Dispositions and Causes (Mind Association Occasional Series)

Dispositions and Causes

MIND ASSOCIATION OCCASIONAL SERIES This series consists of occasional volumes of original papers on predefined themes. The Mind Association nominates an editor or editors for each collection, and may cooperate with other bodies in promoting conferences or other scholarly activities in connection with the preparation of particular volumes. Publications Officer: M. A. Stewart Secretary: R. D. Hopkins

Dispositions and Causes

Toby Handfield

CLARENDON PRESS · OXFORD

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Great Clarendon Street, Oxford ox2 6dp Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trademark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York  Toby Handfield 2009 The moral rights of the authors have been asserted Database right Oxford University Press (maker) First published 2009 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available Typeset by Laserwords Private Limited, Chennai, India Printed in Great Britain on acid-free paper by Biddles Ltd., King’s Lynn, Norfolk ISBN 978–0–19–955893–3 10 9 8 7 6 5 4 3 2 1

Preface As philosophical inquiry becomes more specialized, there is an increasing likelihood that practitioners of one sub-discipline will fail to notice the relevance of insights gained in another. In recent years there have been two relatively distinct research communities, one in philosophy of science and one in metaphysics, both with an interest in dispositional properties and causation, but working in some degree of isolation from each other. The idea for this collection emerged from a conference held at the University of Bristol in December 2005, organized by myself and Alexander Bird. Part of our aim, in convening the conference, was to counter the growing isolation between those research communities. This collection is similarly motivated. The authors are addressing a variety of projects, and do not all aim to address the same questions, but they share an interest in dispositional properties and causal relations. In the first chapter—which serves in part as an overview of recent work on the metaphysics of causes and dispositions, and in part as an introduction—I discuss each of the papers individually, and identify some of the thematic connections between them. The original conference was made possible by the generous support of the British Academy, the Australian Academy of the Humanities, the Institute for Advanced Studies at the University of Bristol, and the Mind Association. In addition to those organisations, I wish particularly to thank the Department of Philosophy at Bristol for hosting my visit there, and Alexander Bird for his assistance and support in organizing that visit. The effort to develop a coherent and unified volume of papers meant that only three of the original conference papers could be included in this collection, but I would like to thank all of the original conference participants for making it such a successful, stimulating event.

vi preface My main debt is to the contributors. I am very grateful that they have had the confidence to entrust their papers to me for publication, and they all showed great patience throughout the process of reviewing and revising the papers. Professor M. A. Stewart, publications officer of the Mind Association, provided a great deal of helpful advice to an inexperienced young editor, and I warmly thank him for it. Two anonymous referees for Oxford University Press gave very detailed and thoughtful comments, which have certainly contributed to making this a better volume. Ole Koksvik and Robyn McNamara gave able research assistance to me in compiling the collection, and Alan Crosier did an excellent job copy-editing the introduction. I am also grateful to the Australian Research Council and to the Monash Research Fund, both of which have supported my research over the period of this project with postdoctoral fellowships. T. H. School of Philosophy and Bioethics Monash University April, 2008

Contents List of Contributors

1. The Metaphysics of Dispositions and Causes

ix

1

Toby Handfield

2. Dispositions, Causes, and Reduction

31

Jennifer McKitrick

3. Causal Structuralism, Dispositional Actualism, and Counterfactual Conditionals

65

Antony Eagle

4. Leaving Things to Take their Chances: Cause and Disposition Grounded in Chance

100

Stephen Barker

5. Causal Laws, Policy Predictions, and the Need for Genuine Powers

127

Nancy Cartwright

6. How is Scientific Analysis Possible?

158

Richard Corry

7. Agent-Causal Power

189

Timothy O’Connor

8. Structural Properties Revisited

215

Alexander Bird

9. Causal Nominalism Ann Whittle

242

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contents

10. Why do the Laws Explain Why?

286

Marc Lange References Index

322 339

List of Contributors stephen barker is Associate Professor and Reader in Philosophy at the University of Nottingham. alexander bird is Professor of Philosophy at the University of Bristol. nancy cartwright holds professorial positions at both the London School of Economics and the University of California, San Diego. richard corry is Lecturer in Philosophy at the University of Tasmania. antony eagle is Lecturer in Philosophy at the University of Oxford, and Kneale Fellow and Tutor in Philosophy at Exeter College, Oxford. toby handfield is Lecturer in Philosophy and an Australian Research Council Postdoctoral Research Fellow at Monash University. marc lange is Professor of Philosophy at the University of North Carolina at Chapel Hill. jennifer mckitrick is Associate Professor of Philosophy at the University of Nebraska–Lincoln. timothy o’connor is Professor and Chair in the Department of Philosophy at Indiana University. ann whittle is Lecturer in Philosophy at the University of Manchester.

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1 The Metaphysics of Dispositions and Causes Toby Handfield

1.1 Introduction In explaining what happens, we commonly use both dispositional and causal concepts. A historian might refer to the belligerent disposition of a nation-state, and use this to explain why a neighbouring state was so anxious to seek an apparently unwise alliance. A physicist might have occasion to mention the disposition of a metal to expand when heated, and use this to explain why a measurement was inaccurate when taken in abnormally hot conditions. The contexts of explanation—physics and history—are very different, but the concepts are recognizably causal and dispositional in both cases. So philosophers of science, and epistemologists more generally, have ample reason to be interested in these concepts. What presuppositions do we bring to our causal and dispositional talk? Under what conditions might these concepts fail to explain in the way we would like them to? Are they truly universal in their application, or are they the sorts of concepts that ought to disappear once we have achieved a ‘mature’ science?¹ ¹ As Russell (1913) famously suggested was the case with respect to causation in physics.

 toby handfield Metaphysicians, also, have plenty to interest them in these concepts. What exactly are the referents of our disposition-talk and causation-talk? Should we be realists about causes and dispositions? Should that realism be tempered by a sort of reductionism, or should it appeal to some kind of primitive causal or dispositional feature of the world? In addition to the very tangible utility of dispositional and causal concepts in our empirical explanations, they are also of philosophical utility. When we turn to examine attempted conceptual analyses of all manner of phenomena, we frequently find causal and dispositional concepts playing a crucial role. For example, there have been attempts to analyse moral responsibility in terms of a disposition or capacity to choose in accordance with reasons.² There is a famous line of thought in the philosophy of language that attempts to analyse reference as a matter of causal links between our occurrent use of a term and the referent of that term.³ Along similar lines, there are causal theories of perception.⁴ Also, in both philosophy of language and philosophy of mind, some have thought that propositional attitudes such as belief and desire are obviously dispositional.⁵ Finally, in epistemology, causation and dispositions are neatly combined in the reliabilist approach, which analyses warrant as being caused by a reliable mechanism, where reliability is arguably a dispositional concept.⁶ So these concepts often appear together, and both are of marked importance in explaining the world around us, in both philosophical and experiential contexts. Moreover, philosophers have used the same, or similar, analytic approaches to understanding both concepts. Most prominently, it has been tempting to try to analyse both causal concepts and ² E.g., M. Smith 1997, 2003. ³ This idea is strongly associated with the work of Saul Kripke, for instance, though strictly speaking Kripke eschews any attempt to give an analysis of reference (1980: 93). ⁴ Grice 1961. ⁵ This idea has its ancestry in, e.g., Ryle 1949, but is best known in works such as Putnam 1975; Lewis 1972; and Armstrong 1981. ⁶ Goldman 1967.

the metaphysics of dispositions and causes  dispositional concepts in terms of counterfactual conditionals. In the case of causation, the basic thought is that an effect depends counterfactually upon its cause: had the cause not occurred, the effect would not have occurred also.⁷ For dispositions, the obvious thought is that if the object bearing the disposition were to find itself in suitable triggering circumstances, a characteristic manifestation would ensue.⁸ There is no consensus that such conditional analyses can succeed, for either dispositions or causation. However, it is rarely disputed that there is some sort of link between conditionals and dispositions, and between conditionals and causation. Sceptics about conditional analyses usually concede, for instance, that the truth of a certain conditional sentence may point to the instantiation of a dispositional property, a causal relation, or both. Given that there is some rough overlap, then, between these two notions, in the sense that both seem to be interestingly related to counterfactual conditionals, there is a prima facie case that the two are in fact metaphysically connected. But even if we are unconvinced concerning any such hard connection, there is still the thought that we might learn methodological lessons from comparing the two types of analysis. If the analysis of causation has progressed further than the analysis of dispositions, is this because there are techniques being used in the investigation of causation which are unknown to those studying dispositions? Part of the intent of this volume is to sketch a way for those working in different traditions—especially in philosophy of science and in metaphysics—to think about dispositions and causes more ecumenically. Characteristically in analytic philosophy, the papers collected here do not aim at any overt synthesis. A reader looking for a grand unified theory of dispositions and causation will no doubt be disappointed. But the papers are written with an eye to ⁷ See Lewis 1973a for the most influential proposal on these lines. ⁸ Conditional analyses of dispositions have recently been championed in, for example, Lewis 1997 and Mumford 1998.

 toby handfield drawing together the discourse of different sub-disciplines, and to uncovering common themes. In the remainder of this introduction, I shall first discuss, in Section 1.2, the prima facie case for accepting that dispositions and causes are deeply interrelated. In Section 1.3, I canvass some prominent ontological accounts of dispositions and causes and examine how these are connected in such theories. Finally, in Section 1.4, I briefly introduce each of the contributions to this collection, and indicate how they bear on the central themes surveyed here.

1.2 The prima facie case for interrelation Of course, many kinds of things can be said with conditional sentences. From the mere fact that conditionals of one sort have been used in an effort to analyse dispositions, and conditionals of a similar sort have been used in an effort to analyse causation, it does not follow that the underlying mechanisms are the same in all respects. However, there is a strong prima facie case that, at bottom, if there are natural necessities of any kind in the world, they are all to be understood as grounded in the same species of basic fact. Both causation and dispositions do seem to be concerned with some kind of natural necessity. Given the cause, the effect must happen—or at least must have a certain non-zero probability of happening. From the disposition and the stimulus conditions (if any are required), the manifestation must ensue—or at least must have a certain non-zero probability of ensuing. The connection, whether between cause and effect or disposition and manifestation, is not conceptual or a priori. It seems to be the result of a natural process, whose non-occurrence is conceivable without contradiction. But it also seems that there is some substantial connection between these events, and that they are not merely juxtaposed as a matter of coincidence. Whatever this ‘connection’ amounts to, it is plausibly the same in both sorts of case. This is not suggested as a self-evident metaphysical truth, but rather as a hypothesis worth exploring, if only because of the

the metaphysics of dispositions and causes  attractive prospect of unification that it opens up. The explicanda appear to be similar in both cases, even if, in both, it is hard to give a robustly satisfying account of what is happening. So it may be reasonable to proceed on the assumption that the very same metaphysical apparatus are in play in both cases. One way to mediate the required connection might be through laws of nature. Perhaps the thing which unifies dispositions and causes is that both must be backed by law. What then, are laws? We have become familiar with a number of answers to this question over recent years. Some argue for a sort of reduction of laws to facts about regularities.⁹ Others embrace a sort of non-reductivism, arguing that laws are constituted by higher-order nomic relations between properties.¹⁰ And others insist on a more primitivist account of laws.¹¹ In addition to those familiar options, however, another idea has risen dramatically to prominence in recent years: that laws are ultimately founded in the dispositional nature of basic properties. On this view, properties are essentially such as to confer certain causal powers or dispositions. A property like being massive, for instance, confers upon its bearers the power to resist acceleration. It also confers the power to generate gravitational forces—or to interact with the gravitational field. Because these powers are essential to the property of mass, lawlike truths, such as ‘masses attract in accord with the gravitational law’, are necessary rather than contingent. Such views have gone under a variety of names. Sometimes they are referred to as dispositionalist accounts of properties, or as dispositional essentialism.¹² Others have characterized closely related views as causal structuralism, or as the causal theory of properties.¹³ The general view in question is—at least in its usual formulations—at odds with Humean claims about the irreality of necessary ⁹ Lewis 1973b, 1983b, 1994a. ¹⁰ Armstrong 1978, 1983; Dretske 1977; Tooley 1977, 1987. ¹¹ Carroll 1994. ¹² Ellis and Lierse (1994) use the latter term for their position. Armstrong (1997) eschews such a view, but when criticizing it calls it a ‘dispositionalist’ account. ¹³ For causal structuralism, see Hawthorne 2001. For the causal theory of properties, see Shoemaker 1980, 1998.

 toby handfield connections. Many take this to be a very serious drawback. Others consider it to be solidly backed by empirical discoveries. Nonlocality in quantum mechanics, for instance, might be thought clearly to demonstrate that there are necessary connections spanning distinct spatiotemporal regions, so a Humean denial of necessary connections cannot be correct.¹⁴ This dispute aside, the causal theory of properties seems to suggest that the phenomena of causation and at least some lowlevel dispositional properties share the same ultimate ground: the essentially power-conferring nature of the basic properties.¹⁵ That said, no causal structuralist has gone very far towards advancing a detailed theory of causation, explicating it in terms of basic properties that are essentially power-conferring. So it is yet to be seen whether the wished-for unification of causation and dispositions in the metaphysics of properties can be achieved. 1.2.1 Finks, masks, pre-emption, and other nuisances There is another notable reason to think that an attempt to understand dispositions in terms of causes, or vice versa, might be useful. The sorts of counterexamples which have proved most problematic for an analysis of dispositions in terms of counterfactuals appear deeply similar to the counterexamples that have dogged the counterfactual analysis of causation. For dispositions, the paradigm counterexamples involve the manifestation failing to ensue despite the occurrence of the usual stimulus event, for one of two reasons: first, something might interfere with the causal process that normally connects stimulus and manifestation; or secondly, something might opportunely intervene to nullify the causal basis of the disposition, before it can be manifest. The first type of counterexample, known as a mask or an antidote, can be identified in many familiar phenomena of ¹⁴ See Loewer 1996 where this point is raised and the Humean claim reformulated to accommodate quantum entangled states. ¹⁵ This hoped-for unification has perhaps been most tantalizingly discussed in George Molnar’s posthumously published work, Powers (2003).

the metaphysics of dispositions and causes  everyday life.¹⁶ My pot plant is disposed to dry out if left in the sun. The attempted analysis in terms of a counterfactual would be: Were this pot plant left in the sun, it would dry out.

As it happens, the pot plant is left in the sun, but I mask this disposition by diligently watering it. So the antecedent is true, but the consequent is false. Nonetheless, the plant still has the disposition. The second type of counterexample is known as a fink.¹⁷ Suppose a man is disposed to become violent when he is drunk. Knowing this fact, his companion slips a sedative into his beer. When sedated, he will lose the disposition to become violent when drunk. The sedative, moreover, will sedate the man more quickly than the alcohol will make him drunk. Before drinking, then, the man has the disposition to become violent when drunk. But if he does become drunk—by drinking the beer—then he will first become sedated, and lose the disposition. The stimulus condition will occur, but the manifestation will not. In such a case any simple conditional analysis must fail. There are, of course, many efforts to overcome these and other problem cases in the literature. My aim here is not to survey the range of such attempts, but to draw out the structural similarity between cases of these sorts and cases of the sorts that trouble counterfactual theories of causation. There is a large variety of counterexamples to any attempted analysis of causation, and a corresponding array of ingenious proposals for defusing them. At the risk of falling into hasty generalization, however, it seems safe to say that the most recalcitrant sort of counterexample—at least for counterfactual analyses—is the case of late pre-emption.¹⁸ A well-worn example involves two children throwing rocks at a bottle. Both children throw with perfect accuracy. Billy, however, throws more slowly than Suzy. Suzy’s ¹⁶ Masks and antidotes are discussed in Bird 1998, Choi 2003, and Johnston 1992. ¹⁷ The idea of a finkish disposition is due to C. B. Martin (1994). An important later article on the topic is Lewis 1997. ¹⁸ Also known as ‘late cutting’. See Lewis 1973a: 200–7 and Menzies 1989.

 toby handfield rock hits and smashes the bottle. Obviously, Suzy’s throw is the cause of the bottle smashing. However, a simple counterfactual analysis of causation would say that Suzy’s throw is a cause if and only if: (1) Had Suzy’s throw not occurred, the bottle would not have smashed.

And this counterfactual is clearly false. The bottle would still have smashed, because Billy’s rock would have done the job. Now recall the case of masking that I put forward earlier. Unlike a pre-emption case such as we have just seen, in which the effect could have come about one way but in fact came about another way, the story of the pot plant is better described as a case of intervention. In order to stop the manifestation—a dry plant—coming about, I intervened in the causal process to obtain a preferable result. Similarly in cases of finkish dispositions: we cannot assimilate these to the paradigm of pre¨emption, because the finkishness means that a different effect comes about. So there is no obvious way to analyse cases of finkish or masked dispositions in terms of pre¨emption. On the other hand, at a stretch, it appears possible to identify masking in cases of pre¨emption.¹⁹ Consider the system involving Suzy’s rock and the bottle. The counterfactual which was false of this system, but which conveys the basic idea of causal dependence, is (1), above. Now suppose we were to try and associate that counterfactual with a disposition. We get the strange-sounding ascription ‘The system involving Suzy’s rock and the bottle is disposed to leave the bottle unbroken, if Suzy’s rock is not thrown.’ Though the locution is awkward, this does seem like a plausible ascription of a disposition to the system. Certainly, the disposition is not a fundamental one, but it is no less real for that. ¹⁹ This idea has been put forward by Stephen Yablo, in an unpublished paper, ‘Causation as a disposition to lose E on losing C’, presented at the Dispositions and Causes Conference, University of Bristol, 2005.

the metaphysics of dispositions and causes  Billy’s rock, then, represents a sort of mask for this disposition of the system. If you were to try to manifest the disposition—by asking Suzy not to throw her rock—the bottle would still smash. Billy’s rock interferes with the causal processes by which the disposition would otherwise become manifest. Such considerations strengthen the case for taking dispositions and causes to be somehow deeply interconnected. When you try to understand dispositions in terms of counterfactuals, you run into problems. When you try to understand causation in terms of counterfactuals, you also run into problems. Moreover, the problems seem to be of the same genus. A reasonable heuristic assumption, therefore, is that a correct understanding of dispositions would shed light upon the nature of causation, and vice versa.

1.3 Prominent accounts in the literature Let us consider, then, the relations between causation and dispositions in a few prominent metaphysical theories. 1.3.1 Lewis 1.3.1.1 Lewis on causation For David Lewis, causation is—in its most basic incarnation—a relation of influence between distinct events.²⁰ C influences E if and only if a relation of counterfactual dependence exists between them. The counterfactual dependence may be any of the following species: • How E occurs might depend on how C occurs. (Had the cause happened differently, the effect would have happened differently.) ²⁰ Lewis’s mature position is propounded in Lewis 2000. That paper represents the culmination of a program begun in his earlier, seminal paper, ‘Causation’ (Lewis 1973a). Descendants of the pre-emption problem mentioned above still afflict Lewis’s later position (Schaffer 2001a).

 toby handfield • When E occurs might depend on when C occurs. (Had the cause happened earlier or later, the effect would have happened earlier or later.) • Whether E occurs might depend on whether C occurs. (Had the cause not happened the effect would not have happened.) And in addition to these there may be hybrid forms of dependence: whether the effect occurs might depend on when the cause occurred, etc. To illustrate: whether and when conception occurs depends—among other things—on when, whether, and how copulation occurred. So there is a multifarious relation of causal influence between copulation and conception. For Lewis, then, facts about causal influence depend upon facts about counterfactuals. Counterfactuals in turn are analysed in terms of laws of nature: but more about these later. 1.3.1.2 Lewis on dispositions runs as follows:

Lewis’s analysis of dispositions (1997)

(2) x is disposed to give response R to stimulus S if and only if, for some intrinsic property B possessed by x, if x were exposed to S and were to retain B for an appropriate interval, x’s being B would be an x-complete cause of x being R.

The essential idea here is that, to have a disposition, an object must be such that it would manifest the response if exposed to the stimulus. In addition, this manifestation must ensue in virtue of an intrinsic property B which the disposition-bearer possesses. Finally, this idea of ‘in virtue of’ is captured by the thought that x’s being B is an x-complete cause of the manifestation. x-completeness simply captures the idea that no other intrinsic properties of x are required for the manifestation to occur. Obviously, the account involves counterfactuals. Moreover, it involves counterfactual claims about causation. An egg is disposed to break if struck because it has an intrinsic property which, if the egg were struck, would cause the egg to break.

the metaphysics of dispositions and causes

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A full understanding of Lewis’s metaphysics of dispositions and causation, therefore, requires a close look at the analysis of counterfactuals. 1.3.1.3 Lewis on counterfactuals Lewis is well known for championing a possible-worlds semantics for counterfactuals.²¹ Possible worlds are—at least at first blush—theoretical devices used for the semantics of modal languages.²² Something is necessary if true in all possible worlds, and contingent if true in some, but not all, possible worlds. Lewis argued that if we were to define a suitable metric of similarity between worlds, which we may call loosely ‘closeness’, we could analyse the counterfactual locution ‘Had it been that A, it would have been that C’ as follows: (3) The closest worlds where A is true are all worlds where C is true.

So a counterfactual such as ‘had I eaten eggs for breakfast, I would not have been so hungry at lunchtime’ is true if the closest possible worlds in which I ate eggs for breakfast are all worlds in which I am not so hungry at lunchtime. What makes for closeness of worlds? The details need not detain us here. The crucial point for our purposes is that the laws of nature play a very large (though not exclusive) role in determining closeness. Worlds with the same or similar laws are ipso facto very close. When evaluating a counterfactual like that above, we do not consider the possibility that in addition to eating eggs for breakfast, the laws of nature might have been very different, such that eggeating induces enormous hunger. A world like that is exorbitantly far from the actual world, and so is irrelevant to the truth of the counterfactual.²³ ²¹ See especially his 1973b and 1979. ²² I shall set aside the issue of the ontological status of possible worlds. See Lewis 1986b for his notorious defence of realism about possible worlds. ²³ But why think that in a world similar to this, except that I eat eggs for breakfast, there would be any difference in what happens at lunchtime? Surely a difference in what happens at lunchtime is itself going to count against the closeness of the worlds. A world where I eat

 toby handfield Thinking back to the sorts of counterfactuals that must be true for a thing to have a disposition, these counterfactuals evidently must be backed by laws of nature. The fragile egg that will break if struck must have this disposition in virtue of its intrinsic properties, but also in virtue of suitable laws of nature that dictate how things with the properties of eggs respond to being stressed. It is ultimately because these laws obtain that the counterfactuals are true. And much the same can be said about all cases of causation. It is because certain laws obtain that the right sorts of counterfactuals are true, and hence that certain pairs of events are related as cause and effect. It is in virtue of all manner of laws governing chemical and biological events that whether conception occurs depends on when and whether copulation occurs: so that relation of causal dependency itself depends on laws, as do all causal relations. 1.3.1.4 Lewis on laws What then, are these crucially important laws? It is here that Lewis’s neo-Humeanism becomes most evident. Laws of nature, for Lewis, are truths that play a central role in the best systematization of all contingent facts. The best systematization is one that is achieved using an appropriate language,²⁴ which is deductively closed and axiomatized, and which has an optimal trade-off between simplicity and strength (or optimal information content, in other words). The laws are simply the theorems of the best system established by such means.²⁵ eggs at breakfast, but thereafter everything is just as it is in the actual world, would surely be the closest one could get? Not so, for it would—claims Lewis—wreak havoc with the laws to make the history of the world ‘reconverge’ to the actual history, after a divergence such as egg-eating. So the divergence from actual events necessary to bring about an egg-eating can be achieved by a relatively minor violation of physical law, but it would require a much more significant violation of physical law to bring about a reconvergence to actual events. These issues are broached in Lewis 1973b: 75–7, but significantly developed in Lewis 1979. It should be noted that this account has been criticized as insupportable on our current understanding of physical laws (Price 1996: 148–52, Elga 2001). ²⁴ That is, one in which all the predicates involve only natural properties (Lewis 1983b: 41–2). ²⁵ The best-system analysis is first proposed in Lewis 1973b: 73–4. It is further refined in his 1983b: 41–3; 1980: 123–8; and 1994a: 231–6.

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The laws, then, ultimately depend upon the overall pattern of particular events. This is notably in contrast to the intuitive understanding of laws as determining the particular events: the Humean order of explanation reverses the intuitive order, in which the particular events depend upon the laws. Putting concerns with the counterintuitive relationship between laws and particular events to one side, what does Lewis’s account tell us about dispositions and causation? It says that both depend upon laws; and ultimately, this means that both depend upon the overall pattern of contingent events. 1.3.2 Armstrong 1.3.2.1 Armstrong on laws For present purposes, the most salient difference between Armstrong’s system and Lewis’s is that Armstrong has a radically different conception of laws of nature. Armstrong’s account of laws is intended to capture the intuitive order of dependency: laws of nature ultimately determining patterns among particular events. Armstrong claims that laws are relationships, not among events themselves, but among universals (or properties—I shall not make anything of the distinction here).²⁶ An initially helpful way to grasp the profound difference this makes at the level of ontology is to consider non-lawlike relations between properties. Suppose pink is a prettier colour than orange. And suppose also that every instance of pink is prettier than every instance of orange. We now have two purported facts: one about a relation between properties, the other about a relation between the instances of those properties. (4) Pink is a prettier colour than orange. (5) All instances of pink are prettier in colour than all instances of orange. ²⁶ This idea was first proposed by Armstrong in his 1978, then developed at more length in Armstrong 1983; and more recently in Armstrong 1997: chapters 15 and 16. A similar account of laws was independently advocated by Fred Dretske (1977) and Michael Tooley (1977, 1987).

 toby handfield Does (4) explain (5), or does (5) explain (4)? In the case of the present example, it is probably more plausible that the fact about the instances explains the fact about the properties. But if one grants for the sake of the example that pink and orange are real and basic universals, one might expect that the explanation runs from the universals to the instances. It is because of the relation between the colours themselves—the properties—that we observe the regularity among all of the instances. Supposing this sort of explanation is indeed possible, one can see how a relation of lawful connection between universals might generate an attractive and powerful explanation of the connection between instances of those universals. For Armstrong, it is in precisely this fashion that a law explains its instances. A pressing question for Armstrong is whether any of the connections he requires between universals obtain contingently. Quite plausibly, the sort of relation between universals suggested by (4) above is an internal relation. Given the nature of pinkness and the nature of orangeness, their relative prettiness is thereby determined. In order for these universals not to stand in this relation of difference in prettiness, there would need to be some change in the universals themselves. Hence it is plausible that the relation is essential to these colours, and (4) is a necessary truth. In Armstrong’s own articulation of the law-making relation, however, it appears that the very same universals could stand or not in such a relation as a matter of contingent fact. 1.3.2.2 Armstrong on dispositions For Armstrong, like Lewis, dispositions depend upon laws. Roughly, for something x to be disposed to R when S, is just for x to have some property φ and for there to be a law that all
φ & S-things are caused to manifest R.²⁷ ²⁷ Armstrong has also made much of an objection to accounts of dispositions which do not reduce them to categorical properties and laws. See Armstrong 1997: 79. For recent responses, see Bird 2005c; Handfield 2005.

the metaphysics of dispositions and causes

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Armstrong’s laws, like Lewis’s, can be said to ‘support’ counterfactual reasoning; and laws like this are enough to ensure something like a conditional analysis of dispositions. (Armstrong, though, is not committed to the success of any such conditional analysis.) 1.3.2.3 Armstrong on causation Standard causation, for Armstrong, is simply lawlike connection between properties, manifest in individual instances of those properties.²⁸ For example, suppose it is a law that salt dissolves in water. Whenever an instance of this dissolution occurs, there is a token of the lawlike relation between two complex properties: the property instantiated when solid salt is immersed in water and the property instantiated when salt is dissolved in water. This token relation just is an instance of causation.²⁹ So wherever laws are at work—at least in typical cases—there will be causation. Recall that dispositions are always backed by suitable causal laws: dispositions, then, involve causation whenever they are manifest. And causation and dispositions are intimately related through the common root of laws. Putting aside differences over the fundamental metaphysics of laws, we can see a striking convergence between Armstrong and Lewis in this regard. They agree that the manifestation of dispositions involves causation, and that both dispositions and causation ultimately depend on more basic laws of nature. 1.3.3 Dispositionalism In canvassing a third, dispositionalist account of dispositions and causes, I am reluctant to use a single author as an exemplar. For the breadth of vision evident in his work, Brian Ellis certainly stands out as the obvious candidate.³⁰ But there are two reasons for hesitating to conduct the discussion solely in terms of Ellis’s work. First, given ²⁸ Singular causation is also possible, but need not concern us here. See 1997: chap. 14. ²⁹ Armstrong 1997: 218–19. ³⁰ Ellis 1999, 2001, 2002; Ellis and Lierse 1994.

 toby handfield the apparent recent increase in interest in dispositionalism, there are a number of card-carrying dispositionalists in the market; but the differences between their theories are not yet clearly established, and it is not clear how tight a family they will form. Secondly, Ellis’s theory has a number of features which I take to be inessential for our purposes here. In much the same way as I disregarded Lewis’s modal realism, and ignored the debate between Armstrong and Lewis over the standing of universals, I wish here to avoid controversies over the existence of natural kinds, and over the need to embrace an all-pervasive essentialism of the sort that Ellis favours. I am not persuaded, however, that this sort of separation can be neatly effected without doing some injustice to Ellis’s views, so I propose not to take the risk. 1.3.3.1 Dispositionalism on dispositions and laws An important alternative to the views of Lewis and Armstrong is to suppose that the basic properties—what are frequently referred to as natural properties—are themselves essentially dispositional. That is, the properties which would be mentioned in a complete and ideal physical theory, including perhaps such familiar properties as mass and charge, are themselves essentially power-conferring properties. Necessarily, things which instantiate these properties would thereby have certain powers. For instance, mass confers the power to resist acceleration, and also the power to attract other masses in accordance with gravitational laws. This view entails that there is a special sub-class of dispositions—those associated with the natural properties—whose members are fundamental and irreducible. These dispositions are not analysable or reducible in terms of facts about laws and nondispositional properties. Rather, it is simply the nature of these properties to be dispositional. Other dispositions—those which do not seem to be relatively fundamental, but which are multiply realizable, macroscopic, and presumably reducible to something more basic—are prone to be understood by the dispositionalist in a way reminiscent of Lewis

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or Armstrong. These do depend upon the properties of the object which has the disposition, and the laws which govern the behaviour of those properties. This brings us, however, to the status of laws for a dispositionalist. Dispositionalism compels its adherents to accept that at least some of the laws of nature hold necessarily—not as a matter of conceptual or logical necessity, but as an a posteriori metaphysical necessity.³¹ This is because if mass (for instance) is essentially such as to confer the power to resist acceleration, then a statement asserting that things with mass resist acceleration is a necessary truth. So laws such as ‘F = ma’, which we may take to be describing with more precision the disposition of masses to resist acceleration, are similarly necessary. But not all laws are like that. Conservation laws and symmetry principles, for instance, appear not to have a form which would license our ascribing causal powers to natural properties. So on the dispositionalist account these laws may not hold as a matter of metaphysical necessity.³² Dispositionalism, then, radically overhauls the relationship between dispositions and laws. Instead of all dispositions depending upon contingent laws, at least some important dispositions are irreducible features of the natural properties. Moreover, the sorts of laws which are typically used to ground dispositions are—according to the dispositionalist—necessary laws: corollaries of something essential in the natural properties. 1.3.3.2 Dispositionalism on causation The dispositionalist account of causation is much less developed. The broad outlines of the strategy are clear: causation ought not to depend—in Humean fashion—on contingent laws that emerge from the global pattern ³¹ See Ellis 2001: 219–20; Molnar 2003: 199; and also, for further discussion, Bird 2005b and Bostock 2003. ³² This point is raised in Chalmers 1999; see Ellis 2001: §7.9 for an attempted explanation. For a related point, that dispositionalists cannot account for all natural necessities, see Fine 2002.

 toby handfield of events. Rather, in at least their most elementary form, causal relations must be a matter of certain powers—those which are essential to the natural properties—being manifested. One interesting dispositionalist proposal is due to Ellis (2001: 50): he proposes that there is an essential connection between at least the most fundamental dispositional properties and causal processes. The thought appears to be that different types of causal processes form natural kinds. So the process of salt dissolving in water is a natural kind, in that all instances of this process share objective structural features. Ellis’s suggestion is that such features are the dispositional properties which are the constitutive ‘grounds’ of such process-kinds. Perhaps a suitable analogy here is the way in which chemical elements are the ‘grounds’ of certain other natural chemical kinds. Just as you cannot have a protein without nitrogen, you cannot have a process of salt dissolving in water without water and salt! While this might appear to be a triviality, it hints at ways of articulating a dispositionalist account of causation. If there is this sort of link between fundamental causal powers and causal processes, then it might be natural for a dispositionalist to explore the sort of process-based theory of causation first inspired by work of Russell, and developed more recently by Wesley Salmon (1984, 1994) and Phil Dowe (2000).³³ (On Salmon’s account, however, a causal process itself is understood in terms of its distinctive disposition to ‘transmit a mark’. So there may be a final layer of dispositionality underlying any such account.) Whether or not such a project is fruitful, crucial issues for a dispositionalist theory of causation remain unexamined. Suppose a dispositional property becomes manifest in the following scenario: there is a certain basic property P, which confers the power to cause response R upon exposure to stimulus S. An object, ³³ In Handfield 2008 I attempt to use Ellis’s idea that dispositions are necessarily linked to processes to develop a theory combining some of the attractive elements of dispositionalism with the Humean commitment to avoiding necessary connections between distinct existences.

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x, instantiates P and is exposed to S at t1 —call this event ‘C’. Subsequently, at t2 , x instantiates R —call this event ‘E’. So we would—in normal circumstances—ascribe a causal relation to C and E. (6) x’s being P and S at t1 caused x’s being R at t2 . (C caused E.)

According to a more reductivist approach to causation, like that championed by Lewis, (6) is equivalent to a certain fact about E’s being counterfactually dependent on C. That counterfactual dependence in turn depends upon laws, which themselves depend upon the global mosaic of property instantiations. For dispositionalists, the question is how much of this Lewisian picture they must reject. Evidently, they can agree to the first step that a causal claim is equivalent to a counterfactual claim. It is in the further analysis of the counterfactual that the difference emerges. For the dispositionalist, whether or not such an analysis of the counterfactual goes via laws, it must not terminate in a global pattern of property instantiations. Rather, it will terminate in the essentially power-conferring natures of the basic properties. So on the sort of approach just sketched, a dispositionalist might co-opt much of the analytic work of Lewis, and his fellows in the counterfactual school of causation, but reject the Humean analysis of counterfactuals.³⁴ Another option is to reject the entire approach of analysing causation in terms of counterfactuals, and to argue—in similar vein to Armstrong—that causation requires some sort of real ‘physical’ connection between cause and effect. The obtaining of counterfactuals concerning C and E may be a reliable symptom of a case of causation, but cannot be constitutive of that causation. On this second route, however, we encounter a time-honoured and recalcitrant question: what is this ‘real connection’, and how ³⁴ This sort of approach might harmonize especially neatly with that of Ann Whittle (this volume), who attempts to treat essentially power-conferring properties in a nominalist fashion, as simply being the obtaining of conditional predicates.

 toby handfield does it relate to what is essential in the natural properties? It would be an unfortunate drawback of a theory if it required both the concept of a power and the concept of cause to be analysed, ultimately, in terms of primitive ideas that cannot be brought under any common explanatory umbrella. There is little explicit discussion of this sort of issue among dispositionalists. Certainly there is more temperamental affinity between dispositionalism and a primitivist, anti-Humean account of causation. But the matter seems to remain open. 1.3.4 Intrinsicness Another important issue that emerges from the debate between dispositionalists and their opponents is whether or not dispositions are intrinsic properties, and whether or not causation is an intrinsic relation. Despite its apparent intuitive familiarity, the correct analysis of the concept of intrinsicness has been a matter of recent debate.³⁵ Many attempts at definition suggest that an entity instantiates a property intrinsically if and only if the instantiation is independent of how things stand with any other distinct entities. So one way of trying to capture the idea of intrinsicness-as-independence has been to say that a property is intrinsic if and only if it is compatible with loneliness. That is, that a thing can have the property while being unaccompanied by any other contingently existing object.³⁶ Problems with this manner of analysis tend to arise when it is applied to properties that are unlikely to be natural—such as the property of loneliness itself. Obviously, loneliness is compatible with loneliness, but it is very doubtful that it is intrinsic! An alternative strategy for defining intrinsicness, then, is to make an initial presupposition that the most metaphysically basic ³⁵ For example, see Denby 2006; Francescotti 1999; Humberstone 1996; Langton and Lewis 1998, 2001; Lewis 1983a; Marshall and Parsons 2001; Vallentyne 1997; Weatherson 2001; Yablo 1999. ³⁶ This manner of definition is originally due to Kim (1982), and was developed by Lewis (1983a).

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properties—the perfectly natural properties—are all intrinsic.³⁷ One can then define duplicates as objects which share all of their perfectly natural properties. And a property is intrinsic if and only if it is necessarily shared between duplicates. The property of loneliness, then, is clearly not intrinsic, because any lonely thing has a possible duplicate that is accompanied. This approach, however, is metaphysically heavy-handed for two reasons: first, it supposes that there are perfectly natural properties. What if there were infinite complexity in a world, such that there were no perfectly natural properties, but rather never-ending levels of structure, leading us to ever more basic properties, without end?³⁸ Secondly, the account presupposes that all of the perfectly natural properties are intrinsic, which, though it is certainly an intuitive idea, might conflict with a dispositionalist conception of the world, as we shall see below. Whatever approach we take to defining intrinsicness, the concept is familiar enough when applied to monadic properties. The property being a triangle is readily understood as intrinsic,³⁹ and being within a metre of some triangle as extrinsic. When we try to apply the distinction to relations, there are some relations that are manifestly intrinsic (has greater perimeter than), and others that are manifestly extrinsic (has been photographed more often than). In addition, however, are so-called ‘external’ relations, such as is contained within and is one metre removed from, and it is not certain how these should be categorized. It is disputable, for instance, whether such relations are compatible with loneliness, because that will depend upon one’s metaphysical conception of space. Having raised this difficulty with external relations, I shall put it to the side, and simply assume that external relations are intrinsic.⁴⁰ With this introduction completed, we can ask how the various ³⁷ This is the strategy Lewis employed in his 1983b. ³⁸ A possibility of which Lewis was aware, and typically anxious to accommodate. See, e.g., Lewis 1986a. For sceptics about this possibility, the argument for infinite complexity is advanced with relish in Schaffer 2003. ³⁹ Pace Skow 2007. ⁴⁰ With some precedent: see e.g., Lewis’s treatment of relations: 1986b: 62.

 toby handfield theories treat dispositional properties and causal relations with respect to intrinsicness. 1.3.4.1 Intrinsicness of dispositions On a Lewisian theory (as indeed on most Humean theories), all dispositional properties are extrinsic. This is because the dispositions of a thing depend upon that thing’s being subject to a certain sort of law of nature, and, for Humeans, to be subject to a certain law of nature is just to be implicated in a certain global pattern of events—itself analysable as an extrinsic property. To illustrate: a particular cigarette has the disposition to produce smoke if lit. This is in virtue of laws about how the compounds in the cigarette will react in combustion, under conditions of sufficient but not abundant oxygen, at relatively low temperatures, and so on. Whether these propositions amount to laws, however, depends upon whether or not these propositions feature in the best systematization of contingent fact. It is possible that there be a cigarette which is a perfect duplicate of our particular one, but which exists in a world where there is little or no gaseous oxygen, and consequently where there are no events of cigarettes being lit. In such a world, it may not be a lawlike truth that cigarettes produce smoke if lit. So the cigarette might lack the disposition to produce smoke, despite being intrinsically perfectly similar to actual cigarettes. On an Armstrongian theory, it is not as easy to adjudicate whether or not dispositional properties are intrinsic. Like the Lewisian theory, having a disposition is a matter of having a property P, and that property being involved in a law such that P things give response R in circumstances S. In the simplest case, the law would have the form N((P & S), R). Being subject to such a law of nature, however, is less transparently an extrinsic property than it is on the Lewisian theory of laws. Putting aside the question of whether dispositions themselves are intrinsic, recall that, for Armstrong, laws of nature are relations of nomic connection between properties. These relations are external.

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Being external, relations of nomic connection are probably best thought of as intrinsic to their relata: presumably the relata could stand in such a relation, independently of what other things exist. Consequently, fiddling with the global mosaic of propertyinstantiations will do nothing to change whether P, S, and R stand in this relation, and there is no prospect of generating counterintuitive consequences of the sort shown above to arise from the Lewisian account of laws. So on the Armstrongian account, the nature of dispositions is not fully determined by how they are related to concrete particulars like events. However, it still remains possible that there be an intrinsic duplicate of some object O which is not subject to the same laws of nature that O is. This would simply be a matter of instantiating the same natural properties, but in a world where different relations of nomic connection obtain. So a thing’s dispositions depend upon relations to other distinct things, and in that sense dispositions are extrinsic. Finally, on a dispositionalist account, certainly some dispositions might be extrinsic. Non-natural properties, such as vulnerability, might depend on contingent external circumstances in such a way that intrinsic duplicates could differ with respect to these dispositions.⁴¹ But the sorts of properties which are a distinctive feature of the dispositionalist ontology—those conferred by the fundamental properties—look like excellent candidates to be intrinsic. In the first instance, using the Lewisian strategy of defining intrinsicness in terms of naturalness, it will follow by definition that these dispositions are intrinsic, because they are always shared by natural duplicates. But even on definitions that do not tie intrinsicness so closely to naturalness, it is not possible for two intrinsic duplicates to be subject to different laws of nature, because dispositionalists ⁴¹ Jennifer McKitrick (2003a) and Michael Fara (2001, 2005) have both argued for the nomic possibility of extrinsic dispositions in recent times, in the sense that intrinsic duplicates subject to the same laws of nature might differ in what dispositions they have. The nomic possibility of extrinsic dispositions was also evidently presupposed in earlier arguments by A. D. Smith (1977).

 toby handfield are necessitarian about the laws of nature: the laws could not have been otherwise. Hence the strategy of showing that a disposition is extrinsic by considering duplicates which, being in different worlds, are subject to different laws, will be ineffectual. That said, basic dispositional properties do not display complete independence from the existence of other entities or events.⁴² Given a disposition, given that it is exposed to its stimulus event, and given no interference, there is some sort of ‘compulsion’ about this situation which constrains what can happen. The nature of this constraint is easiest to describe if the disposition is deterministic: the manifestation must occur. But if the disposition is non-deterministic it is much harder to say what this constraint consists in. Certainly the constraint is not then very tight. In some sense, anything can happen: it is possible both that the power will manifest and that it will not. On the other hand, we find ourselves wanting to say things like ‘some things can happen more easily than others’. Supposing all dispositions to be probabilistic, then, the dispositionalist can make some case that powers are intrinsic in the sense that they are independent, and that this can be seen in the way the instantiation of a power is to a very large extent independent of what distinct events occur. On the other hand, there is the concern that this independence cannot be total. If it were, then what would distinguish these properties from categorical, non-dispositional properties? Most likely, it seems that a dispositionalist is better off plumping for a restricted account of intrinsicness, which relates it directly to naturalness, without supposing that intrinsicness involves independence. 1.3.4.2 Intrinsicness of causation On the na¨ıve conception of causation opposed by Hume, the truthmaker for a singular causal judgment is an intrinsic relation—a relation of ⁴² Brian Weatherson (2001) argues that the best prospect for defining intrinsicness is precisely in terms of a strong combinatorial independence. Following Weatherson’s approach, it appears that dispositions could not be intrinsic.

