indifferent alternatives. (If so, ‘solo numero’ is a bad way to describe the phenomenon.) On that account, solo numero differences are differences that involve (or would invite thought experiments involving) the switching of haecceities accompanied by no other differences. Now we have spoken along the way as if the interpenetrating difference in (c) involves a solo numero difference. But perhaps we were wrong to do so, on the present proposal. The spinozistic case – containing a single creaturely super-law – is a sort of intermediate case, a next-closest approximation to (c). Interpenetrating additions make a morally relevant change to such facts as the quantity of pleasure (say) between worlds. Two blissful creatures with morally duplicate conscious lives enjoy more pleasure overall than one. The one-substance case does not obviously make a quantitative difference, except insofar as the quantities are parasitic on quantity of substances (e.g. quantity of moral agents). There is not clearly any more or less pleasure involved in a world where a single immanent law encompasses two disparate conscious lives as contrasted with a world where two numerically distinct entities support exactly similar lives. But since, in the spinozistic case, there is not merely a switching of haecceities, but also fewer substances, that may be included as morally significant to God’s choice – this without endangering Leibniz’s claims of moral indifference as between (say) switched and unswitched duplicates. Take seriously now Leibniz’s harmony-theoretic conception of value, according to which harmony requires that ‘‘many things be brought into a kind of unity’’ (Grua ; our emphasis), and there may be some reason for God to choose a world of many substances over a world with one super-law. But one must, alas, surely be sympathetic with a tug in the other direction. Given that harmony increases with both ‘‘the variety and the unity in variety’’ (Grua ), isn’t it the super-law world that truly maximizes harmony, providing as it does for the greatest unity without

Postscript: Kant on Leibniz



threatening any of the variety that matters? The core issue is whether numerical variety, as opposed to qualitative variety, is something worth caring about. In God, after all, are located all the perspectives corresponding to the putative plurality of monads. Doesn’t the world with a super-law come closer to the divine essence than the Leibnizian world, retaining a substantial unity akin to God’s without losing the variety of perspective? Doesn’t the super-law world thus enjoy a greater degree of perfection – and so of ‘‘quantity of essence’’ – than the world Leibniz actually envisages? We leave it to our readers to pursue the abstruse considerations raised here connecting final cause with foundational metaphysics.         :        . . . the Critique of Pure Reason may well be the real apologia for Leibniz, even against his partisans whose eulogies do him no honor. Immanuel Kant,  ⁴¹

Conceived as a thesis about things as they present themselves to the pure understanding, Kant was rather sympathetic with the Identity of Indiscernibles doctrine. Kant recognized that the intellect, insofar as it operates in abstraction from sensory experience (intuition), tells us that relations among foundational beings can’t be what makes them the very beings that they are. Taking the alternative to be internal nature, he takes it that our pure intellect makes internal nature individuate. He writes: Leibniz took the appearances for things-in-themselves . . . and on that assumption his principle of the identity of indiscernibles certainly could not be disputed. (‘‘The Amphiboly of Concepts of Reflection’’: A/B)

Interestingly, Kant may also have understood at some level that a one-substance doctrine was a live option if we are considering things as they are in themselves: the something which underlies the outer appearances and which so affects our sense that it obtains the representations of space, matter, shape, etc., may yet, when viewed as noumenon (or better, as transcendental object), be at the same time the subject of our thoughts. (‘‘Second Paralogism,’’ at A)

Kant should see no special threat in these admissions. For all of the above, it turns out that workaday empirical objects are individuated by their place in the spatio-temporal manifold, and that the thesis that ⁴¹ Kant’s gesammelte Schriften, vol. , p. .



The threat of one substance

there is just one empirical object has no plausibility. Phenomenal objects are individuated by reference to how we experience them, and in particular how we perceive them in sensible intuition. In short, Kant thinks that questions of individuation for empirical objects have no deeper answer than one proceeding in terms of the organizing principles of perceptual experience. If one tries, meanwhile, to abstract away from perceptual appearances, one will be left with issues for which such Leibnizian principles as PII have a grip on the intellect but which are ultimately well beyond us. Insofar as we rely on intuition, questions of individuation are moderately tractable. If we do not, we are left with theoretical issues that lie well beyond the domain of human knowledge. Thinking back to Leibniz now, it is worth asking ourselves how we actually know that there are a plurality of objects. By Kant’s lights, Leibniz is in no position to say that we know such a thing. After all, Leibniz cannot rely on the fact that ‘‘confused perception’’ represents the world as containing a diversity of substances, for there seems to be no good a priori argument that confused perception should in this way match things-in-themselves. And there does not seem to be any convincing a priori argument of a theoretical sort entailing a plurality of substances. What Leibniz does have, of course, are vague moral considerations on the one hand and what he takes to be the content of divine revelation on the other. The vague moral considerations are to the effect that a multitude of created beings is, ceteris paribus, morally superior to just one; and the content of revelation is a tradition of scriptural understanding among believing scholars that takes a plurality of creaturely substances to be rather at the bottom of things. So the plurality-of-substance doctrine emerges as well beyond theoretical knowledge (though still thinkable by theoretical understanding), and instead is the posit either of practical reason or of religious faith. Bizarrely, Leibniz’s metaphysic may serve to accomplish what the Critique of Pure Reason itself was intended to accomplish, namely to ‘‘clear away knowledge in order to make room for faith.’’