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power, energy, or necessary connection—holding as a local matter of fact; whereas on the Humean replacement conception the truthmaker is a complex extrinsic matter determined partly by spatiotemporal relations and partly by global patterns of occurrences in the form of regularities. (Menzies 1999: 313)

As Menzies states, the Humean conception of causation holds that the truthmaker for a causal statement is a matter extrinsic to the causal relata. This is well illustrated on Lewis’s theory. In much the same way as we saw that whether or not an object possesses a disposition depends upon extrinsic facts about the global distribution of properties, so too whether or not a particular sequence of events is causal depends upon that global distribution. So the striking of a match and the subsequent lighting, though causally related in this world, could have happened in precisely the same way—intrinsically speaking—without being causally related. The regularities we typically observe, whereby phosphorus and oxygen react under the stimulus of heat, do not occur in such a world, or at least do not feature in the optimal systematization of contingent fact. Hence there are no laws regarding the combustion of phosphorus, and the relevant counterfactual—‘had the match not been struck, it would not have lit’—is false. Armstrong, as a non-Humean, eschews this extrinsic account of the causal relation, and believes it to be an intrinsic relation (2004: 456). There are further idiosyncrasies of Armstrong’s account, such as his belief that this relation can be perceived, and that it is not necessarily law-governed. But other anti-Humeans, while retaining the core idea that the causal relation is intrinsic, adopt different attitudes to the matters of laws and perception.⁴³ The core feature of dispositionalist accounts of causation is that they all hold that the causal relation is at least sometimes intrinsic to the relata. Sometimes anti-Humeans appear to take the more heroic line that all causal relations are intrinsic; but this ⁴³ Others in this tradition include Anscombe 1971; Bigelow and Pargetter 1990; Fair 1979; Fales 1990; Tooley 1987.

 toby handfield has a serious drawback. It appears that the relations picked out as causal in ordinary talk very often include extrinsic relations. For instance, imagine a golfer who is trying to make a putt. At the last minute a kangaroo jumps onto the green, and is headed towards the ball. If no one intervenes the kangaroo will stop the ball entering the whole. However, a passer-by yells at the ’roo, causing it to swerve away from the ball at the last minute. The ball drops into the hole. Relieved, the golfer points to the passer-by and says: ‘That bloke caused my putt to go in!’ Unless one is prepared to analyse this as not a literal truth, or as not reporting a kosher causal relation, then it has all the appearance of a causal relation that is extrinsic. The truthmaker for the causal claim is not a ‘local matter of fact’ between the yell and the ball’s entering the hole. There is no credible way to construe the causal truthmaker as an intrinsic relation between these events.⁴⁴ Putting these hard cases aside, there are some instances of causation that appear susceptible to being understood intrinsically. Given the anti-Humean motives of a dispositionalist, one would expect such an account to be attractive. Such an account might go as follows: (7) C causes E if and only if: i. C occurs, ii. E occurs, iii. had C not occurred, E would not have occurred.

Conditions (i) and (ii) are both obviously true in virtue of properties intrinsic to the pair C and E. Moreover, for a dispositionalist, (iii) is made true by the nature of the natural properties instantiated in C. So, assuming that all natural properties are intrinsic,⁴⁵ (iii) is also true in virtue of properties intrinsic to C. Therefore the causal relation itself is intrinsic to the relata-pair. ⁴⁴ Schaffer 2004. ⁴⁵ Pace the worries raised about this proposal for dispositionalists above (§1.3.4.1).

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How well such an account can be defended is a matter that has not been adequately examined.

1.4 The papers The papers in this collection represent a diverse range of approaches to the central theme. In this section, I briefly introduce each of them. As already discussed, there is a live question as to the metaphysical relation between dispositions and causes. Jennifer McKitrick, in ‘Dispositions, Causes, and Reduction’, examines the prospects for a straightforward reduction of dispositions to causes, and vice versa. She argues that the prospects of a conceptual reduction, in either direction, are very poor. The attempt at a metaphysical reduction of dispositions to causes, she thinks, will likewise fail; but she concludes that it may be possible to metaphysically reduce causes to dispositions. Other papers in the collection are concerned with related issues of reduction. Antony Eagle, in ‘Causal Structuralism, Dispositional Actualism, and Counterfactual Conditionals’, critically evaluates the prospects of grounding metaphysical necessities in the dispositional nature of natural properties—an ambition of some dispositional essentialists. Eagle argues that the nature of counterfactual conditionals used to characterize dispositionality, being tolerant of exceptions and subject to extrinsic defeating conditions, makes dispositions incapable of grounding any substantive necessary truths. Steven Barker, in ‘Leaving Things to Take Their Chances’, advocates a novel reductionist proposal: to ground both dispositions and causes in chances. This promises to avoid the complications that have been encountered in the past, when dispositions and causation are understood—initially—via a deterministic paradigm, and we only later complicate our understanding by incorporating the possibility of probabilistic causes or dispositions.

 toby handfield The next two papers, by Nancy Cartwright (‘Causal Laws, Policy Predictions, and the Need for Genuine Powers’) and Richard Corry (‘How is Scientific Analysis Possible?’) engage in debate about the requisite ontology to explain the success of scientific inquiry. Both are attracted to a ‘three-level’ ontology. At the bottom are capacities, or properties otherwise understood in terms of their power to generate certain effects. The second level is that at which the capacities are exercised—what Corry calls ‘causal influences’. And finally, through the combined effect of the totality of influences, we see the manifest behaviour of the system. A paradigm example of such an ontology would be Newtonian mechanics, in which there is mass and its attendant capacities to attract other masses and to resist acceleration (at the bottom-level), forces between the masses (the exercise of mass’s capacities), and finally accelerations and changes in motion (manifest behaviour). Cartwright’s primary concern is to argue for the necessity of capacities: that without them the probabilistic generalizations we uncover (which she calls ‘causal laws’) are insufficient to guide our future interventions. Corry argues, first, that views such as Ellis’s dispositional essentialism are inadequate to capture the sort of invariant capacity that scientific analysis presupposes, and second, that Cartwright’s own account fails to be sufficiently realist towards the middle-level of the three-level ontology. The next two papers consider properties that appear—prima facie—to pose difficulties for dispositionalists hoping to give a relatively unified ontology. Timothy O’Connor examines, in ‘Agent-Causal Power’, what sort of causal power is required to explain the phenomenon of free will. O’Connor argues that agentcausal power must be understood as an emergent power, arising from the arrangement of the physical parts of the agent, without being reducible to a purely physical cause. He then tries to show how such an emergent power could be accommodated within a dispositionalist metaphysic.

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(The issue of emergence is also raised in Corry’s paper. Corry acknowledges the empirical possibility of emergence as a threat to the scientific method of analysis, and consequently as a threat to the ontological generalizations he makes. O’Connor’s paper thus throws some light on the sort of phenomena we might expect to be most resistant to scientific inquiry.) Alexander Bird considers another threat to dispositional monism: the possibility that structural properties are non-dispositional. In ‘Structural Properties Revisited’, he examines how to settle the question of whether or not structural properties—such as relations of spatiotemporal displacement—are dispositional or not. He concludes that the prospects of a background-free physical theory—recently championed by some physicists—are encouraging for dispositional monists, as it would appear that backgroundfreedom of a theory constitutes grounds to think that all properties mentioned in it can be characterized dispositionally. Also examining options for a dispositionalist ontology, Ann Whittle, in ‘Causal Nominalism’, suggests that the dispositionalist idea of individuating properties by their essential causal powers be adopted, but without a commitment to realism about universals or tropes. Rather, properties can be understood in a nominalistic fashion, as sets of objects, unified by their dispositional–functional role. Having outlined her account, Whittle proceeds to weigh its plausibility in the light of several objections, such as allegations that the account suffers from vicious circularity, or that it has an unattractive similarity to Rylean behaviourism. Finally, Marc Lange’s paper (‘Why Do the Laws Explain Why?’) is primarily about laws of nature. He argues that laws are best accounted for as a set of counterfactual truths that have a property of ‘stability’ which is a sort of robustness under other counterfactual suppositions. What makes Lange’s paper of direct relevance to the themes of the collection is that his preferred account of laws inverts the ordinary relationship between laws and subjunctive conditionals. For Lange, the conditionals are basic, and explain the laws.

 toby handfield This has some affinity with the dispositional essentialist project, but is less metaphysically burdened by claims about essential natures of properties. Indeed, it most closely resembles Whittle’s nominalist version of dispositionalism, with its pared-down ontology of properties as sets of objects characterized by functional role.

2 Dispositions, Causes, and Reduction Jennifer McKitrick

Dispositionality and causation are both modal concepts which have implications not just for how things are, but for how they will be or, in some sense, must be. Some philosophers are suspicious of modal concepts and would like to make do with fewer of them.¹ But what are our reductive options, and how viable are they? In this paper, I try to shut down one option: I argue that dispositions are not reducible to causes. In doing so, I try not to prejudice the issue by assuming a particular analysis of causation or dispositions. I make the following minimal assumptions about dispositions: they are properties of objects which have characteristic manifestations that occur in certain circumstances, and an object can have a disposition outside of the circumstances of manifestation and hence without the manifestation occurring. I think of causation primarily as a relation between events, though there can be true causal generalizations, and objects might be causes. In Section 2.1, I will try to clarify what it means for one kind of thing to reduce to another. I will then argue in Section 2.2 that dispositions do not conceptually reduce to causes, and in Section 2.3 that dispositions do not metaphysically reduce to causes. ¹ A major motivation for reducing modal concepts is actualism, the view that everything that exists is actual (E. W. Prior 1985: 11–28).

 jennifer mckitrick In Section 2.4, I explore other reductive possibilities, in particular that causes reduce to dispositions.

2.1 Reduction In saying ‘dispositions reduce to causes’ one might mean any of the following: We can define disposition terms with causal terms. Disposition statements can be systematically replaced by causal statements. Causes explain everything dispositions explain. Dispositions can be described completely in terms of causes. Causal statements entail dispositions statements. Disposition facts are nothing over and above causal facts.

These are very different claims concerning different issues, from what our words mean, how we should talk, what explains what, to the relations between facts, what exists, and what the world is really like. It is helpful to distinguish at least three different kinds of reduction in this context: Conceptual/Analytical Reduction of A’s to B’s occurs when we can adequately define A’s in terms of B’s, or systematically replace A-talk with B-talk, etc.² Epistemic/Explanatory Reduction of A’s to B’s occurs when why-questions about A’s can be answered with B’s alone, and/or when B’s explain everything that A’s explain.³ Metaphysical Reduction of A’s to B’s holds when A’s are nothing more than B’s.

If we want to rule out symmetrical reduction, we can add a ‘not vice versa’ clause to each kind of reduction, though in the case ² According to Carnap 1938, ‘If now a certain term x is such that the conditions for its application (as used in the language of science) can be formulated with the help of the terms y, z, etc., we call such a formulation a reduction statement for x in terms of y, z, etc., and we call x reducible to y, z, etc.’ (397). ³ According to Garfinkel 1981, ‘to say that something is reducible to something else is to say that certain kinds of explanations exist’ (443).

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of conceptual reduction, it’s not clear if definitions or systematic replacement should be asymmetrical.⁴ Philosophers discuss other varieties of reduction, such as nomological or inter-theoretic reduction (E. Nagel 1961: 336–97) but since dispositions and causes are not laws or theories, these are not the kind of reduction at issue. We can further explicate the notion of metaphysical reduction in terms of global supervenience (Kim 1993: 68–70). To say that dispositions globally supervene on causes is to say, roughly, there cannot be a difference in dispositions without a difference in causes; any possible world with the same causes must also have the same dispositions. If dispositions don’t globally supervene on causes, they aren’t metaphysically reducible to causes. If two worlds have all the same causes, but different dispositions, then the disposition facts are something over and above the causal facts—no metaphysical reduction. While global supervenience might be necessary for reduction, it is not sufficient. Global supervenience is a reflexive relation; reduction is thought to be irreflexive.⁵ So, while A’s globally supervene on A’s, A’s don’t reduce to A’s. Furthermore, even if a set of properties A globally supervenes on a distinct set of properties B, that might not be because A’s reduce to B’s, but because A’s and B’s independently reduce to the same thing. Though conceptual, explanatory, and metaphysical reductions are distinct, they are closely related. They all contribute to a more economical ontology, decreasing the number of fundamental concepts, explanatory hypotheses, or kinds of things thought to exist in the world. If A’s reduce to B’s in one way, they tend to reduce in other ways as well. If we can systematically replace A-terms with B-terms without loss, that suggests that each A-term ⁴ Trout 1991 points out that the correspondence rules used for reductions typically involve identity statements, but since identity is a symmetrical relation, this won’t do for intertheoretic reduction, for example (387). Putnam and Oppenheim’s 1958 characterization of microreduction (reduction of kinds of things into their constituents) includes an asymmetry clause ‘if B1 reduces to B2 , B2 never reduces to B1 ’ (407). ⁵ For example, Putnam and Oppenheim 1958 stipulates that microreduction must be irreflexive as well as assymetrical (407).

 jennifer mckitrick and each corresponding B-term are both picking out the same things in the world, so A’s are nothing more than B’s. It would also seem to follow that B’s can explain everything that A’s can. But we could have metaphysical reduction without conceptual or explanatory reduction. The B’s to which the A’s reduce might be so complex and complicated that a replacement of A-talk with B-talk, or an explanation of A’s in terms of B’s, might be a distant hope or practically impossible. Molecules might be nothing over and above strings, even if we can’t explain molecules in terms of strings or replace molecule-talk with string-talk. In what follows, I’ll address conceptual and metaphysical reduction of dispositions to causes, and raise points about explanatory reduction along the way.

2.2 Conceptual reduction Can we define dispositions in terms of causes? Not in any simple way. Clearly, ‘disposition’ and ‘cause’ do not have the same referent, like ‘water’ and ‘H2 O’. Dispositions and causes are different kinds of things: A cause is an event, causation a relation between events; a disposition is a property of an object. To see why this is a problem for simple conceptual reduction, consider a flat-footed definition of ‘disposition’ in terms of causation: Def 1: What it is for an object to have a disposition is for one event to cause another.

Obviously, one can’t adequately define an object having a property in terms of two events standing in a relation. A better attempt would introduce some parallelism by attributing both having a disposition and being a cause to the same thing: Def 2: Object x has a disposition iff x causes something.

Or, if you think that objects aren’t causes but events are, you can say: Def 3: x has a disposition iff x is involved in an event which causes another event.

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While these analyses are slightly more plausible, they are still inadequate. An object can have a disposition even if it neither causes anything nor is involved with any event that causes anything. For example, a match can be flammable even if it never ignites. The most obvious fix is to say: Def 4: x has a disposition iff x is disposed to cause something.

But this is circular and non-reductive. The same goes for ‘being prone to cause’ ‘having the tendency to cause’ etc. These are merely synonyms for ‘disposed to cause’. We might try to define ‘being disposed to cause’ as follows: Def 5: x is disposed to cause a type of event iff it is such that x would cause that type of event in certain circumstances.

Ann Whittle espouses a similar analysis of dispositional properties in ‘Causal Nominalism’ (this volume). The similarity is not immediately obvious, since Whittle’s main proposal, that ‘properties could be reduced to facts about particulars and causation’ doesn’t mention reducing dispositions to causes. However, Whittle equates having certain causal powers with standing in certain causal relations, and so her reduction of properties to causal powers is, at the same time, a reduction of powers to causal relations. She says: According to causal nominalism, a is F if and only if a has certain causal powers. Put another way, we can say that a is F if and only if a would stand in certain causal relations, given certain circumstances. (p. 245 this volume)

While Whittle presents the move from properties to causes as one reductive step, we can focus on the second part of that step—the reduction of causal powers to causal relations, as the one at issue in the present paper. If we think of F as dispositional, as it is for Whittle, her suggestion that ‘a is F if and only if a would stand in certain causal relations, given certain circumstances’ is essentially that of Def 5.

 jennifer mckitrick This is the most plausible definition considered so far, and it isn’t obviously circular. But notice that dispositional statements have not been reduced to statements about actual causes, but to conditional causal statements. In other words, dispositions haven’t been defined in terms of actual causes, but in terms of ‘wouldbe’ causes. If the reductionist isn’t committed to any such entity as a ‘would-be cause’, how are we to understand these conditional causal statements? What does it mean to say, not that an object caused or is causing an event, but that the object would cause that event in certain circumstances? One might have thought that to say ‘an object would cause an effect in certain circumstances’ is just to say ‘the object has a disposition to cause that effect in those circumstances’. This intuition is perhaps a consequence of the conceptual connection proposed by Def 5 between having a disposition and being something that would cause an effect. Though the definition isn’t blatantly circular, it seems reasonable to expect that the reductionist should have something to say about the relation of actual causes to wouldbe causes, a task which seems quite similar to that of saying something about the relation of causes to dispositions. The analysis is not complete without some account of conditional causal statements. Similar remarks pertain to slightly more complex analyses which construe a disposition as a property of having some property or other that meets a certain causal specification. According to a ‘secondary property’ account of dispositions: Def 6: x is disposed to cause a type of event iff x has a property F which is such that F would cause (or would be causally relevant to) that type of event in certain circumstances.⁶

Again, what does it mean to say that a property is such that it ‘would cause’ or ‘would be causally relevant’ to some event? These expressions suggest that the property has some causal power, ⁶ A similar account is discussed by Johnston 1992: 229.

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which would seem to make the property dispositional in some sense. If this is right, being disposed is defined in terms of having a dispositional property, which makes the definition more circular than it first appears. On the other hand, one may argue that saying that a property ‘would cause’ or ‘would be causally relevant to’ something is not to say that it has causal powers, but rather that it is subsumable under some causal law. This idea of how to think about conditional causal statements suggests another definition of ‘disposition’: Def 7: x is disposed to cause an event of type G iff x has some property F and there is a causal law that F’s in circumstances C are necessarily followed by G’s.

This is similar to Armstrong’s position (in Armstrong, Martin and Place 1996). Disposition ascriptions are not reduced to singular causal statements, but to ‘categorical’ (non-dispositional) properties and general causal laws. This avoids the suspicion of circularity, but introduces a new modal notion into the analysans, causal laws. I will discuss the metaphysical reduction of dispositions to non-dispositional properties and laws in Section 2.3. 2.2.1 Dispositions, causes, and conditionals Notice that definitions 5 and 6 employ conditionals in their causal analyses of dispositions. Of course, using conditionals to analyze disposition ascriptions is nothing new (Carnap 1936: 444–5; Ryle 1949: 43; Dummett 1978: 50). According to a familiar conditional analysis of dispositions: Def 8: x has a disposition iff if x were in certain circumstances, x would exhibit a certain manifestation.

Since causal statements have often been analyzed in terms of conditionals as well, it may be helpful to consider how conditional analyses of causation and conditional analyses of dispositions

 jennifer mckitrick are related. Consider a counterfactual analysis of causal dependence: Def 9: (i) (ii) (iii)

e causally depends on c iff: c and e both occur, c and e are distinct, and if c hadn’t occurred, e would not have occurred (Lewis 1973a: 165–7).

There are three important differences between definitions 8 and 9. Def 8 is about a relation between an object and a property, while Def 9 is about a relation between two events. It is also significant that Def 8 employs a subjunctive conditional where Def 9 employs a specifically counterfactual subjunctive conditional. This is because, in the analysis of ‘disposition’, the antecedent of the conditional is not necessarily contrary to fact since the circumstance of manifestation can obtain whilst the object has the disposition, but the antecedent of (iii) is necessarily contrary to fact since, if it were true that c had not occurred, there could be no causal dependence of e on c. Relatedly, no equivalent of clause (i) occurs in Def 8, since no such condition is necessary for an object to have a disposition: A thing might have a disposition to cause an effect even if that effect never occurs. Despite these differences, there are certain similarities, which can be summarized as follows: To accept conditional analyses of both causes and dispositions is to hold that disposition facts are a matter of certain conditionals being true about objects, while causal facts are a matter of certain conditionals with false antecedents and consequents being true about events. So, why not reduce dispositions to conditionals? Some philosophers, such as Martin (1994), Johnston (1992), and Lewis (1997), claim that simple conditional analyses of dispositions have been conclusively refuted by a number of counterexamples. One such counterexample is ‘masking’. Imagine a fragile glass that is packed so that it has internal supports that would prevent the glass from warping and therefore from shattering when struck. This glass has a host of intrinsic duplicates which are unprotected, and which are occasionally struck and broken. If you struck the packed glass, it

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would not shatter. The ascription of the disposition is true—the glass is fragile—but the counterfactual claim is false. Another purported counterexample to the conditional analysis is ‘finkish’ dispositions. Lewis 1997 critiques the following simple conditional analysis of dispositions: (SCA) (A) x is disposed at t to give response R to stimulus S iff (B) if x were to be subject to S at t, x would give R.

Once we note that things can acquire or lose dispositions, we can generate counterexamples by supposing that dispositional changes occur at inopportune times and ways. Lewis’s example of a finkish disposition is the fragility of a glass which is protected by a wizard who will immediately render it non-fragile if it is ever struck. A real-world example of a finkish disposition is the instability of the DNA molecule. DNA is susceptible to breaking up due to forces such as radiation and heat. However, forces which would break the molecule also trigger mechanisms within the cell nucleus that maintain the molecule’s structure (Tornaletti and Pfeiffer 1996). An object has a ‘finkish disposition’ if that object has a disposition which it loses in what would otherwise be the circumstances of manifestation. In other words, the same S that would cause x to elicit R instead causes x to lose its disposition D before it can elicit R. In this case, (A) is true: The thing does have the disposition. But (B) is false: If x were to undergo S, it would not give R. So, the analysis fails to state a necessary condition for x’s having a disposition. Johnston (1992) considers a similar type of counterexample he calls ‘altering’. A glass swan is fragile, but a vigilant monitor is equipped with a laser beam and will rapidly melt the swan the moment it would be struck. The conditional is false, but the swan is fragile. Another example is the shy, but intuitive chameleon (Johnston 1992: 231). The chameleon is green and thus disposed to look green, but before anyone can turn on the light and look at it, it blushes red. In both these cases, the conditions of manifestation are such that, if they were realized, the object would ‘alter’ and lose its disposition.

 jennifer mckitrick A related case is a finkish lack of a disposition. When green, the chameleon does not have the disposition to appear red, but when the circumstances of manifestation occur, the chameleon acquires that disposition. In this case, an x which doesn’t have D gains D when exposed to S, and subsequently gives R. Arguably, (A) is false: x does not have the disposition. However, (B) is true: if x were to be subject to S at t, x would give R. This shows that the analysis fails to state a sufficient condition for x’s having a disposition. If both disposition ascriptions and causal statements could be analyzed in terms of conditionals, then they would have similar, but different reduction bases: Dispositions would reduce to subjunctive conditionals about objects, and causes would reduce to counterfactual conditionals about events. This would not go to show that dispositions reduce to causes, but it may satisfy the urge to reduce modal concepts in whatever way works. But it’s far from clear that this way will work. Both conditional analyses of dispositions and causation continue to gain critics.⁷ What about defining dispositions in terms of both conditionals and causes as definitions 5 and 6 do? Well, if a conditional analysis of dispositions were adequate, there would be no need to add causes. And if finks and masks show that a conditional analysis cannot work, adding causes will not help. The counterexamples work just as well against causal conditional analyses as they do against the simple conditional analysis. For example, according to Def 5, what it is for a glass to be disposed to break is for the glass to be such that it would causally contribute to a breaking event in the circumstances of striking. But when the glass is well-padded, or protected by the wizard, the glass doesn’t causally contribute to breaking when it’s struck, since it doesn’t break at all. ⁷ For critics of conditional analyses of dispositions, see Bird 1998; Mumford 2001; Choi 2003. For a survey of objections and replies to counterfactual analyses of causation, see Collins, Hall, and Paul 2004.

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Lewis’s revised conditional analysis (RCA) is a causal conditional analysis that was specifically designed to overcome finks. A slightly simplified version of the account (1997: 157) goes as follows: (RCA) x has a disposition at time t to give response m to circumstances C iff x has intrinsic property B, and if x were to be in C at time t and retain B, then B and C would cause event m.

According to RCA, the activating conditions and an intrinsic property of the bearer of the disposition jointly cause the manifestation of a disposition. In a finkish case, something causes the object to lose the relevant intrinsic property, and subsequently to lose the disposition. The condition that the object retains the intrinsic property is not satisfied by objects with finkish dispositions, and so they pose no counterexample to RCA. The condition that the object must have the intrinsic property is not met by the reverse finks, so that counterexample is defeated as well. RCA reduces dispositions to counterfactuals and causes. Lewis’s analysans also features would-be causes, but Lewis has resources for explaining them (1973a, 1986b). The basic form of a conditional causal statement is: If x were to occur, x would cause y.

Using possible-worlds semantics for counterfactuals, this becomes: In the closest possible world where x occurs, x causes y.⁸

Employing the counterfactual analysis of causation, you get: In the closest possible world where x occurs (call it W ), y occurs, and if x didn’t occur in W , y wouldn’t have occurred in W .⁹ ⁸ I am simplifying here. More accurately, on Lewis’s view, the sentence would get analyzed as ‘Either there is no close enough world where x occurs, or there are close enough worlds where x occurs, and in all of the closest possible worlds where x occurs, x causes y’ (1973b: 16). I continue with my simpler Stalnaker (1968) semantics below, since nothing hangs on these details. ⁹ I am simplifying here as well, since the counterfactual analyzes causal dependence, and causation is the ancestral of causal dependence (Lewis 1973a: 167).

 jennifer mckitrick Applying possible-worlds semantics for counterfactuals again, we derive: In the closest possible world where x occurs (call it W ), y occurs, and in the closest possible world to W where x does not occur, y does not occur.

So, RCA comes to: x has disposition D at time t to give response m to circumstances C in world W iff (i) x has intrinsic property B, and (ii) in W ∗ (the closest possible world to W where C obtains at t and x has B at t) m occurs, and (iii) in the closest possible world to W ∗ where C does not obtain at t or x does not have B at t, m does not occur.

In other words, Lewis can reduce disposition statements to counterfactual causal statements, then to purely counterfactual statements, and ultimately to statements about events in and similarity relations among possible worlds. Though Lewis can ultimately reduce causes and dispositions to categorical properties in possible worlds, he reduces disposition statements to causal statements along the way, and thus his view is one of the targets of this paper. Though Lewis has an account of conditional causal statements and an answer to the finkish counterexample, the analysis can be contested on at least three grounds: (1) It assumes that all dispositions have causal bases and (2) that these causal bases are intrinsic; and (3) it does not address the masking counterexamples. Taking up the second objection first, I have argued elsewhere that dispositions are not necessarily intrinsic to the objects that have them (2003a). Contrary to Lewis, perfect duplicates could differ with respect to having certain dispositions; a thing can lose or acquire dispositions without changing intrinsically. Weight may be dispositional, but it’s not intrinsic. The weight of an object is

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relative to the object’s gravitational field. According to RCA, weight would be defined as follows: An object weighs 100 lbs, i.e., has a disposition at time t to give a reading of 100 lbs in circumstances of standing on a standard scale iff it has an intrinsic property B, and if it were to stand on a standard scale at t and retain B, then B and standing on the scale would cause a 100 lbs reading.

But if the object stood on the scale on the moon at t, its intrinsic properties plus standing on a scale would not cause a 100 lb. reading. One might object that being subject to a certain gravitational field is part of the circumstances of manifestation of weighing 100 lbs. However, this is not in accord with the meaning of ‘weight,’ if ordinary usage is any guide. A visit to the ‘Your Weight on Other Worlds’ website amply demonstrates this.¹⁰ The site asks ‘Ever wonder what you might weigh on Mars or the Moon? Here’s your chance to find out.’ If the circumstances of manifestation of your weight included being in the Earth’s gravitational field, there would be no cause to wonder what you weigh on the moon. I have also argued elsewhere that dispositions do not necessarily have causal bases; there can be ungrounded or ‘bare’ dispositions (2003b). RCA fails to extend to such dispositions. I argue that it neither follows from the concept of a disposition nor from the idea that disposition claims must have truthmakers that dispositions necessarily have causal bases. Others such as Molnar (2003) and Mumford (2005a) attempt to identify a class of ungrounded dispositions in the fundamental properties of subatomic particles. Molnar argues that the nature of these particles is exhausted by their dispositionality, and extensive experimentation has revealed no deeper structure to serve as the intrinsic properties to ground these dispositions (131–2). RCA would seem, therefore, to be inapplicable to the most fundamental properties of the physical world. ¹⁰ www.exploratorium.edu/ronh/weight/

 jennifer mckitrick In addition, RCA still faces the problem of masking. Consider the glass that is carefully packed. According to RCA, to say the glass is fragile is to say that it has some intrinsic property B, and if it were to be in circumstances of striking at time t and retain B, then B and striking would cause breaking. However, the carefully packed glass retains its intrinsic properties, but its intrinsic properties and the striking do not cause the glass to break. I haven’t considered every attempt to conceptually reduce dispositions to causes, but some lessons seem to be emerging: A straightforward definition of dispositions in terms of actual causes is a non-starter. Definitions that do justice to dispositional concepts rely on dispositional or other modal concepts, such as counterfactuals, in addition to causation. But when theorists add conditionals to a causal analysis, they inherit the well-known problems which plague conditional analyses.

2.3 Metaphysical reduction So, what about metaphysical reduction of dispositions to causes? We’ve already seen that dispositions and causes are different kinds of things, so it is not plausible to say that disposition are ‘nothing but’ causes. But perhaps once you have all the causes in the world, you don’t have to add anything else to get the dispositions. Recall that, in order for dispositions to be metaphysically reducible to causes, dispositions must globally supervene on causes. So, do dispositions globally supervene on causes? Here are some reasons to think they might. Consider the question: ‘when, if ever, is one warranted in making a disposition claim?’ To begin to answer that question, you might reason as follows. We are entitled to say that something has a disposition before, and even if it never manifests that disposition. The glass doesn’t have to break in order for us to be justified in claiming that it is fragile. We are correct to say the match is flammable before we strike it. So we don’t have to base our disposition claims on what a thing has caused, or does cause. In those cases, we reason from

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other similar cases: Things of this type have acted like that in these circumstances in the past; therefore, this thing is disposed to act like that in these circumstances.¹¹ So, if we live in a world in which a type of thing has never acted in a particular way, it is hard to see how we could ever be entitled to believe that something of that type is disposed to act in that way. Different causal sequences will warrant different disposition claims and identical histories will warrant the same disposition claims. This suggests that possible worlds which agree on causal facts must agree on disposition facts; global supervenience, a necessary condition for reduction, seems to hold. However, while this line of reasoning might justify explanatory reduction, it is a bit out of place in arguing for metaphysical reduction. The question of which disposition claims we are justified in believing is different from the question of which disposition claims are true—which dispositions things have. Things in this world have not been subject to every possible circumstance. We can, at best, imagine what some of these circumstances would be like, and the way familiar things would behave in these circumstances. We have few if any justified beliefs about these dispositions, yet it seems reasonable to say that things have dispositions we don’t know about. If these dispositions have never been triggered, then perhaps there is a possible world with the same history as ours, in which these latent dispositions are different. That would be a case of two worlds agreeing on the causes, yet disagreeing on dispositions—a counterexample to global supervenience, and thus reduction. The reductionist might reply that he can establish global supervenience without taking the route through justification that provoked my objection. He might appeal to Humean supervenience, claiming that the things that make causal statements true are arrangements of local matters of fact, sequences of events, or ¹¹ Quine 1969 makes much the same point when arguing that disposition ascriptions require a prior conception of similarity (166).

 jennifer mckitrick patterns—A’s always being followed by B’s, regular succession in space and time.¹² Furthermore, the reductionist may claim, these are the very same things that determine which dispositions things have. Thus it would be impossible for two worlds to agree on causal facts but disagree on disposition facts. A necessary condition for reduction, global supervenience, is met. This is a more direct defense of metaphysical reduction of dispositions, but reduction to what? Notice, the metaphysical picture which supports global supervenience of dispositions on causes is not that of reducing dispositions to causes, but one of reducing both dispositions and causes to something else. Again, a reductionist might be happy with this result, but that is not the thesis at issue here. Furthermore, there’s reason for thinking that dispositions don’t globally supervene on causes at all. Intuitively, we can describe different possible words which agree on causes, but disagree on dispositions. Our world and the one like it with different latent dispositions were two such worlds. Or, consider two worlds, one containing, among other things, a certain particle, the other nearly identical world containing another version of the particle in that world. But one of the particles has a certain disposition that the other lacks. Suppose the two worlds are exactly similar with respect to causes and effects. In particular, they are alike in that the particles never find themselves in the circumstances of manifestation for the disposition in question. (They may find themselves in many other circumstances and do many things, but they are never in the circumstances that trigger this particular disposition.) These worlds agree on the causal facts, but disagree on the disposition facts.¹³ The ¹² As Lewis puts it, ‘Humean supervenience is named in honor of the great denier of necessary connections. It is the doctrine that all there is to the world is a vast mosaic of local matters of particular fact, just one little thing and then another’ (1986c: ix). See also Loewer 1996. ¹³ This example is similar to one used in Tooley 1977 to support the idea that there could be underived, uninstantiated laws. He imagines ‘the universe containing two types of particles that never meet’ which nevertheless have laws that would govern their interaction (671). I would add that these particles would also have unmanifested dispositions.

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same feature of dispositions that caused a problem for conceptual reduction causes a problem here: an object can have a disposition even if that disposition never gets triggered. So, disposition facts don’t globally supervene on causal facts. But perhaps dispositions supervene on singular causes plus nondispositional properties. In that case, worlds which agree on the distribution of non-dispositional properties and causes necessarily agree on dispositions. But that would be true if dispositions supervene on nondispositional properties alone. Whatever you think of causation, if you think dispositions reduce to non-dispositional properties, you’re going to think worlds with the same non-dispositional properties have the same dispositions. A fortiori, you’re going to think that worlds with the same non-dispositional properties and causes have the same dispositions. Showing that dispositions supervene on causes plus non-dispositional properties does not show that dispositions reduce to causes. Secondly, if, as I and others have argued, ungrounded dispositions are possible, then there are possible worlds which agree on non-dispositional properties but disagree about dispositions. These worlds could have the same causal history and instantiate the same non-dispositional properties, but differ with respect to a particular instantiation of some latent disposition. Perhaps a more plausible reductionist view is not that dispositions supervene on actual causal sequences, but on causal regularities or laws. Causal laws might be a more promising reduction base for dispositions than singular causal facts are, if, like dispositions, laws might be latent, without manifestations. This harkens back to an earlier suggestion: Def 7: x disposed to cause an event of type G iff x has some property F and there is a causal law that F’s in circumstances C are necessarily followed by G’s.

To put this idea in terms of metaphysical rather than conceptual reduction, the proposal entails that, if worlds have the same laws,

 jennifer mckitrick they have the same dispositions. Given this suggestion, one may argue that the two particle worlds must have different causal laws if one particle is disposed and the other isn’t. So even if the worlds have the same events occurring, they don’t have the same causal laws. In that case, there’s no dispositional difference without a causal law difference. One way dispositions and laws might coincide is if statements of law that are true at a world summarize the disposition facts instantiated in that world. If it’s true that all F’s in C are followed by G’s, that might be because all F’s have the power to produce G-events in C, rather than it being the case that F’s have that disposition because of the law. If the truth of law statements depends on which dispositions are instantiated, then there will be no difference in laws without a difference in dispositions. However, the current question is whether there can be a difference in dispositions without a difference in laws. If the same law statements could adequately summarize different distributions of dispositional properties, then the relation between laws and dispositions suggested above is consistent with there being worlds with the same laws but different dispositions. Returning to the two particle worlds, the suggestion that dispositions supervene on laws entails that these worlds must have different causal laws. But must they? Perhaps not, if they are both worlds in which it is a law that all F’s in C are followed by G’s, but while one particle is F, its counterpart is not F and hence is nondisposed. It’s plausible that worlds with the same laws could differ with respect to a certain particle having a certain feature, either because of different initial conditions in each world, or because the laws in these worlds are indeterministic. These worlds would agree on the causal laws, but differ with respect to dispositions. However, this reply is not true to the reduction suggested by Def. 7, since x having its dispositions to produce a G-event depends not just on there being a law that all F’s in C are followed by G’s, but on the fact that x has property F. If dispositions are really being reduced on this picture, F must be non-dispositional. So, a better

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formulation of this idea is that disposition facts supervene on causal laws plus the distribution of non-dispositional properties. The plausibility of this view depends on the idea that all dispositions, even those of fundamental entities, have a non-dispositional causal basis. The metaphysical picture, on this view, is one in which all metaphysically possible worlds are populated by objects which are inert in themselves, and only become active because they are governed by over-arching laws which push them around.¹⁴ But if there is a possible world in which a particle has a power which has no non-dispositional causal basis, then there could be worlds which agree on non-dispositional facts and laws, but disagree with respect to dispositions. I will now consider some objections to this counterexample. 2.3.1 Objection 1: Causal theories of persistence On some views of persistence, what makes a three-dimensional object at t1 the same persisting object as a three-dimensional object at t2 is a causal connection between the two (Tooley 1984). In other words, each time-stage of an object stands in a causal relation to its next stage. In the counterexample, one world contains an F-particle; the other world contains a non-F-particle. In the first world, an F-particle stage causes the next F-particle stage, and in the second world, a non-F-particle stage causes the next non-F-particle stage. So, one may argue, if the particles have different properties, then the two worlds would have different causal sequences after all, and so this is not an example of a difference in dispositions without a difference in causes. Two sorts of replies come to mind. One is to deny this theory of persistence. Though we are not assuming a particular theory of causation, an intuition one many have about causation is that it is a relation between events that essentially involves change. Kant, for example, conceived of causation as a relation between two sets of objective sequences of appearances, perceived as events (Critique ¹⁴ Stephen Mumford has argued against this view (Laws in Nature, 2004).

 jennifer mckitrick of Pure Reason, B234). On some views, a world without change would be a world without causation and perhaps without time as well. Unless something is out to destroy it, an object just sitting there doesn’t have to do anything to remain in existence. Causation essentially involves doing, making something happen. A different challenge to the causal theory of persistence is four-dimensionalism according to which, for an object with three spatial dimensions to persist is for it to be part of a larger object with a fourth, temporal dimension. It makes no more sense to say that one time-slice of a four-dimensional object causes a future time slice of itself than it does to say that the right half of the three-dimensional object causes its left half. If the relation between one stage of a thing and a later stage is not that of cause and effect, there is no causal difference between the two worlds. An alternative reply is to concede this account of persistence, but argue that the stages of a persisting thing could have stood in the same causal relations even if that thing had been slightly different. In other words, sequences of events do not need to be qualitatively identical in order for them to be alike causally, as long as they have all of the same causally relevant properties. Compare one causal sequence, Oswald shooting Kennedy wearing blue socks, with one in which Oswald shoots Kennedy wearing black socks. Arguably, the pairs of events,
Oswald shooting, Kennedy getting shot, are alike causally despite this trivial difference. Now, compare two particle stages each causing a subsequent particle stage. The only difference is that one of the particles has a certain latent disposition which has no effects. In both worlds, a particle existing at t1 causes a particle to exist at t2 . To this extent, the causal theory of persistence is preserved. Admittedly, ‘the particle’s being F at t1 causes it to be F at t2 ’ is not true at both worlds. But it’s not clear to me that this claim is essential to a causal theory of persistence of objects. If it were true that a time slice of an instantiation of a property causes the next time slice of the instantiation of that property, then any worlds with any duration that differ at all would differ causally. That way

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of getting no dispositional difference without a causal difference also gets you no categorical difference without a causal difference. If this goes to show that dispositions reduce to causes, it equally goes to show that non-dispositional properties reduce to causes. I don’t think the proponent of reducing modalities would want to go there. So, even if the causal theory of persistence is correct, it could be that the F-particle world and the non-F particle world have the same causal relations, but different dispositions; the counterexample to global supervenience of dispositions on causes stands. 2.3.2 Objection 2: Causally relevant properties are essential properties The counterexample proposes that the particle might have lacked a certain causally relevant property—one that figures in causal laws and grounds its dispositions. But perhaps the property F is essential to the particle. For example, the properties being an electron, having negative charge, or having a certain mass may be essential to the particles that have them. Indeed, it might generally be the case that a thing’s causally relevant properties are essential to it. David Braun (1995) argues that causally relevant properties are essential properties of the cause. Braun’s Natural Essentialist Analysis (458) of causal relevance goes as follows: (NEA) If c and e are events, and F is a property, then c’s being F is causally relevant to e iff: c is a cause of e, c is essentially F, and F is a natural property.