Bibliography

Quotations from and citations to Leibniz’s writings, in the text and the notes, are generally indicated by abbreviation or a shortened title. In most cases translations are available: where they are we have used them (with occasional modification, indicated where relevant) and cited the source, leaning rather more heavily on L where possible with the exception of material from LA. If no translated source is cited none is to our knowledge available, and we’ve done our best (with help) to render them properly.  .             A AG C Discourse Disputatio DSR E G GLW GM

Gottfried Wilhelm Leibniz. Sa¨mtliche Schriften und Briefe. Ed. Deutsche Akademie der Wissenschaften. Darmstadt, Leipzig, Berlin: Akademie Verlag,  –. Cited by series, volume, page. G. W. Leibniz. Philosophical Essays. Ed. and trans. Roger Ariew and Daniel Garber. Indianapolis: Hackett Publishing Company, . Opuscules et fragments ine´dits de Leibniz. Ed. Louis Couturat. Paris: Presses Univerisitaires, . Reprint, Hildesheim: Georg Olms, . G. W. Leibniz. Discours de Me´taphysique. Cited by section as in G ,–. English translation in AG and L. G. W. Leibniz. Disputatio Metaphysica de Principio Individui. Cited by section as in G , –. English translation in MLI. G. W. Leibniz. De Summa Rerum. Metaphysical Papers, –. Ed. and trans. G. H. R. Parkinson. New Haven: Yale University Press, . Includes marginal pagination to A .. G. W. Leibniz. Opera Philosophicae quae exstant Latina, Gallica, Germanica omnia. Ed. J. E. Erdmann. Berlin: Eichler, –. Reprint, Aalen: Scientia Verlag, . Die philosophischen Schriften von Gottfried Wilhelm Leibniz. Ed. C. I. Gerhardt. Berlin: Weidmann, –. Reprint, Hildesheim: Georg Olms, . Cited by volume and page. Briefwechsel zwischen Leibniz und Christian Wolff. Ed. C. I. Gerhardt. Halle: Schmidt, . Reprint, Hildesheim: Georg Olms, . Leibnizens Mathematische Schriften. Ed. C. I. Gerhardt. Berlin: A. 

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Grua H L LA

LH

MLI MP NE PLP RB SFL T VE W

Bibliography Asher; and Halle: H. W. Schmidt, –. Reprint, Hildesheim: Georg Olms, . Cited by volume and page. Textes ine´dits d’apre`s de la bibliothe`que provinciale de Hanovre. Ed. Gaston Grua. Paris: Presses Universitaires, . Reprint, New York and London: Garland Publishing, . G. W. Leibniz. Theodicy. Trans. E. M. Huggard. New Haven: Yale University Press, . Reprint, LaSalle, Il: Open Court, . G.W. Leibniz. Philosophical Papers and Letters. Ed. and trans. Leroy E. Loemker. nd edn. Dordrecht: D. Reidel, . The Leibniz–Arnauld Correspondence. Ed. and trans. H. T. Mason. Manchester: Manchester University Press, . Reprint, New York and London: Garland Publishing, . Includes marginal pagination to G ,–. Die Leibniz-Handschriften der Ko¨niglichen O¨ffentlichen Bibliothek zu Hannover. Ed. Eduard Bodemann. Hannover: Hahn, . Reprint, Hildesheim: Georg Olms, . Cited by Bodemann’s numbering and page. Leibniz on Individuals and Individuation. Laurence B. McCullough. Dordrecht: Kluwer Academic Publishers, . Contains an English translation of the Disputatio. G.W. Leibniz. Philosophical Writings. Ed. and trans. Mary Morris and G. H. R. Parkinson. London: J. M. Dent & Sons, . G.W. Leibniz. Nouveaux essais sur l’entendement humain. Cited by book, chapter, and section as in A .. Translated in RB. G.W. Leibniz. Logical Papers. Ed. and trans. G. H. R. Parkinson. Oxford: Clarendon Press, . G.W. Leibniz. New Essays on Human Understanding. Ed. and trans. Peter Remnant and Jonathan Bennett. Cambridge: Cambridge University Press, . Cited by page which corresponds to A .. G.W. Leibniz. Fragmente zur Logik. Ed. and trans. Franz Schmidt. Berlin: Akademie-Verlag, . G.W. Leibniz. Essais De The´odice´e. Cited by section number as in G ,–, indicating ‘‘Discours Pre´liminaire . . .’’ and Causa Dei as needed. Translated in H. G.W. Leibniz. Vorausedition zur Reihe VI (Philosophische Schriften) in der Ausgabe der Akademie der Wissenschaften der DDR. Ed Leibniz-Forschungsstelle der Universita¨t Munster. Munster, –. G.W. Leibniz. Selections. Ed. and trans. Philip P. Wiener. New York: Scribners, .   .                

AT

Oeuvres de Descartes. Ed. Charles Adam and Paul Tannery. Paris: J. Vrin, –. Cited by volume and page.

Bibliography Berton CSM(K)

CWS

Essay ST



R. P. Francisci Suarez: Opera Omnia. Ed. A. Carolo Berton. Paris: Vive`s, –. Cited by volume and page. The Philosophical Writings of Descartes. Ed. and trans. John Cottingham, Robert Stoothoff, Dugald Murdoch (and vol. ) Anthony Kenny. Cambridge: Cambridge University Press, ,  (). Includes marginal pagination to AT. Cited by volume and page. The Collected Works of Spinoza, Volume . Ed. and trans. Edwin Curley. Princeton, NJ: Princeton University Press, . Includes marginal pagination to Spinoza opera (ed. C. Gebhardt, Heidelberg: Carl Winter, ). John Locke. An Essay Concerning Human Understanding. Ed. Peter H. Nidditch. Oxford: Clarendon Press, . Cited by book, chapter, and section. Thomas Aquinas. Summa theologiae. Blackfriars edition. London: Eyre and Spottiswoode, –.  vols. Cited by part, question, and article.

Aristotle. The Complete Works of Aristotle. Ed. Jonathan Barnes. Princeton, NJ: Princeton University Press, . Avicenna. Liber de philosophia prima sive scientia divina  – . Ed. S. Van Riet in Avicenna latinus. Louvain, . The ‘Metaphysica’ of Avicenna. Trans. P. Morewedge. New York: Columbia University Press, . Opera philosophica. Venice: Bonetus Locatellus for Octavianus Scotus, . Reprint, Frankfurt-on-Main: Minerva, . Includes the Logica and Metaphysica. Duns Scotus, John. Ordinatio. In Opera omnia (vols.  – ). Ed. P. Carolo Balic. Civitas Vaticana: Typis Polyglottis Vaticanis, –. Gilson, Etienne. Index Scolastico-Carte´sien. Paris, . Reprint, New York: Burt Franklin, n.d. John of St. Thomas. Cursus philosophicus Thomisticus. Ed. B. Reiser. Turin: Marietti, . Kant, Immanuel. Kant’s gesammelte Schriften, heraus gegeben von der Ko¨niglichen Preussischen Akademie der Wissenschaften. Berlin: De Gruyter,  – . Ockham, William. Opera philosophica. St. Bonaventure, NY: The Franciscan Institute, –. Includes the Summa logicae (vol. , ed. P. Boehner, G. Ga´l, S. Brown). Opera theologica. St. Bonaventure, NY: The Franciscan Institute, –. Includes the Reportatio (vols  – ). Philosophical Writings. Trans. Philotheus Boehner. Edinburgh: Thomas Nelson and Sons, . Reprint, Indianapolis: Hackett Publishing Company, . Includes important selections from the Summa logicae  – . Spade, Paul Vincent. Ed. Five Texts on the Mediaeval Problem of Universals. Indianapolis: Hackett Publishing Company, . Includes translations of Ockham’s Ordinatio d., qq. –, and Scotus’s Ordinatio , d., qq. –.