Braun’s account targets properties of events, but he says that properties of objects can be considered causally relevant on his view, since an event can have the property of involving an object with a certain property (449). If Braun’s account is right, perhaps my counterexample is flawed. I proposed an F-particle, in a world where it is a law that all F’s in C are G’s, has a counterpart which is subject to the same laws, but which is not F. But if the particle’s

 jennifer mckitrick causally relevant properties are essential to it, then it is not true that the particle might not have been F; the particle has no counterpart that is not F. But is Braun right? Intuitively, NEA does not seem to give either necessary or sufficient conditions for causal relevance. Consider the claim: ‘My birth caused my mother’s joy.’ Perhaps my birth essentially involves me, a creature with my genetic code and innate characteristics. Was being the birth of a creature with my genetic code causally relevant to causing my mother joy? That’s unclear. Anything within the range of normal human, male or female, would probably have done just as well. So, the NEA hasn’t given a sufficient condition for causal relevance. Nor has the NEA given a necessary condition. Suppose I pick up a fire poker from a fireplace. It happens to be very hot, and it burns my hand. Being very hot is not an essential property of the poker, and does not seem to be an essential property of the event that consists of my grabbing the poker. The poker could have been cool when I grabbed it. However, the temperature of the poker is surely causally relevant to my burn. So, it seems like accidental properties can be causally relevant. Braun defends his account against such objections with subtle moves regarding event individuation. In a footnote, Braun says ‘Some apparent counterexamples to the Essentialist Analysis can be ‘‘turned aside’’ if we keep in mind that two events with different essential properties can occur in the same place at the same time’ (470). On Braun’s view, many different events occur in same space/time region, each with different essential properties. When I slam the door, it is thought that at least two events occur at the same place and time, one that is essentially a slamming and one that is accidentally a slamming. The event that is essentially a slamming startles Sara. The event that is accidentally a slamming blocks the draft. Being a slamming is causally relevant to startling Sara, but not to blocking the draft (Lewis 1986c: 255). Perhaps these kinds of moves can get around the counterexamples offered above. However, these moves raise prior questions

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about causation and essential properties. Which among the cooccurring events is the cause of e? Braun uses counterfactuals to answer such questions. According to Braun, our counterfactual judgments support the conclusion that at least two non-identical events occurring in the same region of space/time that have different effects (455). If the event that was essentially a slamming had not occurred, the draft still would have been blocked, since the door would have been merely shut instead. However, if the event that was essentially a shutting of the door had not occurred, the draft would not have been blocked. This is supposed to persuade us that the slamming and the shutting are different events with different essential properties and different effects. These moves suggest that even if Braun is right, NEA poses no challenge to my counterexample. As it turns out, a potentially causally relevant property might not be essential to some of the events occurring in a certain region of space-time. Suppose being a slamming is a potentially causally relevant property which figures in causal laws relating it to loud noises and startlings. According to Braun’s view, the event which blocks the draft is not essentially a slamming. So, despite the potential causal relevance of being a slamming, that property is not essential to all of the events which instantiate it. Only the properties which are causally relevant to a certain effect are essential, and furthermore, they are essential only to the cause of that effect and to not the other events that occur at the same place and time as the cause. So, returning to my counterexample to the global supervenience of dispositions on causal laws, even if the particle’s F-ness is a potentially causally relevant property, an event which involved the particle might not have been an event which involved an F. So, for all Braun says, the particle might not have been F. In other words, it can have a counterpart that is not F. If causally relevant properties were essential to the objects that bear them, then it would be harder, if not impossible, to generate an example of a difference in dispositions without a difference in

 jennifer mckitrick causal laws: If two particles differed dispositionally, they would differ with respect to a causally relevant property, and hence couldn’t be counterparts of the same particle. There are reasons to reject Braun’s view that an event’s causally relevant properties are essential to it. But even on Braun’s view, a thing can have a potentially causally relevant property non-essentially, and that’s all F-ness is in the counterexample: potentially causally relevant. So NEA presents no barrier to generating a counterexample to the supervenience of dispositions on causal laws. That’s not to say there are no other barriers. One might think that the causal properties of fundamental entities are essential to them. However, there’s no need to assume that the particles in the counterexample are fundamental particles. Consideration of Braun’s view supports the idea that a thing can have non-essential (potentially) causally relevant properties, including non-essential dispositions. 2.3.3 Objection 3: Other metaphysical assumptions Perhaps I am assuming a certain account of events. According to some accounts, an event is a particular instantiating a property at a time (Kim 1976). So, events can be individuated by specifying a triple consisting of a particular, a property, and a time. On this account, the event that occurs in one of the particle worlds consists of the triple
particle1 , F, t. The corresponding event in the other world,
particle2 , P, t, is not an instantiation of F, so the corresponding events are different events.¹⁵ If this account of events is correct, the two worlds do not include the same event. Arguably, this difference between events can lead to a causal difference. If these two different events have any causes or effects, then there is a causal difference between the two worlds in which they occur. ¹⁵ If particle 1 and particle 2 are different particulars, the corresponding events already cannot be identical. In order to apply Kim’s account to trans-world identity of events, we have to allow that one particular can exist in different possible worlds, or that a counterpart relation of the particular constituent of an event is sufficient sameness of event.

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For example, if an event in the first world caused particle1 to be F at t, but in the second world, no event caused particle2 to be F at t, then the two worlds seem to differ causally. This objection is similar to Objection 1, and my reply is similar as well. One option is to reject this account of events. One problem with it is that it makes an event’s property and time of occurrence essential to it. So, the event of a top spinning couldn’t have been any faster or any later, since the triple
top, spinning at 50 rpm, t is not identical to the triple
top, spinning at 51 rpm, t+e . Another way to reply is to say that this account of events is consistent with the two worlds agreeing causally. It’s possible that t and consequently the particles’ being F or non-F spans the duration of each world, and that these events don’t have any causes or effects, so there is no causal difference between the worlds despite a difference in events. These worlds might be very short-lived, so that many potentialities go unrealized. If these seem like uncommon worlds, that is merely a function of that fact that, given certain metaphysical assumptions, the metaphysically possible worlds in which the example obtains are fewer. However, the fact that the example obtains in any of these worlds goes to show that I am not making the contrary metaphysical assumption. It may also be objected that I am assuming that there can be a world with no F’s in it, in which it is a law that all F’s in C are followed by G’s. That seems to entail some sort of Platonism about the existence of properties. However, that might be acceptable. There could be laws governing emergent properties in worlds where those properties do not emerge (Tooley 1977: 695). But more to the point, I am making no such assumption. I assume there is a possible world in which one particle is not F. That could be a world in which other particles are F, some of which find themselves in C and are followed by G’s, and others that don’t. I also assume there is a possible world in which a particle is F, but never in C. That could be a world in which there are other F particles which wind up in C and are followed G’s.

 jennifer mckitrick 2.3.4 Objection 4: Conceptual, not metaphysical One may object that my example trades heavily on conceptual possibility, and does not clearly speak to the issue of metaphysical possibility. The examples derive claims about what is possible from what is conceivable. What one takes to be conceivable in these instances is partially determined by one’s concepts. Though I claim to not be presupposing particular accounts of dispositions, I am perhaps tacitly appealing to some conception of dispositions that is driving my intuitions. I might thereby be begging the question in favor of a certain non-reductive approach to understanding dispositional concepts. Perhaps on some metaphysical views of dispositions, the possibilities I conceive of are mere pseudo-possibilities. This line of objection opens deep methodological questions. Perhaps I fall prey to the paradox of inquiry here, whereby I cannot search for an appropriate account of dispositions unless I already know what I’m looking for. Though I am not assuming a particular analysis or definition of ‘disposition’, I cannot proceed as if the term holds no meaning for me. I must have some idea of what a disposition is, some concept of a disposition. If I am doing something more than critiquing conceptual analyses, I take my concept to be picking out a kind of thing in the world, which may be given better or worse descriptions by the analyses. However, I don’t think I was tacitly making any illegitimate conceptual assumptions, for no leading conceptual analysis of dispositions contradicts my intuitions. Consider the view that dispositions are irreducible powers. Particle1 has a latent, irreducible power that particle2 lacks. That would be a dispositional difference without a causal difference. What if dispositions are secondary properties along the lines of Def 6? Particle1 has a property F that would cause the manifestation where particle2 lacks that property, and hence they differ dispositionally. If I am right that there is no causal difference, there is a failure of global supervenience. What if having a disposition was a matter of a certain conditional statement being true? The

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conditional ‘if C were to obtain, it would exhibit m’ is true of particle1 , but not particle2 . If that’s consistent with the two worlds having the same causal sequences, then there’s a dispositional difference without a causal difference. What if having a disposition were a matter of having some non-dispositional property that is subsumed by some causal law? We’ve already considered the possibility that particle1 is F, subject to the law that all F’s in C are necessarily followed by G’s. I argued that particle2 could be non-F, and hence non-disposed, without there being any causal difference in the worlds. It makes no difference which particular analysis of ‘disposition’ is assumed. How is it that conceptual analyses of dispositions in terms of causes are consistent with there being a dispositional difference without a causal difference? Because every analysis of ‘disposition’ that has any plausibility does not analyze disposition ascriptions in terms of statements that a cause occurred, but in terms of wouldbe causes or conditional causal statements. Perhaps there is some concept of a disposition that is inconsistent with my intuitions. For example, if what it is for an object to have a disposition is for that object to be a cause of some effect, then there would be no dispositional difference without a causal difference. But as we have seen, that is an inadequate conception of a disposition. One need not assume a specific analysis of ‘disposition’ to preserve this essential feature of the concept—dispositions can be latent, or unmanifested. This is the key difference between dispositions and causes that my example plays on. As long as one is working with a concept of ‘disposition’ that has this feature, which I would argue one must unless one is to change the subject, then the counterexamples can be generated.

2.4 Other reductive possibilities In response to the proposal that dispositions globally supervene on causal laws, I suggested that the F-particle world and

 jennifer mckitrick the non-F-particle world could have the same laws and causal sequences if the difference in F-ness were part of the initial conditions of those worlds. If this is right, perhaps dispositions globally supervene on causal laws plus initial conditions. Perhaps two worlds with the same laws and initial conditions necessarily have the same dispositions. However, these laws would have to be deterministic, since two possible worlds with the same probabilistic laws and initial conditions could diverge and subsequently instantiate different dispositional properties. If dispositions globally supervene on causal laws, or causal laws plus conditions, that still leaves the question: where do these causal laws come from? Perhaps they are derived from (supervene on, reduce to) particular sequences of events, patterns of kinds of things in succession in space and time. Possibly, these are the same kinds of things that make disposition claims true. So, again, even if disposition facts globally supervene on causal laws, that might not be because dispositions reduce to causal laws, but because both dispositions and causal laws reduce to something else. There is some reason to think that the world cannot contain both unreduced dispositions and laws (McKitrick 2005; Mumford 2005b). If the world were law-governed, then what objects do would be determined by the laws that govern them. Their dispositions could be nothing over and above their acting in accordance with laws. On the other hand, if objects had genuine powers, then causal laws would be, at most, generalizations about the kinds of powers things have. If causal laws are necessary for causation, then there’s a tension between having both dispositions and causes in the world without reducing one to the other. Since generalist theories of causation which take causal laws as fundamental clash with unreduced dispositions, a singularist view of causation is most compatible with unreduced dispositions and causes. A singularist view of causation takes singular causal facts as fundamental, and causal generalization as derivative (Sosa and Tooley 1993: 17–19). There is no obvious incoherence in imagining objects having irreducible dispositions, and events standing in irreducible causal relations.

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However, we may want to be more conservative in the number of irreducible entities, properties, and relations we postulate. 2.4.1 Reducing causes to dispositions How might one define causes in terms of dispositions?¹⁶ One idea is that causation is a matter of a disposition manifesting. The view could be put roughly like this: Def 11: a causes b iff a has a disposition to produce b in circumstance C, and C obtains.

Without going through successive permutations, let me point out several difficulties for this approach. First of all, if a and b are names of events, it’s not clear that events are the bearers of dispositions rather than objects, and it is not clear that anything can have a disposition to produce a particular event rather than a type of event. Secondly, it is possible that a has a disposition to produce b in C, C obtains, and yet b does not occur. The counterexamples of masks and finks work here as well. (The fragile glass is disposed to break when struck, but it is packed with Styrofoam, or protected by a wizard, so that when it is struck, it doesn’t break.) And if b does not occur, a did not cause b, so the definition does not give a sufficient condition for causation. Thirdly, it seems conceptually possible that a causes b even though a didn’t have a disposition to produce b. A fall from a flying airplane isn’t disposed to cause one to get up and walk away, yet it has happened. Fourthly, ‘to produce’ is a synonym for ‘to cause’. So, ‘cause’ has essentially been defined in terms of a disposition to cause, which is not reductive. This circularity cannot be easily avoided. What is a disposition a disposition for, but for causing the manifestation? Most expressions for the relationship between a disposition and its manifestation are causal, such as ‘produce’, or ‘elicit’. If causation is presupposed as part of the concept of a disposition, then a definition of causation in terms of dispositions is not reductive. ¹⁶ Suggestions appear in Cartwright 1999: 67; Harr´e 1970: 97.

 jennifer mckitrick To avoid the circularity, one might try to rid the characterization of ‘disposition’ of causal notions by defining it in terms of a conditional. So, if disposition statements were reducible to conditionals, we could reduce causal statements to disposition statements and then reduce disposition statements to counterfactuals. It’s not clear if this will work given the different kinds of conditionals traditionally involved in analyzing dispositions and causes, and the problems involved with such analyses discussed in Section 2.2.1. But if it did, it’s not clear what, if anything, would be gained by letting dispositions playing the middle man in a counterfactual analysis of causation. What about metaphysical reduction of causes to dispositions? Do causal facts globally supervene on disposition facts? We can use the same sorts of thought experiments used against the reduction of dispositions to causes to try to answer this question. Suppose a rubber band is stretched and resumes its former shape in one world, but in a very similar world, the rubber band has yet to be stretched. In the first world, a causal sequence has occurred which has no counterpart in the second world. However, it seems possible that the same disposition claims are true at both worlds—in both worlds the rubber band is elastic. So, there’s a difference in causes without a difference in dispositions, a failure of global supervenience, and hence no reduction. The dispositions-to-causes reductionist might argue that effects are manifestations of dispositions, so a world never has a difference in effects without a difference in the dispositions of causes. He might insist that there must be a dispositional difference between these two worlds. If someone stretched the rubber band in the first world, he had the disposition to stretch it, and that disposition was lacking in the second world. Or, if the rubber band stretched on its own accord, it had the disposition to stretch that the other rubber band lacked. In response, the example can be elaborated as follows. In both worlds, at time t1 , the rubber band is in the hands of someone with a disposition to stretch it. In W1 , the rubber band is stretched at t2 ;

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in W2 , the rubber band isn’t stretched until t3 . So, at t2 , the worlds differ causally, but not dispositionally. The reductionist may counter by saying at t1 , the two worlds must have differed dispositionally in order for their futures to diverge. Perhaps the person in W1 had a more powerful and urgent disposition to stretch the rubber band, or the person in W2 had a disposition to attend to his itchy elbow first. However, such a response won’t work for probabilistic dispositions. Suppose two worlds each contain a lump of uranium that has a disposition to emit particles 50% of the time under certain circumstances. One lump emits a particle, but the other doesn’t. To insist that there must be a dispositional difference between the two lumps of uranium is to deny the possibility of probabilistic dispositions. I can anticipate one further, and perhaps decisive, rejoinder on behalf of the causation-to-dispositions reductionist. In W1 in which the rubber band is stretched at t2 , the stretched rubber band has a number of dispositions at t3 : it is disposed to break if pulled a little harder; it is disposed to make a ‘twang’ sound if it is plucked; and it is disposed to shoot across the room if one of its ends is released, etc. The flaccid rubber band in W2 at best has the disposition to acquire these dispositions if stretched. So, the two worlds disagree dispositionally after all. The possibility of probabilistic dispositions makes no difference here. The world where a lump of uranium emits a particle then has a particle flying around in it, which is disposed to trigger a Geiger counter, to bombard other uranium atoms, and so forth. This world differs dispositionally from the world in which no particle is emitted. So, after the manifestation occurs, the worlds differ dispositionally as well as causally. This feels like something of a cheat, but what can the antireductionist say? In order to maintain her position, she must insist that there is a point at which the two words differ causally but not dispositionally. But this most recent objection shows, as soon as the effect or manifestation starts to occur, the two worlds start to

 jennifer mckitrick differ dispositionally. So, perhaps there’s a crucial moment after the cause occurs but before the effect starts to occur. Since no cause occurs in the other world, the two worlds would disagree causally at that point. But how could a cause be occurring in one world and not the other without the two worlds differing dispositionally? For example, suppose that prior to emitting a particle, an event which is the cause of the particle emission occurs in the lump of uranium. While the uranium lumps might have agreed dispositionally earlier, at the moment when the cause of the emission has occurred but the emission has yet to occur, the two lumps differ dispositionally as well as causally. One lump is disposed to emit a particle in the next micro-second, the other is not. So, it seems that we cannot describe two worlds that agree disposition-wise, but disagree cause-wise. If causal facts globally supervene on disposition facts, a necessary condition for the metaphysical reduction of dispositions to causes is met. Is this because dispositions and causes reduce to the same thing? I think not. If both causes and dispositions reduced to the same thing, we should not be able to describe worlds which agree causally but disagree dispositionally. However, unless all dispositions necessarily have a non-dispositional causal basis, it seems that we can describe worlds which agree about causes and non-dispositional properties, but disagree about dispositions, as I argued in Section 2.3. So, this suggests it is not the case that global supervenience of causes on dispositions holds because both causes and dispositions reduce to the same thing, but because causes reduce to dispositions. Another possibility for causal to dispositional reduction is a reduction of causal laws to dispositions. Assume that objects have inherent powers, which are activated in various circumstances. We may be able to generalize about what kinds of things have what kinds of powers in which circumstances: Protons have the power to attract electrons at certain distances and velocities; massive objects have the power to attract other massive objects, etc. Such generalizations would be our causal laws.

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One may object that it is metaphysically possible that no such generalizations are true. A world in which no causal generalizations are true would be a world in which the powers are too chaotic to have any causal laws. However, if that is indeed a possibility, it is no objection to the reduction of laws to dispositions. Chaotic worlds would merely be worlds with no laws to reduce. If causal laws are generalizations about powers, then worlds which agree on dispositions will agree on causal laws—whether they have them and what they are. However, not all worlds that agree on causal laws will agree on which dispositions are instantiated, since true generalizations underdetermine particular patterns of instantiation of dispositions. For example, the generalization ‘All F’s in C become G’s could be true in a world with twenty F’s in C that become G, a world with five F’s in C that become G and six F’s not in C, a world in which F’s are never in C, and infinitely many others. So, there would be global supervenience of causal laws on dispositions, but not dispositions on causal laws.

2.5 Conclusion There are several options regarding dispositions, causation, and reduction. My main objective was to argue against reduction of dispositions to causes. The general problem for a reductive relationship between causes and dispositions comes to this: Causes are active; dispositions are potentially latent. Reducing one to the other threatens to obscure this crucial difference. The best arguments for global supervenience of dispositions on causes, a necessary condition for reduction, proceed by providing a common reduction base for dispositions and causes. Since causal laws are possibly uninstantiated, they are a better reductive fit with dispositions. But in which direction? Recall that a reduction of dispositions to causal laws plus conditions requires deterministic laws. If we want to allow for the possibility of probabilistic laws, then reducing causal laws to dispositions is a better prospect. However, my inability

 jennifer mckitrick to provide a convincing example of a causal difference without a dispositional difference raises the intriguing possibility that causes reduce to dispositions.¹⁷ ¹⁷ The following people have provided useful feedback on earlier versions of this paper: Toby Handfield, John Gibbons, Joe Mendola, Al Casullo, Roderick Long, Eric Marcus, an anonymous referee, and attendees of the Southern Society for Philosophy and Psychology Annual Meeting 2006, the University of Nebraska–Omaha Philosophy Colloquium, the University of Nebraska–Lincoln Philosophy Graduate Student Colloquium, and the Dispositions and Causes Conference at the University of Bristol.

3 Causal Structuralism, Dispositional Actualism, and Counterfactual Conditionals Antony Eagle

3.1 Properties and modality It is a truism that objects act as they do at least in part because of how they are. Though there may be outside forces that influence how the object behaves, the most significant determiners of that behaviour are the intrinsic properties that the object itself possesses. The role of properties in determining behaviour is so important that we frequently individuate properties by the characteristic behaviours to which they give rise. This is most obvious in the case of dispositions: fragility, for example, just is that property which contributes the characteristic behaviour of breaking when appropriately struck to its possessors. Orthodox Humean views hold that the connection between properties and behaviour, even in the case of dispositions, is contingent. For example, Lewis adopts a modern version of Hume’s denial of necessary connections when he advocates a principle of recombination according to which patching together parts of different possible worlds yields another possible world. (Lewis 1986b: 87–8)

 antony eagle Using this principle we can easily sever any link between intrinsic properties and behaviour: recognizing that any non-overlapping regions of spacetime count as distinct existences, one may apply the principle of recombination to determine that it is possible that any event in a given region may be spatially or temporally adjacent to any other. The fact that an object which is wholly contained within one such spatiotemporal region has certain intrinsic properties therefore places no constraint on the contents of any other region. If a region is spatially extended but instantaneous, the contents of that region do not constrain the contents of temporally adjacent extended and instantaneous regions. So the properties of an event and its participants do not necessitate the subsequent course of events. In particular, the fact that an object possesses at one time certain intrinsic properties does not determine the subsequent behaviour of that object, for there are possible situations in which an intrinsic duplicate acts differently by giving rise to a different subsequent course of events. So although properties might be actually characterized by their behaviour, this is a matter of physics or circumstances being such as to make it the case that every actual instance of the property will display the characterizing behaviour under the appropriate conditions. They are not necessarily characterized by this behaviour. So, at least, the Humean story goes: ‘there is nothing in any object, consider’d in itself, which can afford us a reason for drawing a conclusion beyond it’ (Treatise, Book I, Part 3, Section 12). 3.1.1 Causal structuralism But many have found this Humean story implausible. For one thing, the Humean picture is committed the thesis of quidditism: that there is something to a property over and above any secondorder properties that a property has, and thus over and above its causal profile. For example, if having mass actually confers the power to attract other massive objects, the Humean believes that ‘being massive’ possibly confers the power to repel other

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masses. So ‘attracts other massive objects’ is a contingent secondorder property of being massive. According to the Humean, every (non-logical) second-order property is contingently possessed by the properties which have it; which means that for any first order property P, there is a possible world w in which P lacks every second-order property that it actually possesses. What, then, makes P actually the same property as P in w? The answer must be that there is some ground to that identity, a shared essence to the two instances which is called a ‘quiddity’. The quiddity is independent of the causal or behavioural role that P actually occupies, so that role can arbitrarily vary even while the property retains its identity. That properties have quiddities hasn’t been widely accepted. The best argument I’ve come across against quiddities is that they are methodologically otiose. John Hawthorne gives forceful expression to this objection with respect to the property of negative charge: All scientific knowledge about negative charge is the knowledge about the causal role it plays. Science seems to offer no conception of negative charge as something over and above ‘the thing that plays the charge role’. If there were a quiddity ... it would not be something that science had any direct cognitive access to ... Why invoke what you don’t need? Unless certain logical considerations forced one to suppose that properties are individuated by something over and above their causal role, then why posit mysterious quiddities? (Hawthorne 2001: 368–9)

Without stopping to evaluate this or other anti-quiddistic arguments (Black 2000; Mumford 2004), we may still take them as motivation enough to explore a non-Humean alternative conception of properties on which the causal/behavioural profile of a property is not merely contingently attached to that property. This alternative conception is difficult for the Humean to accept at least partly because the paradigm examples upon which the Humean rests her account are categorical properties. Take again the example of being red. The natural way to think of this property is as giving certain features to the object which has it; but how

 antony eagle other objects respond to those features, for instance how observers respond to it, is not part of specifying the property itself. Categorical properties are naturally understood as passive in a certain sense: events occur because other objects respond to the presence of a categorical property. If the paradigm property is categorical, then it is easy to understand how contingency of causal role is an appealing thesis. If, however, we adopted dispositional properties as the paradigm, a quite different conception of properties seems natural and appealing. A disposition is specified by its stimulus conditions and the manifestation it makes in response to that stimulus: as fragility, on the traditional view, is characterized by a stimulus of being struck with sudden force and a manifestation of breaking. The disposition looks explicitly as if it is specified in terms of its causal profile, and the powers it contributes to objects which have it: the power to produce the manifestation under the stimulus conditions. This causal power looks necessary for the property to be the property it is: an object could not be fragile if it did not have the power to break when struck. If we began thinking of dispositions as the paradigm, then one might regard the causal profile as necessary to the property in every case, not just in the dispositional case. The resulting view of property identity is that what makes a property the property it is, what determines its identity, is its potential for contributing to the powers of things that have it. ... if under all possible circumstances properties X and Y make the same contribution to the powers of the things that have them, X and Y are the same property. (Shoemaker 1980: 212)

In the absence of any agreement on what ‘making a contribution’ to a power might be, we can adopt the thesis that properties just are causal powers, and have an essential causal profile. This view about properties leads to the thesis of causal structuralism (Hawthorne 2001): the thesis that at least some properties, whether natural or less than perfectly natural, have a causal profile that is essential

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to them. Mumford (2004: §10.6) defends the similar thesis that properties are intrinsically powerful, as does Molnar (2003). Causal structuralism is also the cornerstone of the thesis of dispositional essentialism (Ellis and Lierse 1994; Bird 2005a): the view that all the most natural properties—perhaps those delivered to us by fundamental science—have an essential causal profile. In Bird’s formulation, the properties mentioned in the laws of nature are individuated by their causal role. In Ellis’s formulation, natural kind membership is determined by possession of properties that are individuated by their causal role. Whether these formulations lead to different views, or whether they amount to the same view (as might be if, for example, the laws of nature govern the behaviour of natural kinds), I won’t here say. Dispositional essentialism entails causal structuralism, but is not entailed by it.¹ Lewis once claimed that ‘it can plausibly be said that all perfectly natural properties are intrinsic’ (Lewis 1986b: 61). Despite their differences of formulation, all causal structuralists accept this thesis of intrinsicness when applied to perfectly natural properties with essential causal profiles (if there are any): ‘Powers are intrinsic properties of their bearers’ (Molnar 2003: 129), and intrinsicness is ‘one of the crucial appearances which has to be saved by an analysis’ (Molnar 1999: 3). Ellis elaborates: The intrinsic properties and structures of things are what make them what they are. They explain how things are disposed to behave, just in virtue of how they are constituted ... (Ellis 2001: 31)

Perhaps not all dispositions or powers are intrinsic, as McKitrick (2003a) has argued, using examples like ‘vulnerability’ (the Mona Lisa was vulnerable to vandalism before it was covered with ¹ While I think it’s possible to accept causal structuralism without accepting dispositional essentialism—and will argue in this paper that doing so is clearly the preferable option—defenders of that package in the literature are sparse. Mumford (2005a: 424–5) does claim to accept causal structuralism without dispositional essentialism, but there is reason for considerable scepticism regarding his position, as he seems to base his objections on a non-standard conception of what it means for a natural kind to have an essential property.

 antony eagle bulletproof glass). Yet even these extrinsic dispositions ‘are reducible to fundamental potencies that are intrinsic’ (Bird 2007: 125). The intrinsicness thesis entails that intrinsic duplicates have the same perfectly natural powers or dispositions. There are good reasons for causal structuralists to suppose that whatever perfectly natural powers there happen to be are intrinsic (and, I imagine, to suppose that perfectly natural relations, like spatiotemporal relations, are external²). For dispositional essentialists it is obligatory: if any perfectly natural property were extrinsic, intrinsic duplicates with that property needn’t have the same causal behaviour, so that the causal profile of this perfectly natural property would not be invariable between instances, contrary to the dispositional essentialist assumption that all perfectly natural properties are causally characterized powers. For causal structuralism in general, the issue is more subtle, as it is compatible with causal structuralism that some perfectly natural property might be amongst those which do not have an essential causal profile. No plausible candidate springs to mind; nevertheless, it may be so. Yet the hypothesis that there is a perfectly natural property that intrinsic duplicates need not share is at least puzzling. Consider the thesis of object separability: the claim that the complete physical state of the world supervenes on the intrinsic character of all of the objects in the world plus their spatiotemporal relations. In a world where there was a perfectly natural but extrinsic power, this intuitively plausible thesis would be violated.³ This isn’t compelling—many ² Using ‘external’ here in the sense of Lewis (1986b: 62), whereby internal and external relations are both, in some sense, intrinsic relations. ³ It is true that a related doctrine to object separability has been questioned recently. Maudlin (2007) has argued that entangled quantum systems violate what we might call point separability, the doctrine that the complete physical state supervenes on the intrinsic character of each spacetime point. Object separability is much weaker than this thesis, as extended objects whose properties didn’t supervene on the properties of their parts could still obey object separability. And indeed the examples Maudlin uses, of entangled ‘pairs’ of electrons, seem to be of this type—I’m not at all sure that spatially extended entangled systems really should be counted as having distinct objects as parts rather than being extended simples or multiply located individuals. So I don’t think these examples violate object separability, and they may even support it if it turns out to be true even in the strange world of quantum theory. In any case I’m not inclined to discuss these quantum

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intuitively plausible principles are incorrect—but in the absence of a clear and compelling example of a perfectly natural intrinsic property to substantiate the falsity of the otherwise attractive principle of object separability, I don’t find the purely theoretical possibility of such a property very moving. I thus regard it as far more reasonable for the causal structuralist to also accept that perfectly natural powers are intrinsic, and adopt the intrinsicness thesis. Indeed, further reflection on the above considerations suggests that the causal structuralist should probably accept Lewis’s stronger thesis that all perfectly natural properties are intrinsic, powers or not. At least for the time being, then, I’m going to assume the intrinsicness thesis (I will reconsider it in Section 3.4). Causal structuralism relies on a notion of ‘sameness of causal profile’. A causal profile is basically the complete record of the behaviours that a property does and would give rise to under any possible circumstances. Some properties, like fragility, have quite a simple causal profile, as there is only one type of circumstance (exertion of force), and one characteristic behaviour (breaking). Other properties might have many more complicated causal profiles: perhaps there are many possible circumstances in which the property makes a distinctive contribution, or perhaps the property can indeterministically give rise to more than one possible behaviour in a given circumstance. In all these cases, causal structuralists believe that there is an essential link between properties and certain counterfactual conditionals, those which specify some circumstances (the stimulus) in the antecedent, and specify the behaviour that property gives rise to under those circumstances (the manifestation) in the consequent. Causal structuralists accept, therefore, the thesis of conditionality: each causal structural property P supports a characteristic stimulus-manifestation counterfactual conditional for the objects which possess P. mechanical examples much, mostly because I find them too controversial at present to have much dialectical force, particularly since most of the debate over causal structuralism has taken place against a neutral background with respect to discussions of quantum theory.

 antony eagle Causal structuralists are careful to note that the possession of the property does not necessitate the truth of the corresponding conditional. Following on from plausible counterexamples given by Martin (1994), Bird explains that the claim that perfectly natural sparse properties are essentially linked with characteristic subjunctive conditionals [only requires] that the kind of ability that a disposition (strictly, its instantiation) has to make a conditional true in this world (when it is true) is repeated with respect to the same conditional in all other possible worlds. In another possible world the disposition might not in fact make the conditional true, but that will be because ... circumstances are not suitable ... (Bird 2005a: 438)

It is worth noting the reappearance of the intrinsicness thesis: the link between properties and counterfactuals holds in virtue of the intrinsic properties—those which are repeated in otherwordly instantiations of the very same disposition, assuming that the disposition is natural. Yet it may be the case that other instances of the disposition occur in worlds where the extrinsic circumstances disrupt that instance ‘making true’ the conditional (whatever that might mean). While the link is not necessary, it is ‘essential’, as the counterfactual characterizes the essential causal profile of the property. We shall consider further below what this essential but non-necessary link could consist in. 3.1.2 Dispositional actualism in the metaphysics of modality Accounting for modality has long been a major project in metaphysics, and some, but by no means all, causal structuralists have seen a possible solution to the problem of modality in their views about properties. We can see why they have held this hope if we look at a controversial thesis that many causal structuralists accept: that the laws of nature are necessary. Take the essential link that a property P has with its stimulusmanifestation counterfactual. For example, that if some object x has P, then Sx
Mx. As the link is essential, this conditional

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holds for every x, in every possible world. So, necessarily, ∀x(Px → (Sx
Mx)). If a counterfactual is true, so too is the corresponding material conditional. Hence, necessarily, ∀x(Px → (Sx → Mx)). And this necessarily true generalization fits the profile of what many have called a law of nature.⁴ The causal structuralist who accepts this line of argument seems in so doing to conjure a robust necessity out of facts about the pattern of stimulus and manifestation for a given property—a pattern which, despite its rich modal consequences, is apparently empirically discoverable and hence requires only actual facts to ground it. It is not logical necessity: it is not a theorem of any formal calculus that ∀x(Px → (Sx → Mx)). Nevertheless, it is a kind of necessity, which some have called natural necessity, and it has a certain modal invariance despite its basis in facts about the actual causal profile of the property P in question. Given this result, there is a perfectly natural temptation to think that this natural necessity is to be identified with metaphysical necessity. From there it is very attractive to propose that the grounds for metaphysical necessity and possibility are therefore to be found, not in an independent realm of possibilia, but in the constraints that the essentiality of actual causal profiles of properties place on the space of possibility. To put it another way, the identity of the properties in question can be discovered by looking at their actual causal profile; once assured that this identity is essential, because the causal profile is necessary, we know how possible objects with the same properties would behave, and thus deduce modal claims from claims purely about actuality. Quite what to call the resulting position on the metaphysics of modality is unclear. I plump for ‘dispositional actualism’, for the reason that this view grounds, or discovers truthmakers for, metaphysical modality in the actual causal profile of occurrent properties. I do not think that dispositional actualism follows from ⁴ Bird 2005a: 442. Set aside, for the time being, our reservations about counterexamples to the essentially linked counterfactuals.

 antony eagle causal structuralism, and I think that almost any view on the metaphysics of modality can be rendered compatible with causal structuralism.⁵ Nevertheless, many causal structuralists, especially the dispositional essentialists, do accept something very much like dispositional actualism. Consider In virtue of being powerful, [properties] provide natural necessity and possibility and are fit to be the truthmakers for modal truths. (Mumford 2004: 170)

Again, necessities in nature ... require truthmakers, and it seems that it will be real powers which provide such truthmakers ... (Molnar 2003: 223)

Finally, Ellis gives a more sophisticated dispositional account: p is necessarily true iff p follows from the essential nature of some natural kind, where, as before, that nature is characterized by some property with an essential causal profile (Ellis 2001: 275). With this account of natural and metaphysical necessity in place, he explicitly contrasts his actualism with Lewis’s acceptance of mere possibilia: Either one accepts Humean Supervenience and possible worlds realism ... or one rejects them both, as I do, and seeks to ground causal modalities and nomological connections in basic dispositional properties (Ellis 2001: 245)

Those who propose this dispositional actualist view may also be seduced by remarks that other essentialists of a quite different stripe have made, notably Kit Fine: Indeed, it seems to me that far from viewing essence as a special case of metaphysical necessity, we should view metaphysical necessity as a special case of essence. For each class of objects, be they concepts or ⁵ For instance Molnar (2003: §12.2) is apparently a causal structuralist who is a primitivist about modality; in his terms I suppose dispositional actualism would be a reductionist doctrine. I must confess I do not understand his ‘primitivism’: he claims modal operators are primitive, and yet modal claims hold in virtue of powers and supervene on powers. (To avoid confusion, note that this is not the kind of primitivism I discuss in connection with CP-laws in Section 3.4.2.)

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individuals or entities of some other kind, will give rise to its own domain of necessary truths, the truths which flow from the nature of the objects in question. (Fine 1994: 9)

Given that self-described essentialists of one kind favour the reduction of alethic modality to truths about essence, there is precedent and inspiration for the causal structuralist to ‘reduce’ natural necessity to truths about property essences. The dispositional actualists are well aware that this proposal will call for revisions in our intuitive understanding of modality. Contingency of laws is widely accepted, and abandoning it must be seen as a cost, whatever fixes are available to save the appearances (Handfield 2004). For much the same reason, many counterfactuals will involve considering possible situations which involve violations of law, at least on the Lewis–Stalnaker semantics. If there are no law-violating possibilities, then these counterfactuals will be vacuously true, and this is a gross revision. So it is incumbent upon the dispositional actualist to give an alternative account of the semantics of counterfactuals that secures their ordinary truth values. We now turn to this project; I think a serious difficulty arises for the combination of causal structuralism and dispositional actualism when it comes to counterfactuals.