Bibliography

Suarez, Francisco. Disputationes metaphysicae. In vols.  and  of Berton. On the Essence of Finite Being as Such, On the Existence of that Essence and Their Distinction [Metaphysical Disputation XXXI]. Trans. Norman J. Wells. Milwaukee, WI: Marquette University Press, . On Formal and Universal Unity [Metaphysical Disputation VI]. Trans. J. F. Ross. Milwaukee, WI: Marquette University Press, . Suarez on Individuation. Individual Unity and Its Principle: Metaphysical Disputation V. Trans. Jorge J. E. Gracia. Milwaukee, WI: Marquette University Press, . On the Various Kinds of Distinctions [Metaphysical Disputation VII]. Trans. Cyril Vollert. Milwaukee, WI: Marquette University Press, . Thomas Aquinas. ‘On Being and Essence by St. Thomas Aquinas. Trans. Armand Augustine Maurer, C.S.B. Toronto: The Pontifical Institute of Medieval Studies, . De ente et essentia. Ed. Raymundi M. Spiazzi. Turin: Marietti, . Expositio super librum Boethii De trinitate. Ed. Brudon Decker. Leiden: E. J. Brill, . Faith, Reason and Theology: Questions I-IV of ‘‘Comentary on ‘De Trinitate’ of Boethius’’. Trans. Armand Maurer. Toronto: Pontifical Institute of Mediaeval Studies, . Summa contra gentiles. Ed. Ceslai Pera et. al. Turin: Marietti, . Truth (De veritate). Ed. and trans. Robert W. Mulligan. Chicago: Henry Regnery, .                  Adams, Marilyn McCord. William Ockham. Notre Dame: University of Notre Dame Press, . Adams, Robert M. ‘‘Primitive Thisness and Primitive Identity.’’ Journal of Philosophy  (), –. ‘‘Actualism and Thisness.’’ Synthese  (), –. Leibniz: Determinist, Theist, Idealist. Oxford: Oxford University Press, . Angelelli, Ignacio. ‘‘The Scholastic Background of Modern Philosophy: Entitas and Individuation in Leibniz.’’ In J. J. E. Gracia, ed., Individuation in Scholasticism, –. Armstrong, D. M. Universals and Scientific Realism. Volume I: Nominalism and Realism. Cambridge: Cambridge University Press, . A Combinatorial Theory of Possibility. Cambridge: Cambridge University Press, . A World of States of Affairs. Cambridge: Cambridge University Press, . Ba¨ck, Allan. ‘‘The Islamic Background: Avicenna and Averroes.’’ In J. J. E. Gracia, ed., Individuation in Scholasticism, –. Bartha, Paul. ‘‘Substantial Form and the Nature of Individual Substance.’’ Studia Leibnitiana  (), –. Bennett, Jonathan. A Study of Spinoza’s ETHICS. Indianapolis: Hackett Pub-

Bibliography



lishing Company, . Events and Their Names. Indianapolis: Hackett Publishing Company, . Black, Max. ‘‘The Identity of Indiscernibles.’’ Mind  (), –. Bobik, Joseph. Aquinas on Being and Essence: A Translation and Interpretation. Notre Dame, IN: University of Notre Dame Press, . Bochenski, I. M. ‘‘Sancti Thomae Aquinatis de Modalibus Opusculum et Doctrina.’’ Angelicum  (), –. Broad, C. D. Leibniz: An Introduction. London: Cambridge University Press, . Brody, Baruch. Identity and Essence. Princeton: Princeton University Press, . Brown, Gregory. ‘‘Compossibility Harmony, and Perfection in Leibniz.’’ The Philosophical Review  (), –. Carriero, John. ‘‘Leibniz on Infinite Resolution and Intra-mundane Contingency.’’ Studia Leibnitiana  (), –. Carroll, Lewis. ‘‘What the Tortoise Said to Achilles.’’ Mind, ns  (), –. Castan˜eda, Hetor-Neri. ‘‘Leibniz and Plato’s Phaedo Theory of Relations and Predication.’’ In M. Hooker, ed., Leibniz: Critical and Interpretive Essays, –. Chisholm, Roderick M. ‘‘Possibility without Haecceity.’’ In P. French, ed., Studies in Essentialism, –. Clatterbaugh, Kenneth. Leibniz’s Doctrine of Individual Accidents. Studia Leibnitiana, Sonderheft  (). Cleland, Carol E. ‘‘Space: An Abstract System of Non-supervenient Relations.’’ Philosophical Studies  (), –. Couturat, Louis. ‘‘On Leibniz’s Metaphysics.’’ In Frankfurt, ed., Leibniz, –. An edited translation by R. Allison Ryan of ‘‘Sur la Me´taphysique de Leibniz,’’ Revue de Me´taphysique et de Morale  (), –. Cover, J. A. ‘‘Relations and Reduction in Leibniz.’’ Pacific Philosophical Quarterly  (), –. ‘‘Reference, Modality and Relational Time.’’ Philosophical Studies  (), –. ‘‘Non-Basic Time and Reductive Strategies: Leibniz’s Theory of Time.’’ Studies in History and Philosophy of Science  (), –. Cover, J. A., and John Hawthorne. ‘‘Leibniz on Superessentialism and WorldBound Individuals.’’ Studia Leibnitiana  (), –. Cover, J. A., and Mark Kulstad, eds. Central Themes in Early Modern Philosophy. Indianapolis: Hackett Publishing Company, . Curley, Edwin. Spinoza’s Metaphysics. Cambridge MA: Harvard University Press, . Curley, Edwin and Gregory Walski. ‘‘Spinoza’s Necessitarianism Reconsidered.’’ In R. Gennaro and C. Huenemann, eds. New Essays on the Rationalists. Oxford: Oxford University Press, . D’Agostino, Fred. ‘‘Leibniz on Compossibility and Relational Predicates.’’ In R. Woolhouse, ed., Leibniz: Metaphysics and Philosophy of Science, –.