3.2 Counterfactual conditionals According to the standard Lewis–Stalnaker semantics for counterfactuals, a counterfactual conditional ‘if it had been that A, it would have been that C’ is true in a situation just in case there is no relevantly similar situation in which A is true but C false. Obviously a lot more needs to be said about ‘relevantly similar’, but on any reasonable understanding of that notion most of the intuitively valid principles of counterfactual implication follow. One of the more interesting principles of counterfactual implication is that the rule known as ‘strengthening the antecedent’ fails. That is, even if

 antony eagle ‘A
C’ is true, it needn’t be that ‘(A ∧ B)
C’ is true. So this sentence is pretty clearly true: (1) If kangaroos had no tails, they would fall over. Yet adding an additional conjunct to the antecedent leads to a false sentence: (2) If kangaroos had no tails, and were held up by scaffolding, they would fall over. This is in contrast to strict implication: if ‘
(A → C)’ is true, then we can strengthen the antecedent, because ‘
((A ∧ B) → C)’ will also be true. One way to put this point is as follows. If A strictly implies C, then whatever makes A true thereby makes C true regardless of any specification of further facts additional to those that make A true (so A’s truthmaker intrinsically makes C true). The same is not true of counterfactual conditionals. The dependence between A and C exists not just in virtue of A, but also on the other facts that hold in the worlds in which A is true. The standard semantics makes the default assumption that the other facts are as much as possible like the facts that hold actually. But explicitly specifying further facts that must also be held fixed, as when new conditions are added to the antecedent, can disrupt a de facto dependence that holds in situations very similar to actual situations, by rendering the resulting situation quite dissimilar to actuality. In any case, the point is clear: fixing the facts that make A true and the facts that make C true is not yet enough to fix whether or not there is a counterfactual dependence between A and C; for that you need to know something about the situation in which A and C are embedded. That is, whether C counterfactually depends on A is extrinsic to A and C, so that counterfactual dependence is an extrinsic relation, the obtaining of which does not supervene on the individual or joint natures of the relata (Lewis 1986b: 62). This familiar feature of counterfactuals leads to trouble in the present context. The causal structuralist who is also committed

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to dispositional actualism—like Bird, Ellis, Molnar, and Mumford—accepts the following claims: • Perfectly natural properties have an ‘essential’ link to certain characterizing counterfactuals (Conditionality). • Perfectly natural properties are intrinsic (Intrinsicness). • The truthmaker for the characterizing counterfactuals is the instantiation of the perfectly natural property (follows from Dispositional Actualism). We can use a favoured example of the causal structuralist to explore these claims: the property of being negatively charged, N. Suppose, for the time being, that N is essentially linked to something like the following counterfactual:⁶ (3) If e has N, and e had been placed sufficiently near a body e such that Ne , e would have moved away from e . Whether or not a body e has N is intrinsic to e—negative charge is a perfectly natural property if anything is. Finally, what makes any instance of (3) true is that ‘e’ denotes an object which has N. The truth conditions for the counterfactual claim, therefore, do not refer to anything other than the instantiation of the dispositional property that is essentially linked to (3). But it is easy to see that this story cannot be right as it stands. Consider a situation in which we place a negatively charged particle e sufficiently near a negatively charged particle e , but then place a positively charged particle p between e and e . In this situation, e will be attracted by p and so will not move away from e . In this physically plausible situation, (3), the characterizing counterfactual of N, is false. This is not due to any intrinsic alteration in e or in the nature of N, but is wholly due to extrinsic facts in the situation in which e happens to be located, the obtaining of which interferes with the dependence between negative charge and repulsive motion away from like charges. ⁶ We shall revisit this supposition later.

 antony eagle This is, in effect, just the well-known phenomenon of masking of dispositions carried over to properties more generally (Johnston 1992). This simple example illustrates again the way that the truth of counterfactual conditionals can depend on facts that are not explicitly mentioned in the conditional. In this case, the truth of (3) depends not only on the nature of e but also that there are no interferers around to distort (‘mask’) the manifestation of N’s nature. Masking makes for a difficulty for the dispositional actualist who hopes to ground alethic modality in dispositions and not in some independently given modal reality. The dispositional actualist would reject the talk of possible worlds and similarity rankings that the Lewis–Stalnaker semantics requires, and would provide alternative truth conditions for counterfactual claims that depend only on the presence of the appropriately linked disposition: Many subjunctive conditionals are true ... What makes such conditionals true is often the existence of a dispositional property. (Bird 2005a: 437)

But, intuitively, this alternative proposal gives the wrong result in the present case. For the dispositional property N is present in e in an unaltered fashion, and since N is essentially linked to (3), the dispositional actualist predicts that (3) is true in every situation in which an intrinsic duplicate of e is present. This is true even in the second situation we considered, with the interfering positive charge p. Hence the dispositional actualist predicts that even in that situation (3) should be true. But the material conditional ‘if e is placed sufficiently near e , then e moves away from e ’ is false in that situation, so the counterfactual is false in that situation too, not true as the dispositional actualist maintains. Ellis, to his credit, attempts to give alternative truth conditions for counterfactuals that do respect the Lewis–Stalnaker semantics. In fact he regards all counterfactuals as false, basically because they

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can be interfered with. But even a false counterfactual can be acceptable for Ellis just in case there are no countervailing dispositional properties ... that are strong enough to overcome or swamp the display of the dispositional property having the outcome [mentioned in the consequent]. (Ellis 2001: 282)

This proposal is somewhat unclear, as it is difficult to understand how a false counterfactual could adequately characterize the causal role of a property—especially how any particular false counterfactual could do so better than any other false counterfactual. But set that aside: if the countervailing properties are intrinsic to the individuals mentioned in the antecedent or consequent, this will be equally subject to the occurrence of extrinsic interferers as the more orthodox analysis of counterfactuals. And if the countervailing properties are extrinsic, it seems that the characterizing counterfactual will not be acceptable in those situations, and hence the property will not be essentially linked to that characterizing counterfactual. Further light can be shed on this unfortunate result by examining the kind of contribution to observed behaviour that negative charge is supposed to make. The negative charge on some particular particle is supposed to make a distinctive contribution to the systems of which it is a part. That contribution might take the form of a repulsive force on other negatively charged particles, or an attractive force on positively charged particles; in any case it is supposed to be a component force. There has been considerable discussion recently about whether component forces are anything more than a convenient means of representing a physical system (Cartwright 1983), but what is certainly clear is that the causal structuralist about negative charge who adopts dispositional actualism ends up grounding every counterfactual in component forces exerted by the objects mentioned in the counterfactual. So in our above example, the counterfactual (3) was supposed to be made true by the contribution made by e in virtue of its possessing negative

 antony eagle charge N. But what the situation with the additional positive charge shows is that explicitly introduced component forces are not enough to determine the resultant force exerted on a particle, and this net resultant force is what is important for the overall behaviour of objects in a given situation. Counterfactual claims about forces are made true by the component forces exerted by the objects explicitly mentioned in the counterfactual (like e and e ), and by the lack of distorting further forces in the background. The Lewis–Stalnaker theory ensures the absence of distorting forces by appealing to similarity, which ensures a kind of de facto neutrality of the background. But because the dispositional actualist restricts themselves to intrinsic properties of the bearers of dispositions, they have no obvious way to ensure the neutrality of the background, and thus cannot distinguish situations in which the manifestation of the component forces is straightforward, and those in which it is compromised. On this account, (3) should be true in (at least) those worlds where e and e exist and possess the same intrinsic properties (alternatively, all those worlds in which intrinsic duplicate counterparts of e and e exist). But the world with the positive charge p is one such world, and in that world the counterfactual is false. The dispositional actualist could say that the presence of p changes e (or e ) intrinsically; but this is antecedently implausible unless we have already accepted the dispositional actualist/causal structuralist package (though see Section 3.4). They can say that e (or e ) is such as to cause like charges to move away in the absence of interferers; this, while true, doesn’t look like it depends only on intrinsic properties of e to result in the truth of (3), because we would have to be assured additionally of the lack of interferers. If these complaints are valid, the dispositional actualist cannot account for the truth conditions of (3). All this discussion of component forces might naturally suggest that the problematic results are an artifact of a poorly chosen example, and that some other characterizing conditional is appropriate for N. This thought cannot be sustained. For example,

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consider the obvious and popular option of selecting a characterising counterfactual which is explicitly restricted to component forces: (4) If e has N and e had been placed sufficiently near to an e such that Ne , e would exert a repulsive force on e . This counterfactual respects the intrinsicness thesis, and may well characterize the causal role of negative charge in some sense. But it does not characterize the causal role of negative charge in the robust sense that the causal structuralist requires. For the mere fact that N makes this kind of causal contribution to the situations in which it is instantiated entails nothing that is not itself hedged or conditional about how the objects which possess it will behave in that situation; for all that (4) tells us, negatively charged particles might move towards or away from other negative charges. As such, an object with N might behave in any way whatever if the circumstances are appropriate. Very little can usefully be said about how negatively charged objects will behave simply in virtue of their having N, and arguably the circumstances will make just as important a contribution to the overall behaviour of the object in question as its intrinsic nature, which circumscribes precisely how the circumstances will cause the object to behave.⁷ One might reply that there is no reason to suppose, as I have, that characterizing conditionals like (4) need tell us much about how the objects with the dispositions will in fact behave. But this reply concedes too much. For consider (3) again: whether this is true, or false, seems to depend on how in fact e behaves under counterfactual circumstances. If the dispositional actualist cannot say much about this behaviour in virtue of the dispositions that e has, then surely there are counterfactuals, like (3) itself, that the dispositional actualist cannot give an account of. This is one reason ⁷ Similar arguments, though used for a different end, can be found in Cartwright, this volume: §7, who argues that nothing in the specification of a causal law, and the capacities that law is linked to, entails that the occurrent behaviour will be in accordance with that capacity.

 antony eagle why I devoted so much time to (3), which strikes many as an improper rendering of the characterizing conditional for N: Even if the dispositionalist rejects the use of conditionals like (3) to characterize the natural properties, she still encounters a problem in providing the truth conditions for conditionals like (3). And it is supposed to be one of the hallmarks of dispositional essentialism that it can provide a superior account of the truth conditions of counterfactuals of all stripes. For similar reasons, there is no hope of using (4) to ground other alethic modalities. It may be necessarily true but it does not tell us what will necessarily happen consequent upon the exertion of the forces mentioned in (4), which is surely what would be required to ground natural necessity in actual dispositions. This undermines a thesis that many causal structuralists subscribe to: that the laws of nature are necessary (Bird 2005a: 442–3). If at least some laws are about observable behaviour of negatively charged particles, then those laws may be violated even if negative charge necessarily always makes the same contribution, for the simple reason that nothing intrinsically about those negatively charged particles ensures that their contribution will result in similar consequences. Even if a law of nature did turn out to hold of necessity, the causal structuralist would have no resources to explain this! For an additional fact, that the power in question was unable to be interfered with, is needed to bridge the gap between the actual contribution of the property and the necessity of the manifestation of that property, and that extra fact is not intrinsic to the bearer of the property. And it is no use to abandon the claim that at least some laws concern observable behaviour, for then it looks like the laws are insufficient to describe or predict observable behaviour, which seems to make them substantially incomplete.⁸ ⁸ Of course it may be that what happens depends on the totality of facts about forces, including all instances of (4), and many other claims. But this serves to make the same point again: for what ensures that any given set of such facts is the totality of all such facts cannot be a fact about any particular individual force-exerter, but must be a global fact—just like

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This is all even more obvious when we consider the connections between necessity and counterfactual conditionals. As Williamson (2007: §3) has recently argued, the following claim holds on any plausible account of counterfactuals and necessity (where ‘⊥’ stands for an arbitrary contradiction): (5)
A ≡ (¬A
⊥). If the laws of nature were necessary, it follows by Williamson’s argument that, for the conjuction of all laws of nature L, ¬L
⊥. If L didn’t describe what would observably happen in worlds in which it obtains, it is difficult to see how this would follow, as the lawhood of L would in that case be compatible both with things happening as L says, and as it does not. So laws must describe what happens in worlds in which they obtain. So either of two things hold: (a), (4) isn’t a law (if the forces mentioned are supposed to manifest in appropriate motion), and the best candidate for a law is (3), but, as we have seen, the causal structuralist who subscribes to dispositional actualism cannot account for the truth conditions of (3). Or, (b), (4) is a law, but it must be supplemented by another law that describes how forces manifest in observable behaviour; and this second law will be false (and so not necessary) without an additional non-necessary extrinsic claim that there are no interferers. Either way, there is a claim supposed to be a law that is not necessary. So it does not follow from the dispositional essentialist position that the laws of nature are necessary. Either way, whether the causal structuralist adopts (3) or (4) as the paradigm characteristic counterfactual for negative charge, they will have difficulty grounding robust modal truths in the intrinsic nature of powers alone. This was to be expected: a shifty modal claim like a counterfactual just doesn’t seem to be the right kind of thing to ground a non-shifty alethic necessity, unless one simply identifies the counterfactual with a strict conditional and does gross injustice to our intuitions about counterfactuals. The the fact about the lack of interferers in a particular case. The view that these global facts are all there are is discussed in Section 3.4.

 antony eagle combination of causal structuralism and dispositional actualism is, in a certain sense, self-undermining. The causal structuralist needs certain counterfactuals to characterize the causal profile of a given property. What the preceding arguments have shown is that causal structuralists may adopt the dispositional actualist account of natural necessity if and only if they abandon the attempt to give appropriate truth conditions for these characteristic counterfactuals. Dispositional actualism undermines causal structuralism.

3.3 Hedged conditionals Before abandoning the package of causal structuralism and dispositional actualism, recall that most causal structuralists aren’t particularly happy with using conditionals to characterize the causal role of a property in any case. So when they talk of an ‘essential’ connection between a property and a role, it may be that they don’t intend that role to be characterized by a counterfactual conditional. The most common suggestion is that the role should be characterized by a hedged conditional. So Bird suggests (almost in passing) that the link is between properties and ceteris paribus conditionals (Bird 2005a: 443), while Mumford (1998: §4.9) argues that the appropriate way to characterize dispositions uses ‘conditional conditionals’, where the antecedent is a specification of ideal conditions and the consequent is the stimulus-manifestation counterfactual. I have no problem with hedged conditionals, in themselves. But I’m far from convinced that the causal structuralist who also accepts dispositional actualism has the resources to give an account of these hedged conditionals. Let a hedged counterfactual be analysed as a regular counterfactual in the scope of a hedging operator. Taking Bird’s proposal as our starting point, let the basic hedging operator be the ceteris paribus operator, ‘CP’.⁹ In this framework the causal ⁹ Mumford’s conditional conditional approach can be implemented in this framework: simply let ‘CP(x)’ be true if and only if ‘ideal conditions
x’ is true. I don’t much

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structuralists’ ‘essential connection’ between a property and a stimulus-manifestation conditional S
M turns out to be a necessary connection between a property and the hedged claim CP(S
M). The claim is supposed to be necessary, in that every situation in which the counterfactual S
M is false will be one in which, though the property is present, the surrounding circumstances aren’t appropriate for it to manifest properly. Returning to our example, negative charge will be necessarily linked with the claim that ‘other things being equal, negative charges will move away from each other if placed in close enough proximity’. This hedged claim will not be false in the situations I described above, for those cases in which there is a distorting charge in the vicinity are not cases in which other things are equal. This, at least, is the intuition the causal structuralist relies on. The most pressing worry about hedged conditionals is that they might turn out to be circular and hence trivial. That is, the best analysis we might be able to give of the semantics of the CP operator might require a ceteris paribus operator. At worst, the everyday truth conditions of ‘ceteris paribus, negative charges repel’ might turn out to be just those for ‘Negative charges repel, as long as there are no distorting factors’. This latter sentence entails nothing independently about what constitutes a distorting factor, rendering the analysis of such factors in terms of ceteris paribus clauses circular—distorting factors are a mere shorthand for circumstances not being equal. One proposal which seems clearly threatened by the trivial circularity objection is Mumford’s ‘ideal conditions’ analysis. Mumford argues that we have an independent grasp on what it means for conditions to be ideal for a given property, so whether we need to mention ‘distorting factors’ in the semantic analysis of ceteris paribus clauses is neither here nor there. The problem is that intuitively, ideal conditions are those in which possible distorting influences like his proposal, because the supposition that ideal conditions obtain will typically require consideration of very distant possibilities that evaluating a regular CP claim seems not to involve.

 antony eagle are not present. As such, truth conditions for a ceteris paribus clause involves specifying which factors need to be absent to make for ideal conditions. As Fara (2005: 52–3) argues, genuinely ideal conditions are those in which nothing interferes in any way with the manifestation under the stimulus conditions—just those, of course, in which the stimulus-manifestation conditional for the property in question are satisfied. Once again, the conditions under which a property is successfully linked with a conditional seem to boil down to simply the conditions under which the conditional is true. Similar triviality worries occur with weakened (or ‘fainthearted’) conditionals (Morreau 1997), or appeals to implicit context, or appeals to implicature—all appear to come down to a certain proviso, viz. that normal conditions obtain, but without any independently plausible account of what such normal conditions amount to that is both contentful and non-circular (Fara 2005: 53–61). What we need instead, if we are not to allow the causal structuralist special pleading in this case, is an analysis of the CP operator that is non-circular, and that uses only the resources that dispositional actualism makes available. In particular, the analysis should eschew the use of ideal conditions that can only be accounted for in terms of CP clauses. If ideal conditions are to be mentioned, they should be cashed out independently of the given property in question so that the analysis has a non-circular content. The analysis should also eschew the use of possible worlds as an independent notion, and make do with the primitive causal powers that the dispositional actualist regards as the true basis for understanding and analysing modal claims. This rules out a na¨ıve (and antecedently implausible) account of CP(p) in terms of the majority of possible situations being such that p obtains. But it also rules out a rather more attractive position on ceteris paribus conditionals. This is the view that counterfactuals are already implicitly ceteris paribus conditionals. The CP operator, at least when it operates on a Lewis-style counterfactual, is a null operator. The plausibility of this view rests on the idea that the correct way to understand ceteris paribus is as a kind of similarity: p holds,

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ceteris paribus, if p holds actually and in all similar possible worlds. In that case, a ceteris paribus conditional is true iff the material conditional has no counterexamples either actually or in nearby possible worlds; that is, if the counterfactual is true.¹⁰ This view is fairly plausible in some respects, as the counterfactual does give a good analysis of the de facto dependence of consequent upon antecedent that nevertheless can be disrupted in peculiar situations. It has the apparently unfortunate feature that nothing that actually occurs can ever violate a true ceteris paribus claim (unless there can be some fact true of the actual world but true at none of the most similar worlds, which would be odd). But its primary defect is that it relies on a Humean analysis of modality in terms of possible worlds, and this is not compatible with dispositional actualism. Even if the dispositional actualist can give an account of ‘possible worlds’ talk, the story would succumb to the circularity worry, as the analysis of CP in terms of possible worlds would be required to give the analysis of modality in terms of dispositions and their characterizing counterfactuals. A precisely similar worry would undermine any attempt by the causal structuralist dispositional actualist to adopt the account of CP claims in Lange 2002. Lange claims that CP claims are connected with ‘reliable’ counterfactuals, but the account needs an independent theory of counterfactuals, one that cannot be given by the dispositional actualist. So far, I’ve argued that several ways of understanding CP claims are unavailable to the causal structuralist who accepts dispositional actualism. These proposals have been of varying degrees of plausibility as analyses; importantly, none of my arguments have expressed any kind of general scepticism about the existence or content of CP claims—in contrast to the negative view of CP claims urged by Woodward (2002). In fact, I’m cautiously optimistic that an account of CP claims can be given in terms of generic sentences, to which I now turn. But, once again, I’ll argue that this proposal ¹⁰ There is, I suppose, a variant which maintains that a CP counterfactual is true if the counterfactual is true actually and in nearby worlds; I neglect this view in what follows.

 antony eagle is unavailable to the dispositional actualist. The upshot is that no non-trivial account can be given of the hedged conditionals that the causal structuralist requires. 3.3.1 Habituals and generics A generic claim is a kind of generalization that is true in virtue of what typically or normally happens to the kinds of objects the claim is about, rather than what exceptionlessly happens to those kinds of objects. For example, if some deformed tigers are born with only three legs, then the universally quantified claim ‘all tigers have four legs’ is false. Nevertheless, the generic generalization ‘tigers have four legs’ can still be true, since it is normal for a tiger to have four legs, and three-legged tigers are abnormal. Because generics are tolerant of exceptions in this way, they hold some promise in giving an account of ceteris paribus claims. Recently, this line of approach has been followed by Nickel (2008). Nickel’s account is aimed at understanding ceteris paribus laws, but we may be able to apply it to the conditionals that are our main topic. His proposal amounts to the claim that ‘CP(∀x(Ax → Cx))’ is true in w iff ‘every x that is produced by a process characteristic for A’s in w is a C’ (Nickel 2008: 12–4). (Of course the causal structuralist thinks that the characteristic processes are necessary, to ensure essentiality of causal role.) For counterfactual conditionals, this straightforward extension should suffice: ‘CP(∀x(Ax
Cx))’ is true in w iff in all the most similar worlds to w, every x produced by a process characteristic for A’s in those worlds is a C, so that ‘CP(∀x(Ax → Cx))’ is true at all the most similar worlds to w. If we analyse the CP counterfactuals in this way, it seems, we can associate with each property a generic claim about its characteristic behaviour. Crucial to the viability of this proposal is the idea of a characteristic process for A’s in w. There are two ways to understand this notion, and both of them lead to trouble. Firstly we could understand ‘characteristic’ intrinsically, meaning common or alike to the majority of cases. Yet for a common process to result in

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the right outcome requires that the process not be interfered with, which throws us right back into the problem we examined in Section 3.2 of having a property instantiated but the characteristic process failing to occur for extrinsic reasons. The more interesting way to understand ‘characteristic’ is as including some extrinsic features as well, so that it will be built into the definition of a characteristic process that it results in the right outcome. We can, and do, often understand ‘characteristic’ in this way: think of the characteristic process of development of a human child, where we have little difficulty in agreeing that it is characteristic of that process to result in individuals with ten fingers, even though development can be disrupted in ever so many ways to prevent that outcome. But once again circularity is a significant threat, as there seems little prospect of analysing ‘characteristic’ without involving an open-ended unspecified prohibition on possible interferers. Moreover, while this proposal might help with abnormal origins of some A failing to make it a C, it has no grip on the original problem. For we can certainly imagine an electron produced in the most characteristic manner but that nevertheless fails to move away from another paradigm electron, for reasons having nothing to do with the characteristic process that produces them. The basic problem with the foregoing proposal is that the kind of exception of which generics are tolerant seems to involve uncharacteristic members of a kind. But the interferers/masks objection involves counterdispositional behaviour of a single individual in some circumstances, though it may be perfectly characteristic in other ways. Let us use the term ‘habitual’ to denote a sentence that, like a generic, is tolerant of exceptions, but unlike a generic sentence doesn’t concern consistent behaviour within a kind, but rather concerns consistent behaviour in an individual over time. The canonical form of a habitual sentence is something like: ‘
Object
Verbs when
Circumstances’, as in (6) a Jack drinks when he’s stressed. b Glass breaks when it’s struck firmly.

 antony eagle The semantics for such habitual claims is somewhat involved (Krifka et al. 1995), but that needn’t detain us, as it is quite apparent that we do understand sentences like (6a) and (6b) regardless of what the correct semantic story turns out to be. What is attractive, from our perspective, is that these sentences correspond nicely to dispositions—in the case of (6b), the disposition of fragility—while they also admit of non-falsifying exceptions. In fact Fara (2005) has recently made a strong case that the best way to characterize a disposition is via a habitual sentence. Perhaps some of the problems we’ve run into can be sidestepped by analysing the characterizing causal role of a property directly in terms of habituals (rather than link properties to regular conditionals and then analyse the CP operator). For instance, we could propose that x has the disposition characterized by ‘A
C’ iff C habitually happens to x when A happens to x. Better still, we could simply propose that a property is necessarily linked, not to a conditional, but to a habitual claim. This proposal looks promising already: habituals do resemble conditionals in some respects,¹¹ and this may account for why it has been thought that conditional analyses of causal roles are appropriate. So while it must be admitted that this proposal does away with the letter of causal structuralism because it abandons the essential link to conditionals, it may yet suffice to give a good account of what a causal role is. Yet while habitual sentences make for a very promising analysis of disposition ascriptions, they serve the dispositional actualist’s purposes very poorly. And both of these facts can be traced to the exception-tolerance of habituals. Dispositions can exist despite occasionally being interfered with, so exception tolerance ¹¹ In this connection the popular thesis that habituals involve an implicit generic adverb of quantification GEN is particularly noteworthy (Heim 1982). This proposal connects with the thesis that some apparently conditional claims involving an ‘if ’ clause do not feature a conditional connective, but rather merely serve to highlight the restrictor (Lewis 1975). (Kratzer (1986) goes further, and argues that no conditional features a conditional connective.) If this is right, and the evidence for it is persuasive, the mistake of regarding dispositions as linked to conditionals instead of habituals is readily explicable.

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is necessary for a correct characterization of when a disposition exists. But if our aim is to characterize all natural necessity in terms of dispositions, as the dispositional actualist intends, exception tolerance is a bad feature. For one of the characteristics of genuine necessity is that is truly exceptionless. To fix ideas, consider the following na¨ıve characterization of necessity in habitual terms: (7) ‘Necessarily Fx’ is true iff x Fs under any circumstances. If this is a genuine habitual, we should expect x to habitually satisfy F —but also if on occasion x failed to F, that needn’t falsify the habitual. But of course if, on at least one occasion, x fails to F, then we know that it is not necessary that Fx. Because any necessity operator
exhibits the characteristic feature that
p |= p, if ever it occurs that ¬p we can conclude ¬
p. Moreover, there seems no way of modifying the simple account of (7) to secure genuine exceptionlessness—no matter what conditions one inserts, it is always possible that a genuine habitual could be true even if the object fails to manifest in those conditions. Things are not better with ‘possibly’, as the obvious analysis is such that ‘possibly Fx’ holds iff it is not the case that x fails to F under all circumstances. So ‘possibly Fx’ is false iff the right hand side of this biconditional is false; iff the habitual sentence is true; and the habitual sentence can be true even if x does sometimes satisfy F. But we then get the implausible result that even if x does F sometimes, it can still be impossible that Fx! It may be that some uses of ‘necessary’ share this exception tolerance with habitual claims. After all, consider the following use of ‘always’, which is a temporal analogue of an alethic necessity: (8) Jack is so unhealthy; he’s always smoking. (8) can be true even if Jack sometimes doesn’t smoke. But even if there are uses of ‘always’ that basically express habituals, that doesn’t mean that every use of ‘always’ does, so an across the board

 antony eagle habitual-based account of ‘always’ must fail. The same is true of ‘necessary’, with the additional feature that cases like (8) involving ‘necessary’ are much harder to generate. Consider: (9) To obtain a grant it is necessary to complete an application form. It is perhaps possible to read (9) as being compatible with someone getting a grant without applying. But it is much more plausible to regard (9) as straightforwardly incompatible with the possibility of a grant without application. So while generics and habituals might provide a good account of CP and causal roles, they do not do so in a way that is suitable for the needs of the dispositional actualist. I conclude that some other approach is necessary for the causal structuralist and dispositional actualist to avoid the problem of interferers in an acceptable manner. 3.3.2 Primitivism Some causal structuralists who are tempted by dispositional actualism recognize the problems I’ve raised. Here, for instance, is Brian Ellis acknowledging that properties are susceptible to interference and masking: [W]hat dispositional properties do is dispose the things that have them to behave in certain ways, depending on the context. (Ellis 2001: 129)

No guidance is given about how we might separate what is contributed by context from what is contributed by the disposition, and one might well think that if the resulting behaviour depends on context that will make the link between property and behaviour contingent, precisely what the causal structuralist objects to in the Humean picture. (And while the Humean says explicitly that the relevant contextual factors under which a property leads to a behaviour are the laws of nature, Ellis says nothing much about his ‘contexts’.)

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Elsewhere, however, Ellis is a bit more explicit about the kinds of impact that context can have: [T]hings may not interact as they are intrinsically disposed to interact. For other forces may come into play. But then the laws of nature we call ‘‘causal laws’’ allow for this. The causal laws are not contingent universal generalisations about how things actually behave, but necessary truths about how they are intrinsically disposed to behave. (Ellis 2001: 239)

The new concept introduced here is of being ‘intrinsically disposed’ to behave in a certain way. Of course, as Ellis recognizes, this is not the same as being disposed simpliciter, because the latter kind of disposition would necessitate a conditional that could be interfered with. Ellis therefore is proposing instead that a property is to be necessarily linked with a description of its intrinsic disposition, so that a property P is characterized by a new kind of hedged conditional—a conditional prefixed with ‘intrinsically’, so that anything instantiating P is such that intrinsically (S
M), even if it is not the case that S
M. This proposal is somewhat obscure, to say the least. Ellis (2001: 28) does give an account of intrinsicness in his causal sense: G is a causally intrinsic property of x iff x would display G iff there were no external influences affecting the display of x’s properties. I suspect that this merely describes the problem of interfering conditions, rather than answering it. The proposal also seems susceptible to counterexample: the property ‘x is not under external influences that affect the display of x’s properties’ seems to turn out causally intrinsic but is, extremely plausibly, extrinsic.¹² Even if the proposal was explanatory, and survived the counterexamples, the definition tells us only when a property is intrinsic. There seems no straightforward way to derive from this the semantics of the one-place sentential operator ‘intrinsically’ that Ellis seems to be appealing to in the above quotation. ¹² I believe this counterexample is due to Josh Parsons.

 antony eagle A charitable reading of this passage takes Ellis to be advocating a kind of primitivism. This is the doctrine that the connection between a property and its characterizing conditional is not to be analysed or understood in terms of other, more primitive notions. The main problem facing this interpretation of Ellis’s proposal is that we have no independent understanding of how his new ‘intrinsically’ operator works. Normally, ‘intrinsically p’ is factive, and simply states that the basis for the truth of p is intrinsic to some object. But Ellis’s operator is not factive, as the characterizing conditional in the scope of ‘intrinsically’ can be false even while, presumably, the whole claim is true. It is thus difficult to see how any evidence we might have for the falsity of the conditional could ever lead to the falsity of the ‘intrinsically disposed’ ascription, and this seems rather to undermine Ellis’s claim that the discovery of the essentially dispositional properties of natural kinds is the main task of science. Until we have more details on what Ellis’s proposal involves, it is impossible to accept it. A more plausible kind of primitivism is to be a primitivist about ceteris paribus claims. At least in this case one can claim that the various difficulties that people have faced in giving accounts of the CP operator do motivate taking it as a new primitive, completely independently of dispositional actualism. Yet even setting aside the methodological unpleasantness of simply taking the CP operator as a new primitive, this move will not help. Primitivists will maintain that, even despite the impossibility of an analysis, there will be some way to understand the behaviour and function of CP operator. Presumably this understanding will be provided by our ordinary familiarity with the idea of ‘other things being equal’. This causes problems for the combination of causal structuralism and dispositional actualism, because as a thesis primarily about perfectly natural properties, most of the properties it is centrally concerned with are not going to be manifested in isolation from other properties. In that case, it seems intuitively plausible that other things are never equal: there are always actually interfering factors. If other things are never equal, the CP operator seems, intuitively,

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to give trivial results in this case: CP(p) is true for any claim p involving perfectly natural properties (even if CP is not trivial for claims about higher-level phenomenological properties). If the intuitive understanding of CP renders any property-specifying conditional trivially true, we can reasonably claim that no genuine property specification has been given. If the causal structuralist wishes to retain a contentful version of their conditional thesis, they should wish for an understanding of CP which does not give this trivial result. As such primitivism is not an option, and we must see whether the causal structuralist can provide a non-trivial analysis of the CP operator. This is practically important for the causal structuralist too. Many causal structuralists regard their position on property identities as the only scientifically respectable one: any other view, involving mysterious quiddities, seems to have little empirical support. But unless the concept of ceteris paribus conditions can be spelled out in an independent fashion, there will be little empirical content to causal structuralism either. For suppose we witness a manifestation M in circumstances S; do we conclude that a property P is present which has the characteristic conditional S
M? We should not, unless we are antecedently convinced that conditions are ideal and thus that it is really S that M depends on (rather than S plus some interfering background conditions). So there seems no way to fix the identity conditions for properties without a way of characterizing CP conditions. And, as we have seen, there is no currently plausible theory of CP claims that is acceptable to the causal structuralist who accepts dispositional actualism.

3.4 Everything is connected? The problem of interferers (or masks) arises because the intrinsic nature of some object places no constraints on its surroundings, and thus the manifestation of the characteristic behaviour of that object can be prevented in many cases. We saw in the previous section that there is no acceptable way for the dispositional

 antony eagle actualist to rule out all and only these interference situations. But some dispositional essentialists have countenanced a more radical response: denying that there is a distinction between an object and its surroundings. This amounts to abandoning the thesis of object separability discussed above (Section 3.1.1). Ellis, for one, gives hints that he accepts something like this claim. At one point he makes the offhand remark that the Humean picture of the world as a collection of loose and separate entities is in conflict with quantum mechanics, and that the correct picture of our world should be more ‘holistic’ (Ellis 2001: 52). (Perhaps the source of this view lies in Popper’s (1990) view that the only non-arbitrary ground of probabilities in quantum mechanics lies in a propensity of the whole world to produce a certain outcome.) Whatever its provenance, the view is highly controversial as an interpretation of quantum mechanics, and for that reason alone doesn’t provide strong support for the denial of object separability. Regardless of its scientific merits, this view is radically revisionary of our ordinary practices in using counterfactuals—so revisionary as to be unacceptable. What we attempt to capture using counterfactuals is a kind of robust dependence between the antecedent and consequent: a dependence that persists through external disruptions. If there are no external disruptions, because all properties are global properties of the whole world, then it is hard to see how our practices in using counterfactuals can even make sense. Moreover, as our discussion of habituals shows, we can make sense of ascribing regular habits to localized individual objects; the response to the existence of localized claims is not to deny that they make sense, but to deny the overly holistic approach advocated (albeit in passing) by Ellis.

3.5 Conclusion So far, I’ve argued that the combination of causal structuralism and dispositional actualism is subject to the problem of interferers: that the characterizing conditionals for properties aren’t going

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to hold whenever the property is instantiated. I argued in the previous section that the most plausible strategies for hedging these characterizing conditionals are unavailable to the dispositional actualist. In the absence of plausible alternatives, I conclude that one of the three claims (§2) that characterize causal structuralism and dispositional actualism has to be given up. But which? The discussion of habitual claims, I suggest, shows that it can make sense to ascribe habits to individual objects in relative isolation from their environments. If habituals can be used to analyse dispositions, then I think causal structuralism is a viable option: perfectly natural properties are to be individuated by the habits they convey to intrinsic duplicates which possess them. The culprit, rather, is dispositional actualism: the claim that necessity and possibility are grounded in perfectly natural dispositional properties. It was dispositional actualism that gave rise to most of the trouble in Section 3.3, and by abandoning it, and keeping a more Humean understanding of modality, the causal structuralist has the resources to give a plausible account of property identity. Few causal structuralists will be happy with this option, I suspect. I don’t think this is because causal structuralism is itself in tension with a Humean picture of modality. Rather, I think many actual adherents of causal structuralism (including dispositional essentialists like Bird and Ellis, and powers-theorists like Molnar and Mumford), are in the grip of a non-Humean picture of the world, one consequence of which is causal structuralism. For many dispositional essentialists, the Humean picture is of a ‘dead’ world, moved from without by laws of nature. By contrast they wish to maintain that powers within objects animate the world and explain why things happen as they do; causal structuralism follows as the most natural way to individuate these animating powers. On reflection this seems to take a very robust view of properties as things, acting and causing observed behaviours. Such a robust view seems to inherit many of the objectionable features of quidditism, particularly the idea that properties somehow are

 antony eagle something over and above the behaviour of the objects which have them. By contrast, a more minimal causal structuralism does away with a robust commitment to properties as things, perhaps proposing rather that having a property is just satisfying a habitual sentence.¹³ None of the more radical anti-Humean aspects of dispositional essentialism seem to follow from this view alone. There is no commitment to properties as entities. There needn’t be commitment to the necessity of the laws of nature: while salt might habitually dissolve in water, there may be exceptional cases. And the recognition of the possibility of exceptional cases shows that there mustn’t be a repudiation of possible worlds, whether concrete or ersatz, as we shall need some such possible situation to be one in which there is an exception to the habitual claim. It follows, I suggest, that arguments for dispositional essentialism that appeal to causal structuralism beg the question—they only appear to lead to the controversial dispositional essentialist view because some aspects of the latter view are implicitly presupposed when characterizing causal structuralism. In this paper I’ve been concerned to articulate what causal structuralism by itself is committed to. I’ve argued that the problem of interferers (or masks) means that causal structuralists cannot explain counterfactuals purely in terms of dispositions; and no weaker hedged conditional can fulfil the dual role of characterizing properties and explaining alethic modalities. So I conclude that there is excellent reason even for a causal structuralist not to attempt a reductive account of modality in terms of dispositions. It follows that the dispositional essentialists and powers-theorists were too quick to repudiate a Humean conception of modality, as no acceptable alternative conception is available to them. In that ¹³ A similar, overtly nominalist option is explored by Ann Whittle (this volume); many aspects of her position are reflected in my discussion above, particularly the observation that a causal structuralist can tread a middle way between realism and phenomenalism. However, she appears more resistant to the independent appeal to facts about possible situations that I think is the fundamental upshot of this discussion.

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case, many of the supposed ontological economies of powers and dispositional essentialism disappear, and many of the arguments from causal structuralism to dispositional essentialism fail. The question then becomes: what arguments can these philosophers give for their position if causal structuralism doesn’t entail it? My suspicion is that no such arguments exist; but I don’t have space to defend that here.¹⁴ ¹⁴ Thanks to audiences at La Trobe, Oxford, and the Dispositions and Causes workshop at the University of Bristol; thanks also to Toby Handfield for many helpful comments, and John Poland for discussion.

4 Leaving Things to Take their Chances: Cause and Disposition Grounded in Chance Stephen Barker

Chances, causes, counterfactuals, and dispositions are related in some way that is revelatory of their natures, but which way? Impressed by the power of counterfactuals as an analytic tool, many have thought that both cause and disposition are grounded in counterfactual facts. Think of causes as facts to do with what wouldn’t have been if certain events had not occurred. Think of dispositions as analysed in terms of facts about what would have been if certain events had occurred. Now refine this idea by bringing in chances to deal with indeterministic elements that may attend both cause and disposition, and contrive more complicated counterfactual conditions to cater for pre-emption, finks, antidotes, and other disruptive phenomena. One has therein the current counterfactual-theoretic program to tame cause and disposition. Its practitioners don’t agree about how it should work, or whether it really can. I shall argue that the question of its fate does not rest with their sorting out the details; it turns on a deeper matter. A closer look at chance shows that the whole counterfactual reductive program starts on the wrong foot.

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My contention is that cause and disposition are both grounded in chance. Cause is not grounded in counterfactual chance-raising facts, as in the orthodox program, but more directly in the nature of chance itself. Cause is a form of realized chance, where a realized chance is an instantiated chance property—the chance of e at t —whose event subject matter, e, obtains. More precisely, c causes e if and only if there is a realized chance of e at tc , the time of c, issuing in a chance process linking c to e. A chance process is a set of events whose members are ordered in terms of relations of chance realization. Cause has this relation to chance because (a) facts of chance imply, in themselves, facts of cause, and (b) this implication cannot be explained by the hypothesis that chance is reducible to cause; it is cause that is reduced to chance. In this scheme, dispositional properties are properties that contribute to the fixation of chance properties. Chances are determined by conditional chances. The properties that feature in conditional chances are the dispositional properties. Neither the facts of cause nor the facts about dispositions are constituted by counterfactual facts. Rather, counterfactuals are mere symptoms of more fundamental facts of chance and disposition. They are analytic epiphenomena in this domain.

4.1 The arrow of cause and the arrow of chance Counterfactual analyses of causation aim to explicate cause through facts of counterfactual chance-raising. For example: had a cause c not been, the chance of effect e would have been lower than its actual chance.¹ If we invoke chance in a counterfactual chanceraising theory it seems we have in mind single case objective chances. We need these because we need some kind of modally robust chance—not something fixed by mere contingent relative ¹ See for example, Lewis (1973a); Noordhof (1999); Schaffer (2001a); Ramachandran (2004).

 stephen barker frequencies. We need them to be single case because facts of causation can be single case. We think of chances, in this sense, as propensities about the single case.² Are chances proportions of branching worlds or properties fixed by the platitudes we affirm about chance, or something else? I will not attempt to offer an answer here. No theory of chance will be given. Rather, my goal is to describe what the relation is between cause, chance, and disposition. I contend that the arrow of chance and the arrow of causation are one and the same. Where there is a causal process, there is, what we might call, a chance process. If the causation is directed towards the future, then the chances are directed towards the future; if the causation is directed towards the past, then the chances are pastoriented. Does that mean that chance is a kind of partial potential causation, or that causation is nothing but a form of realized chance? I shall urge the second alternative, but first let us examine more closely the linking of the arrows of chance and cause. The coalescence of the arrows of chance and cause is distilled in the following Cause–Chance principles: CC1: If c causes e, c contributes to the chance of e at tc , the time at which c occurs. CC2: If at a time t, there is a non-zero chance of e and e obtains, then at least some of the conditions at t that determine the chance of e at t, caused e.

In defending these principles I allow, first, that there might be backwards chances, and backwards causation, so an event e might lack an earlier cause, and thereby lack an earlier chance—more about that in a moment. Secondly, there is no a priori temporal continuity condition for either cause or chance. This means that we allow in principle situations in which an event e occurs, where e has a prior causal history, but there are times t prior to e such that there is no cause of e at t, although there are causes of e before ² They are not dispositions to produce a certain frequency of outcomes given repetition of a certain chance set up.

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t, and after t. In such cases, the cause process leading up to e is temporally discontinuous, with a discontinuity at t. There is no chance, physically speaking, of e at t. Nevertheless, armed with the facts about earlier causes of e, we can assign a probability of e at t, but this probability will not mirror a chance of e at t. CC1 states that causes imply chances. Nearly all cases of cause we know of are directed towards the future, and the corresponding chances are also directed towards the future. The pushing down of the plunger causes the explosion seconds later: the pushing down of the plunger contributes to a future-directed chance of an explosion. Contributes here means that the plunger-pushing event is part of the explanation of why at t there is a certain chance of an explosion. The general argument for CC1 might be summed up thus: causes explain their effects. If c causes e, then c explains e, and thus, at time t, c is a potential explanation of e. How then can c at t not contribute to fixing the chance of e at t? We do not think that cause is necessarily future-directed; there may be backwards causation. According to CC1, where causes go, there go chances, and so where there is backwards cause, there is backwards chance. If we accept de Beauregard’s (1977) hypothesis that the correlations between separated twin particles that are in a quantum entangled state are such that the measurement of one causes its twin to have had a certain spin value earlier, then we commit ourselves to backwards causation. But if we accept that causes influence the chance of their effects then, in the case of backwards-directed cause, the chance of the effect must be a backwards-directed chance. But here there is an objection. For Lewis (1980), the chances of an event after t are 1 or 0 according to whether or not the events occurred or not; there are no values in between 0 and 1. The subjective probability of some past event, might, given someone’s evidence, be between 0 and 1. But for Lewis, the objective chance will never fall there. All backward chances are trivial. The spirit of CC1 is that there may be non-trivial backwards-directed chances. Lewis then must be wrong to have taken this line. Indeed, it is not

 stephen barker clear why he takes it. Lewis accepts a chance-raising view about causation, and embraces the conceptual possibility of backwards causation. If no explicit temporal order is built into causation, then it cannot be so built into chance. Rather, the temporal order of any particular case of causation, and that of any particular chance, emerge from facts that do not, as such, assume facts of temporal direction.³ Another source of concern about CC1 is the prospect of events that are possible and have causes but have chances of degree zero. Consider a roulette wheel that has continuum many physically concrete points on its perimeter. Spinning the wheel causes some point on its perimeter to be aligned with a point on the structure supporting it. Suppose spinning is a genuinely stochastic process. One might argue that the objective probability of the wheel stopping on any of its perimeter points is zero. If so, the spinning of the wheel caused the wheel to stop on π, but did not contribute to a non-zero chance of its stopping on point π. Thus, c causes e, but c does not make a contribution to a non-zero chance of e. This is not specifically a problem for CC1, but for any view that c’s causing e implies c raised the chance of e at tc . Had there been no spinning there would still have been zero chance of the wheel stopping on π. However, there is reason to suspect that there must be greater chance in the actual case, than in the counterfactual case. Treating the chance in the actual case as not zero but infinitesimal would respect that thought—see Lewis (1973a, postscripts). An infinitesimal chance is positive, in which case CC1 is not contravened. Unlike CC1, CC2 is bound to be controversial. Yet, it is not devoid of intuitive appeal. Suppose that at time t there is a positive chance of a match lighting later. Let us suppose that our explanation of this chance, the properties at t that ground it, are that it is being struck at t, that O2 is present, that the match and ³ See Lewis (1979) for an explication of cause’s arrow in terms of de facto physical features of the universe.

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ambient conditions are dry, etc. Nothing else contributes positively to the chance of lighting. Suppose that the match lights. Then the conditions that made some positive contribution to the match’s lighting are contributors to the cause of the match’s lighting. Thus, the presence of O2 , the dryness, the striking, etc., are all causes of the match’s lighting. The arrow of chance, given that chance is actualized, is the arrow of causation. As I will show below, it is not the case that every chance contributor is a cause, but amongst all the events that are chance contributors, some will be causes. This is a case of future-directed chance. But what of backwardsdirected chance, which we are not ruling out? At time t in the history of the universe, there are a vast set of effects f , and they probabilize, possibly to degree one, earlier causes c. These probabilities are objective, since they do not depend on any ignorance of facts holding at t. But, if these backwards-directed probabilities are deemed real chances, then, by CC2, there is all-pervading backwards causation, where, evidently, there is none. Let me offer a reason, independent of CC2, for thinking that such backwards-directed objective probabilities cannot be chances. Whether or not we are theoretically attracted to a counterfactual chance-raising analysis of causation, we should admit that there is some link between chance-raising and cause. I hazard that the principle RC, below, states correctly what that link is. In a world devoid of redundant causation—causal set ups such as pre-emption—if c counterfactually raises the chance of e, c causes e: RC: Where c and e occur, if the chance at tc of e would have been lower, had c not obtained, then if there is no redundant causation in operation, c caused e.

Consider now the following simple case of an effect probabilizing some earlier cause. The existence of a certain decay product P at time t makes it probable that there was earlier on a decay event D. If there had been no product P, then the probability of an earlier decay event D would have been much lower. But

 stephen barker by RC, given that there is no redundant causation between P and D, the presence of P caused D. But that is absurd. If so, the past-directed probability of D, generated by P, cannot be a chance. Generally speaking, RC implies that past-directed probabilities of effects, generated by causes, are not real chances. If they are not real chances, then CC2 cannot be applied to commit us to bogus backwards causation. An objection not unrelated to that just given is the problem of inverse chances. It seems we should accept that there are conditional chances, since properties instantiated at times can determine chances at those times. Let ‘Ch(e) = m’ mean that the chance of e’s obtaining is m, and ‘Ch(e|c) = n’ mean that the chance of e’s obtaining, given that c obtains, is n. But now suppose that chances are probabilities that conform to the probability calculus. If so, Bayes’s theorem holds for conditional chances: Ch(c|e) = (Ch(e|c) · Ch(c))/Ch(e) But if Bayes’s theorem holds for chances, then where Ch(e|c) has a value, so does Ch(c|e). The problem is that although the value Ch(e|c) may look like the value of a conditional chance, the value of its inverse Ch(c|e) may not—see Humphreys (1985). Let us assume that the condition e of the inverse chance Ch(c|e) = m obtains. Then there is a chance Ch(c) = m, which may lack the causal implications required by CC2. CC2 will be contravened. Indeed, given RC, it can be argued, in a way analogous to that just rehearsed, that the inverse chances will generate the same problem that our pseudo backwards chances generated: they imply through RC bogus causation. What should the response be? Humphreys (1985) and Fetzer and Nute (1980) accept that chances are not probabilities; they are not modelled by the axioms of the probability calculus, and so don’t conform to Bayes’s theorem. There is no a priori reason to think that they should. If so, we can block the threat to CC2 by denying that these inverse probabilities are chances.

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For Lewis (1980), the chance of an occurring event e at the time te of e is 1. But doesn’t that contravene CC2? Nothing at te causes e, since it is e itself that confers a chance of 1 at t on e occurring at te . But such chances, I suggest, are merely degenerate cases. We do not think of these things as propensities in the same sense that a set up, prior to te has a propensity to issue in e. One final reason for objecting to CC2 is spontaneous, apparently uncaused events. Consider a single radioactive isotope I with some half-life. I has a chance at time t of decaying by t∗ —say 0.6. Say I decays. Then there is a realized chance. But where is the cause? What fact or event at t caused the decay? If no causal fact can be identified, then CC2 is in trouble. But we should ask: why isn’t it that the isotope I’s having a certain structure, which is the ground of the chance of decay at t, also the cause of the decay? I has a certain configuration of protons and neutrons, bound by nuclear forces. It is this structure, the fact that I has the property of possessing such a structure, that produces the chance. If so, why isn’t it the fact that I has this structure that is the cause—admittedly indeterministic—of its decay? The mere fact that this might be an essential property should not deter us: essential properties can be causally efficacious. On the other hand, in the case of isotope I, there is a 0.4 chance that no decay event occurs by t∗ . Suppose that this chance is realized. What is the cause of non-decay? It is not the presence of I: one could not say that there was no decay because I was present. One could, however, say that there was no decay because there was not a constant stream of heavy particles bombarding I. (Such a stream of bombardment would have grounded a higher chance of decay.) That, admittedly, is to introduce an absence to explain another absence, but causation by absence is apparently a form of causation. If so, we can expect chance by absence. 4.1.1 Explaining chance–cause correlation I think we have good reason to think CC1 and CC2 hold: the arrow of cause goes with the arrow of chance. Our question now

 stephen barker is why? An explanation might take one of two alternative routes: (A) analyse chances by appeal to cause—some kind of probability combines with cause to produce chance; (B) analyse cause in terms of chance. Dowe’s (2002) proposal falls into category A. He explains chance in terms of what we might call nomological probability. Nomological probability is the kind of partial determination that facts at a time and laws provide, for both past and future events. Think of it as physical degrees of determination that facts at a time bestow upon both past and future events. Some nomological probabilities are not chances; for example, the degrees of physical determination imposed by effects on earlier causes are not chances. But some nomological probabilities are chances. According to Dowe, a chance is simply the nomological probability that causes give effects. Dowe must mean potential causes here rather than actual causes. Chance is then analysed as follows, where PrC (e) is the nomological probability fixed by a set C of obtaining states of affairs at t that are potentially causes of e: Cht (e) = PrC (e) Evidently, this approach to chance cannot utilize a counterfactual chance-raising analysis of cause, since cause is being used to analyse chance. Dowe (2000) has his own theory of cause: a process theory combined with a counterfactual approach to cause by omission and by prevention. Details do not concern us here. My objection to Dowe’s approach concerns interpretation of PrC (e). He calls this a partial probability. But what is that? One gets the impression that Dowe thinks that for every set of possible states of affairs S at t and event e not at t, the laws will assign a probability value n, this being the probability of e conditional on S. And so, for any set of potential causes C of e at time t, the laws will assign a probability to e given C. But this idea is wrong. Not every state S at t will in itself impose a probability on e. Take the case of isotope I in a box. In this case consider the possible state of affairs that there are alpha particles in the box by

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time t∗ . One way this could come about is that I decays and emits alpha particles. Another way is that some other isotope is in the box decays and emits particles or some isotope penetrates the box and decays releasing alpha particles. But suppose there are no such other isotopes. Under the circumstances there is a set of conditions that act together as the potential cause of alpha particles in the box. These are: (i) I has such and such internal structure. (ii) Nothing is going to annihilate I before t∗ . These facts in themselves will not fix a nomological probability of there being alpha particles in the box before t∗ . We need to supplement them with the fact: (iii) There is no other isotope in the box, nor any isotope outside the box that can penetrate the box. It is the conditions (i)–(iii) which fix a nomological probability—the nomological probability 0.6 that there are alpha particles in the box by t∗ —not simply conditions (i)–(ii). First note that the required further totality fact (iii) is not a potential cause of there being alpha particles in the box. Thus if alpha particles appear in the box, we cannot say that this event was caused by the fact that I was the only isotope in the box, nor by the fact that no other isotope penetrated the box. These look simply false as causal claims. In short, although it is true that where there is a realized chance of e, amongst the determiners of the chance there are facts that will cause e, it does not follow that all determiners of chance are potential causes. But Dowe’s theory assumes this. The obvious response to this difficulty is the following modification: a chance at t of e is a nomological probability whose determinants include potential causes of e. Fine. But what conditions have to be met by a set of state of affairs S, including potential causes, to fix a nomological probability? If we look at the conditions (i), (ii), and (iii) we see that they fix a nomological probability only because they embody a fact of totality. So, generally speaking,

 stephen barker S must be a kind of totality state; it must specify all the factors relevant at t to the determination of a probability. With this admission, however, we can begin to sow serious worries about Dowe’s theory of chance. Chances are meant to be nomological probabilities. Importantly, they are meant to be the partial ones fixed by potential causes of e. But this is incompatible with Dowe’s approach. If chances are nomological probabilities they can only be properties of totality states distilling all the physically relevant features at a time. This requirement, that determining factors be total, destroys his theory when it comes to chance in the context of backwards causation. Consider unrealized backwards-directed chances. Say at t that Major Tom is about to leap into a time machine. The time travel is chancy. It depends on whether Major Tom survives the journey through the wormhole and that depends on whether the wormhole will collapse. We ask: will Major Tom get there or not? We use will here because we are concerned with internal or personal time in Lewis’s (1976) sense. Say that the chance is 90%. There is a 90% chance that Major Tom will appear 100 years ago. Tom enters, but, unfortunately, the wormhole collapses. Tom never gets to the past. The chance is unrealized. Our concern now is to explain what is the chance property at t of getting to t∗ a hundred years ago. What objective conditional probability yields 90%? We need a condition S that represents a totality condition at t such that PrS (Major Tom survives) = 90%, where S includes potential causes of Tom’s survival. The state S cannot be (iv) below—where D is the set of features that will determine the state of the worm hole: (iv) Major Tom has just entered the time machine. The time machine is in state D. That is not a totality state. It includes all the potential causes, but, as we noted above, potential causes in themselves do not fix nomological probabilities. We need a totality state capturing all the physical features relevant to the nomological probability. We

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cannot simply restrict them to potential causes! Unfortunately for Dowe’s theory, the totality state that does that is not one that assigns 90% to Major Tom’s presence 100 years ago. It assigns almost zero to that state of affairs, since there are no traces of Tom’s being in the past 100 years ago. Tom never made it, and that fact is etched into the present time t. Thus the nomological probability is close to zero, whereas the chance is meant to be 90%. If there are backwards chances then they cannot be a species of nomological probability. Chances have to be something different. Intuitively, (iv) is the kind of fact that one invokes to ground the chance of Major Tom getting to the past. That shows that (iv) is a totality condition in this sense: it is all the relevant chance-producing features at time t. But this means that chance isn’t nomological probability. What is relevant to chances is not identical to what is relevant to nomological probabilities. I conclude that the attempt to reduce chance to a form of nomological probability fails. I cannot see any other way of analysing chance in terms of some other notion of probability and cause.⁴ I conclude that analysing chances in terms of cause and some form of objective probability won’t work as a way of explaining CC2. Alternative A above fails. 4.1.2 Option B: Counterfactual chance-raising analyses of cause Alternative B was that we explain causation in terms of chance, and thereby explain CC1 and CC2. The orthodox counterfactual chance-raising view of causation is one way in which people have thought cause is reducible to chance. I now argue that this won’t work in explaining CC2. Take the basic counterfactual chanceraising account: c causes e if and only if c and e obtain and had c not occurred the chance of e would have been lower than its actual ⁴ For example, a proposal that the chance is Cht (e) = the nomological probability at t that something at t causes e, will not work for much the same reasons that Dowe’s proposal fails.

 stephen barker chance. In terms of this analysis the right hand side of CC2—that there is an event c at t, contributing to the chance of e, that causes e —is equivalent to the conjunction: (i) At a time t, there is a non-zero chance n of e, and e obtains; (ii) There is an event c, which obtains at t, and had c not obtained, the chance of e at t would have been m, and n > m. The conjunct (i) is the antecedent of CC2; it is the statement that there is at t a realized chance of e. The conjunct (ii ) is some further thesis of counterfactual dependency. If so, CC2 is equivalent to the statement below—where → is entailment: [(i) is the case] → [(i) is the case & (ii) is the case]. Obviously, any proposition entails itself. The issue, then, is whether (i) entails (ii). I maintain it does not. If (ii) is true it is because: (a) e has some actual chance at t of n, determined by physical conditions at t; (b) certain further conditions hold that determine that the counterfactual probability of e is m; (c) n > m. The problem is that (i) can only entail (a), since (i) amounts to (a). (i) cannot entail (b), since (b) is about other facts holding under the circumstances. Evidently, (a) itself does not entail (b). But for (i) to entail (ii) it must entail (a), (b), and (c). Matters will not be improved by looking at other versions of the counterfactual chance-raising account, since any such accounts will provide analyses of the consequent of CC2 that are equivalent to conjunctions of the kind above. That is, one conjunct will be of the form (i), with the other conjunct being some specification of a counterfactual condition.⁵ ⁵ Noordhof (1999) offers a counterfactual chance-raising analysis in which the chances raised are not at tc , the time of c, but at the time just before e, the effect. On this analysis CC2 would not reduce to an entailment of the form described above. Still, there would be

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If this is right, the counterfactual chance-raising analysis of cause cannot explain CC2.⁶ Therefore, counterfactual chance-raising analyses of causation must be false. I think the real explanation of CC2 is not by appeal to counterfactual chance-raising, but by appeal to something basic about chance. Causation is itself just a form of realized chance. I will elaborate this view in the next section, but first let me indicate, in general terms, the intimate relation between chance and cause suggested by reflection on an important feature of chance: the law of large numbers. The law of large numbers states that the long run relative frequency of positive outcomes of repeated identical trials converges on the chances of individual positive outcomes of the trials.⁷ We can expect such convergence only if we take it that events come about because, and only because, of the properties that determine their chances. In other words, CC2 must be true: if an event e happens, then the events that are its causes at t are found amongst the properties that determine that it has some positive degree of chance at t. Note that these determining properties will be perfectly ordinary, and in themselves, non-chancy properties. It is just that they are chance-determining, and it is amongst a problem. Why would CC2 hold at all? One problem is that Noordhof ’s analysis assumes that if c causes e, there is a chance of e just prior to e. But there is no reason why that should be if cause functions at a temporal distance. A second problem is that from the fact that at tc there is a chance of e, and e occurs, why would anything follow about a counterfactual chance-raising condition regarding a chance just before e? ⁶ In arguing for CC2, I invoked the principle RC. I note that RC does not commit us to a chance-raising analysis of cause, since, it is not a reductive principle about chance-raising in relation to cause. ⁷ More technically, the law of large numbers states that if independent trials with the same chance n of success in each trial are repeated, the likelihood that the percentage of successes differs from the chance n by more than a fixed positive amount, e > 0, converges to zero as the number of trials m goes to infinity, for every positive e. Perhaps the proponent of single case objective probabilities ought not to believe that the relative frequency of positive outcomes will necessarily converge on the chance n. Rather they should have a degree of belief differing infinitesimally from 1 that the relative frequency of positive outcomes will converge on n. That’s because it is physically possible that there is non-convergence, though, one might judge, the chance of non-convergence is infinitesimal. I will not consider this refined view in the main text.

 stephen barker these chance-determining properties that the causes of events are found. I am not seeking to explain the law of large numbers as some fact realized in physical reality, but merely to show that there is a constraint on its acceptance as more than just a mathematical truth. If we do not accept CC2, then we have positive reasons not to accept the law of large numbers, thought of as the claim that if we were to repeat certain chance set ups infinitely, then relative frequencies would converge on chances. To illustrate the idea, consider a world of isotopes, with half lives of some specific value. The chance of decay of any such isotope within, say, one day is also some specific value n. The law of large numbers says that in the long term, relative frequency of trials in which an isotope is left for a day and decays to the total number of trials will converge on the chance of decay n. But say God is inclined to intervene causally in this world through supernatural agency. Indeed, God, at regular points throughout the life of this universe, induces isotopes to decay. If this is so, the long term relative frequency of decay will not correlate with the physical chance of decay n. Why is that? With God intervening there will be a causal source for decay events other than the properties explaining their physical chances. The isotopes are not being left to take their physical chances. That means that the properties that are potential causes of decay events are not just the properties that contribute to the physical chance of decay events. Rather, the properties that are potential causes of decay events include supernatural properties, unconnected with those that determine physical chances. This is a universe in which CC2 fails. It is false that when there is a physical chance at time t of decay within one day, and that chance is realized by a decay event, we shall find the causes of the decay event amongst the conditions that explain the physical chance of decay. That is false, because God, a non-physical potential cause, may be the cause of the decay. Because CC2 is false, the law of large numbers is contravened.

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4.2 Components of chance and chains of chance My thought then is that CC2 is explained by the fact that chance itself is already causal in the sense that cause is a kind of realized chance. As we have already seen, not every fact that contributes to a realized chance property for an event e is a cause of e. For the chance view of causation to proceed, it needs to provide a criterion for determining, amongst facts contributing to a realized chance of e, which facts are causes of e and which are not. Consider the simple isotope case. The conjunctive fact (1) below, determines an overall chance of 0.6 of there being alpha particles in the box (hereafter, ‘alpha particles’), and a chance of 0.4 of no such particles being in the box: (1) Isotope I has such and such physical structure; there is no isotope-destroying system in the box; there are no other isotopes inside our outside the box; and no stream of heavy particles is bombarding I. In other words, there is a conditional chance Ch(alpha particles|(1) obtains) = 0.6, and Ch(no-alpha particles|(1) obtains) = 0.4. To say that (1) determines that there is a 0.6 chance of there being alpha particles and a 0.4 chance of there being no alpha particles is to say (1) physically necessitates these chances: it is a nomological matter. The physical necessitation by (1) of these chances is not a causal necessitation. The facts mentioned in (1) do not cause a 0.6 chance of there being alpha particles. Rather it is a non-causal bringing about of a chance. We explain why there is a 0.6 chance of there being alpha particles—a 0.4 chance of there being no alpha particles—by pointing to (1). Explanations appeal to worldly connections. And in this case, the worldly connection is the noncausal connection between (1) and the chances.⁸ Represent this as: ((1) obtains) ⇒ (There is a 0.6 chance of alpha particles), ⁸ For some discussion of non-causal explanation in this volume, see Lange.

 stephen barker where ⇒ represents non-causal connection. The introduction of ⇒ requires nothing more than admitting that chances are nomological. This is to say that there are laws governing the relation between properties and the chances that arise with their instantiation. (1) is a conjunctive condition some of whose components are potential causes of there being alpha particles and some of whose components are potential causes of there being no alpha particles. (2) below is the potential cause of there being alpha particles. (3), which is entailed by the last conjunct of (1), is the potential cause of there being no alpha particles: (2) Isotope I has such and such physical structure. There are no isotope-destroying systems. (3) There is no stream of heavy particles bombarding I. What determines the fact that (2) and (3) have these causal powers? My proposal is this: (2) is a potential cause of there being alpha particles in the box because it contains facts that explain why there is a positive chance at t of alpha particles. The obtaining of (2) brings it about, in the non-causal sense just described, that there is a positive chance of alpha particles, that is, ((2) obtains) ⇒ (There is a positive chance of alpha particles.) This claim does not conflict with the assertion above that (1)’s obtaining determines that there is a 0.6 chance of alpha particles. (2) in itself does not determine that there is a 0.6 chance of alpha particles. It just determines that there is a positive chance of alpha particles, or, more precisely, that it is at least 0.6. But that the chance is exactly 0.6 requires further factual constraint not available in (2) itself. On the other hand, (3) is not a potential cause of there being alpha particles in the box. However, it is a potential cause of there being no alpha particles. The reason for this is that (3) explains why there is a positive chance of there being no alpha particles in the box. That there isn’t a constant bombarding of I by heavy particles—(3)—brings it about that there is a positive chance of there being no alpha particles in the

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box. Thus: ((3) obtains) ⇒ (There is a positive chance of no alpha particles).⁹ Generally speaking, c is a potential cause of an actualized e, if and only if c is part of a set of facts (..., c, ...), that physically determines that there is a positive chance of e. That is: ( ... , c, ... ) ⇒ (There is a positive chance of e). I say potential cause, for, as we shall see in a moment, actual causes have to meet a further condition. Note also that nothing proposed here implies that c can only cause e if c is a necessary condition of e. The potential cause c is not part of any necessary condition for e having a positive chance. Rather, c is a necessary condition in a sufficient condition for e having a positive chance. Let us call the above specified condition for being a potential cause positive impact. Positive impact seems to have some affinity to the thesis of the counterfactual chance-raising theorist that causes raise chances. It does. The impact story, I claim, is the kernel of truth that the counterfactual chance-raising account is attempting to get at. Let’s not be tempted, however, by the idea that positive impact is counterfactual chance-raising in disguise. First, facts of impact reduce to certain facts of non-causal physical necessitation. But there is no reason to see such facts as counterfactually based. Indeed, there are strong reasons not to. Secondly, to treat impact as reducible to counterfactual chance-raising would be to drift again towards an attempt to analyse cause in terms of counterfactual chance-raising. But we have already seen that such an analysis ⁹ There is an asymmetry in relation to (2) and (3). (2) has a more intimate relation to the strength of the chance than does (3). (2) determines that there is at least a 0.6 chance of alpha particles in the box, whereas (3) does not fix any particular strength. Why? (2) is associated with a process potentially leading to there being alpha particles, which involves physical change: I’s decay. Whereas (3) is not associated with a physical process leading to there being no alpha particles. This contrast in chance reflects a contrast in the corresponding facts of causation. If there are alpha particles, then (2)’s causing alpha particles involves a physical process: decay and alpha particle emission. If there are no alpha particles, then (3)’s being a cause of there being no alpha particles does not involve causation by a physical process; it is causation by omission of an absence.

 stephen barker cannot work, since it cannot explain CC2. Thirdly, the proposal is consistent with chance lowering causes. The potential cause c can explain where, in fact, there is a positive chance of e; namely, where it has positive impact in my sense. But that is perfectly consistent with its being the fact that had c not occurred, the chance of e would have been lower. Explanation here is decoupled from counterfactual dependencies. 4.2.1 Chance processes We can say that there where c make a positive impact on the chance of e at t, and that chance is realized, then c is a potential cause of e. It does not follow that c is a cause of e. We bridge the gap between potential cause and actual cause by appeal to chance process. What is required is that the process through which c would issue in e is uninterrupted. Thus the chance of e at t is fixed overall by more than one source—that is, sets of positive contributing factors, but one of these factors is prevented from fully completing the process associated with it. For example, consider a standard case of pre-emption. Fred goes into the desert. His enemy, Zack, intends to poison him by putting poison in his water-bottle; his enemy Mack intends to cause him to die of dehydration by knocking a hole in his bottle. Both these events occur and the water runs out and Fred dies of dehydration. Thus, Mack’s knocking a hole in Fred’s bottle caused his death, not the poisoning of the water. In this case there is a realized chance, at t0 , of death. The time t0 is the time, say, a little after the poisoning. Say it is a chancy matter just when the water runs out—depending on bodily movements of Fred, and it is a chancy matter when Fred gets thirsty, and chooses to drink. We have two sources of chance in this case: holing and poisoning. Each in themselves defines a set of properties that, independently, provides factors that positively impact on the chance of death. However, although poisoning has positive impact, it is not a cause. Thus, a fact c’s being a positively impacting factor in relation to the chance of an actually occurring event e, does not, in itself, imply that c causes e.

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Here again purveyors of counterfactual theories may hope that counterfactuals are needed to explain why poisoning of water, although a positive contributor to the chance property Cht (death), is not a cause of death. That is, one might look to counterfactual theories that specify conditions that isolate causal chains from preempted causes; some pattern of counterfactual dependency fixes causal chains. Alternatively, hope might be placed in some completely different theory of causal processes; for example, Dowe’s (2000) theory, which brings in conserved quantities. No such articulations of processes are required. Our concept of chance already provides us with the materials to define process in the requisite sense, that being what I have called chance process. Take the poisoning pre-emption case. Schematically, we can represent the process structure as follows. The dark circles on the extreme left represent the events of holing and water poisoning. These are two chance sources for the chance of death. The top dark line represents an uninterrupted chance process, of which the intermediate filled circles are actualized stages. The lower line is an interrupted chance process—the first light coloured circle is the water bottle being empty, the second light circle some later unactualized stage (see figure). t0

t1

t2

tn−2

tn−1 tn

holing

death

poisoning

 stephen barker The two sources of chance, poisoning and holing, are identified as two distinct sources of positive impact on the chance of death. We have the following conditions: (The water contains poison ... ) ⇒ (There is a positive chance of death) (The bottle is holed ... ) ⇒ (There is a positive chance of death)

This means the facts concerned are potential causes. To be an actual cause the source concerned needs to be associated with a realized chance process. There is a process type associated with these sources. A chance process is a set of events that are linked by conditional chance relations. We can define a chance process in the following terms: A set¹⁰ of occurring events E is a chance process between c and e iff: (i ) Events in E form a temporal ordering, <, which may be before or after; (ii) The events c and e are such that c ∈ E and e ∈ E, and for all x ∈ E, where x = c, c < x, and for all x ∈ E where x = e, e > x; (iii) For any two events Sk < Sn such that Sk , Sn ∈ E, there is a conditional chance Ch[Sn |Sk , b] > 0, where b is some set of conditions; (iv) Where there are no intermediate events f ∈ E, such that Sk < f < Sn for a given pair Sk –Sn , then there is no physical chance of Sn defined at tf . Thus (i) is the condition that there is an ordering, allowing for temporally forward or backwards processes; (ii) is that c and e are temporal extremes; (iii) is the conditional chance condition; (iv) is the condition that either there is chance continuity all the way ¹⁰ The set may be finite—in which case the process is a set of discrete events—or non-countably infinite—if the process involves chance continuity. If the set is finite, then the chance process is temporally grainy either because, (a) it results from graininess in the quantum world or (b) because the events themselves bring their own grain. For example, it makes no sense to talk of mental events occurring at a geometrical point-sized moment of time.

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down, or there is grain, in which case, intermediate times do not provide chance properties for succeeding events. There is a question about how we might get to know about chance chains so defined. The answer is not by prior causal knowledge. Rather, we know them through our powers as beings who can intervene in reality. We know about minimal conditional chances by intervening to set up states that induce probabilities. By combinatorial sorting we know that certain conditions are necessary components of propensities. By isolating chance sources, and by intervening so as to reduce them to zero chances, we gain knowledge about chance processes.¹¹ The structure of chance processes is a completely empirical matter. It is not required that there is continuity: there is no general argument against action at a temporal or spatial distance. We now can define a condition for an interrupted chance process. There is an unrealized stage in the chain, qua possible development. That is, all possible developments are such that they are only partially realized, where partial realization means that only a sub-set of their stages are actualized. We now see the significance of the diagram in the pre-emption poisoning case above. There is a fully realized chance process linking holing to death. There are at most only partially realized chance processes from water poisoning to death. There is a fully realized chance process from holing to there being no water in the bottle: represented by the middle dark arrow. We can now state the principle that links chance to cause, and articulates the chance theory of cause, the idea that causes are a form of realized chance: Where (i ) Cht (e) = n, and n > 0, (ii ) c is at t, (iii ) c makes a positive impact on Cht (e), and (iv) c is part of an unbroken chance process leading to e, then c is a cause of e.

This is the chance view of causation in essence.¹² ¹¹ I draw some of these ideas about intervention from Woodward (2003). ¹² On the proposed theory of cause, cause is not transitive. Thus although c contributes positively to the chance of e and e positively to the chance of f , it does not follow

 stephen barker If single case objective probabilities require the existence of chance processes, and chance processes imply causal facts, then the whole project of analysing causation in terms of counterfactuals, is, quite simply, dead in the water. Counterfactuals are at most symptoms of metaphysically prior facts, including facts of chance.¹³

4.3 Dispositions I have argued that counterfactuals do not play any explanatory role in relation to causation, rather chance does that. How do these results bear on the project of analysing dispositions? If counterfactuals do not yield a theory of cause, then that might render it doubtful that they yield a theory of dispositions. That is confirmed by the fact that attempts to reduce dispositional facts to counterfactual facts have not been entirely successful (see recently Martin 1994; Lewis 1997; and Bird 1998). These difficulties may be overcome by incorporating some of the techniques that have been deployed by counterfactual theorists treating redundant causation (Yablo 2002). I will not comment on the prospects of providing an extensionally correct analysis of dispositions using such tools in the terms in which such writers have framed the problem of dispositions. Rather I will dispute how they have framed the problem of dispositions. Counterfactual approaches to dispositions have tended to focus on a subset of the real class of dispositions. They have tended to consider only what we might call necessitating dispositions: if there is a disposition from S to R, then its manifestation requires R. For example, solubility in water that c contributes positively to f . Thus, placing a bomb in Fred’s room contributes positively to the chance of Fred’s leaving, given Fred was disposed to notice changes in his room. And indeed, the placing of the bomb caused Fred’s moving away. Fred’s moving away positively impacts on the chance of his being healthy the next day, and indeed the former is a cause of the latter. But placing a bomb does not positively impact on the chance of being healthy the next day. Placing of the bomb has, rather, a positive impact on the chance of Fred’s not being healthy. So placing of the bomb cannot be a cause of his being healthy the next day. (On the issue of transitivity see McDermott 1995.) ¹³ This fits in with a general line I have argued elsewhere. See Barker 1999, 2003a, 2003b.

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is something sugar might have, since were it put in water it would dissolve. Thus theorists have focused on counterfactuals of the form If S had obtained, R would have obtained, which reflect a link of necessitation between stimulus and response, thought of as an event. But such dispositions are only a special case. If quantum mechanics is right, then, then there is some small chance that salt in pure H2 O at room temperature might not dissolve. Thus we can speak only of a chance less than 1, though very near it. Generally, a disposition is best characterized as a relation between stimulus and a chance of an event. Necessitating dispositions are just the case where the chance happens to be 1. How then could we use counterfactuals to analyse chancy dispositions? It would seem that straight counterfactuals won’t work. We need counterfactuals about chances. A seemingly attractive idea is that we explain facts about dispositions in terms of counterfactual chance-raising, as in: O has a dispositional property π to give response R to stimulus S iff the actual chance of R is x, and if S had been the case, the chance of R would have been y, and y > x.

But this also won’t work, even leaving aside finks and antidotes. First, there can be chance lowering dispositions just as there are chance lowering causes. But even if we could exclude such cases, by adding counterfactual clauses analogous to those used in the counterfactual analysis of causation, this analysis leaves out something essential: that chancy dispositions come in strengths. It could be that the fragility of one vase is greater than that of another. Both have exactly the same size and geometry, but differ with respect to material constitution. If dropped in precisely the same way, and under identical circumstances, one is more likely to shatter than the other. By the above analysis, both vases share the same disposition—but clearly they have different dispositions, differing in strength. Mere facts about counterfactual chance-raising do not capture what there is to being a disposition: we need some quantitative measure rather than merely a qualitative measure.

 stephen barker A simple minded way of introducing a quantitative measure would be something like this: O has a dispositional property π to give response R to stimulus S, of strength n, iff the actual chance of R is x, and if had S been the case, the chance of R would have been y, and y − x = n.

But this simple idea fails miserably. Say the actual chance of O’s dissolving in water is 0.25 because there is a 0.5 chance it will be inundated in water in the next instant, and a 0.5 chance of dissolving once it is immersed. The difference between actual and counterfactual chance is 0.25. But the disposition’s strength is 0.5. This case shows that in order to obtain a quantitative measure of dispositions we need a way of isolating the chance contribution of the dispositional property so as to reveal what its strength is. In other words, supplemented by S, a dispositional property π makes some particular contribution to the overall chance of R. That contribution is the strength of the disposition. If we cleave to a counterfactual analysis of dispositions, the only way of seemingly articulating this thought is as follows: O has a dispositional property π to give response R to stimulus S, of strength n, iff were there to be no chance-bestowing property present except for π, then had S been the case, the chance of R would have been n.

Unfortunately this analysis is inadequate because counterfactuals do no work in eliciting an understanding of what dispositions are. The concept of a chance bestowing property already contains all we require to provide an account of dispositional properties: counterfactuals are redundant. A chance-bestowing property is a property that is a positive contributor in a conditional chance, and that’s just what a dispositional property is. A bit more explicitly: A property π is a dispositional property to give response R to stimulus S, of strength n, iff there is a conditional chance of the form Ch[R|c1 , ... , π, ... , cn ] = n, where S is (c1 , ... , ci−1 , ci+1 , ... , cn ), and π makes a positive impact on the chance of R.

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Deterministic dispositions are simply those where the chances are 1. The present treatment of dispositions is analogous to the functional treatment of Mumford (1998: chapter 9). In asserting that X is fragile one asserts that X has a property that enters into such a conditional chance and is a positive contributor. To say that X is more fragile than Y is to assert that X and Y have properties that enter into such conditional chances, and that generally, the chances in the case of X are greater than those for Y . This theory is consistent with some dispositions having no stimulus conditions.¹⁴ So an isotope has the disposition of spontaneously decaying, which is to say, that it has a property π that enters into a conditional chance where the antecedent condition is simply that an object has π. The theory also accords with the idea that there are constantly manifested dispositions.

4.4 Conclusions I have argued that chance is the foundation of both disposition and cause. I have offered no theory of chance here—nor can I point to any theory currently proposed in the literature that is without its problems. My goal has merely been to make a case for the central importance of chance to both causes and dispositions. The account also invokes what I have called non-causal connection, represented by ‘⇒’. But connection in this sense must be admitted by anyone who believes that chances are nomologically tied to properties; that the obtaining of non-chance physical properties at time-slices of the world explains the chance properties that hold at those time slices. Finally, a brief word about how this account relates to some of the other approaches in this volume. In my account, counterfactuals are downplayed as tools of philosophical explanation. Marc Lange argues, in contrast, that the laws are fixed by prior counterfactual ¹⁴ See Molnar 2003: 85–7.

 stephen barker facts. One might have doubts about how this works for laws of chance, since, I suggested, counterfactuals about chances may not deliver in themselves facts about what degrees of chance are associated with given dispositions. More congenial to this account is Ann Whittle’s proposal that powers are given by functional or causal facts. I believe that what is proposed here is consistent with the kind of nominalism she defends, provided the functional roles are articulated in terms of chance rather than counterfactuals. Lastly, I have presented a picture in which non-chance facts nomologically generate chances. It may be that we have to analyse the structure of that generation of chances in terms of capacities or influences, in the sense of Nancy Cartwright and Richard Corry. They label these influences causal. But perhaps their linkage to chance is more basic.¹⁵ ¹⁵ Thanks to Michael Clark, Phil Dowe, Paul Noordhof, and Toby Handfield for helpful discussions and suggestions relating to this paper.

5 Causal Laws, Policy Predictions, and the Need for Genuine Powers Nancy Cartwright

5.1 Introduction Knowledge of causal laws is hard to come by; it is expensive. Yet we make enormous effort to obtain it. Why? What is the use of knowing causal laws? I have always supposed that knowing causal laws will help us to change the world and in a very immediate way: we can read off—defeasibly of course—from the causal laws ways to manipulate the world to achieve the effects described in the laws. Nor have I been alone in this supposition; it is, I think, at the heart of various manipulation theories of causality as well as much of our practical effort to obtain causal-law knowledge. Unfortunately I now believe it is mistaken. Knowledge of causal laws cannot play the special role I expected of it. In this paper I will attempt to explain why. I will also provide two special cases where causal knowledge is backed up in just the right way to make it of use in the way envisaged: the case of nomological machines and the case where capacities are at work. There is a cost with respect to the latter, however, at least for the die-hard Humean. For the notion of capacities that does the job is a metaphysically heavy notion that cannot be cashed out in terms of lawful relations among ‘occurrent’ properties, a notion with one of the central characteristics that made

 nancy cartwright Hume despise powers. Much of my discussion will focus on my worry about the usefulness of causal-law knowledge for policy prediction. I turn to capacities, with their similarities to Hume’s much despised powers, as a solution in the last few sections. For purpose of illustration I shall consider deterministic causal laws that are expressed in a system of linear equations of a familiar sort: System of linear deterministic causal laws x1 c= u1 ... xn c= 1 n−1 ani xi + un .

Here the u’s represent quantities not caused by any of the x’s, and the symbol ‘c=’ means that the left and right-hand side are equal and that the factors on the right are a complete set of causes of those on the left. (Reference to the population and circumstances is repressed as is usual in presentation.) In the case of yes–no variables the analogue is J. L. Mackie’s famous formula for INUS conditions, supposing that all factors on the right-hand-side are genuine causes of the one on the left: Boolean deterministic causal law E c ↔ A11 A12 ... ∨ A21 A22 ... ∨ An1 ... Anm .

Analogously with c=, the symbol c↔ means that the left- and right-hand sides are equivalent and the factors on the right are all causes of those on the left.

5.2 What is a causal law? I have my own preferred view of what causal laws are. It is not everybody’s cup of tea but it has a number of virtues I explain below. If one disagrees that causal laws do have the characteristics I describe, then what I describe still needs a name and my worries still arise for it. That’s because something very like what I describe

laws, predictions, and powers  looks to be the appropriate result of many of our favoured—and ‘expensive’—methods of causal inference. So, causal laws or not, we need to figure out what can be the good of them. And of course not all these features are necessary to make my problem real; they are, though, what I have argued gets the best balance of practice and principle in providing an account of what a causal law is. So ... I argue that causal laws have a number of specific features (cf. Cartwright 1989): • They are population-relative. They describe relations that hold among quantities in a particular kind of population in particular kinds of circumstances, though this relativization to population and circumstance is often left to context to supply. • The primacy of singular causation. The causal relation they report is not primitive, say an abstract relation between universals. Rather, causal laws describe what singular causal processes will or can occur in the specified circumstances whenever the prescribed causes are instantiated. • In keeping with the fact that a causal law reports what singular causal processes will or can occur, a causal law picks out at least one complete set of causes: the specified set is enough to produce the effect and nothing more need be added. • The causes reported in a causal law may produce the prescribed effect with a variety of frequencies. The laws may be deterministic—the causes always produce the designated effects in the prescribed populations in the prescribed circumstances; they may be probabilistic, where the effect is produced with some fixed probability; or the effects may even be produced by hap, with no fixed probabilities. (It should be noted that what we say about probabilistic laws depends on our views about probabilities. Do we want, for instance, to say that the effect will occur with the relevant limiting relevant frequencies in some mythical infinite sequence or instead that it can occur or that it has a certain propensity to occur?)

 nancy cartwright • Causal laws may use a peculiar modal form familiar in daily life but not much studied in philosophy: the specified causes can produce the designated effect—they are enough to do so—but they may not, with nothing more to be said. There may be no fixed probabilities with which the effect occurs nor any further reasons that work in a systematic way to pick out when it should occur and when not. • Factual effects. Causal laws specify that effects will (or can, in the relevant sense of ‘can’) genuinely obtain when the specified causes obtain. In particular causal laws do not describe counterfactual effects that would (or could) obtain in different populations or for sets of causes that are not represented by variables not in the law. Nor do they presuppose that the specified causes are produced in any special way unless that is stated in the description of the situation to which the law is relativized. (Note that, as I shall discuss in Section 5.7, this does not mean that the effects need be occurrent in some narrow ‘Humean’ sense of ‘occurrent’). To illustrate, a law xn c = 1 n−1 ani xi + un from a linear deterministic system relative to situation S says that in every individual instance in S, xi taking the value Xi and un taking the value Un whenever instantiated causes xn to take the value 1 n−1 ani Xi + Un . This account of causal laws has a number of virtues. 1. It tells us what causal laws say. Many contemporary treatments of causality in philosophy of science do not do so, including common versions of the probabilistic theory of causality, related Bayes-nets theories and some versions of manipulation and invariance-under-manipulation accounts. Consider Judea Pearl’s account (2000), which begins with a set of causal equations like those of the linear deterministic system of Section 5.1. His work supposes that the equations say at least that in any system of the kind under study the values of the quantities in the equations are always related as the equation describes. But there is

laws, predictions, and powers  more, an asymmetry; the causal equation tells us that the quantities on the right are causes of those on the left. But what does a law say in telling us that? The Bayes-nets axioms, relating causal laws and probabilities, put constraints on the set of causal laws: only some sets of causal laws are admissible for any given probability distribution. This is not enough to answer the question. Beyond asserting that the specified functional relation holds in the system under study no matter what values of the quantities are instantiated, what more does the causal equation say? I have already explained my answer. Wolfgang Spohn (2001) supplies a different answer, one that will be dear to the hearts of those who think causal language is a veil. Roughly, Spohn maintains that causal laws are summaries of the kinds of complicated patterns of conditional probability relations among time-ordered quantities represented in a Bayes net. So it becomes important to Spohn to make the axioms relating causal laws and probabilities strong enough so that only a single set of causal laws is consistent with a given probability. Otherwise different, and incompatible, sets of causal laws would be equally appropriate for summarizing the same probabilistic facts. An alternative might be to claim that a causal law says that a certain abstract relation holds between universals, the universals that are represented by the variables in the equations. Consider too the probabilistic theory of causality for yes–no variables. One fairly good attempt at formulating it says that C is a cause of E in test population K for situation S if and only if in S, P(E|C&K) > P(E|¬C&K), where a test population is one in which all other sources of variation in the probability of E are held fixed barring C.¹ C causes E in S simpliciter if it does so in any test population in S. Hence it can be true in S both that C causes E and

¹ The formulation I give here still isn’t quite right because K must not hold fixed any causal intermediaries by which C causes E on a given occasion. My own best attempt relies on reference to singular causings even in the formulation of the probabilistic theory. See Cartwright 1989, chapters 2 and 3 and Cartwright 2007 for a fuller discussion.

 nancy cartwright that C causes ¬E. (Once some particular form for the causal laws in question is specified it becomes possible to say more concretely what counts as other sources of variation of the probability of the effect.) There are at least two understandings of this theory.² On the one hand we can see it as an answer to my question about what a causal law says. The law ‘C causes E in S’ says that P(E|C&K) > P(E|¬C&K) for some test population K ∈ S. On the other hand we can see it as a sufficient condition for the truth of a claim that says something else more immediately about causation. That’s what I try to do. I offer an account of what the law says in terms of singular causings that will (or ‘can’) occur ‘in the long run’. Then I show for various kinds of causal systems that when the probabilistic theory is formulated appropriately for them, the increase in conditional probability is indeed sufficient for the related causal law to be true. These two understandings of the probabilistic theory can also help make clearer my concern that we should, if we can, offer an account of what causal laws say. Many discussions nowadays settle for describing some central ‘characterizing’ features of causal laws. Often these descriptions themselves refer to causal laws, as in the probabilistic theory, which refers to other causal laws true in the situation in order to characterize K. In this case the descriptions cannot serve as definitions. That is not the concern I am raising, however. I myself take this kind of ‘circularity’ to be a virtue of an account since, I argue, we have good reasons to think that causality is endemic, that many causal relations are as basic as anything can be and that we have good epistemic access to various kinds of causal relations. What I want to know is what a causal law says, and what it says could very well include something about other causal laws. On neither understanding can the probabilistic theory provide a noncircular definition of a causal law. Only the first ² I would like to thank John Worrall for pointing out to me the importance of making clear these two different understandings of the probabilistic theory.

laws, predictions, and powers  provides an answer to my question, albeit an answer that seems to me to be mistaken. 2. The account I offer of causal laws is empiricist in what I take to be the most important sense, that stressed by Otto Neurath: it is this-worldly. Causal laws do not describe relations between universals nor structures behind the happenings; they describe what happens when the causes are instantiated. (Though note again that, as I shall point out in Section 5.7, there are a great many more things that I take it we have good reason to count as ‘this-worldly’ than a narrow ‘Humean’ does.) 3. This account of what causal laws say dovetails with a panoply of our most favoured methods for testing causal laws: various statistical methods used in econometrics and other social sciences, the mark method, randomized control trials, controlled experiments and tests looking for invariance under controlled interventions. For a number of these, formal proofs can be provided that positive results on the test—if the test is ideally conducted in the appropriate setting—is sufficient for the truth of the causal law as I interpret causal laws.³ I take this to be a strong argument in favour of this interpretation of what causal laws say since it seems to me essential to good philosophy and to good scientific practice that metaphysics and methodology can be shown to be mutually supporting. I am at pains to explain what I take causal laws to say since causal laws are the topic of my concerns in this paper. I am worried that, contrary to expectation, causal laws cannot after all provide us with the kind of information we need to predict what will happen as we attempt to change the world. For this reason an account of causal laws that meshes with methodology matters, since what we seem to assume is that what we establish with our best methods for testing casual laws carried out in the best circumstances is ³ The proofs naturally require assumptions about features of singular causings. Also the singular causal reading of causal laws is not unique in having this virtue, at least for some of the methods. Holland and Rubin (1988) for instance show that in the right kinds of populations, positive results in a randomized controlled trial are sufficient for a causal law, supposing that the law makes claims about the occurrence of singular counterfactual differences.

 nancy cartwright knowledge that we can use directly: in knowing the causal law we know how to change effects by changing their causes and we can make precise predictions about the results of so doing. Perhaps the reader will have a different view about what causal laws say. Much of my argument in what follows applies to other views as well, but here we have at least one articulated view to keep in mind that maintains the all-important connection between metaphysics and methodology.