Bibliography

Fitch, Gregory W. ‘‘The Nature of Singular Propositions.’’ In D. F. Austin, ed., Philosophical Analysis. Dordrecht: Kluwer, , –. Fleming, Noel. ‘‘On Leibniz on Subject and Substance.’’ The Philosophical Review  (), –. Frankfurt, Harry, ed. Leibniz: A Collection of Critical Essays. Garden City, NY: Doubleday, . Frege, Gottlob. Die Grundlagen der Arithmetik. Translated by J. L. Austin, The Foundations of Arithmetic. nd. rev. edn. Oxford: Basil Blackwell, . French, Peter A. et. al., eds. Midwest Studies in Philosophy XI. Studies in Essentialism. Minneapolis: University of Minnesota Press, . Garrett, Don. ‘‘Spinoza’s Necessitarianism.’’ In Y. Yovel, ed., God and Nature: Spinoza’s Metaphysics. Leiden: E. J. Brill, , –. Gracia, Jorge J. E. Introduction to the Problem of Individuation in the Early Middle Ages. Munich: Philosophia Verlag, . Gracia, Jorge J. E. ed. Individuation in Scholasticism: The Later Middle Ages and the Counter-Reformation,  – . Albany, NY: SUNY Press, . Gracia, Jorge J. E. and John Kronen. ‘‘John of St. Thomas.’’ In J. J. E. Gracia, ed., Individuation in Scholasticism, –. Grandy, Richard. ‘‘Anadic Logic and English.’’ Synthese  (), –. Hampshire, Stuart. Spinoza. New York: Penguin, . Hartz, Glenn A. and J. A. Cover. ‘‘Space and Time in the Leibnizian Metaphysic.’’ Nouˆs  (), –. Henninger, Mark G., SJ. Relations: Medieval Theories –. Oxford: Clarendon Press, . Hintikka, Jaakko. ‘‘Leibniz on Plenitude, Relations and the ‘Reign of Law’.’’ In Frankfurt, ed., Leibniz, –. Hooker, Michael, ed. Leibniz: Critical and Interpretive Essays. Minneapolis: University of Minnesota Press, . Ishiguro, Hide´. Leibniz’s Philosophy of Logic and Language. Ithaca, NY: Cornell University Press, . ‘‘Leibniz’s Theory of the Ideality of Relations.’’ In H. Frankfurt, ed., Leibniz, –. Jolley, Nicholas. Leibniz and Locke: A Study of The New Essays Concerning Human Understanding. Oxford: Clarendon, . Kaplan, David. ‘‘How to Russell a Frege-Church.’’ Journal of Philosophy  (), –. Kennedy, L. A., C.S.B. ‘‘Thomism at the University of Salamanca in the Sixteenth Century: The Doctrine of Existence.’’ In Tommaso D’Aquino nella Storia del Pensiero, vol. . Napoli, , –. Kim, Jaegwon. ‘‘Causation, Nomic Subsumption, and the Concept of an Event.’’ Journal of Philosophy  (), –. ‘‘Events as Property Exemplifications.’’ In M. Brand and D. Walton, eds., Action Theory. Dordrecht: Reidel, , –. Kripke, Saul A. Naming and Necessity. Cambridge, MA: Harvard University Press, .

Bibliography



Kulstad, Mark. ‘‘A Closer Look at Leibniz’s Alleged Reduction of Relations.’’ Southern Journal of Philosophy  (), –. Leibniz on Apperception, Consciousness and Reflection. Munich: Philosophia Verlag, . ‘‘Did Leibniz incline toward Monistic Pantheism in ?’’ In Leibniz und Europa. Vortra¨ge, VI Internationaler Leibniz-Kongress. Hanover: G. W. Leibniz Gesellschaft e.V, , –. Lewis, David. ‘‘Counterpart Theory and Quantified Modal Logic.’’ Journal of Philosophy  (), –. ‘‘Extrinsic Properties.’’ Philosophical Studies  (), –. On the Plurality of Worlds. Oxford: Basil Blackwell, . McCullough, Laurence B. Leibniz on Individuals and Individuation. Dordrecht: Kluwer Academic Publishers, . McRae, Robert. Leibniz: Perception, Apperception, and Thought. Toronto: University of Toronto Press, . Mates, Benson. ‘‘Individuals and Modality in the Philosophy of Leibniz,’’ Studia Leibnitiana  (), –. The Philosophy of Leibniz: Metaphysics and Philosophy of Language. New York and Oxford: Oxford University Press, . Matson, Wallace. ‘‘Steps Toward Spinozism.’’ Revue Internationale de Philosophie  (), –. Mehlberg, Henry. ‘‘Essai sur la the´orie causale du temps.’’ Studia Philosophica  (), –. Time, Causality, and the Quantum Theory. Vol. : Essay on the Causal Theory of Time. Dordrecht: D. Reidel Publishing Company, . Includes a translation of ‘‘Essai sur la the´orie causale du temps.’’ Mercer, Christia. Leibniz’s Metaphysics: Its Origins and Development. Cambridge: Cambridge University Press, forthcoming. Mondadori, Fabrizio. ‘‘Reference, Essentialism, and Modality in Leibniz’s Metaphysics.’’ Studia Leibnitiana  (), –. ‘‘Leibniz and the Doctrine of Inter-World Identity.’’ Studia Leibnitiana  (), –. ‘‘On Some Disputed Questions in Leibniz’s Metaphysics.’’ Studia Leibnitiana  (), –. Morton, Adam. ‘‘Complex Individuals and Multigrade Relations.’’ Nouˆs  (), –. Mugnai, Massimo. Leibniz’ Theory of Relations. Stuttgart: Franz Steiner Verlag, . O’Leary-Hawthorne, John, and J. A. Cover. ‘‘Framing the Thisness Issue.’’ Australasian Journal of Philosophy  (), –. ‘‘A World of Universals.’’ Philosophical Studies,  (), –. ‘‘Infinite Analysis and the Problem of Lucky Proof.’’ Unpublished manuscript. Parkinson, G. H. R. Logic and Reality in Leibniz’s Metaphysics. Oxford: Clarendon, .