5.3 Add-on versus intrinsic accounts of causal laws Economists at least from the time of J. S. Mill have worried about the usefulness of causal laws for policy prediction due to their instability. Mill worried about naturally occurring variations in both the background arrangement of causes and in the underpinning structures that support causal laws. Early econometricians and more recently Chicago School economists like Robert Lucas worried more about the likelihood that active policy intervention would undermine the structural arrangements that support the causal laws. The worries I raise here about the usefulness of causal laws for policy prediction echo these earlier worries about the stability of causal laws by economists. To explain my worry I shall review a few recent accounts that aim to provide central characterizing features of causal laws, focussing on accounts that treat economic causes since these are most alert to the problem. Begin by considering the probabilistic theory of causation, described in Section 5.2, which I claim provides a provably sufficient condition for the designated cause to appear in a true causal law. For a given population S let us focus on some particular test (sub)population K so we can repress K in the conditional probability. Consider what use we can make of knowledge of the law that C causes E in K for policy predictions about the effects in K on E of changing C. The probabilistic account of causality seems

laws, predictions, and powers  ideal for providing an answer: increase the probability of C and the probability of E will increase because P(E) = P(E|C) P(C) + P(E|¬C) P(¬C). So if P(C) increases in K so too should P(E) supposing P(E|C) > P(E|¬C), in K. But this is not the case. The formula above is for a given probability measure P. P(C) cannot change without the measure P changing and if P changes to some new probability P ∗ , the fact that P(E|C) > P(E|¬C) determines nothing about the relation between P ∗ (E|C) and P ∗ (E|¬C). Knowing that C causes E in K and hence knowing that P(E|C) > P(E|¬C) does not help us predict the effects on E of manipulating C in K. It turns out that this is exactly the problem that concerns econometrician David Hendry (Engle, Hendry, and Richard 1983; Hendry 2004) when he gives an account of causation. As with the theory of probabilistic causality, Hendry focuses on the conditional probability of the effect on the hypothesized cause, P(E|C). His primary attention is to cases where C is strictly exogenous to E. This means that the conditional probability, P(E|C), can be estimated without attention to the marginal probability, P(C). For the relation between C and E to be causal however, Hendry requires super-exogeneity: P(E|C) must be invariant across the envisaged policy changes. So Hendry stipulates that ‘C causes E’ is not to be counted as a causal law unless P(E|C) remains fixed across the manipulations envisaged to change C. This is an example of what I call an add-on account of causality par excellence (Cartwright 2006). A criterion that is sufficient to guarantee a causal law on its own is provided—as I indicated, the probabilistic theory is provably sufficient for a causal law to obtain. Then invariance is added on top as a second demand before the label ‘causal’ is allowed. One can of course quarrel with my account of what a causal law says, insisting that the account is not complete until invariance is added on. This is essentially what Hendry does (and also James Woodward as we shall see shortly). But recall my

 nancy cartwright claims to a connection between the content of a causal law and our best methods of testing for causal laws. The additional invariance requirement is not part of most standard methods, not just for those based on the probabilistic theory but also for a host of conventional methods for establishing causal laws, from the mark method to randomized controlled trials.⁴ James Woodward (2003) also has an add-on account.⁵ When it comes to causality Woodward focuses on systems of linear equations of the kind I described in Section 5.1. For Woodward two demands must be fulfilled before equations like these can properly be labelled ‘causal’. First Level invariance: the equation must remain invariant under any changes on right-hand-side variables ‘by intervention’.

‘Intervention’ is hard to define properly; it is something like a ‘miracle’ from the Lewis account of counterfactuals, a change in the cause at the last stage that affects nothing other than the cause and things causally downstream from it. Woodward defends this as a condition on causality with a number of examples in which it is violated by relations known to be spurious. What we would like to know is whether all spurious relations violate it; that is, is level invariance a sufficient condition for causality? I have a kind of representation theorem to show that it is (see Cartwright 2007). I begin with some axioms that a set of causal laws should satisfy—like asymmetry, irreflexivity and the assumption that any functional relations that hold are generated by genuine causal relations.⁶ The theorem shows that any functional ⁴ Though some methodologists, especially in economics, now frequently add on tests of invariance. ⁵ See also Mitchell (2003), who stresses the need for invariance without a detour through causality. ⁶ I take these axioms to be fairly innocuous and to be true of causal laws even if my singular-causings account of causal laws is mistaken. I should note that there has been some objection that the axioms are not so innocuous because a transitivity axiom is included. But the transitivity axiom assumes only that if x appears as a cause of y in a linear deterministic causal system, we still have a causal law for y if we substitute for x the right-hand side of any causal law that has x as effect. I think this is necessary unless we are willing to assume

laws, predictions, and powers  relation generated by a set of causal laws will be one of those causal laws if and only if it is level invariant. So I am happy with level invariance as criterion of causality. But Woodward is not. He demands in addition Modularity: there must be at least one way to change the other causal relations in a system that leaves any genuine causal relation invariant.⁷

The effect of this requirement is that each variable in a system⁸ can be changed (by changing the law that governs it) without changing anything else except the effects of that variable. This again is a ‘miracle’-like change. What justifies this as a condition on causality? Woodward is clear:⁹ this addition allows us to use the relation in question for manipulation. That I take it is why Woodward calls his account of causality indifferently an ‘invariance’ account and a ‘manipulability’ account. As an answer to my worries it is far less satisfactory than Hendry’s condition, however. For it underwrites the use of causal laws for predicting the outcomes of manipulations not for the manipulations we might be envisaging, as with Hendry, but only for very special kinds of ‘surgical incisions’. These are the kinds of manipulations that are demanded in a controlled experiment. That, I believe, is how they come to play such a special role in Woodward’s account. They are good for a very special way of testing for causal laws. But they are no good for showing why knowledge of causal laws is useful for policy predictions. Woodward’s account also shares the central defect of Hendry’s when it comes to addressing my worries. Modularity, just like that causation in nature is not continuous in time, so that there is a notion of direct causal law (the ‘last’ law in operation before the effect is produced) that is not representation relative and that it is this notion of direct causal law that we are trying to characterize. ⁷ See Woodward’s definition of modularity, 2003. ⁸ I.e., any variable that appears as an effect in a law in the system of laws. ⁹ Actually, he gives the same reason—causes must be usable to manipulate their effects—for both level invariance and for modularity. I cite it only for modularity because level invariance does not provide manipulability unless modularity is added and I at any rate have an alternative defence of level invariance.

 nancy cartwright the requirement of superexogeneity, is an add-on. Level invariance already provides a sufficient condition for licensing causal laws. But if we want to use those laws for predicting what happens as we manipulate the causes, to think of causal laws as useful for policy prediction, we must add on invariance.¹⁰ To reinforce this, turn to an account of causality offered by macroeconomist and methodologist Kevin Hoover that is not an add-on account.¹¹ Hoover defines causality directly in term of the effects that can be achieved by manipulation. Hoover: C causes E iff anything we can do to fix C partially fixes E but not the reverse.

Although this definition secures a connection between causation and manipulation and does so with no add-ons, the kinds of relations it calls ‘causal’ would not count as causal in everybody’s books—like probabilistic theories of causation, causal process theories or Lewis-style counterfactual accounts. The figure provides an example of a simple mechanism to illustrate, where the u’s are ‘policy levers’—quantities we can manipulate, and the solid lines with arrows depict pure ‘mechanical’ causation, like pushing on a lever at one end to trip a switch at the other. The dotted line depicts ‘Hoover’ causation. So Hoover does not need add-ons. If he is right about what causation is, we can see why causes by their very nature can provide predictions about strategies for manipulating the world. But many ¹⁰ Though note that Woodward’s condition doesn’t really do the trick since we are guaranteed by him just that there is at least one way to change the cause that leaves the causal law invariant and this may well not be among any of the ways we envisage implementing policy. Moreover for Woodward the one way that is guaranteed could be just an ‘in principle’ way to change the cause, not a way that is at all accessible to us. If so, no connection at all with policy prediction is secured. What the ‘in principle’ manipulation is good for is an ‘in principle’ test that the causal law obtains. ¹¹ See Hoover 2001. I should note that the description I give here of Hoover’s account is not one he is happy with. I claim it is what his definitions say and take the kind of causal relation described by the definitions as a very important one different from more ‘mechanical’ kinds of causal relations. He maintains that he intends his account to cover the more conventional notion of ‘mechanical causation’ and that various caveats he offers allow his definitions to do so. For further discussion, see Cartwright 2007.

laws, predictions, and powers  ux

x

y

uz

z

will not want to allow that Hoover’s is an account of causation at all. Where then is the expected connection between knowledge of causal laws and our ability to predict the consequences of manipulating causes? It seems it is not there. The requisite predictive capacity is not provided by a causal law. It is achieved by adding on a further assumption, an assumption whose sole motivation seems to be to achieve this connection.

5.4 What then is special about knowledge of causal laws? So, what’s wrong with adding on a Hendry-like invariance assumption? We can add it on as an additional requirement for the use of knowledge of a causal law. ‘Warning: do not use this product for predictions about the consequences of manipulations without ensuring that it is invariant under those manipulations.’ But it would be a bad idea to add it on as a requirement on the truth of causal laws for a number of reasons. • As I have already stressed, this would break the connection between the metaphysics of causal laws and our standard methods for testing them.

 nancy cartwright • It relativizes the concept to the manipulations under which it is supposed to be invariant. We could perhaps suppress the relativization if the set contained only one kind of member, like Woodward’s miracle-like manipulations. But this does not go very far in establishing the usefulness of causal knowledge for predictions about the results of manipulating causes. • It breaks with standard usage of the concept of causal law that we put to other purposes. We want to know about the causal laws for systems that are shaky, where attempts to manipulate the causes may undermine the laws: snowflakes and spider webs, undefusable bombs and old-fashioned children’s toys that break if wound up too tightly; and also for systems that we never intend to manipulate or never could manipulate, like the processes in the sun that produce light and heat, the planetary system and the innards of my car engine and computer, where I firmly intend never to go. We want to know because we want ways to ascribe responsibility about what is happening in the system, because what happens there may be analogous to what happens elsewhere, because we want to be able to repair the system or dismantle it, because how the system operates may have side effects, because it is a central feature of human nature to be consumed with curiosity about how the world around us operates, etc., etc., etc. Knowledge of causal laws is thus valuable in dozens of different ways, even if it does not provide direct predictability about how we can achieve effects by manipulating causes, as we might have unreflectively supposed. So forsaking it would be foolish and relabelling it by demanding the add-on requirement of invariance under some set of manipulations leaves us in need of another label for what seems to me to be the original concept. All this leads me to conclude that adding-on is a bad idea. Yet knowledge of causal laws without adding on invariance does

laws, predictions, and powers  not help with policy predictions in the desired way. But the situation is far worse even than this for causal knowledge. Once we allow invariance to be added on, causal knowledge seems to have no special role at all. Any claim that is invariant under a proposed manipulation of some factor will provide correct predictions about the results of manipulating that factor. Look again for instance at a law from a linear deterministic causal system, where for years many of us have been keen to insert a symbol like ‘c=’, not just an equality sign: xn c= 1 n−1 ani xi + un . If we insist that the functional relation be invariant under a particular manipulation, say of xi , the fact that the equation expresses a causal law is irrelevant to what we can predict about xn . If we insist on invariance of the relation, any relation is as good as a causal relation for predictions about results of the manipulation. And if we do not insist on invariance of the relation, causal relations have no guarantee to do the job. So we return to my central worry—what is so special vis-`a-vis policy prediction about knowledge of causal laws? Perhaps it is an empirical fact that causal laws are always stable under manipulations, even if this is no part of the concept of causal law and no part of what the causal law says. This is clearly false. I think even Woodward’s far weaker—and far less useful—claim that there is always some manipulation that leaves the causal law invariant is false. Moreover, if true it goes a long way to showing that exactly the same thing is true of certain spurious relations that then have the same claim to usefulness as genuine causal laws. Consider again the Hoover diagram, with causal laws x c= ux , y c= ayx x and z c= azx x + uz . Then the ‘spurious’ relation z = azx (y|ayx ) + uz is also functionally true. According to Woodward’s modularity thesis, there is some manipulation that can change x and leave the two causal laws between x and y and between x and z unchanged. In the Hoover diagram that manipulation could be by manipulating ux . But then the very same manipulation is also a way of changing y whilst leaving the spurious relation between

 nancy cartwright y and z unchanged. So if the manipulation ux is accessible to us and provides a way to change x without threatening the power of the causal law z c= azx x + uz to predict what happens to z as we change x, it is equally a manipulation that is accessible to us and that provides a way to change y without threatening the power of the spurious relation z = azx (y|ayx ) + uz to predict what happens to z as we change y. This manipulation does not of course satisfy Woodward’s definition of an intervention on y. It is not a miracle-like change of y since it also involves a change of a cause, x, of another variable, z, in the system that is not an effect of y. That means it is not good for testing whether y is a cause of z. But testing is not our issue. We are here interested in the usefulness of causal knowledge not in the testing of it. And if the manipulation ux makes the causal law z c= azx x + uz useful for policy predictions about the effects on z of changing x (via ux ), it does exactly the same for the spurious relation z = azx (y|ayx ) + uz for predicting the effects on z of changing y (via ux ). So even if we disregard the facts that Woodward’s modularity demand may well be false as an empirical assumption and that the one manipulation it claims to exist may well not be one we can—or wish to—exploit, the modularity requirement provides no special role vis-`a-vis policy prediction for knowledge of causal laws over knowledge of spurious relations. Yet again we have failed in our hunt for what is special about causal knowledge. There is further reason to be suspicious about a widespread difference in stability of causal laws over spurious relations of this kind. Nature is rife with what I call nomological machines (1989, 1999), from clocks and vending machines to seeds and caterpillars. The machines of interest here involve a relatively stable arrangement of parts which gives rise to a number of interconnected causal processes inside the machine plus some kind of skin or shield that limits access to the internal variables under a variety of common circumstances. We put the coins in and get out a packet of crisps; we do not perform key-hole surgery on the vending machine to jiggle the levers and chutes inside. We water the seed and plant it

laws, predictions, and powers  in the right kind of soil at the right time; we do not reach in and shift about the internal make-up that will produce the seedling.¹² In these cases the causal processes inside can be very stable. But then all the spurious relations are stable as well and for the very same reasons. Often even our efforts to achieve a desired result are directed by our recognition of a spurious relation in total ignorance of the causal laws. For instance, as an undergraduate I was paid to keep the needle centred on a dial at the cyclotron lab in Pittsburgh. The point was to keep the beam on target. When the beam drifted so did the needle; and what one did to adjust the needle adjusted the angle of the particle gun producing the beam. No-one was expected to manipulate the particle gun in the right way directly, we just had to keep the needle centred. The relation we relied on to get the job done was entirely spurious. There are a vast number of other examples as well. Medicine provides many: we frequently successfully treat a mild symptom in order to relieve a severe symptom of the basic malfunction without understanding the causal processes involved. The structure is like the common cause structure from the Hoover diagram I considered a few paragraphs back in discussing modularity. We rely not on causal knowledge but on knowledge of a stable correlation, a correlation that is stable presumably because within a reasonable range whatever we are doing to relieve the mild symptom passes through the basic malfunction that causes the more severe symptom. I take it then that causal laws are not universally stable and that a great many situations that guarantee the stability of causal laws also guarantee the stability—and sometimes the equal usefulness for policy prediction—of non-causal relations. Perhaps instead the answer to my worry is just that causal laws are more frequently stable than other relations. Maybe so, but without more ado this does not provide much predictive certainty, especially if there are ¹² Though my recent gardening experiences suggest that what I am doing with sweet pea seeds must be like taking a sledgehammer to the vending machine.

 nancy cartwright no markers to indicate which are stable and which are not. I think we can do better if we focus instead, not on the frequency with which causal laws are stable, but rather on what kinds of situations make for stability and, very centrally, on whether we can recognize them. Now that I have become gripped with despair about the general uselessness of our hard-won causal knowledge but have come to see some hope in the idea of recognizable markers, I realize that I have studied two different kinds of situations that can relieve the problem: situations in which capacities are at work and nomological machines. Nomological machines are not my central concern here so I will turn to them later and only briefly, concentrating instead on capacities.

5.5 Capacities Capacities, I claim, are a source of stable causal laws. When a capacity is properly triggered it will regularly exercise itself in a canonical way. For example, I am irritable; I have the capacity to be angered easily: if I find my daughter has piled the dishes in the kitchen and not washed up, I am apt to lose my temper. Triggering may not be essential for a capacity, however. For example, the capacity of one massive object to attract another seems to act continuously and without need of a trigger. Nor does the capacity described in quantum mechanics for an atom in an excited state to emit a photon seem to need triggering even though it is exercised only sporadically. As I use the term capacity, the connection between a capacity and its exercise or the potential for its exercise is analytic.¹³ For ¹³ What then of what have come to be called ‘finkish’ dispositions (see Martin 1994)—those that are thwarted the instant they start to work? From my point of view we can treat these in at least three different ways, at least the first two of which have long been available in the philosophy of science literature. (1) The disposition is not really there although its putative marker is. The marker is merely putative; a more correct description of it would exclude the possibility of interference (though there may be no way to characterize the exclusion other than ‘nothing interferes with the operation of the disposition’).

laws, predictions, and powers  many capacities we do not need the second phrase, ‘potential for its exercise’, since they are universally exercised when properly triggered; the gravitational capacity to attract a massive object is a case in point—and it does not even need triggering. But the exercise of a capacity need not occur universally upon triggering even when nothing interferes. Some capacities are probabilistic, like the (quantum) capacity of an excited atom to emit a photon. (As with causal laws themselves, what we say about probabilistic capacities vis-`a-vis their exercise depends on our views about probabilities. Do we want, for instance, to say that these capacities will be exercised with the relevant limiting relevant frequencies in some mythical infinite sequence?) And some may just be exercised by hap, without even fixed probabilities. In these cases the analytic connection is only with the potential for exercise and to talk about them we use a modal form familiar in daily life but not well studied by philosophers: triggering my irritability can produce anger but it may not; and perhaps there is nothing more to be said. There may be no real probabilities for the irritability to be exercised nor further reasons that work in a systematic, reliable way to pick out when it is exercised and when not. It may even happen that the capacity is there all my life and never exercised: I have moral luck; I am irritable and occasions arise that can trigger the irritability but this chancy capacity happens never to be exercised. The important point is that the presence of a capacity guarantees that the matching causal law obtains, whatever be the form of that law: triggering the capacity causes (or causes with some fixed probability or can cause) the exercise of the capacity; and sometimes, as with gravity, just the presence of the capacity can cause it to be exercised. This is not enough to allow us to predict what happens under manipulations, however. To do that we need to have some way of ascertaining when a capacity obtains and when it does not. But (2) Finkish dispositions are really cases where one and the same factor or arrangement has mixed dispositions that cancel out each other’s effects. (3) The finkish disposition is indeed exercised; what fails is the manifest result.

 nancy cartwright for many capacities we do have just this kind of information. Mass is associated with the capacity to attract massive objects; negative charge with the capacity to attract positive charges and with the capacity to repel negative charges; etc. Capacities can be useful to us just because in many cases Nature supplies secure ways to recognize when they obtain: there are features that we have independent means of identifying that guarantee (or make probable or possible¹⁴) the presence of the capacity. Unlike the connection between a capacity and its potential for exercise, I take it that this connection is not analytic. There are a number of important metaphysical issues that ultimately need to be resolved but that we can sidestep for many philosophy of science purposes and especially for the purposes for which I introduce capacities here. These include 1. What is a capacity? A property? A second-order property? A material mode concept that expresses only a formal mode distinction about how we identify properties? ...? 2. What is the connection between the capacity and the ‘occurrent’ property with which it may be associated? Must there be such an occurrent property for every capacity? Must the association be universal or can it be ceteris paribus, probabilistic or chancy? What is central for my purposes here are the two facts I have described: Capacities are analytically connected with causal laws. For a vast number of capacities we have learned how to tell when they are present and when not. They are associated in a systematic way that we know about with features we know how to identify independently.

Together these two facts guarantee that we can make reliable predictions about the results when we manipulate causes. ¹⁴ For instance, ‘Eating shredded wheat can improve your heart health.’ Just as the connection between the triggering of a capacity and its exercise might be chancy, I see nothing to rule out the possibility that the connection between the more readily identifiable markers and the capacity might also be chancy. Even if chancy the connection can still be important to know, especially if we do not know any more reliable connections.

laws, predictions, and powers  We manipulate the presence or absence (or the degree) of the associated ‘occurrent’ feature. The presence of the feature guarantees (or makes probable, etc.) the presence of the capacity and that in turn guarantees a causal law underwritten by the fact that the capacity will be exercised if the specified feature is present or if properly triggered (or that it will be exercised with some designated probability or that it can be exercised). So capacities make knowledge of causal laws useful for predicting the results of manipulations. So, too, I have claimed, do nomological machines. But beware: it is not the relations inside the machine that matter. Although nomological machines support the stability of both causal and non-causal relations inside the machine, these, as I have stressed, are not generally of direct use to us. Many, however, also support input–output relations that are of considerable use.¹⁵ We water the seed in the right temperature and light conditions and that causes a seedling to grow. We put a pound coin in the vending machine and that causes a packet of crisps to come out. In the next section I shall review in more detail what is in common about capacities and nomological machines that makes for usable causal-law knowledge.

5.6 What makes knowledge of causal laws useful? Capacities and nomological machines share several important features that allow them to serve as guarantors of the predictions that ¹⁵ Recall that on my account causal laws are population and situation relative. Many causal laws, I argue, arise from the operation of a nomological machine; the input-output laws that many machines give rise to are an example. In this case the relativization of the causal laws is to the proper operation of the nomological machine. For capacities the situation is more complicated. Since I take the connection between the capacity and the related causal law to be analytic, the causal law that connects the obtaining or triggering of a capacity with its exercise cannot be population or situation relative. In this case the laws that are population or situation relative are the empirical laws that hold in many cases, linking the presence of a capacity with some other independently identifiable feature. These are indeed very often population or situation relative even if a few (like the examples I cite from basic physics) may be thought to hold tout court.

 nancy cartwright causal laws suggest about the results of manipulations, some of which I have already talked about with respect to capacities: 1. Characterizability. There are available reasonably good characterizations of what a capacity and a nomological machine are. A philosophical account of capacities piggybacks on an account of dispositions and, despite the fact that we know there are many outstanding problems about dispositions, the notion is well enough developed that we can have confidence that some analogue of it holds in reality. Similarly with nomological machines. These may not be well enough characterized in my work but we can also draw on discussions of mechanisms by philosophers like William Bechtel and Jon Elster¹⁶ for reassurance that it is not an empty notion. 2. Underwriting of causal laws. Both guarantee that specific kinds of causal laws obtain and continue to obtain so long as they are in place. So long as a capacity obtains, so too will the causal law that connects the obtaining or triggering of the capacity with its exercise. So long as a nomological machine is intact, not only are the relations inside maintained, both causal and non-causal, but so too are the input–output relations. 3. Identifiability. In many cases there are markers by which the presence of the capacity or the nomological machine can be identified. 4. Recognizability. Very often both the markers and the conditions for safe use—use that leaves the relevant causal laws intact—can be recognized independently. I have argued extensively that discovering these markers in the case of capacities is one of the central achievements of science (Cartwright, 1989). (Recall as an example that negative electric charge brings with it the capacity to repel other negative charges and the capacity to attract positive charges.) For nomological machines the case is more complicated. ¹⁶ See Craver and Bechtel (2005) and Elster (1998). Other views of ‘mechanism’, like Stuart Glendening’s or Woodward’s, may not be close enough to help here.

laws, predictions, and powers  Some—seeds and caterpillars and the planetary system for instance—are given by Nature; we learn to recognize them, and to recognize what can and cannot be done to them without harm, both by experience and by theory. Others we build ourselves and for many, identification is made easy; we put labels on them and even instructions for proper use (e.g. ‘Do not overwind’, ‘Keep in a cool place’). 5. Usability of associated causal laws. In many cases the causes that are referred to in the causal laws guaranteed by a capacity or a nomological machine are ones we can recognize and know how to manipulate without undermining the existence of the capacity or the machine that gives rise to the law that we will use for predicting the outcomes of our manipulations. So both these categories provide simultaneously a metaphysical and an epistemological basis for the usability of causal-law knowledge. • When a capacity or a nomological machine obtains, there will not only be a stable causal law, but there will also be a reason why the law is stable and in many cases we can recognize when this reason holds and when not and what kinds of manipulations will jeopardize it. We do not learn just that this law seems stable under this set of manipulations but not that; that another law has been observed stable under a particular manipulation but we have no basis to speculate about others; that yet another seems not very stable at all. Where capacities or nomological machines obtain, our knowledge about the stability of this or that law—if we have it at all—is not haphazard and inexplicable. It becomes systematic, thus easier to remember, to understand and to generalize from. • When there are recognizable markers we can come to learn when this system of knowledge applies and when not. • With some understanding of the sources of stability we can come to learn and to respect the ways in which our manipulations must be carried out. (For instance, we do not rely so confidently on the assumption that striking the key

 nancy cartwright labelled ‘T’ on a computer keyboard will produce a T on the screen if, when we strike the key, we inadvertently knock over a cup of coffee onto the keyboard.) • When there are understood sources of a causal law, we can often repair the causal law when it breaks down or remove it if it becomes undesirable. Still, life is not easy. Nomological machines must not be breached if they are to do their job and sometimes it is difficult to tell if they have been damaged. That’s my trouble with sweet pea seeds. I think I have kept them dry, not too hot, not too cold, have not mashed them nor irradiated them nor ... Yet when I put them in soil of the right temperature at the right time and water them in the right way, they still do not germinate. Something has gone wrong inside but I have no clue what. The difficulty of recognizing when the support for a causal law has been breached can be considerably less problematic with capacities. Nature seems to have provided many with relatively sure markers that we have learned to identify reliably—consider again the negative charge that marks the capacity to repel other negative charges, or mass, which marks the capacity to attract other massive bodies. But capacities introduce their own troubles, which I mentioned in the Introduction, at least for those who believe in some robust notion of occurrent properties. I do not know what these are really supposed to be but if they are anything at all, the exercise of a capacity should not be among them—and it is the exercise of the capacity that appears as the effect in the causal law that the capacity underwrites. I turn to this issue in the next section.

5.7 Capacities as powers¹⁷ Return now to my warning in Section 5.1. Why do I say that the notion of capacity necessary to understand how scientific ¹⁷ A lot of the material in this section repeats earlier work. But I think it is worth repeating here for two reasons. First, many readers will probably not be familiar with it. Second,

laws, predictions, and powers  knowledge supports policy and planning is a metaphysically heavy power notion? Hume taught that it makes no sense to distinguish between the obtaining of a power and its exercise¹⁸. But this is just what is required to characterize the facts we need about capacities. By ‘metaphysically heavy’ here I mean that the notion of capacity and the use to which I put it requires the threefold distinction between • The obtaining of the capacity • Its exercise • The manifest (‘occurrent’) results. Gravity has the capacity to make heavy objects fall. The attraction of a heavy body constitutes the exercise of the capacity; the motion of the heavy body is the actually manifested result when the capacity is exercised. What matters here is that the canonical behaviour after which the capacity is named may be seldom if ever the actually occurring—or, as I use the term, the actually manifested—result and the actually manifested result may have no systematic connection with the presence of the capacity. The systematic connection is between the obtaining of the capacity and its exercise. Massive objects—that is, objects with the gravitational capacity—always attract other bodies even should the other bodies never move closer. and more important for my theses in this paper, I have never before seen or described explicitly how capacities serve as the guarantors of the usability of causal laws. Indeed I have not seen before how useless causal-law knowledge is in and of itself. My earlier work on capacities stressed instead how capacities explain how we can export knowledge from special ‘experimental’ situations to ones with new settings (not particularly the same settings with new methods for introducing causes) and how we can deploy knowledge of what happens in these ‘experimental’ settings to construct totally new situations in which totally new laws emerge. ¹⁸ In his A Treatise of Human Nature Hume deduces from his definition of a cause that not only the distinction between moral and physical necessity is without foundation but also that: ‘The distinction, which we often make betwixt power and the exercise of it, is equally without foundation’ (Book I, Part III, Section XIV). Later in his Treatise Hume restates this doctrine: ‘It has been observ’d in treating of the understanding, that the distinction, which we sometimes make betwixt a power and the exercise of it, is entirely frivolous, and that neither man nor any other being ought ever to be thought possest of any ability, unless it be exerted and put in action’ (Book II, Part I, Section X).

 nancy cartwright We should not be misled by this overfamiliar example. In the case of gravity the Humean is apt to retort that the effect produced by the presence of a massive body is that other massive bodies become subject to a gravitational force. I agree. Indeed that is my point. What is the causal law at stake? Not that the gravitational capacity in an object, which is guaranteed by empirical law to be there whenever the object has a mass, causes this or that specific motion in another object—the manifest or ‘occurrent’ result. Rather the presence of the gravitational capacity is enough to cause that capacity to be exercised, that is, to cause a ‘force’ to be created; what motions occur depends on the environment in which the capacity is exercised. Irritability is the same. What my being irritable guarantees is that if triggered I can get angry easily. That is the causal law. What are the manifest results when the capacity is exercised, that is when I ‘get angry’—my feelings, my behaviour, my words, my body language, my facial expressions—all depend on the environment in which the capacity is exercised. ‘Getting angry’ here is like ‘force’. It does not in this case name some inner feeling or some spectrum of outer behaviours. Rather it labels the exercise of the capacity of irritability, which exercise combines with other facts about the environment to account for the manifest results, my feelings and behaviours, which may differ dramatically from one occasion of exercise to another. Perhaps we can think of force as the ‘exercise of a power’, it might be argued, but if we do, it does not violate Hume’s strictures since being subject to a gravitational force is an ordinary occurrent or manifest result, like having a mass or moving with a certain velocity. This raises the sticky issue of what an occurrent property is supposed to be, which I maintain has no interesting answer. Of course the force ‘occurs’ in many senses of ‘occur’. (It is, for example, certainly factual as opposed to counterfactual.) Most notable perhaps is the fact that it can be measured, and very precisely. But we measure it ‘indirectly’, as we do in science, by looking for its causes—yes, the massive body was there to

laws, predictions, and powers  produce it, or by looking for its effects—the second body moves differently from how it would move were the first body not there (unless something tricky is substituted for it). We do not, though, ever measure it by inspecting the impressions it creates in us. So I am keen to admit that the exercise of a capacity is a genuine empirical ‘occurrence’. But then I do not think there are any cogent arguments against admitting all sorts of ‘non-Humean’ features into the knowable empirical world in the first place, features like causings and powers, and exercises of powers and interferences with those exercises. I do not think, however, that those who find ‘occurrent’ an interesting category—let’s call them ‘Humeans’ here for the sake of a label—should be so glib about sweeping all these exercisings of capacities into that category. Recall that Gilbert Ryle in The Concept of Mind warned against positing a single thing—say ‘grocing’—that occurs when a grocer performs any of the myriad jobs (the manifest results) that she does qua grocer—weighing coffee, wrapping cheese, stocking shelves. We do this all the time in science, however. And I think we do it just because it allows an accurate statement of the causal laws we have discovered. That though does not make these happenings ‘occurrent’ in the right sense for the ‘Humean’, I expect, whatever that sense is. To see the source of my hesitation, look at two more cases in science, one where the exercise does not seem to be occurrent in whatever is the intended sense and one in which it is. In the case of force, what it seems reasonable for a ‘Humean’ to count as an occurrent or manifest result in terms of force is the total force. That after all is linked by well-understood laws with the actual motions. What then of the force of gravity or the Coulomb force, which I take to be the exercisings of the gravitational and electromagnetic capacities respectively? These are called ‘component’ forces and many ‘Humeans’ take this as a justification for the claim that they are occurrent in the appropriate sense: they are there because they are the parts that make up the total force. But are they there in the right sense? Let us look at

 nancy cartwright some capacities in circuitry that seem to be exactly analogous but where to answer ‘yes’ to the same question would be a real stretch. Capacitors have the capacity to affect the flow of electricity in a circuit; it is called the ‘capacitance’ and is given in a well-established formula. Inductors too have a capacity to affect the flow, called the ‘inductance’, and resistors, the ‘resistance’, both with their characteristic formulae. When these act together in a complicated circuit there is no simple way to ‘add’ their effects, no analogue of the ‘total’ force in which the separate ‘effects’ can be naturally seen as parts that make up the whole. Rather the net effect on the current is calculated from the structure of the circuits and the formulae for inductance, capacitance and resistance by a series of rules that reduce complex circuits to simple ones; then a final rule calculates the net effect in the simple circuit. This is a case where there are a number of distinct capacities at work. The formulae give the causal laws that connect the triggering of the capacity with its exercising. The rules give a way to calculate what the current will be when all the exercisings occur together. Of course the exercisings occur in some sense or there would not be the same final effect. But there is no sensible way in which we can see them as part of that effect. Nor can I imagine any other way to count them as ‘occurrent’ in some restricted ‘Humean’ sense. Contrast a case where the exercisings really do occur in the same sense and same way as the overall effect, that is, as the analogue of the overall effect—the motions—in the case of force or the final characteristics of the current in the case of circuitry. Many economic models describe economic processes by sets of simultaneous equations. Each is said to represent a separate ‘mechanism’. For instance consider a simple familiar supply–demand equilibrium model: Qs = aP + us Qd = bP + ud Qs = Qd

laws, predictions, and powers  where Qs is quantity supplied, Qd is quantity demanded, P is price; a is positive, b negative, and us and ud represent other factors than price that affect the quantity supplied and quantity demanded respectively. I take it that the first equation describes the exercising of a supply capacity. This is a particular capacity that obtains in (specific kinds of ¹⁹) equilibrium situations whenever the price is P. It tells us that the exercise of this capacity is a quantity effect of size aP. Similarly for the second equation. It tells us that the effect of the demand capacity that obtains whenever the price is P is a quantity effect of size bP. Here the ‘Humean’ is perfectly entitled to infer that both effects are occurrent in almost any strong sense of ‘occurrent’ that might be intended. That’s because the model is a simultaneous-equations model. The rules for what happens when a number of capacities are exercised at once is that all the separate equations must be satisfied together. What happens overall must be consistent with the actual obtaining of each of the separate effects. Notice how different this is from the vector addition of forces. Say we have two negatively charged masses, with the gravitational and Coulomb forces just balanced. Motions, which I take to be the overall outcome, the manifest result, in this case are uncontroversially occurrent in anyone’s books. The gravitational capacity should produce a motion of the two towards each other; the Coulomb, motion away from each other. In fact the two are motionless. Are we prepared to say the two separate motions exist in the motionlessness? If they do, it is certainly in a much weaker sense than the two quantity effects exist in the equilibrium model. And for the circuits, the claim that the separate effects are ‘occurrent’ in some restrictive ‘Humean’ sense is even more far-fetched. ¹⁹ Exactly what the causal laws are relativized to is generally not discussed, which gives rise to a standard problem in philosophy of economics—to what situations in the real world is a given economic model supposed to apply?

 nancy cartwright

5.8 Conclusion Work by economists like Robert Lucas and David Hendry and more recently by philosophers like James Woodward and Sandra Mitchell, reminds us that for policy and planning we need something invariant, something that can be relied on across the policies to be implemented. But the idea that causes, or causal laws, are linked to strategy directs us to look in the wrong place for the desired invariance. There is nothing about the fact that one thing makes another happen in a situation that means that it will continue to do so if we start changing the methods by which the cause is introduced. Stability is nice when it happens and it is useful to know. But it does not follow from the causal relation itself and that is reflected in the fact that standard accounts of causal laws need to add it on if they want to get it. Yet we do succeed in prediction and planning—and by using our knowledge of causal laws. Other people grow glorious sweet peas from sweet pea seeds, all of us rightly expect our lights to turn on when we flip the switch, it is surely correct to expect that the magnet may retrieve the metal earring from between the floorboards and even I, despite my failures at gardening, can generally succeed in getting a packet of crisps from a vending machine. Causal laws—but causal laws with very special sources—vouchsafe these predictions. Nomological machines generate causal laws between inputs and predictable outputs. Capacities guarantee causal laws as well, though in this case we shall have to adopt some metaphysical distinctions that Hume abjured. In both cases, happily, there are frequently recognizable markers by which we can tell that the causal law in question can be relied on for the manipulations we propose to make. So—causal-law knowledge is not in general useful for policy and planning, despite our huge investments in obtaining it. It can, however, be useful if the causal laws are generated in the right way. But what then about the link between methodology and

laws, predictions, and powers  metaphysics? If we think of causal laws as I do, then there is a clear link between what a causal law says and how we go about justifying causal-law claims. But I have argued that knowledge of causal laws is not then of immediate use in the way we generally suppose unless the laws are generated in very special ways. Where is this reflected in our methodology? Econometricians like Hendry who insist on add-on tests for invariance, or social scientists who worry about the ‘external validity’ of claims from the environments in which they are established to those where they may be used, worry about just this question. But the efforts here are thin and unsystematic. In methodology we have manuals and courses on how to establish causal laws. The US government with respect to its so-called ‘No Child Left Behind’ legislation is firm in its policing of what will and will not be allowed to count as evidence for a causal claim; so too is the UK government, for instance in manuals of best medical practice by the National Institute for Health and Clinical Excellence (NICE). Philosophers too are right in the centre of the fray. We have at least a dozen different accounts of causal laws on offer, most of which are read off from some one or another methodology for licensing causal laws. But where is the methodology for determining if the laws are generated in the right ways to make them stable and usable for policy predictions? And what can we philosophers say—beyond the handful of sketchy suggestions here—about when causal knowledge will be stable—and recognizably so—and when not?²⁰ ²⁰ Research for this paper was supported by the AHRC grant for ‘Contingency and Dissent in Science’. I am grateful to the AHRC for this support and to the LSE research group associated with the project for help in thinking through the issues discussed here.

6 How is Scientific Analysis Possible? Richard Corry

6.1 Introduction One of the most powerful tools available to science is the analytic method. The method involves studying fairly simple systems in relative isolation, and then applying our knowledge of these systems to explain and predict the behaviour of more complex systems. Not only does this method give us a foothold in our understanding of complex systems, it allows us to extend our understanding to new systems, and to unify our understanding of different systems. Furthermore, it is this same analytic method that allows us to put together complex systems from parts that we understand in order to produce useful and predictable technologies. The importance and success of the analytic method raises an interesting question: What must the world be like for the method to work? What, if any, are the metaphysical presuppositions of this methodology? I will argue that the analytic method presupposes a kind of entity that does not appear in standard ontologies. I begin with a brief discussion of the analytic method in Section 6.2. In Section 6.3 I show that the method presupposes an invariant of some kind, and argue that there is nothing in standard Humean ontologies that can fill this role. In Section 6.4 I consider non-Humean ontologies that include powers, capacities and the like, and suggest that

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these non-Humean elements will not solve our problem either. In Section 6.5 I put forward my suggestion for the invariant that grounds the analytic method. Section 6.6 compares my position with that of Cartwright, and considers some objections Cartwright has made to the kind of position I am proposing. Finally, Section 6.7 deals with a further worry one may have about my proposal.

6.2 The analytic method On occasion, as a party trick, I have been known to rub a balloon against my head and then press this balloon against a wall. To the delight of any children (and even adults) who have not seen the trick before, the balloon will defy gravity and stick to the wall. Why is this so? The explanation for this extraordinary behaviour seems to be that in the process of rubbing, the surface of the balloon picks up electrons from my hair. The resulting excess of electrons on the balloon means that the attraction between the positively charged protons in the wall and the negatively charged electrons on the balloon are not balanced by an equal repulsion between the electrons in the balloon and those in the wall. Thus the balloon sticks. This explanation takes advantage of the analytic method. We explain the behaviour of a system like the balloon and wall by identifying relevant subsystems (electrons and protons in this case) and then applying our knowledge of these subsystems to explain the behaviour of the complex system. Of course, to do this, we need to have some knowledge of the subsystems. This knowledge is gained by conducting experiments on similar subsystems under controlled (and typically fairly simple) conditions. Note that the analytic method allows us to do more than successfully explain or predict the behaviour of a system like the balloon on the wall. The method allows us to unify our understanding of the balloon’s behaviour with our understanding of a huge variety of other phenomena, ranging from lightning strikes to chemical reactions. Even if you do not agree with Friedman (1974) and Kitcher (1989) that unification is the ultimate

 richard corry basis of scientific explanation, you must surely agree that such unification should be regarded as a Good Thing. Furthermore, because the analytic method allows us to predict the behaviour of such a large range of systems based on a unified theory of the components of those systems, this unified theory is capable of much more rigorous experimental testing than would be possible for theories that did not analyse the complex systems, and so did not refer to commonalities between them. Note also that the analytic method is not confined to physics; it is ubiquitous in the sciences and in everyday life. Chemists explain the action of acids in terms of the interactions of individual H+ and OH− ions. Evolutionary biologists explain the distribution of traits in a population in terms of the interactions of the individuals bearing those traits. Political analysts explain and attempt to predict election outcomes in terms of the voting preferences of groups of voters. Economists explain changes in the market by referring to the buying and selling preferences of individual agents. The success of the analytic method in such diverse fields suggests that the method really has latched onto something about the way that the world is structured. This is no trivial observation for there are ways that the world could be that would not support the method. Timothy O’Connor (1994, 2000, this volume), for example, has argued for the possibility of emergent properties—properties of complex systems that cannot be understood in terms of the properties of the components of the system. If all properties of complex systems were emergent in this sense, then the analytic method would not be applicable anywhere. Another way that the analytic method might fail is suggested by a type of explanation that sometimes appears in biology. It is not unusual in biology to explain the properties of some part of an organism by reference to the role that part plays in the organism as a whole. So, for example, many properties of the human heart can be explained, and possibly even predicted, by the fact that the role of the heart is to pump blood. If the world was such that subsystems had the properties they do only because they are part of

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a bigger whole, then once again, the analytic method would not be appropriate. So what must the world be like to support the analytic method?

6.3 Invariance and composition When applying the analytic method, we use our knowledge of how the components of a system behave individually to make inferences about how they will behave together. If this strategy is to work, then our knowledge of the components as individuals must continue to apply in some sense when these individuals are part of the larger system. But this epistemic assumption only seems justified if a corresponding metaphysical assumption is true. That is, the analytic method presupposes that something about the components of the system remains constant when these components are put together in the larger system.¹ What is this metaphysical invariant? What is it that remains constant from one situation to another, in virtue of which we can apply our knowledge of the components as individuals to the components as parts of a complex system? I will shortly consider a number of possible answers to this question, but first, let us note that whatever this invariant is, there are three constraints it must satisfy: (1) The invariant must actually be invariant across the relevant contexts. (2) The invariant must be something we can learn about whilst studying a system in relative isolation. (3) The knowledge gained by studying the invariant in the simple context must be useful for understanding behaviour in the complex context. ¹ I am only claiming that the existence of such invariants is necessary for the success of the analytic method, not that it is sufficient. In addition we will need laws that tell us how these invariants combine in complex systems. Such composition laws have been the focus of attention in much of the previous discussion of what makes the analytic method possible—particularly in the debate between holism and methodological individualism in the philosophy of social science (see, for example, Brodbeck 1958 and Addis 1966). I discuss laws of composition in Section 7 below.

 richard corry With these constraints in mind, let us turn our attention to the candidates. 6.3.1 Behaviour Let’s warm up by considering the na¨ıve view that it is the behaviour of the components that remains invariant between contexts. What I have in mind by the term ‘behaviour’ is simply the temporal sequence of properties (including relational properties) the system actually possesses. The suggestion that it is simply behaviour that is invariant between relevant contexts has two things going for it: (1) We learn about systems (whether in complex or simple contexts) by observing their behaviour. (2) It is the behaviour of systems that we wish to predict and/or explain by employing the analytic method. Thus, if behaviour were invariant between the relevant contexts, then it would certainly serve the purposes of the invariant that is presupposed by the analytic method. The problem, of course, is that behaviour (or at least the relevant aspects of behaviour) is typically not invariant between relevant contexts. Newton’s theory of gravitation, for example, tells us that a massive body in isolation will move in a straight line, while a massive body in the presence of another will move in a curved line. So massive objects behave differently in different contexts and thus behaviour cannot be the invariant that grounds the analytic method in gravitational physics. Similarly, human beings behave very differently in groups than they do in isolation, so behaviour will not be the invariant that grounds the analytic method in sociology or economics. There may, of course, be some domains where the relevant behaviour of the relevant systems remains constant between simple and complex contexts. In such a domain mere behaviour could ground the analytic method. For in such a domain, the behaviour of the complex system would simply consist in the characteristic behaviours of the individual components all happening at once. So if we learn the characteristic behaviour of the individuals

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(say, by studying them in isolation) we can predict the behaviour of the complex whole. Mass in Newtonian physics may provide an example of such a situation. The mass of a Newtonian particle does not change from one context to another, so the mass of a complex of many particles simply consists in the occurrence of all the individual characteristic masses. In Newtonian physics, then, behaviour with respect to mass could serve as the invariant that grounds applications of the analytic method to explain or predict the mass of a complex system. However, in any interesting complex system there will be causal interaction between the parts, and the relevant behaviour of these parts in combination will not be the same as their behaviour in isolation. From now on, I will only be concerned with such interesting cases. The crucial point is that we can and do successfully apply the analytic method in many such cases. Since the behaviour of the subsystems is not invariant in these cases, behaviour cannot be the invariant that grounds the successful application of the analytic method in any interesting case.² 6.3.2 Laws of nature Laws of nature, perhaps, are a more likely candidate for the invariant that grounds the analytic method. For, as usually understood, part of what makes a law of nature a law is precisely that it is invariant—the true laws of nature do not change from one context to another. If we can learn the laws that govern a component system by observing it in isolation, and if these laws remain invariant, then surely we can (at least in principle) use these same laws to explain or predict the behaviour of the component when it is part of a compound. Let us put aside any Humean worries we might have about how we might come to learn about the laws of nature, and consider whether the laws we learn by studying a system in isolation will ² J. S. Mill seems to disagree, asserting that in all cases where the analytic method works, the behaviour of a complex system simply consists in all of the components doing what they would have done in isolation. I find this position quite implausible but will discuss it further below.

 richard corry actually be of any help in understanding what is going on when that system is part of a more complex whole. It is a common thought that the standard form for a law of nature is a universal conditional. Hempel and Oppenheim, for example, state that a law of nature usually ‘makes an assertion to the effect that universally, if a certain set of conditions, C, is realized, then another specified set of conditions, E, is realized as well’ (1948: 153). Although laws are hardly ever explicitly stated in this way, the conditional form reflects the fact that almost all laws of nature—whether from physics, biology, economics, or wherever—tell us what will happen only if we supply them with a set of initial (or final, or intermediate) conditions. But the conditional form of such laws leads to trouble for the analytic method. For suppose that we study a system in isolation and learn that it obeys a certain law. That is, we learn that under conditions C (in which the system is isolated) behaviour E always occurs. This knowledge can be of no use to us when we want to know what the system will do as part of a complex—that is, when we want to know what will happen when conditions C no longer obtain. The problem, then, is that although the laws we might discover by studying a system in isolation may be invariant, the laws we learn this way seem to be the wrong ones for explaining how the system will behave in a more complex situation. One might object to my assumption in the previous paragraph that conditions C (isolation) will no longer obtain when the system is part of a complex. For it is possible to specify a set of conditions C that will obtain both when the system is in isolation and when it is part of a complex (as a trivial example, let C be the condition that 2 + 2 = 4). If a law refers only to such conditions, then it will continue to apply when the system is part of a compound. In response I accept that there may be such laws, but let us follow through their consequences. If the law governing the component system states that ‘if a certain set of conditions, C, is realized, then another specified set of conditions, E, is realized as well’, and if C is realized both when the system is in isolation and when it

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is part of a compound, then E will be realized both when the system is in isolation and when it is part of a compound. That is, the relevant behaviour of the system will not change from one context to the other. But I have already considered situations in which behaviour remains invariant, and have set such situations aside as uninteresting.³ In interesting situations, the behaviour of our component system will not be invariant, and hence the relevant conditions C cannot be realized both when the system is in isolation and when it is part of a compound. Perhaps a more sophisticated view of laws will help. Consider Newton’s Second Law: f = ma. This law is not equivalent to a universal conditional of the sort suggested by Hempel and Oppenheim; rather it is equivalent to an infinite number of such conditionals, one for each possible value of f and m. Thus, if we can learn that a system obeys this law by studying it under one set of conditions, we might still be able to apply the law when the system is subject to a different set of conditions. Unfortunately, the move to a more sophisticated view of laws does not really help. The same problem simply raises its head in another guise. The problem we face is one that has been pointed out on numerous occasions by Nancy Cartwright (see, for example, her 1980, 1983, 1989, 1999). Cartwright observes that the standard view of laws of nature is that they describe regularities in behaviour. But she says, such regularities are exceedingly rare in nature; the actual behaviour of a system depends on the environment it is in, and there will often be external influences that disrupt any lawlike regularity. Thus laws of nature—conceived of as statements of regularity in behaviour—will most likely be false. ³ Perhaps I am being a little unfair labelling these situations ‘uninteresting’. As Cartwright points out in this volume, complex systems modelled by a system of simultaneous equations might be interpreted in such a way that each equation specifies the characteristic behaviour of a component system. Since a solution to a system of simultaneous equations is one in which each individual equation is satisfied, one might argue that such solutions describe cases where the characteristic behaviours of the components all occur simultaneously. I don’t really mean to suggest that all such systems are uninteresting. What I really mean is that they are not the systems I am interested in here.

 richard corry So, for example, taking a sophisticated view of the laws of classical mechanics, we might interpret these laws as stating that massive bodies will accelerate towards each other at a rate proportional to the product of their masses and inversely proportional to the distance between them. Thankfully, however, I can report that the computer I am typing on at this moment is doing no such thing. The computer is not accelerating towards the Earth because it is supported by a desk. The desk seems to have destroyed the supposed regularity. Relating this example back to the analytic method, the problem is this: if I study two massive bodies in isolation, I will find that they obey a law which states that the bodies will accelerate towards each other at a rate proportional to the product of their masses and inversely proportional to the distance between them. However, when I place these two bodies into a more complex system involving non-gravitational forces (such as electromagnetic forces in the case of the desk), they will no longer obey this law. Thus the law is of no use to the analytic method (at least this is true if we conceive of the law as describing a regularity in the behaviour of a system—I will consider other ways to conceive of laws shortly). Before giving up on laws of nature, let us consider an objection that Cartwright briefly considers and rejects. This objection suggests that what we need to do is employ a more complex ‘super law’ which takes into account all the relevant interactions into which a system can enter. In the example above, the relevant super law would be one ‘which says exactly what happens when a system has both mass and charge’ (Cartwright 1980: 81). There are two problems with this suggestion. The first problem is that the way we actually come up with such a super law is by studying the interactions involved in isolation. Once we know how the individual interactions work, we put this knowledge together to formulate a super law. So our knowledge of the super law is a result of an application of the analytic method, and so cannot be something we rely on in that very application. The analysis that produces the super law must rely on an invariant other than the super law itself.

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The second problem with the super law suggestion is that, as Cartwright points out, ‘if we fail to describe the component processes that go together to produce a phenomenon, we lose a central and important part of our understanding of what makes things happen’ (1980: 81). The reason we miss this important part of our understanding is that super-law explanations are simply not examples of the analytic method. 6.3.3 Dispositions We have seen that neither behaviour nor laws can play the role of the invariant that grounds the analytic method. The next obvious candidate to consider is that it is the dispositional properties of component systems that plays this role. The thought would be that we observe the components of a system individually under various different circumstances and thereby learn about their dispositions to behave. We then apply our understanding of these dispositions to explain the behaviour of the components when they interact to form a larger system, and thus explain the behaviour of the complex whole. Unfortunately, however, dispositions—as standardly understood—cannot be the invariant we are looking for either. To see why this is so, let’s take a closer look at what we are ascribing when we ascribe a disposition to something. The standard analysis of dispositions proceeds in terms of subjunctive conditionals something like the following: ‘X is disposed to behave in manner B under conditions C iff were X to be placed in conditions C it would behave in manner B.’ Although this straightforward conditional analysis has been elaborately modified to avoid certain objections (see e.g. E. W. Prior 1985; Lewis 1997; Malzkorn 2000; and Mellor 2000), the basic strategy is still to analyse dispositions in terms of the behaviour that would occur if certain conditions held. But if we analyse dispositions in terms of conditionals, then we will run into exactly the same problem that faced laws of nature. When we observe a component in isolation, we learn

 richard corry about its dispositions to behave under certain conditions C. But to explain the behaviour of a compound system, we need to know how the components are disposed to behave under very different conditions C  , conditions in which the component is part of the larger system. Furthermore, we have seen that in any interesting case, the actual behaviour of the components in the system will differ from their behaviour in isolation. Thus the differences between conditions C and C  are clearly relevant to the dispositions in question. In short, the problem is that any behavioural dispositions we discover when a component is in isolation will be dispositions whose antecedent is not satisfied when the component is part of the larger system. Thus, although the dispositions of the components may remain invariant from one situation to another, the dispositions we learn about when studying the components in isolation will not be the dispositions that are manifested when the components are placed into a complex. Simple dispositions, as standardly understood, cannot be the invariant that grounds the analytic method. Just as there is a sophisticated view of laws of nature according to which a law corresponds to an infinite set of conditionals, there is a sophisticated view of dispositions according to which a disposition corresponds to an infinite number of conditionals. So, for example, we might say that when affected by a force of f Newtons, an electron is disposed to accelerate at a rate of 9 × 10−31 f meters per second per second. Complex dispositions like these could be regarded as a kind of multi-track disposition (see Ellis and Lierse 1994: 29; Bird, this volume). Ultimately, I think that complex dispositions of this sort are a step in the right direction. However, we are not out of the woods yet. For so long as we analyse dispositions in terms of conditionals which state what behaviour will occur when certain conditions are satisfied, each disposition will correspond one-to-one with a lawlike regularity, and hence will be subject to the same problems that faced laws of nature. For example, an electron will have a disposition to behave one way in the presence of massive objects,

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and a disposition to behave another way in the presence of charged objects, and neither of these dispositions will be manifest when the electron is in the presence of a massive charged object. We might try to solve the problem by positing a ‘super disposition’, but this will face the same problems as a super law.

6.4 Towards a solution: capacities and non-Humean dispositions At this stage I believe that we have exhausted the possibilities available to what we might call a Humean ontology. The Humean view I am referring to is the view that fundamental reality consists of objects with categorical (i.e. non-dispositional) properties and that is all. Laws of nature, on this view, are descriptions of contingent regularities among these objects and properties. Dispositions are descriptions of contingent regularities in the behaviour of the object having the disposition. Thus laws and dispositions must be analysed in terms of conditionals like those considered above. What I think our discussion so far has shown is that the scientific method assumes an ontology richer than the sparse world described by the Humean.⁴ So the question is: What must we add to the Humean ontology in order to ground the analytic method? A number of authors (e.g. Ellis and Lierse, Ellis, Cartwright, Molnar, Harr´e) have suggested, for various reasons, that what is lacking from the Humean ontology are Tendencies, Powers, Capacities and such like. I believe that the addition of such non-Humean concepts is a step in the right direction; however, not just any old non-Humean Tendency, Power, or Capacity will do the job. In order to see what is needed, I think it will be useful to consider the views of Brian Ellis and Caroline Lierse on the one hand, and Nancy Cartwright on the other. Let us begin, then, with Ellis and Lierse. ⁴ And what O’Connor (this volume) brands the ‘second-order Humean metaphysics’ of David Armstrong (1997) and Michael Tooley (1997) will, I believe, face the same objections.

 richard corry 6.4.1 Ellis and Lierse on dispositions and powers It is common to distinguish dispositional properties from nondispositional, or ‘categorical’ properties (so called since they do no more than categorize their bearers).⁵ The Humean view described above holds that all dispositional properties supervene on categorical properties together with the laws of nature. This view—which Ellis and Lierse (1994: 30) call ‘categorical realism’—takes the analysis of dispositions in terms of conditionals as a definition. Understood this way, the analysis can provide a path to reduce dispositional properties to non-dispositional properties plus laws of nature. So, for example, on this view to say that a glass is fragile is simply to say that if certain circumstances obtain the glass will (or is likely to) break, and the reason the glass will (or is likely to) break in such circumstances is that the glass has a certain structure and there are laws of nature that imply that when objects with this structure are placed in these circumstances they will (or are likely to) break. Categorical realism is probably the dominant view among philosophers today. Ellis and Lierse deny categorical realism, arguing that some dispositions cannot be reduced to a categorical basis. Their thought is that the conditional analysis is not a definition of what it is to have a dispositional property, but, rather, a means of identifying such a property. The dispositional property is what makes the conditional true, but it is not simply reducible to the conditional.⁶ With this non-Humean view of dispositions under their belt, Ellis and Lierse define causal powers, capacities, and propensities as special kinds of dispositional property: A causal power is a disposition of something to produce forces of a certain kind. Gravitational mass, for example, is a causal power: it is the power of a body to act on other bodies gravitationally. A capacity is a disposition of a kind distinguishable by the kind of consequent event it ⁵ Though note that Mellor (1974, 1982) argues that the distinction is incoherent. ⁶ Similar ideas can be found in Harr´e 1970; Harr´e and Madden 1973, 1975; Shoemaker 1980; Swoyer 1982; Fales 1990; and Fara 2005.

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is able to produce. Thus, for x to have the capacity to do Y is for x to have a disposition to do Y in some possible circumstances. Inertial mass, for example, is a capacity. It is the capacity of a body to resist acceleration by a given force. A propensity is a disposition which a thing may have to act in a certain way in any number of a very broad range of circumstances. For example, the propensity of a radium atom to decay in a certain way in a certain time is a disposition which the atom has in all circumstances. (Ellis and Lierse 1994: 40)

These powers, capacities, and propensities are prime candidates for the invariants we have been hunting. For it is at the very least plausible to suppose that these properties of a system remain constant from one situation to another, even though the behaviour they produce might change. Indeed, Ellis and Lierse argue for ‘dispositional essentialism’, the view that at least some dispositional properties are essential to the entities that have them. That is, having certain dispositional properties is part of what makes an entity the kind of thing that it is. If dispositional essentialism is true, then the essential powers, capacities, and propensities of a system must, by necessity, remain invariant as the system is taken from one situation to another. Furthermore, it seems natural to suggest that we can learn about the powers, capacities and propensities of a system by studying that system in simple controlled circumstances. Finally, Ellis and Lierse have freed these dispositions from Humean analysis in terms of conditionals, so maybe their view will avoid the problems I outlined above for the standard account of dispositions. Unfortunately, nothing is quite so simple, for it is not at all clear that Ellis and Lierse’s account of dispositions does avoid the problems of the standard Humean account. Although they reject the conditional analysis of dispositions, dispositions are nonetheless only identifiable via conditionals; the disposition to E in circumstances C is simply that property that is responsible for the fact that its bearers would (normally) E in circumstances C. So, suppose that we take a system x and investigate it under a range of simple, controlled conditions C. We find that in circumstances C, x tends

 richard corry to E. Following Ellis and Lierse we ascribe a dispositional property P to the system x, where P is the property responsible for the fact that in circumstances C, x tends to E. The problem is that this is all we know about P. In particular, we do not know what behaviour P will tend to produce in circumstances other than C. Consider now an application of the analytic method. Suppose that I study the way that electrons interact with other electrons by studying pairs of electrons in isolation. I will discover that electrons are disposed to accelerate away from each other. According to Ellis and Lierse, what I have discovered is that electrons have a dispositional property P that is responsible for them accelerating away from other electrons when the two are isolated from other interactions. But what happens if we take the pair of electrons and put them into a more complex system? The answer depends on the details of the system. The two might still accelerate away from each other, they might remain motionless relative to each other, they might even accelerate towards each other. So, can knowing that the electrons have the property P help us predict what will happen? I think not. It is true that the electrons’ behaviour in the complex system could be the result of the same dispositional property P that led to the electrons accelerating away from each other in isolation. The problem is that all we learn about P by studying the electron pair in isolation is that possessing P implies a conditional: in situations C (where the pair is isolated) they will exhibit behaviour E (accelerating away from each other). But we have already seen, in our discussion of Humean dispositions, that such a conditional is no use in predicting what will happen in situations other than C. By interpreting the conditional as a means for identifying the property P rather than an analysis of P, Ellis and Lierse simply shift the problem from metaphysics to epistemology. 6.4.2 Cartwright on capacities Nancy Cartwright is another supporter of capacities, powers, and tendencies, but she has a slightly different interpretation of the

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notion than Ellis and Lierse. In particular, Cartwright argues that capacities should not be straightforwardly understood in terms of dispositions. Dispositions, she says, are usually tied one-toone with lawlike regularities, they are identified with particular manifestations. Capacities, on the other hand, are ‘open ended’ and give rise to varied behaviours (Cartwright 1999: 59, 64). If we must think in terms of dispositions, she says, we should think of capacities as being what Gilbert Ryle has called ‘highly generic’ or ‘determinable’ dispositions, in the same class as ‘being humorous’, or ‘being a grocer’. Quoting Ryle (1949: 118) she says that such generic dispositions ‘signify abilities, tendencies, propensities to do, not things of one unique kind, but things of lots of different kinds’ (Cartwright 1999: 64). When interpreting Cartwright, we are faced with a dilemma. Either what she has in mind are simply multi-track dispositions of the sort that Ellis and Lierse describe, or they are something else. If Cartwright is simply talking about non-Humean multi-track dispositions of the Ellis–Lierse stripe, then surely her view cannot do any better than Ellis and Lierse’s in helping us understand the analytic method. If, on the other hand, Cartwright has something different in mind, the question is what? However Cartwright answers this question, she is going to face difficulties. For the one thing she does tell us is that the behaviour a capacity gives rise to is highly varied. In particular, objects with a given capacity may behave very differently in one circumstance than they do in another. But now we are faced with the same old problem again: if the behaviour that a given capacity produces can change from one circumstance to another, then how is it that learning about the exercise of a subsystem’s capacities in isolation can tell us anything at all about how these capacities are exercised in the differing circumstances of the compound system? Moving from ordinary old dispositions to highly generic dispositions just seems to make our problems worse, for we just add extra variability from one situation to another. The fact that the capacity itself remains

 richard corry invariant is of no use to us if we have no way to know what behaviour the capacity will produce.

6.5 Causal influence When I wrote the original draft of this paper I did not think that Cartwright had the tools to answer this objection. However, I may have been too quick to draw this conclusion, for in her contribution to this volume Cartwright clearly lays out just the kind of distinction that I think will solve the problem. In her paper in this volume, Cartwright too is concerned with a kind of invariance, namely the conditions under which causal laws remain invariant (and hence useful). She argues that it is capacities that guarantee the usability of causal laws, and that they do this both by underwriting these laws and by allowing us to characterize the situations in which the laws will fail to hold. In the course of this discussion, Cartwright tells us that only a metaphysically heavyweight, non-Humean notion of capacity will do the job. According to Cartwright (this volume, p. 151), what is needed is a threefold distinction between: (1) The obtaining of a capacity (2) Its exercise (3) The manifest (‘occurrent’) results. I believe this threefold distinction is just what we need in order to understand the analytic method (as opposed to the two-fold distinction made by Ellis and Lierse between non-Humean dispositions on the one hand, and the Humean behaviour they produce on the other). This threefold distinction is essentially the same as that made by George Molnar (2003) who distinguishes (1) Powers, (2) Manifestations of powers, and (3) Effects of powers. In what follows I will focus on Cartwright’s version of the distinction and provide an interpretation of it that is geared towards what I ultimately think is the correct story. I will return very briefly to Molnar’s view at the end of Section 6.6.

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The expression ‘manifest results’ refers to the kind of properties that Humeans would be happy to allow into their fundamental ontology—properties like position and size. I will take the ‘obtaining of a capacity’ to denote the existence of a non-Humean, essentially dispositional property. Recall that Humeans analyse dispositional statements as being nothing more than conditional statements regarding the manifest results one will see if other (manifest) conditions are realized. Thus a Humean seeks to understand dispositions in a way that keeps everything at level (3) of Cartwright’s metaphysical hierarchy. So, by positing a capacity that is separate from, and responsible for, these manifest results, Cartwright is positing a non-Humean property similar to the kind that Ellis and Lierse endorse. To avoid confusion I should clarify this last claim. As we shall see shortly, Cartwright views capacities as dispositions that are manifested at level (2) of the hierarchy. Ellis and Lierse do not seem to recognize level (2), hence we must suppose that they view causal powers and the like as dispositions that are manifested at level (3). What Cartwright shares with Ellis and Lierse is the view that capacities and/or powers are essentially dispositional—they cannot be analysed away in terms of, or reduced to, the behaviours they produce. Cartwright, like Ellis and Lierse, must therefore place capacities into a metaphysical category that is separate from level (3). What Cartwright gives us that Ellis and Lierse do not (at least not explicitly) is a second non-Humean element: the exercise of a capacity. We will see what this amounts to in a moment, but just note why we might be interested in this extra level of complexity in the context of the analytic method in science. I have argued that we cannot make sense of the analytic method if we focus only on level (3) of the hierarchy. Nor can we make sense of the analytic method if we add dispositions at level (1), at least not if we understand them as dispositions to produce level (3) behaviour. The problem in both cases is that the behaviour at level (3) typically does not remain constant from one situation to another. So, in order to understand the analytic method, it seems we are forced to

 richard corry posit another metaphysical level of some kind, and I believe that Cartwright’s level (2) is just what we need. Note that, to support the analytic method, level (2) cannot be reducible to, or analysed away in terms of, either levels (1) or (3). For nothing in level (1) or (3) is invariant in the way that will be required from level (2). In particular, although we might follow Cartwright and identify elements of level (2) as exercisings of capacities at level (1), levels (1) and (2) are ontologically distinct. So what are these things on level (2)? Cartwright gives us the following illustration: Gravity has the capacity to make heavy objects fall. The attraction of a heavy body constitutes the exercise of the capacity; the motion of the heavy body is the actually manifested result when the capacity is exercised. What matters here is that the canonical behaviour after which the capacity is named may be seldom if ever the ... actually manifested ... result and the actually manifested result may have no systematic connection with the presence of the capacity. The systematic connection is between the obtaining of the capacity and its exercise. Massive objects—that is, objects with the gravitational capacity—always attract other bodies even should the other bodies never move closer. (This volume: 151)

So gravitational forces are examples of the exercisings of capacities, as would be electromagnetic, strong, and weak nuclear forces. But the notion is more general than the notion of a force. Cartwright suggests that getting angry is the exercising of the capacity of irritability. As further examples I would suggest that resisting acceleration is the exercising of the capacity of inertia, and influencing an election is the exercising of one’s capacity to vote. What all these have in common, I believe, is that they are all cases of exerting an influence over the behaviour of a system. From now on, I will refer to the entities at level (2) as causal influences rather than exercisings of a capacity.⁷ ⁷ I have three reasons for choosing this terminology. The first reason is purely aesthetic. The second reason is that I have already used this terminology in Corry (2006), and the

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The crucial point is that causal influences are metaphysically distinct from both the capacity itself and from the behaviour that results. They are distinct from capacities because an object could have a capacity without that capacity being ‘triggered’. For example, massive objects have the capacity to influence the motion of other objects, but if there were no other objects there would be no causal influences. Similarly, causal influences are distinct from the manifest behaviour that results, because the same influence can lead to very different behaviour in different circumstances. So how might these causal influences help us with the problem of understanding the analytic method? My thought is that the analytic method assumes that systems have certain causal powers, capacities, tendencies, and the like, understood as follows: (a) Causal powers, capacities, tendencies and the like are dispositions, but they are dispositions to produce causal influences (at level 2) not dispositions to produce manifest behaviours (at level 3). (b) These dispositions are invariant under all conditions: if the disposition is triggered the corresponding causal influence will come into effect. (c) The conditions that are sufficient for the triggering of these dispositions are positive states of affairs (i.e. they don’t involve negations). We will see the point of assumption (c) shortly. I note here, however, that we do have independent reasons for thinking that nature does not pay attention to negative facts—see Armstrong 1997 for discussion of this issue. To see how these conditions come together in the analytic method, consider the following example. concept I have in mind is very similar to the concept introduced with this name in Creary 1981. The third reason is that, as we shall see, one could hold an ontology that includes levels (2) and (3) but not level (1). I therefore want my terminology to reflect this independence between levels (2) and (3).

 richard corry Suppose we observe a 1 kg sphere of gold under various controlled conditions and come to the conclusion that it has the capacity to attract other massive objects. We find that there is a systematic relation between the strength of this attraction, the mass, m, of the other object and the distance, r between the two. The relation is characterized by the equation f = Gm/r 2 . In line with assumption (a) we interpret this capacity as a complex disposition which implies that if an object of mass m is at a distance r meters from the gold sphere, then there will be a causal influence of attraction between the two objects whose strength is Gm/r 2 Newtons. Suppose further that our gold sphere happens to have a net negative charge. By observing the interaction of the sphere with other charged objects, we find that it has a capacity to repel other negatively charged objects, and that the strength of this repulsive influence follows a similar inverse square law.⁸ Now for the crucial part. Suppose that we place our gold sphere in the vicinity of a second identical sphere. What should we expect to happen? By assumption (b) the spheres retain their disposition to attract other massive objects. Thus, there will be an attractive causal influence between the two spheres, so long as the conditions are right to trigger the disposition. But the disposition states that all that is required for an attraction of strength Gm/r 2 is that there is another mass m at distance r, and by assumption (c) that is the end of it—we cannot add the condition that the disposition is triggered only if the other mass is not charged. Thus we are led to conclude that there will be an influence of attraction between the two spheres. But by a similar reasoning we should expect an influence of repulsion between the two spheres. What actually occurs is the result of these two influences working against each other. If each ⁸ Unfortunately, all these charged objects will also have mass, so the observations of the repulsive causal influence due to charge will never truly be made in isolation from the attractive causal influence due to mass. In practice we observe the influence our sphere has on very light charged particles, since we know that the gravitational influence will be correspondingly small.

how is scientific analysis possible?  √ of the spheres has a net charge of − (Gk) Coulombs, the two influences are of equal strength, and so cancel each other out. The point of assumption (c) here is that it ensures that if conditions are right for the exercising of a capacity, they will remain right even if we make the environment more complex (so long as we don’t remove the original conditions in the process). Thus it is not only the capacity that remains invariant from simple situations to complex ones; the influence that the capacity has can also remain invariant. If the influences can remain invariant from simple systems to complex ones, then we can learn what influences will be in play in a complex system by studying the simple systems from which it is composed (assuming that there are no emergent influences at play). To put the analytic method to use, all we need to do now is figure out what manifest behaviour will occur when the system is subject to more than one causal influence. Given the diverse nature of causal influences, it may not always be easy to combine different influences, and so the analytic method may not always be useful even if the assumptions above are satisfied. However, there are realms within which we already have rules for combining such influences. In an election, for example, we simply stipulate such rules. When dealing with influences that are trying to produce accelerations, we call them forces, model them in a vector space, and combine them via vector addition.

6.6 Cartwright and the status of level (2) The purpose of this paper so far has been to spell out in detail why the analytic method presupposes an invariant that is distinct both from dispositional properties and from standard ‘Humean’ properties. We have seen that on this point I am largely in agreement with Cartwright, and that it seems natural to identify the element I am proposing with level (2) of Cartwright’s metaphysical hierarchy. However there does seem to be an important difference

 richard corry between Cartwright and myself: in my opinion she does not take level (2) of her hierarchy seriously enough. One indication of the difference between Cartwright’s position and the one I am advocating here can be seen by noting that nothing in my argument requires level (1) of Cartwright’s hierarchy. Recall that level (1) contains dispositional properties, including dispositions to produce causal influences. We should only posit level (1) as a distinct, irreducible ontological category if we think that these dispositions are irreducibly dispositional in the way that Ellis and Lierse describe. But nothing in our discussion so far requires this. In particular, given the existence of influences at level (2), one could choose to analyse the disposition ‘to have a causal influence of type X in circumstances C’ in terms of a conditional just as Humeans do—the only difference being that the conditional will mention elements at levels (2) and (3) instead of just the Humean level (3). If we take this route, we can do without the kinds of thing that Cartwright, Ellis and Lierse all seem to agree are necessary: irreducible causal powers, capacities and the like. Now I am not suggesting that we should take this route—I am personally rather fond of causal powers, and there may be other good reasons for endorsing them—my point is that nobody seems to have noticed this possibility. In particular, I believe that Cartwright’s failure to notice this possibility is a symptom of her strangely dismissive attitude towards level (2). The true nature of my disagreement with Cartwright is best seen by comparing our attitudes to component forces. Both Cartwright and I place forces at level (2) of the hierarchy. Now, if I am right, the role of level (2) is to provide an element of invariance as circumstances change. In particular, then, component forces must lie at level (2), for it is only these component forces, and certainly not the total force, that have any chance of remaining invariant. Thus I am committed to the claim that component forces are real existants. Cartwright, however, seems to deny the reality of component forces. This denial is perhaps clearest in her earlier work:

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The vector addition story is, I admit, a nice one. But it is just a metaphor. We add forces (or the numbers that represent forces) when we do calculations. Nature does not ‘add’ forces. For the ‘component’ forces are not there, in any but a metaphorical sense, to be added; and the laws which say they are must also be given a metaphorical reading. (1980: 78)

But the denial continues in more recent work. In The Dappled World, for example, she considers the force between a pair of charged particles and says: We say that Coulomb’s law gives the force that is due to their charge [as opposed to their mass]. But this is no concept for an empiricist. What we mark when we say that there is a coulomb force at work is not the presence of an occurrent force whose size is that given in Coulomb’s law, but rather the fact that the charged bodies have exercised their capacity to repel or attract. Coulomb’s is never the force that actually occurs. (1999: 82)

Furthermore, the denial of the reality of component forces seems to be a central pillar of Cartwright’s major thesis that ‘the laws of physics lie’. For example, if component forces are not real, and only resultant forces are, then laws such as Newton’s law of gravitation (which says there will be an attractive force of strength Gm1 m2 /r 2 between any two masses) will be contradicted by Coulomb’s law (which states that there is a force of strength q1 q2 /r 2 between any two charged particles) in cases involving particles that have both charge and mass.⁹ Given that the argument I have outlined in this paper concludes that science presupposes causal influences such as component forces, and given that my argument seems very similar to arguments that Cartwright has given in a number of places, I am at a loss to ⁹ Cartwright’s argument applies to a particular view of the content of laws of nature, namely that they are universal generalizations concerning level (3) behaviour. I will not here enter into the debate over the adequacy of this view except to say that we can keep the idea that a law is a universal generalization, yet avoid Cartwright’s negative conclusions, if we allow the generalizations to include elements from level (2). See Corry (2006) for further discussion of this point.

 richard corry understand what she has against component forces. So let us turn to her reasoning. In ‘Do the Laws of Physics State the Facts?’ (1980), Cartwright considers John Stuart Mill, who held that component forces are real. Mill states that If a physical body is propelled in two directions by two forces, one tending to drive it to the north and the other to the east, it is caused to move in a given time exactly as far in both directions as the two forces would have separately carried it; and is left precisely where it would have arrived if it had been acted upon first by one of the two forces, and afterwards by the other. (A System of Logic, Book III, chap. 6, §1)

Cartwright responds that Mill’s claim is ‘unlikely’: ‘When a body has moved along a path due north-east, it has travelled neither due north nor due east ... no pure north motion can be part of a motion which always heads north-east’ (1980: 79). The lesson is even clearer, she says, in cases of equilibrium. Considering a system like the two charged gold spheres described above, Cartwright says: The gravitational capacity should produce a motion of the two towards each other; the Coulomb, motion away from each other. In fact the two are motionless. Are we prepared to say that the separate motions exist in the motionlessness? ( This volume: 155)

Cartwright suggests that the answer is clearly no. I have no quibble with Cartwright’s response to Mill. I too baulk at the claim that the motionlessness of a particle could consist in a motion to the left simultaneous with a motion to the right. But showing that Mill’s reasons for countenancing component forces are no good does not show that we should not countenance component forces. In particular, it does not show that there is something wrong with component forces considered as causal influences at level (2) of our metaphysical hierarchy. For Mill’s position and Cartwright’s objection are all aimed at level (3) of the

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hierarchy. The principle Cartwright is invoking is that motions (at level 3) are not resolvable into component motions (also at level 3). This does nothing to show that a motion (at level 3) cannot be the result of multiple component influences at level (2). In fact, Cartwright’s argument here actually leads us towards the conclusion that we must accept component causal influences as real. For her claim that motions cannot be resolved into components in the way Mill suggests is just a special case of something I assumed as a premise of my argument at the beginning of this paper, namely that in interesting applications of the analytic method, the behaviour (at level 3) of subsystems will not remain invariant from simple situations to complex ones. In particular, the motions of subsystems in a complex situation will not simply consist in the occurrence of the motions that would have occurred if the subsystems were in isolation. What Cartwright’s examples show is that the invariant presupposed by the analytic method cannot lie at level (3). So Cartwright gets things the wrong way around. She dismisses component forces because there are no component effects at level (3). But it is precisely because there are no component effects at level (3) that we posit the existence of invariant influences at level (2). To ground the analytic method, causal influences must be distinct from, but at least as real as, capacities and powers on the one hand and the behaviours they produce on the other. But causal influences are clearly not dispositions, and they are different in kind from the sorts of properties or events that we would normally term ‘behaviour’. Thus the analytic method assumes a whole new kind of entity, something that mediates between the powers something has and the behaviour those powers produce; between cause and effect. Entities of this kind do not appear in standard ontologies; however they have been advocated for similar reasons by Creary (1981). As mentioned previously, Molnar (2003: §12.1.3) also describes something very like my causal influences under the title ‘manifestations’. Molnar intends that his manifestations do the same sort of work as my causal influences, however he seems to draw back from granting manifestations any ontological reality. He says: ‘While

 richard corry ontologically there is nothing over and above individuals and their properties (actions), causally there is’ (2003: 198). I have no idea what it means for something to exist causally but not ontologically.

6.7 Composition of causes The main point of this paper has been to track down the invariant that grounds the analytic method in science. My conclusion is that causal influences are what do the job. However, I should probably say a few more words about the second stage of the analytic method—the composition of component causal influences. As Brodbeck (1958) stresses, laws of composition are empirical laws, and there is no reason why the same laws should apply in all cases. I have already noted that when the causal influences are forces (i.e. they are influences that are trying to bring about accelerations) we have a clear rule for combining multiple influences: we form the vector sum of the various forces, and the system will behave as if this sum were the only force in play. Similarly precise models can be found in fields as diverse as evolutionary biology, ecology, and econometrics. Unfortunately though, in many other situations we do not have such precise rules of composition for causal influence. Does this mean that the analytic method cannot be applied in these other situations? No. Even without precise mathematical models telling us how to compose causal influences we may have rough and ready rules. For example, acids tend to turn litmus paper red, bases turn litmus paper blue. What happens if I place litmus paper into a mixture of an acid and a base? I do not have a precise rule for composing the influences of the acid and the base, but if I know that the acid is strong and the base weak, then I can predict that the litmus paper will tend towards the red end of the spectrum. But as Creary (1981) points out, even when we do not have any idea how to compose the influences at play, the analytic method can still be of use in providing post facto explanations. Suppose that I were to mix an acid and a base together in some unknown proportion. Suppose also that I had no idea about the relative

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strengths of the acid and the base. In such a situation I would be in no position to predict the outcome of placing litmus paper in the resulting solution. But suppose that I place the litmus paper in the solution and find that it goes red. I can conclude that it went red because the influence of the acid in the solution was stronger than the influence of the base. Note that this explanation is only available to me if I assume the influences of the acid and base are invariant. However, there must be some restrictions on the form that the laws of composition can take if we are to be able to apply the analytic method. From a practical standpoint, if the laws are too complex, then we will not be able to learn or apply them. But there is a metaphysical worry here too. I have argued that invariant causal influences together with laws of composition can ground applications of the analytic method. But if we allow any old laws of composition, then it seems we will be able to ground the analytic method in all circumstances, including circumstances where we would intuitively think the method was inappropriate. To see why this is so, note that a law of composition is simply a function that takes component influences as inputs and then outputs some means for predicting the resultant behaviour (the output could be a specification of the resultant behaviour, it could be a ‘resultant force’, a probability distribution over behaviours, or some such). But given any set of behaviours and any assumed component influences, there will be a function that maps those components to the appropriate behaviour. Thus, if we allow any old rule of composition, then we can analyse any behaviour in terms of constant component influences. We will effectively rule out the possibility of true emergent properties and behaviours. Whilst I think that it would be wrong to rule out the possibility of emergence in this way, the more pressing concern is that if any behaviour is capable of analysis in terms of any set of component causal influences, then this would seem to trivialize the whole notion of analysis. Certainly it would cast doubt on my reasons for accepting the reality of causal influences.

 richard corry What we need, then, is a natural way of limiting the possible rules of composition available to the analytic method. The whole point of introducing causal influences was to fill the role of the invariant assumed by the analytic method. It is natural, then, to insist that the laws of composition respect this invariance. So, for example, if two influences that pull in the same direction are combined, the resultant influence should also pull in that direction. One of the nice features of Newtonian mechanics is that the composition of forces is linear. This mathematical property models the fact that forces are independent of each other—the strength and direction of a force is not affected by the existence of other forces, which is to say that forces are invariant. In general, composition laws that are linear can easily be interpreted as respecting the invariance of the causal influences they range over. But it is not true that linearity is a necessary condition. Consider, for example, an election for a single seat in parliament. Suppose that there are 10,000 voters, two candidates, and that the result is determined by simple majority. If Thor receives 2,000 votes, and Winifred receives 8,000, then Winifred will win. Exactly the same outcome will be produced if Thor receives 3,000 votes and Winifred 7,000. Thus the composition of votes is clearly not linear. Nonetheless, it makes perfect sense to regard each vote as having (or constituting?) an invariant influence on the outcome, with neither the strength nor direction of the influence dependant on the other votes cast. Of course one could choose to interpret things differently. One might claim that a vote has no influence at all unless it is part of the majority. Interpreting the influences as invariant allows us to apply the analytic method—we can explain and predict the outcome of elections in terms of the voting behaviour of individual voters. If, on the other hand, we assume that a vote has no influence unless it is in the majority, then we can only explain and predict election outcomes in terms of which side gets a majority, not in terms of the behaviour of individual voters (we will, of course, be tempted to explain which side gets a majority in terms of the voting behaviour of individuals, but this

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would require us to assume that individual votes have an invariant influence on who gets the majority). Despite the nonlinearity of composition in this case, we can (and indeed ought to) apply the analytic method by assuming invariant component influences.¹⁰ It would be nice to have an exhaustive mathematical articulation of all the constraints that a composition law must satisfy if it is to respect the invariance of causal influences. Unfortunately, I have no such articulation—it may be that there is no such exhaustive list. I hope to investigate these constraints further on another occasion. In the meantime I can only suggest that we judge each case on its merits. Can the composition law (whether it is in physics, biology, economics, or wherever) be interpreted as respecting invariant component influences? If so, do these invariant influences support successful and explanatory applications of the analytic method? If the answer to both questions is yes, then we have some reason to believe in the reality of the component influences.