Bibliography

‘‘Leibniz’s Paris Writings in Relation to Spinoza.’’ Studia Leibnitiana Supplementa  (), –. Rescher, Nicholas. The Philosophy of Leibniz. Englewood Cliffs: Prentice-Hall, . Robinet, Andre´, ed. Malebranche et Leibniz: Relationes personelles. Paris: Vrin, . Rosenkrantz, Gary S. Haecceity: An Ontological Essay. Dordrecht: Kluwer Academic Publishers, . Russell, Bertrand. Our Knowledge of the External World. Chicago and London: Open Court, . A Critical Exposition of the Philosophy of Leibniz. nd. ed. London: George Allen & Unwin, . Rutherford, Donald. Leibniz and the Rational Order of Nature. Cambridge: Cambridge University Press, . Sleigh, Robert C., Jr. ‘‘Notes on Harmony.’’ Originally appearing in Proceedings of the Fourth International Leibniz Congress, , –; reprinted in R. S. Woolhouse, ed., G. W. Leibniz: Critical Assessments, vol. . London: Routledge, , –. Leibniz and Arnauld: A Commentary on Their Correspondence. New Haven: Yale University Press, . ‘‘Leibniz on Malebranche on Causality.’’ In J. A. Cover and M. Kulstad, eds., Central Themes in Early Modern Philosophy, –. ‘‘Leibniz on Divine Foreknowledge.’’ Faith and Philosophy  (), –. Stein, Ludwig. Leibniz und Spinoza. Berlin: Reimer, . Van Fraassen, Bas. An Introduction to the Philosophy of Time and Space. nd. ed. New York: Columbia University Press, . Van Inwagen, Peter. Material Beings. Ithaca, NY: Cornell University Press, . Wilson, Catherine. Leibniz’s Metaphysics: A Historical and Comparative Study. Princeton: Prnceton University Press, . Wilson, Margaret. ‘‘Possible Gods.’’ The Review of Metaphysics  (), –. ‘‘Compossibility and Law.’’ In S. Nadler, ed., Causation in Early Modern Philosophy. University Park: Pennsylvania State University Press, , –. Winnie, John. A. ‘‘The Causal Theory of Time.’’ In J. S. Earman et. al., eds., Foundations of Space-Time Theories: Minnesota Studies in the Philosophy of Science, Vol. . Minneapolis: University of Minnesota, , –. Woolhouse, R. S. ‘‘The Nature of an Individual Substance.’’ In M. Hooker, ed., Leibniz, Minneapolis: University of Minnesota Press, , –. Woolhouse, R. S., ed. Leibniz: Metaphysics and Philosophy of Science. Oxford: Oxford University Press, . Wong, David. ‘‘Leibniz’s Theory of Relations.’’ The Philosophical Review  (), –.

Index

accident(s), , , , , , , , , , , , , , , – proper, , ,  relational, , , , , , , –, , – their relation to substance, , , , , , –, , , , , , , ,  action creaturely, , , n. divine,  see also freedom activity principle of, , ,  see also change, inner principle of; force, active actualism, Russellian, –, n. Adams, Marilyn McCord, n. Adams, Robert M., n., , n., , , n., , n., n., n., n., n., n., , n., n., n., , n., , , , n., , n., n. aggregate, ,  n. monadic (body as), , , , n., , world as,  analysis, infinite, , , , , , , , ,  Angelelli, Ignacio, n. angels, , , , , , , , , , ,  annihilation, , , , , , , , , ,  see also miracles anti–haecceitism, , , –, , , , , , n., ,  see also generalism Aquinas, St. Thomas, , n., , n., n., n., , n., , , , n., , , , , , , , , , , n.

Archimedes, ,  Aristotelian, , , , , , , , , , , ,  Aristotle, , n., n., , n., , , , , , , , n., ,  and scholastic themes, –, n., –,  Armstrong, D. M., , , n. Arnauld, Antoine, –n. Leibniz to (the correspondence), , , , , , , , , , , , , n., , n., , , ,  Aurioli, Peter,  Avicenna, , n., n., , –n., n., ,  Ba¨ck, Allan, n. Bartha, Paul, n., , ,  Bayle, Pierre, ,  being, vs. knowing, –, , , , ,  beings, incomplete, n., –,  Benardete, Jose´,  n., Bennett, J., , n., n., n., , , n., n., n. Bernoulli, John,  bivalence, ,  see also conventionalism Black, Max, ,  black worlds, , n.,  bond, substantial, , ,  Bourget, Louis, , , ,  Broad, C. D.,  Brody, Baruch, n. Brown, Gregory, n., n. Buridan’s ass, n., n. Carriero, John, n., n. Carroll, Lewis, n. Castan˜eda, Hector–Neri, n. causal efficacy/power in substances, , , , , 



 causal (cont.) realism,  see also change, inner principle of cause divine, as a kind of giving, – final, , , , , ,  immanent, asserted or presumed, , , chapter  passim inter–substantial, denied, ,  change, , , , , –, ,  inner principle of, , , –, ,  over time, see identity, diachronic qualitative (of accidents), , ,  real (vs. relational), ,  substantial, , , ,  Chisholm, Roderick, n. Christian(s), ,  see also Lutheran; Theology Clarke, Samuel Leibniz to (the correspondence), , , , , , ,  Cleland, Carol E., n. co–location, –,  see also interpenetration common motion (of parts of bodies) – nature(s), , , , , , , ,  communicability, , , –,  see also incommunicability complete concept(s), , , , , , n., , , ,  contents of, , , , , , –, n., , , , , – the doctrine of, , , , n., , , , , , ,  and essentialism, –, , , , , ,  God’s grasp of, , , , – and individual/singular nature or essence, , , , , , , ,  and individuation, , , , , , , ,  and law–of–the–series, , , –, –, ,  motivations for the doctrine of, – natural interpretation of (as list), , , – substance defined by contents of, , , , , , –,  thick vs. thin, , –,  n., ,  component/composite view of substance? , , , , –, –, , , , –

Index compossibility, –, , n., ,  see also incompossibility concept containment, –, , , , – individual: see complete concept concurrence, , , n. condensation (rarefaction), ,  connectedness spatio–temporal, of possible worlds, , , , n., conservation , , , , , , n. contingency, ,  n. and infinite analysis, , , , , , , ,  continuity, , , , ,  vs. contiguity,  Contradiction Principle/Law of, , , , , – conventionalist, , , , ,  corporeal substance, , n., –, n., , , , ,  monad as a (one–substance view), , , , ,  counterfactual, , , , , , , ,  identity: see identity, transworld (TWI) counterpart theory, , , , , –, , , , n. and infinite analysis, –,  see also semantics, modal Couturat, Louis, n., ,  Cover, J. A., n., n., n., n., n. creation, n., , , , , , , –, , ,  n. Curd, Martin, n. Curd, Patricia, n. Curley, Edwin, n. D’Agostino, Fred, ,  decidability, – deduction and entailment, –,  and Leibniz’s rationalism, , ,  of relational properties, , –,  from singular subject? ,  definition nominal,  real, , , , ,  Socrates lacks a, n.,  Democritus, , n. demonstrative, , , ,  see also reference denomination

Index extrinsic, , –, , , , , , , , ,  intrinsic, , –, , , , , ,  n., , , ,  de re modality, , , , , , , , , , , n., , , , –, , , , , n., , , ,  vs. de dicto, –, , ,  and general propositions, –,  see also essentialism; haecceitism; transworld identity; world–bound individuals Des Bosses, Bartholomew, , , , n. Descartes, Rene´, , n., n., , , –n.,  description, definite, , ,  determinism, n., –,  De Volder, Burcher, , , n., , , , ,  diachronic identity: see identity, diachronic difference primitive relation of, , , n., , , , ,  qualitative, , ,  solo numero, , , , , , , ,  transworld (TWD), , , ,  distinction formal, n., , –, ,  n., , ,  modal, n., n. numerical, , , , , , , , , , , , , , , , , , ,  rational/mental (of reason), , n., , –,  n., , ,  real, n., n., n., , , , , , n.,  divine concurrence, , , n. conservation, , , , , , , n. creation, n, , , , , , , , , –, n. freedom, , , , ,  ideas, –, , n., ,  knowledge, , ,  mind, , , , , n., , , ,  perfections, ,  power, –,  will (vs. nature), , , – wisdom, , ,  divine preference argument: see Identity of Indiscernibles, divine preference



argument for division, –, ,  from itself, ,  see also communicability; incommunicability Duns Scotus, John, , n., , n., , , , , , , n.,  and individuation, , , n., , , ,  entailment, , , ,  see also deduction entelechy, , , , ,  epistemology vs. metaphysics: see order equivalence objections (to reduction of relations), – essence, n., ,  n., ,  vs. accident, ,  vs. existence, , –, ,  possible creaturely, , ,  vs. propria, – as real possibility of a thing,  specific (species–), – ‘essential’, different senses of, –, n., n., , n., – essentialism, , –, , , chapter , ,  moderate, , n., –,  strong, , , , , –, , , , , , , , , ,, , , , , , , ,  super-, , –,  n., , , , , , , , , , , , , , , n., , , ,  Eucharist, , , n., –,  Eustachius a Sancto Paulo, n. events, , – expression, , , , , –, , , ,  see also perception; harmony extension, (vs. intension) of ‘individual’/‘substance’, ,  extension (Cartesian), , , , ,  extrinsic denomination: see denomination, extrinsic first state the puzzle of the, – Fitch, Gregory, n. Fleming, Noel, n. force, , ,  active, , , , , , , , , , ,  passive, 



Index

form(s), , , , ,  as active, , – and force, , , , ,  and law–of–the–series, , , –, , , , , ,  –plus–matter view of substance, , –, –, ,  substantial, , , , , , , , , , , , , , – formal distinction, n., , –, , n., , ,  unity (i.e. specific), , , n.,  Foucher, Simon,  freedom creaturely, , , , ,  divine , , , ,  Frege, Gottlob, n. function,  mathematical, as model, , , –, –, – Galileo,  Garber, Daniel,  Garrett, Don n. generalism, –, –, n., n., , n. see also anti–haecceitism God and complete concepts, , , , , ,  doing/creating the best, , , , , –, , n., ,  and the first/initial state, , , ,  and the metaphysics of possibility, – mind of, , , , , n., , ,  and possible worlds, –, ,  and relation to substances, – and transworld identity, – see also creation; divine ideas; divine will; divine wisdom Gracia, Jorge J. E., , n. haecceitism, –, ,  and the Identity of Indiscernibles, , –, , , , ,  pressures against, – salvaging Leibniz’s, – strong, , ,  and switching arguments, , , –n. weak, –, , , ,  haecceity, , , , , , , , ,

, , , , , , –, ,  grasping of, ,  Leibniz’s (= Haecceity), , , , , , , , , ,  Scotistic, , , , , , ,  i.e. thisness, , n., , , n.,  Hampshire, Stuart, n. harmony , , n., ,  as a basis of per se unity? , ,  of perceptions, , , , ,  pre–established, , , , , , , , , n. relational laws of, , , n., , –, , , ,  Hartz, Glenn A., n., n. heaven, , n. Platonic, , ,  Henninger, Mark G., n., ,  Hintikka, Jaakko, n., n. Horne, Conrad, n. Hume/Humean, , , n., , n.,  humor, n. hypothetical necessity: see necessity, hypothetical and moral ideas, divine, –, ,  n., ,  identity criteria of, – diachronic, , –,  n., , ,  n.,  personal, – transworld (TWI), , , –, , , , , , –, –, , n. , , , , , , , ,  Identity of Indiscernibles (PII), , , , , ,  n., ,  n., , , , n., , ,  divine preference argument for, n., n., –, , –, , , , , , , ,  and haecceitism, , –, , , , ,  inter–world, , , , n. intra–world, , , , , , ,  modal strength of, –, – no reason argument for, n., n., –, , –, , , , , , , ,  Russell and, , –, – immanent causal source of change, see causation, immanent

Index functions, –, –,  universals, , , n.,  impredicability, –, , n.,  incommunicability, , , ,  incomplete beings, n., –,  independence, see separability indexical(s),  n., ,  indexing (to times, worlds), , ,  indiscernible(s), , , n., , , n., ,  and switching, see switching see also Identity of Indiscernibles individual nature, , , ,  and complete concept, , n., , , ,  individuation Aquinas on, n., n. blueprint approach to, –, ,  (see also component view of substance) and complete concept, , , , , , , ,  via component/constituents of substance, , , , , n., , – contemporary approaches to, – and counting (How many?), , , ,  and difference (i.e. numerical), , , , , , –,  epistemology vs. metaphysics of, ,  (see also being, vs. knowing) and incommunicability (indivisibility) , , , , –,  internal vs. external principle of, , , , –, , , , , , , , –,  modal approach to, –, , , , , , ,  and negation, , , ,  and relations, , , , , , – scholastic approaches to, –, –, –, , , ,  Scotus, Scotistic haecceity and, , , n., , , , , – spatio–temporal, , , , , , , , , n., , –, – Suarez on, , , ,  whole–entity view of (Leibniz’s), , , , , , –, , , , , , , , ,  infinite analysis, , , , , ,  and counterpart theory, –,  intellect relation of formal/specific unity and common nature to, , , , , , – intension



of ‘individual’/‘substance’, , –, , , , , , ,  interpenetration, –, –, ,  intrinsic denomination, see denomination, intrinsic monadic state/history, , , , , –, , , , , , ,  property, see property, intrinsic intrinsicalness: see superintrinsicalness Ishiguro, Hide´: n., n., n., , n.,  n.,  John of St. Thomas, n. Jolley, Nicholas, n., n. Kant, Immanuel, , , , n., – Kaplan, David, –, n., , ,  Kim, Jaegwon,  Kripke, Saul , , Kripkean, n.,  n., , n. knowing vs. being, –, , , , ,  Kulstad, Mark, n., n., n., n., , n. Law(s),  and compossibility, , , ,  of harmonious expression, n., , , , , –, , , , ,  of nature, , , , , , , n. as supervenient, , , n., ,  n., ,  Law–of–the–series, , , ,  and complete concept, , , –, –, ,  as essential, n., , , ,  and form and force, , ,  functional model of, , , –, –,  giving rise to states of substance, , , , , , , – and Haecceity (Leibnizian), – and identity of persisting substance, , , ,  and laws of nature, n., – many needed, or one sufficient? , – and marks and traces, – permanent/persisting, in substance, , , , , ,  and substantial form, , , , ,  Lelong, J.,  Leibniz’s Law, , 



Index

Levey, Samuel, n. Lewis, David, n., , , , , , n., n. list complete concept or sense of a name as, , , , , n.,  Locke, John, n., , , ,  Lutheran, n., n.,  McCullough, Laurence B., n., n., n., n., , n., , , , n. Mc Rae, Robert, n. Malebranche, Nicolas, n. marks and traces, , –,  and the predicate–in–subject doctrine, , , ,  mass noun, n., – Mates, Benson, n., n., , , , , n., n., , , n., , n.,  mathematical function, as model, , , –, –, – representation of truth and validity, , – Matson, Wallace,  n. matter, , ,  and individuation, n., n., , , –, – –plus–form view of substance, n., , –, –, , – primary (Leibniz), n., ,  prime (Aristotelians), , ,  secondary ,  maximality, of worlds, , , , , ,  meaning,  of names/singular terms, n., , , ,  medieval(s), see scholastic(s) Mehlberg, Henrik, n. Meinongian, ,  Mendelssohn, Moses, n. mental distinction: see rational distinction Mercer, Christia, n. metaphysics component–style (of substance), , , , , –, n., –, , , , , , , , ,  of individual substance, – and the nature of possibility, – mind divine, , , , , n., , , , 

relation of formal/common natures to, , , , , , – (see also nominalism) miracles , , n., n., –,  and essentialism, – mirroring, , ,  see also harmony modal approach to individuation, –, , , , , , ,  operator, ,  realism, ,  semantics, , , , –, , – modality de dicto vs. de re, –, , ,  de re and qualitative clothing, , , , – (see also generalism) moderate essentialism, see essentialism, moderate Mondadori, Fabrizio, n., n., n., n., n., n., n., , , , n., n., n. moral necessity: see necessity, hypothetical and moral status of worlds, , , , , ; see also cause, final; God, doing/creating the best Morton, Adam, n. Mugnai, Massimo, n. multiplication of worlds (haecceitistic), , , n., n. Mundy, Brent, n. name(s), , , , , ,  meaning/sense of, , , ,  of worlds,  see also term(s), singular nature: common/formal/specific, see common nature individual, and complete concept, , n., , , , , , , ,  laws of, see laws of nature necessitarianism, , , , , , ,  necessity absolute/per se, , , n. hypothetical or moral, , , , , , n.,  of origins (Kripkean), , n., , ,  negation, , –,  as principle of individuation, , ,  Newtonians, , 

Index nominalism, , ,  and Aquinas,  in Leibniz, , , ,  in Suarez, n., , ,  No Reason argument: see Identity of Indiscernibles, No Reason argument for occasionalism, , , ,  Ockham, William, , n.,  O’Leary–Hawthorne, John, n., n., n. one–substance threat, –, –, – Russell on the, – order of knowing vs. of being, –, , , , ,  Parkinson, G.H.R., n., n., n. passivity, n., ,  perception, , , –,  harmonious, , , , ,  perfections simple/positive/compatible, , , ,  permanent/persisting (substance), , , , ,  law-of-series as: , , , , ,  per se vs. per accidens, , , n.,  unity, , , , , n. phenomenalism, n.,  Plato /–nist, , , , , , n. possible in–its–own–nature, , ,  the metaphysics of the, – substances (i.e. non–actual), , ,  (see also essence, possible creaturely) possible world(s) best of all, , –, , n. and compossibles, –,  as creation scenario(s), , ,  and generalism, – God’s relation to, , , , –, ,  maximal? , , ,  moral status of, , , , ,  haecceitistic multiplication of, , , n. spatiotemporal connectedness of? –, n. predicate relational, , , , –, , , ,  (see also properties, relational) –in–subject doctrine, , n., n., , –, , , , , , ,



–,  pre-established harmony: see harmony, pre–established primitive i.e. basic/simple, properties, – modal predicate,  relation of difference, , , n., , , , ,  thisness (haecceity), n., , n., ,  world–names,  Principle of Sufficient Reason (PSR), , , , ,  and haecceitism, , –, , ,  and Identity of Indiscernibles (PII), –, – modal status of, –, –,  and predicate–in–subject doctrine, – privative, , ; see also negation properties basic, , – intrinsic, , n., , , , , , , , , , , , , ; see also superintrinsicalness monadic, , , , , , ,  qualitative, , , ,  relational, , , n., , , , , n., , , , , , , ; see also predicate, relational proposition(s) general, , , , , , , , , , , ,  Russellian, , n., , ,  relational, see truths, relational singular, , , n., , , , , , , , , , , , ,  Protestant: see Lutheran puzzle of the first/initial state, – qualitative, ,  nature of substance, and de re modality, –, – similarity/difference, , ,  thisness, ,  rational distinction, , n., , –,  n., , ,  rationalism, –, , , , , , ,  real definition, , , , ,  distinction, n., n., n., , , , , , n. (see also separability) presence, , 



Index

realism, , ; see also nominalism causal,  extreme modal ,  Scotus read by Leibniz as committed to? n., – substance–accident , ,  reason senses of,  sufficient: see Principle of Sufficient Reason (PSR) reduction, , – and relations: see relations, reductionism about reference, n., n., , n. and the complete–concept doctrine, –, ,  demonstrative, –n., ,  via descriptive profile, , ,  direct,  relation(s), , , , ,  (see also denomination, extrinsic) and (external) individuation, , , , , ,, – of primitive difference, , , n., , , , ,  reductionism about, , , , , , n., –, , n. scholastic views of, , –, – spatial/temporal, , , , , , , , , ,  and supervenience, , , –, , – (see also relations, reductionism about) relational accidents, see accidents, relational predicates, see predicates, relational properties, see properties, relational truths/facts, see truths, relational Remond, Nicolas, n. Rescher, Nicholas, n., n., , n. Richard of Mediavilla,  Rosencrantz, Gary S., n. Russell, Bertrand, n., , , –, , , , , , , , n., , –, , , ; see also actualism, Russellian; propositions, Russellian Rutherford, Donald, n.,  n., , , , n. semantics modal, , , , –, , , – separability (separation), –n., , , , , –, , , , , , , , n., , , , , , , , , , , 

scholastics, , , , , , , , , , , , , , n.,  and Aristotle, –, n. and individuation, –, –, , –, , , – and relations, , , –, , – Scotistic haecceities: see haecceity, Scotistic; primitive thisness Scotus: see Duns Scotus, John simplicity, –,  of basic predicates/properties, , , , , ,  singular concepts,  propositions, see propositions, singular term(s), , , , ; see also names Sleigh, Robert C., n., , n., n., n., n., n., , n., , , n., , , , n., n. soul, n., , , , , ,  spatio–temporal connectedness of all worlds? , , , n. features as individuating, , , , –, , , , n., – relations, , , , , , , , , –, –,  species, , , , , , , ,  specific unity, see unity, formal Spinoza, Baruch, , , ,  and necessitarianism, , , , , ,  and the one–substance doctrine, –, – Spinozism, , , , , , n. Stalnaker, Robert, ,  Stein, Ludwig, n. Suarez, Francisco, , , , –, n., , ’ nominalist sentiments in, n., , ,  and individuation, , , ,  substance Aristotelian account of, n. defined by sum of predicates in complete concept? , , , , , –,  component/composite approach to, , , , , –, –, , , , – corporeal, , n., , , , , , , n., , , , , , ,  on the model of a function, –, –, – incomplete, n., – law–of–the–series as permanent/persisting

Index in, , , , , ,  simplicity of, –, –,  see also form substantial bond (vinculum) see bond, substantial substantial form and communicability, – and law–of–the–series, , , , ,  and numerical unity/difference, , , , , ,  in scholastics, , ,  see also form suchness, ,  sufficient reason: see Principle of Sufficient Reason (PSR) superaddition, , ,  superintrinsicalness, , –,  supervenience of laws, , ,  n., , n., ,  of numerical difference?  n.,  of relational facts, , , –, , –,  of singular truths on general, , , , ,  (see also weak haecceitism) switching, , , n., , n., , , –n., , , – syntactic system ,  Temmik, Aloys, n. Theism, n.,  Theology/theological, , n., –, n., , , ,  n., , , ,  thisness, see haecceity Thomas Aquinas, see Aquinas, St. Thomas Thomistic, n., , , , ,  Time, – see also spatiotemporal Tournemine, Rene´–Joseph de,  traces, see marks and traces transubstantiation, , , – see also Eucharist transworld difference (TWD), , , , , transworld identity (TWI), , , –, ,



, , , , –, –, , n. , , , , , , , ,  and God: – and haecceitism, –, , , , , , , , , , , truths general, , , , , , , , , , , ,  monadic, , , , , , ,  relational, , , , , , , , , , n., , , , , , n.,  singular, , , n., , , , , , , , , , , , ,  unity,  formal (specific), , , n.,  numerical, –, , ,  per se, , , , , n. and variety (simplicity and richness), n., , , ,  universals, , , ,  immanent, , , , n.,  Leibniz on, – see also common natures; nominalism Vailati, Ezio, n. van Fraassen, Bas n. van Inwagen, Peter, n. variety, , ,  vinculum substantiale, , ,  Walski, Gregory, n. whole–entity, , , , , , –, , , , , , ,, , ,  Williamson, Timothy, n. Wilson, Catherine, n. Wilson, Margaret , , , , –, ,  Winnie, John A. n. Wong, David, n., Woolhouse, R. S.  world–bound individuals (WBI) –, , , , , , , , , ,  worlds: see possible worlds