6.8 Conclusion What I would have liked to have done here is produce a transcendental argument for the existence of causal influences. Such influences, I would like to say, are necessary presuppositions of one of the most useful and successful (and I might suggest essential) methods we have for understanding the world. The difficulty, of course, is proving necessity. It is always possible that there are ways to make sense of the analytic method without recourse to causal influences. What I believe I have shown is that the method requires some constant element or other, and that the usual suspects (laws, dispositions, and powers) cannot play the role required whilst causal influences can. ¹⁰ To avoid confusion, I should note that although I have argued for the addition of primitive non-Humean influences to our ontology, I do not mean to suggest that all causal influences are primitive. The influence each voter has on the outcome of an election will, no doubt, be analyzable in terms of familiar physical and/or psychological processes. However, if I am right, the analysis will eventually bottom out in primitive non-Humean causal influences of the kind I have described.

 richard corry Causal influences are no ontological free-lunch (to steal a term from Armstrong 1997), so I can see the temptation to do without them. But if I am right that causal influences are assumed by the analytic method, then the spectacular success of this method gives us good reason to believe in them. In fact, given that the analytic method can be grounded by causal influences without level (2) dispositions, but not vice versa, we have more reason to believe in causal influences than we do in (currently popular) causal powers, capacities, and tendencies. But an ontology that includes causal influences can do more than simply ground the analytic method. As Creary (1981), Spurrett (2001), and Corry (2006) point out, accepting the reality of component causal influences allows us to block Cartwright’s argument that there are no true laws of nature. For similar reasons causal influences allow us to block Russell’s (1913) arguments against causal laws (see Corry 2006). Who knows what else causal influences might do for us.¹¹ ¹¹ Thanks to Toby Handfield for some very helpful comments on previous drafts of this paper.

7 Agent-Causal Power Timothy O’Connor

Our universe is populated, at bottom, by a vast number of partless particulars of a few basic kinds. Each of these particulars instantiates some of a small range of primitive qualities and stands in primitive relations with other particulars. We may conceive of qualities as immanent universals that are numerically identical in their instances, along the lines championed by David Armstrong (1978), or as ‘tropes’ that are non-identical but exactly resembling in their instances, following C. B. Martin (1997). (Nothing of what follows hangs on which alternative one prefers.) In calling these qualities ‘primitive’, we are contending that they are real existents whose being does not consist, even in part, in the existence or instantiation of other entities. The nature of these qualities is irreducibly dispositional: they are tendencies to interact with other qualities in producing some effect, or some range of possible effects. (Or, in certain cases—as we shall consider below—they may instead confer upon their possessor a tendency towards, or power to produce, some such effects.) It may be that the dispositional profile of a quality does not exhaust its nature, so that it has a further ‘qualitative character’, or quiddity. Here again, we may be neutral on this question for present purposes.¹ ¹ For discussion, see especially Molnar 2003; Heil and Martin 1999; and Hawthorne 2001.

 timothy o’connor The formal character of a feature’s dispositionality may be variable. For a couple of centuries after Newton, it was usual to conceive dispositions deterministically: given the right circumstances, causes strictly necessitate their effects. But fundamental physics since the early twentieth century encourages the thought that dispositions may be probabilistic, such that there are objective probabilities less than one that a cause will produce its characteristic effect on a given occasion. On this view, deterministic propensities are simply a limiting case of probabilistic ones. What is more, it seems possible to conceive pure, unstructured tendencies, ones that are nondeterministic and yet have no particular probability of being manifested on a given occasion. The qualities of composite particulars (if we do not here embrace eliminativism) are typically structural, consisting in the instantiation of qualities of and relations between the composite’s fundamental parts.² Very often, the terms we use to refer to features of composites do not pick out such structural properties, since they are insensitive to minor variation in the composite’s exact underlying state. (A water molecule’s being in a structured arrangement of hydrogen and oxygen atoms persists through small-scale changes in its microphysical composition and state. Of course, there are also much more dramatic cases of underlying variation across instances consistent with applicability of the same macroscopic term, with functional terms providing obvious examples.) Here, we should say that the concept is satisfied in different cases in virtue of the instantiation of different structural qualities. Despite superficial ways of speaking, there is no distinctive causal power attached to the satisfaction of such a concept, as that would require the causal powers theorist to accept an objectionable form of double counting of causes, one for the macroscopic structural property (itself nothing over and above ² David Armstrong has been the key contemporary figure in developing the idea of structural properties as part of a ‘sparse’ ontology. Nonetheless, he waffles a bit in his understanding of their reducibility. He speaks of them as something subtly ‘extra’—distinct from the underlying instances of properties and relations but strongly supervening upon them (Armstrong 1997: 37). But this is hard to square with his adamant contention that they are an ‘ontological free lunch’. (See the discussion on 34–45.)

agent-causal power  the instantiation of microscopic properties and relations) and one for the putative multiply-realized functional ‘property.’ Such are some central elements of a causal powers metaphysic. There are many disputes of detail among its adherents—to the disputed matters already noted, we should add the nature of primitive external relations and the substantiality of space or spacetime.³ Such disputes aside, the causal powers metaphysics stands opposed both to the neo-Humean vision that David Lewis (1983b, 1986c) popularized and the second-order Humean metaphysic of causal realism without causal powers defended in recent years by David Armstrong (1997) and Michael Tooley (1987).⁴ In what follows, I shall presuppose the ecumenical core of the causal powers metaphysics. The argument of this paper concerns what may appear at first to be a wholly unrelated matter, the metaphysics of free will. However, an adequate account of freedom requires, in my judgment, a notion of a distinctive variety of causal power, one which tradition dubs ‘agent-causal power’. I will first develop this notion and clarify its relationship to other notions. I will then respond to a number of objections either to the possibility of a power so explicated or to its sufficiency for grounding an adequate account of human freedom.

7.1 The problem of freedom and agent-causal power Central to the notion of metaphysical freedom of action, or free will, is the thought that what I do freely is something that is ‘up ³ On the nature of fundamental external relations, see Molnar 2003: ch. 10; Ellis 2001; and the skeptical discussion in Armstrong’s contribution to Armstrong, Martin, and Place 1996. ⁴ I characterize the Tooley-Armstrong view as a gratuitously complicated kind of Humeanism because, despite their intentions, second-order relational structure to the world (their N(F, G) necessitation relation) cannot explain first-order facts (instances of G regularly following instances of F) since the second-order relations presuppose the supposed explananda. Were God to construct a Tooley-Armstrong world, determining the distribution of first-order F and G facts must precede decisions about N(F, G) facts.

 timothy o’connor to me’, as Aristotle says. A familiar, disputed line of reasoning, which turns upon the principle that where certain truths that are not up to an agent logically (and so unavoidably) entail some further truth, the latter truth is itself not up to the agent, concludes that nothing of what we do would be up to us were our actions to be embedded within a strictly deterministic universe.⁵ But if determinism would threaten our freedom, so would the complete absence of any intelligible causation of our actions. So one might steer a middle course by supposing that the world is governed throughout by unfolding causal processes, just not deterministic ones. In particular, one might suppose that our free actions are caused by our own reasons-bearing states at the time of the action. An action’s being ‘up to me’, on this view, consists in the nondeterministic causal efficacy of certain of my reasons: I might have performed a different action in identical circumstances because there was a non-zero (and perhaps pronounced) chance that other reasons-bearing states had been efficacious in producing the action which they indicated.⁶ However, according to many critics (myself among them), indeterminist event-causal approaches falter just here, in the fact that the free control they posit is secured by an absence, a removal of a condition (causal determination) suggested by the manifestly inadequate varieties of compatibilism. If there is no means by which I can take advantage of this looser connectivity in the flow of events, its presence can’t confer a greater kind of control, one that inter alia grounds moral responsibility for the action and its consequences.⁷ Given the causal indeterminist view, if I am faced with a choice between selfish and generous courses of action, each of which has some significant chance of being chosen, it would seem to be a matter of luck, good or bad, whichever way I choose, since I have no means ⁵ Peter van Inwagen has heavily influenced discussion of this argument over the last thirty years by his careful formulation of the argument. See van Inwagen 1983 and O’Connor 2000 for a friendly amendment. ⁶ The most prominent advocate of this view of freedom has been Robert Kane. Kane has developed his view in a number of writings, culminating in The Significance of Free Will. ⁷ A few preceding sentences are borrowed from O’Connor and Churchill 2004.

agent-causal power  directly to settle which of the indeterministic propensities gets manifested. The familiar considerations just sketched lead certain philosophers to conclude that the kind of control necessary for freedom of action involves an ontologically primitive capacity of the agent directly to determine which of several alternative courses of action is realized. In these instances of agent causation, the cause of an event is not a state of, or event within, the agent; rather, it is the agent himself, an enduring substance. I will not defend the claim that any actual agents have such a capacity. The philosophical claim is that agents must exercise such a capacity if they are to have metaphysical freedom, but it is an empirical claim whether human agents do exercise such a capacity (and thus do in fact act freely). Our concern is what such an agent-causal power would be, and, given the analysis, whether any agents could possibly have it, given fairly modest assumptions about the agents and their embeddedness within an environment. We begin by considering what the notion of agent causation requires us to assume concerning the nature of the agent having such a power. It is commonly supposed that the notion requires a commitment to agents as partless and nonphysical entities. A radically distinct kind of power, the thought goes, requires a radically distinct kind of substance. And this seems further encouraged by my earlier contention that the causal powers metaphysics pushes one to regard typical ‘high-level’ features as structural properties wholly composed of microphysical properties arranged in a certain way. But there is more to be said. While the tidiness of substance dualism has its appeal, it is in fact optional for the metaphysician who believes that human beings have ontologically fundamental powers (whether of freedom or consciousness or intentionality). For we may suppose that such powers are emergent in the following sense: (i) They are ontologically basic properties (token-distinct from any structural properties of the organism); (ii) As basic properties, they confer causal powers on the systems that have them, powers that non-redundantly contribute to the system’s collective

 timothy o’connor causal power, which is otherwise determined by the aggregations of, and relations between, the properties of the system’s microphysical parts. Such non-redundant causal power necessarily means a difference even at the microphysical level of the system’s unfolding behavior. (This is not a violation of the laws of particle physics but it is a supplement to them, since it involves the presence of a large-scale property that interacts with the properties of small-scale systems.) In respects (i) and (ii), emergent powers are no less basic ontologically than unit negative charge is taken to be by current physics. However, emergent and microphysical powers differ in that (iii) the appearance of emergent powers is caused (not ‘realized’) by the joint efficacy of the qualities and relations of some of the system’s fundamental parts and it persists if and only if the overall system maintains the right kind of hierarchically-organized complexity, a kind which must be determined empirically but is insensitive to continuous small-scale dynamical changes at the microphysical level.⁸ One cannot give uncontroversial examples of emergent properties. Though there are ever so many macroscopic phenomena that seem to be governed by principles of organization highly insensitive to microphysical dynamics, it remains an open question whether such behavior is nonetheless wholly determined, in the final analysis, by ordinary particle dynamics of microphysical structures in and around the system in question.⁹ Given the intractable difficulties of trying to compute values for the extremely large number of particles in any medium-sized system (as well as the compounding error of innumerable applications of approximation techniques used even in measuring small-scale systems), it may well forever be impossible in practice to attempt to directly test for the ⁸ Concepts of emergence have a long history—one need only consider Aristotle’s notion of irreducible substantial forms. Their coherence is also a matter of controversy. For an attempt to sort out the different ideas that have carried this label, see O’Connor and Wong 2006. And for a detailed exposition and defense of the notion I rely on in the text, see O’Connor and Wong 2005. ⁹ For numerous examples of such phenomena, see Laughlin, Pines, Schmalian, Stojkovic, and Wolynes 2000.

agent-causal power  presence or absence of a truly (ontologically) emergent feature in a macroscopic system. Furthermore, it is difficult to try to spell out in any detail the impact of such a property using a realistic (even if hypothetical) example, since plausible candidates (e.g., phase state transitions or superconductivity in solid state physics, protein functionality in biology, animal consciousness) would likely involve the simultaneous emergence of multiple, interacting powers. Suffice it to say that if, for example, the multiple powers of a particular protein molecule were emergent, then the unfolding dynamics of that molecule at a microscopic level would diverge in specifiable ways from what an ideal particle physicist (lacking computational and precision limitations) would expect by extrapolating from a complete understanding of the dynamics of small-scale particle systems. The nature and degree of divergence would provide a basis for capturing the distinctive contribution of the emergent features of the molecule. As sketchy as the foregoing has been, we must return to our main topic. I have suggested that we can make sense of the idea of ontologically emergent powers, ones that are at once causally dependent on microphysically-based structural states and yet ontologically primitive, and so apt to confer ontologically primitive causal power. If this is correct, then the fact that agent causal power would be fundamental, or nonderivative, does not imply that the agent that deploys it be anything other than a mature human organism. It is simply an empirical question whether or not the dispositions of the ultimate particles of our universe include the disposition to causally generate and sustain agent-causal power within suitably organized conscious and intelligent agents. One important feature of agent-causal power is that it is not directed to any particular effects. Instead, it confers upon an agent a power to cause a certain type of event within the agent: the coming to be of a state of intention to carry out some act, thereby resolving a state of uncertainty about which action to undertake. (For ease of exposition, I shall hereafter speak of ‘causing an intention’, which is to be understood as shorthand for ‘causing an event which is the

 timothy o’connor coming to be of a state of intention’.) This power is multivalent, capable of being exercised towards any of a plurality of options that are in view for the agent. We may call the causing of this intentional state a ‘decision’ and suppose that in the usual case it is a triggering event, initiating the chain of events constituting a wider observable action. Following agent causalists of tradition (such as Thomas Reid), I conceive agent-causal power as inherently goal-directed. It is the power of an agent to cause an intention in order to satisfy some desire or to achieve some aim. How should we understand this goal-directedness? One way is a variation on a familiar view in action theory, the causal theory of action. The rough idea behind developed versions of the causal theory is that the agent’s having a potential reason R actually motivated action A (and so contributes to its explanation) just in case R is a salient element in the set of causes that ‘nondeviantly’ produce A. (R might be, e.g., a belief–desire pair or a prior intention.) In line with this, one might be tempted to say that R actually motivated an agent’s causing of intention i just in case R is among the set of causes that nondeviantly produce it. However, it is not clear that anything could (in strict truth) produce a causally-complex event of the form an agent’s causing of intention i. On the causal powers theory, causation consists in the manifestation of a single disposition (limiting case) or the mutual manifestation of a plurality of properties that are, in C. B. Martin’s term, ‘reciprocal dispositional partners’ (typical case). We sometimes speak of an external event’s ‘triggering’ a disposition to act (as when the lighting of the fuse is said to trigger the dynamite’s disposition to explode). And this way of speaking might tempt one to assert, in more explicit terms, that the lighting of the fuse directly caused the causally-complex event, the dynamite’s emitting a large quantity of hot gas caused the rapid dislocation of matter in its immediate vicinity. But neither of these statements can be taken at face value when it comes to the metaphysics of causation. The unstable chemical properties of the dynamite’s active substance

agent-causal power  (nitroglycerin) would be involved in any number of effects relative to an appropriate wider circumstance. However, in each case, a variety of conditions C are exercising a joint disposition towards the particular effect, E. And nothing directly produces their producing of the effect, as this could only mean that the conditions C did not, after all, include all the factors involved in producing E. Granted, there is a perfectly good sense in which a prior event that produces one or more of C’s elements may be said to indirectly cause C’s causing E, in virtue of causing part of C itself to obtain. (So, the lighting of the fuse did lead more or less directly to the rapid burning process of the chemical substance, which event caused the production of the hot gas, which in turn caused the surrounding matter to be rapidly pressed outward.) But this indirect causing of a causal chain by virtue of causing the chain’s first element cannot apply to instances of agent causation, for the simple reason that here the first element within the causal chain is not an event or condition, but a substance. It is not the event of the agent’s existing at t that causes the coming to be of a state of intention—something that could have a cause—but the agent himself. The notion of causing a substance, qua substance, has no clear sense.¹⁰ Thus, we cannot coherently suppose that the obtaining of a reason in the agent may be said to be among the factors that causally produce the agent’s causing an intention. But perhaps we can sensibly stop a little short of this supposition by supposing instead that the obtaining of the reason appropriately affects (in the typical case, by increasing) an objective propensity of the agent to cause the intention. On this latter suggestion, while nothing produces an instance of agent causation, the possible occurrence of this event has a continuously evolving, objective likelihood. Expressed differently, agent causal power is a structured propensity towards a class of effects (the formings of executive intentions), such that at any given time, for each causally possible, specific agent-causal event-type, there is a definite objective probability of ¹⁰ See O’Connor 2000: 52–5, for further discussion.

 timothy o’connor its occurrence within the range (0, 1), and this probability varies continuously as the agent is impacted by internal and external influences. To emphasize: events that alter this propensity do not thereby tend toward the production of the agent’s causing the coming to be of an intention (in the sense that they potentially contribute to the causing of this latter event). Even where the event promoted occurs, the effect of the influencing events is exhausted by their alteration of the relative likelihood of an outcome, which they accomplish by affecting the propensities of the agent-causal capacity itself. Where reasons confer probabilities in this manner, I will say that the reasons causally structure the agent-causal capacity. It will perhaps be helpful to clarify what I have and have not just said. I am at this point taking it as provisionally given that we have a decent grasp on the very idea of agent causal power. I argued in the penultimate paragraph that we cannot coherently suppose reasons to constrain agent-causal power in one familiar way, that of tending to produce agent-causal events. I then tried to explicate another (albeit less familiar) way, that of structuring a propensity of an agent to produce an event without thereby tending toward the production of the agent’s producing said event. However, I have in no way suggested that one could not coherently jettison the idea of agent causation in favor of an event-causal theory of action on which the having of reasons does indeed tend directly towards the production of one’s executive intentions to act. This is the guiding idea of causal theories of action and, unlike some agent causationists such as Richard Taylor, I do not maintain that it is impossible to give a satisfactory theory of action along these lines. I would only insist that such a theory cannot capture the more ambitious notion of freedom of action. Here, I maintain, purely event-causal theories (whether deterministic or not) will inevitably fail. Thus, I am committed to supposing that there is more than one broad sort of way that the having of reasons might influence an intentional action. As with other propensities, the effect of events constituted by the having of reasons to act depends on surrounding circumstances. The agent-causal account I am advancing suggests

agent-causal power  that the presence of agent-causal power is one very important determinant on such effects. In the presence of such a power, the causal contribution of the having of reasons is exhausted by the alteration of the probability of a corresponding agent-causal event. With this idea in hand, we can specify one way in which agentcausal events are inherently purposive. Necessarily, when an agent causes an intention i to occur at time t1 , he does so in the presence of a motivational state whose onset began at a time t0 < t1 and which had an appreciable influence on the probability between t0 and t1 of his causing of i. Let us say that when a reason R satisfies this description, the agent freely acted on R.¹¹ The controverted metaphysics of agent causation aside, this sufficient condition for acting on a reason is quite minimal. Some would contend that it is objectionably weak because it allows that I may act on a reason of which I am entirely unconscious. In such a case, it will be claimed, the reason is exerting a brutely causal influence, and not a rational influence.¹² In my view, this objection mistakenly seeks to assimilate all cases of reasons-guided activity into a single framework. I agree that some free actions manifest a heightened degree of conscious control and I try to capture what this might consist in immediately below. But we need to recognize that not even all free actions are created equal—freedom itself comes in degrees. If a reason inclines me to undertake an action but its content is unknown to me (if, say, I am aware merely that I have an inclination to undertake the action), the latter fact diminished my freedom, since I am thereby unable to subject my motivation to rational scrutiny. Nonetheless, if it remains open to me to undertake the action or not, I exhibit the goal-driven self-determination that is the core element of freedom of the will.¹³ Agents who act freely to any degree, then, directly produce the intentions that initiate and guide their actions, acting on ¹¹ I first developed the distinction in the text between acting on and acting for a reason in O’Connor 2005. ¹² Nikolaj Nottelmann raised this objection to me in discussion. ¹³ For further discussion of the idea of degrees of freedom, see O’Connor 2005.

 timothy o’connor an inclination that is the causal product of certain reasons they acquired (and subsequently retained) at some point prior to this causal activity. But sometimes, it would appear, there is more to be said about the way that reasons motivate freely undertaken actions. Often enough, not only am I conscious of certain reasons that favor the course of action I am choosing, I expressly choose the action for the purpose of achieving the goal to which those reasons point. This goal enters into the content of the intention I bring into being. In such cases, I cause the intention to A for the sake of G, where G is the goal of a prior desire or intention that, together with the belief that A-ing is likely to promote G, constitutes the consciously-grasped reason for which I act. Now, since I freely and consciously bring the intention into being and thus give it just this purposive content, that purpose cannot but be one for which I am acting. What is more, a further explanatory connection between that reason and the choice is forged beyond the reason’s influence on the choice’s prior probability. This connection consists in the conjunction of the external relation of prior causal influence and the purely internal relation of sameness of content (the goal G). There may be several reasons that increase the likelihood that I would cause the intention to A. In the event that I do so, each of these reasons are ones on which I act. But if I am conscious of a particular reason, R, that promotes a goal G (and no other reason promotes that goal), and I cause the intention to A for the sake of G, then R plays a distinctive explanatory role, as shown by the fact that it alone can explain the goal-directed aspect of the intention’s content. It alone is one for which I act. It is commonly objected to nondeterministic accounts of human freedom that, despite what I’ve just said, undetermined actions cannot be explained by the agent’s reasons since those reasons cannot account for why the agent performed action A rather than B, one of the alternatives that were also causally possible in the circumstances. This objection fails to appreciate that explanation need not always be contrastive. If there are truly indeterministic quantum mechanical systems capable of generating any of a plurality

agent-causal power  of outcomes, whatever results is not absolutely inexplicable. A perfectly good explanation may be given by citing the system and its relevant capacities that in fact produced the outcome, even if there is no explanation at all of why that outcome occurred rather than any of the others that might have. Similarly, if an agent is capable of causing any of a range of intentions that would result in different corresponding actions, the reason(s) that inclined the agent to do what he in fact does serve to explain it even though there may be no explanation of why he did that rather than any of the alternatives.

7.2 Arguments for the impossibility of agent-causal power The possibility of agent causation has been widely doubted, especially in recent philosophy. Sometimes, the claim is that it is absolutely, or metaphysically, impossible insofar as it posits conditions that contradict certain necessary truths about certain ontological categories, such as that of event or substance. Other times, the form of impossibility is epistemic: agent causation, it is held, is incompatible with what we have excellent reason to believe are basic truths concerning the physics of our world; or with the relationship between the physics and any high-level processes to which basic physics gives rise; or with a general sort of ontological economy that obtains in our world (no superfluous explanatory features). I will now consider four reasons that some have put forward as grounds for doubting the coherence of agent causation, either absolutely, or with respect to some such general feature of our world. 7.2.1 From the timing of actions C. D. Broad’s oft-cited objection to the possibility of agent causation runs thus: I see no prima facie objection to there being events that are not completely determined. But, in so far as an event is determined, an essential factor in its total cause must be other events. How can an event possibly be

 timothy o’connor determined to happen at a certain date if its total cause contained no factor to which the notion of date has any application? And how can the notion of date have any application to anything that is not an event? (1952: 215)

Broad’s objection, or something like it, would have considerable force against an agent-causal view that maintained that nothing about the agent at the time of his action was explanatorily relevant to its performance. Such an ‘action’ would indeed seem freakish, or inexplicable in any significant way. But no agent causationist imagines such a scenario. On the version of the view advanced here, the agent’s capacity to cause action-triggering events is causally structured by the agent’s internal state, involving the having of reasons and other factors, before and up to the time of the action. These events within the agent suffice to explanatorily ground the agent’s causing the event to happen ‘at a certain date’ without collapsing the view into one on which those events themselves produce the action. Randy Clarke, an erstwhile defender of an agent-causal account of freedom, has recently claimed that a modified version of Broad’s objection has some force.¹⁴ Events, but not substances, are ‘directly’ in time in that their times are constituents of the events. By contrast, he maintains, ‘a substance is in time only in that events involving it ... are directly in time’. (This is supposed to be directly parallel to a reverse contention with respect to space, on which substances occupy space directly whereas events in their careers occupy a location only via its constituent object.) From this, he suggests, one can argue that the fact that effects are caused to occur at times ‘can be so only if their causes likewise occur at times—only, that is, if their causes are directly in time in the way in which events are but substances are not’ (2003: 201). ¹⁴ 2003: 201–2. Clarke does not claim that this argument is individually decisive. Instead, he presents several considerations, including some that I present below, that he believes to tell against the possibility of agent causation and that cumulatively make the impossibility of agent causation more likely than not. I will argue to the contrary that none of the main considerations he adduces has significant force.

agent-causal power  The contention that drives this argument is obscure. It can easily be taken to suggest that events are ontologically more fundamental than objects, a contentious claim that any agent causationist will reject out of hand. But if this is not being claimed—as the reverse contention regarding occupation of space confirms—the point is unclear. What does it mean, exactly, to say that an object exists at a time ‘only in that’ events it undergoes exist at that time? It cannot be the claim that the object’s existing at that time metaphysically depends on the event’s existing, as the object might have undergone another event at that time instead. If we weaken the claim to the plausible observation that, necessarily, an object exists at time t only if there is some event or other involving it that occurs at t, the dependence is no longer asymmetrical: for any event occurring at t that involves an object, O, necessarily, that event exists at t only if O exists at t. Since I can think of no other way of explicating the ‘exists only in that’ relation, I do not see here a promising basis for Broad’s assertion that the cause of an event can only be another ‘datable’ entity. 7.2.2 From the uniformity of causal power A second objection on which Clarke puts a great deal of weight begins with the following observation. If there is such a thing as agent causation, then there is a property or set of properties whose dispositional profile is precisely to confer on the agent a capacity to cause an intention to act. Notice how this contrasts with other causal powers in a very basic respect: the obtaining of properties that constitute ‘event-causal’ powers themselves tend towards certain effects (conditional on other circumstances). Hence, Event-causal powers are tendencies towards effects, i.e., the powers themselves are disposed to produce effects. Agent-causal power confers a capacity upon agents to produce effects, i.e., the power is not disposed to produce anything, it merely confers on its possessor a generic disposition to cause effects.

 timothy o’connor The uniformity objection to the thesis of agent causation is simply that it is doubtful that there can be any such property that fundamentally ‘works differently’ (by conferring a power on its possessor to cause an effect) (2003: 192–3). If true, ‘causation would then be a radically disunified phenomenon’ (2003: 208), and this is evidently a bad thing. We may read this objection as making the claim that the ontological category of property has an abstract functional essence that includes the tendency in the presence of other properties towards the direct, joint production of certain effects. Is there reason to think that this is so? One reason to doubt it stems from the variety of property theories philosophers have advanced: transcendent vs. immanent universals vs. tropes; pure powers vs. Humean non-dispositional qualities vs. a ‘dual-aspect’ combination of the two. In the face of serious commitment to and elaboration of such diverse positions, one might think that the range of possibility is correspondingly broad. However, this sort of reason for rejecting the uniform dispositional essence thesis is not compelling. Nearly all philosophers holding one or another of the competing theories of properties just noted believes the truth of their favored theory to be necessary, with the other alleged entities judged to be impossibilities. And that seems the right thing to say, whatever one’s view. In particular, if one rejects Humean qualities in favor of either the pure powers or dual aspect theory, then one should hold that, whatever the variation across possibility space when it comes to the specific kinds of properties there are, they all conform to the general features of one’s property theory.¹⁵ Thus, one who maintains the uniformity thesis may allow that figuring out the right conception of properties is difficult while ¹⁵ A complication here is that one version of the causal powers theory maintains that there are two fundamental kinds of properties and relations: those whose nature is dispositional and certain ‘framework’ relations such as spatio-temporal relations. (See Ellis 2001.) Suppose this is correct. Even so, one may argue for the abstract functional uniformity of all properties falling on the powers side of this division.

agent-causal power  contending that, once we have embraced a general approach (here presumed to include irreducible dispositionality), we should presume an absolute unity of nature at a suitable level of abstraction. But at what level of abstraction should the thesis be applied? Consider that, in the advent of statistical laws in fundamental physics, many metaphysicians are now comfortable with the notion that there are nondeterministic dispositions varying in strength along a continuum, with deterministic potentialities merely being a limiting case. Consider further that, while properties typically work in tandem towards effects, a natural way of interpreting the phenomenon of radioactive particle decay is as an entirely self-contained process whose timing is radically undetermined by any sort of stimulus event. Finally, some adhere to the truth of (and still others to the possibility of) a view that all or many conscious mental properties are intrinsically intentional while this is true of no physical properties. None of these claims concern free will, and yet all posit a kind of variability in the nature of dispositional properties that warrants classifying them into different basic types. Given these examples, it is hard to see why there may not be a further partition of types of the sort envisioned by the agent causationist. Doubtless there is a unity across these divisions at some level of abstraction. But assuming the agent causationist’s position is otherwise motivated, he may reasonably contend that it must be sufficiently abstract as to encompass the division his theory requires. Indeed, why may not the unity of basic dispositional properties simply consist in their making a net addition to the pool of causal powers? 7.2.3 From the connection between causation and probability-raising A third consideration for doubting the possibility of agent causation (also given by Clarke 2003) takes as its point of departure that causation is somehow bound up with probability raising. As Clarke notes, it is difficult if not impossible to state a very precise thesis here. In most cases of indeterministic event causation, the obtaining

 timothy o’connor of a causally relevant feature to some degree raised the probability of the effect in question—but not, or at least not obviously, in all cases. Given the fact that the obtaining of potential causes may screen off other factors that would otherwise potentially influence an outcome, we can readily imagine cases where something that actually contributed to an effect nonetheless rendered it either no more or even less likely than it would have been had that factor not obtained.¹⁶ Still, he contends, there is ‘considerable plausibility’ to the claim that a cause must be the sort of entity that can antecedently affect the probability of their effects. But an agent, as such, is not this sort of entity—clearly, only an event or enduring state could be. So the thesis of agent causation runs contrary to a plausible constraint on indeterministic causation by positing agents who are indeterministic causes of certain effects while necessarily not having a direct influence on the prior probability of those effects (2003). In reply, I suggest that Clarke’s proposed constraint on admissible causes is at best a rough, first pass at capturing a conceptual connection between causal factors and probability transmission. And to the extent that there is a plausible intuition underlying it, my structured tendency account of agent causation conforms to it. On this account, agent causation is not something wholly disassociated from the evolving chain of probabilistic causes constituting the world’s history. Agent causes act on the basis of prior factors that confer a positive objective probability on their occurrence. This should suffice to conform to any independently plausible, refined thesis that is intended to capture the vague intuition that probability transmission is a fundamental feature of causation. We may grant that, if one already believes on independent grounds that agent causation is impossible, then Clarke’s more specific claim is a reasonable way to express the intuition. But in the present context, it seems to me a gratuitous strengthening of a general ¹⁶ Clarke cites (2003) putative illustrations in Dowe 2000: 33–40; Salmon 1984: 192–202; and Ehring 1997: 36. For a deft and thorough development of a theory of indeterministic event causal powers, see Hiddleston 2005a.

agent-causal power  intuition in a way that arbitrarily precludes the possibility of agent causation. 7.2.4 From the superfluity/unknowability of agent causing that is probabilistically constrained By constructing a picture on which agent causal power is causally structured by reasons and other factors, I have tried to integrate the view of human freedom it anchors into a view of the wider world as an evolving network of interacting powers. Critics of traditional, less constrained versions of the view have understandably complained that it depicts a godlike transcendence of natural forces. The present project suggests that the objectionable aspect is inessential, since it is possible to give freedom a human face.¹⁷ To other critics, however, that merely opens up other vulnerabilities. Eric Hiddleston charges that the view of agent causation as probabilistically structured renders it superfluous for explanatory purposes (2005b: 552–3). Any event that one might explain as caused by an agent whose power was probabilistically structured by reasons R1 and R2 might equally well and more economically be explained by the direct causal efficacy of R1 and R2, acting nondeterministically. Furthermore, the agent causal theorist practically invites such an alternative explanation when he allows that in some cases, reasons do in fact bring about actions (though these would not be directly free actions). An initial reply simply notes that the agent causationist will expect that cases where reasons directly bring about actions differ in detectable ways from those in which agent causal power is at work. Viewed from another direction, there is no reason to suppose that an agent whose agent-causal power was rendered inoperative with all else being left untouched would simply carry on exactly as before. ¹⁷ Another recent effort along these lines is O’Connor 2005. Randolph Clarke 2003 is similarly an attempt to give a recognizably human version of the agent causal account of freedom. John Churchill and I give reasons for rejecting Clarke’s approach in our 2004.

 timothy o’connor But Hiddleston, I believe, would wish to persist as follows: why would we have reason to posit agent causal power in the first place instead of a causal theory of action on which reasons are productive? It seems that nothing in the observable pattern of events could, even in principle, require us to ascribe certain events to agents as causes.¹⁸ In reply, I first question the premise that there are no distinctive features of agent-causal processes as against possible cases in which reasons nondeterministically produce actions. First, just given the way highly deliberate and unpressured choices seem to us to unfold, it seems doubtful that our reasons fix a probability for the precise timing of the action which they promote. At most, there is an interval of time in which a possible choice is likely to occur, with the likelihood being subject to fluctuation as the agent deliberates. It seems, on some occasions, that I am capable of putting off decisions or continuing to search for reasons pro and con various courses of action, and that there are not fixed probabilities of my ceasing to dither at particular moments. (This is consistent with assuming that there is a high conditional probability for the agent’s causing intention i at t1 on i’s occurring at t1 .) One might construct a model analogous to the way physicists model particle decay, on which a sample of a radioactive substance of a given mass has an associated probability distribution that measures the likelihood for each moment over an interval of its having lost half its mass by that time. But any such model generally applied to the case of freely making a choice would seem contrived. Second, the agent causationist can plausibly suppose that while there is a probability of an agent’s causing an intention to A, there is no particular probability of that intention’s having a further goal-directed content in the sense I spoke of as acting for, and not just on, a reason. That is, there may be a probability of 0.6 that an agent will, within a specified interval of time, cause an intention to ¹⁸ Clarke (2003: 206) endorses the undetectability claim while denying that it gives reason to reject the possibility of agent causation.

agent-causal power  A, but no probabilities to its having the precise content of simply A, A-for-the-sake-of-G1, or A-for-the-sake-of-G2. I put forward these two suggestions with some diffidence, as they are grounded in vague intuitions concerning how actions seem to us to unfold. A more firmly-grounded response to the ‘no evidence’ objection is that, even if there weren’t these differences from possible cases of indeterministic causation by reasons, we have a general explanatory reason to accept that agents are sometimes causes. The thesis that agents are sometimes causes, in my view, best reflects the phenomenology of many of our actions and it is required by our (related) native belief that most human adults are free and morally responsible agents. In general respects, the explanatory appeal to agent causation is similar to the appeal to causal realism. The skeptical Humean insists that all we need are the observable patterns among events, (allegedly) conceived nondispositionally. According to the realist, we must go deeper, explaining the patterns themselves in terms of the structured propensities of the world’s basic features. Humean complaints that primitive causation is an ‘occult’ metaphysical relation are just so much throwing dust in the air and complaining that one cannot see. We have an intuitive grasp—albeit one that is highly general, needing elucidation—on the idea of causal power and it is fundamental to our na¨ıve conception of the world around us. Now, Hiddleston himself is no Humean. As it happens, however, he endorses Nancy Cartwright’s (1989) idiosyncratic claim to provide a purely empirical, neutral case for the existence of eventcausal dispositions, a case that turns on the nature of successful scientific practice in isolating causal influences. (And so he thinks there is a principled asymmetry concerning the possibility of evidence for event and agent causal dispositions.) Here, I can only join hands with many others in confessing not to understand exactly how Cartwright’s argument is supposed to go—how it is that the convinced Humean cannot give an alternate interpretation (however perverse to my realist eyes on non-empirical grounds) of what is observed and the empirical inferences and theorizing based upon it.

 timothy o’connor Many philosophers (including Hiddleston) dispute the claim that our experience of acting in any way supports the thesis that human agents are sometimes (literally) causes. Randy Clarke writes: I do not find it a credible claim that ordinary human agents have any experience, or any belief arising directly from experience, the content of which is correctly characterized in terms of agent causation ... Ordinary human agents, it seems plain, lack the concept of substance causation. A representation of free action as substance-caused (or as consisting in the substance causation of some event internal to the action) is a sophisticated philosophical construction ... (2003: 206–7)

Now, something in the neighborhood of Clarke’s remarks is surely correct. It takes philosophical reflection to attain a clear grasp on the idea of agents qua substance as causes, as distinct from either events internal to the agent as causes or the bogus Humean surrogate of patterns of (actual or counterfactual) regularity among events internal to the agent. But, for all that, it may be (and I contend, is) the case that (a) the content of the experience-inacting of ordinary human agents involves a fairly inchoate sense of themselves as bringing about their actions and that (b) the reflective account that best captures this inchoate content is the agent-causal account. I observe that this position on the ordinary experience of agency is supported by Daniel Wegner, a prominent cognitive psychologist, who goes on to argue that our experience of agency is deeply illusory.¹⁹ 7.2.5 From the insufficiency (for freedom) of agent causing that is probabilistically constrained Recall that an apparent difficulty facing an alternative, causal indeterminist account of human freedom—an account that eschews agent causation in favor of a nondeterministic causation of choices by one’s reasons—is that it appears to be a matter of luck which ¹⁹ See Wegner 2002, chapter 1. I criticize Wegner’s case for the illusory character of what he terms ‘conscious willing’ in my 2005: 220–6.

agent-causal power  of the undetermined possibilities is realized in a particular case. Given the presence of desires and intentions of varying strength, making certain outcomes more likely than others, the agent possesses no further power to determine which outcome in fact is brought about. The determination is a product of the propensities of the agent’s states, and the agent doesn’t seem to directly control which propensity will ‘fire’. If we imagine two identical agents in identical circumstances, with one agent nondeterministically choosing alternative A and the other choosing B, it seems a matter of luck from the standpoint of the agents themselves which alternative occurs in which person. Supposing there is a power of agent causation has the virtue that it seems to avoid this ‘problem of luck’ facing other indeterministic accounts.²⁰ Agent causation is precisely the power to directly determine which of several causal possibilities is realized on a given occasion. However, Derk Pereboom has recently argued that this is so only if agent causation does not conform to pre-given indeterministic tendencies.²¹ He writes: ... to answer the luck objection, the causal power exercised by the agent must be of a different sort from that of the events that shape the agent-causal power, and on the occasion of a free decision, the exercise of these causal powers must be token-distinct from the exercise of the causal powers of the events. Given this requirement, we would expect the decisions of the agent-cause to diverge, in the long run, from the frequency of choices that would be extremely likely on the basis of the events alone. If we nevertheless found conformity, we would have very good reason to believe that the agent-causal power was not of a different sort from the causal powers of the events after all, and that on the ²⁰ In addition to causal indeterminist and agent causal theories of freedom, there is noncausal indeterminism, on which control is an intrinsic, noncausal feature of free choices or actions. For versions of this view, see Goetz 1988; Ginet 1990; McCann 1998; and Pink 2004. ²¹ Others have recently argued that agent causation does not necessarily avoid the problem of luck (or, as it sometimes put, the ‘problem of control’). See Haji 2004; Widerker 2005; and Mele 2006. I will not here address their ways of pressing the issue, though I find their arguments even less compelling than the one by Pereboom that I discuss in the text. Pereboom (2005: 243–4) also rejects the arguments of Mele and Haji.

 timothy o’connor occasion of particular decisions, the exercise of these causal powers was not token-distinct. Or else, this conformity would be a wild coincidence ... (2005: 246)

Though Pereboom expresses the matter in epistemological terms, I take it that he intends to be making a linked pair of metaphysical claims, as follows. If agent-causal power is to truly enable the agent directly to determine which causally-possible choice obtains, and so overcome the luck objection plaguing other accounts of freedom, then it must be a different sort of power from event-causal powers such as the propensities of one’s reasons, such that its exercise is token-distinct from the exercise of any of these event-causal powers. And the latter condition can be met only if the outcomes of agent-causal events are not strictly governed by the propensities of any relevant set of obtaining event-causal powers. The agent causationist readily endorses the first of these conditionals, on a straightforward reading of ‘different sort of power’ and ‘token-distinct exercise’. After all, the view posits a fundamental, irreducible power of agents to form intentions. But the second conditional directly rejects the viability of any account on which agent causal power is probabilistically structured by reasons. Why does Pereboom assert it? His thought seems to be that if the event of one’s having certain reasons along with other prior events ensure that one’s choices will fit a certain pattern—more accurately, make the pattern-fitting likely, given a sufficiently large number of cases—then one’s supposed agent-causal power in choosing is at best a shadowy accompaniment to the event-causal power. In truth, it is no power at all, as it adds nothing to the mix of factors already in play. With no authority to act on its own, its presence makes no discernible difference to what occurs in the aggregate. If it would be a matter of luck, beyond my direct control, which of my indeterministic propensities happens to be realized on any given occasion, were the causal indeterminist account correct, then adding the ability to ‘directly determine’ the outcome wouldn’t help if I am ineluctably constrained by those very propensities.

agent-causal power  It is easy to feel the pull of this thought, but it should be resisted. First, we insist upon the importance of the distinction between (the persisting state or event of one’s having) reasons structuring one’s agent-causal power in the sense of conferring objective tendencies towards particular actions and reasons activating that power by producing one’s causing a specific intention. On the view I have described, nothing other than the agent himself activates the agent causal power in this way. To say that I have an objective probability of 0.8 to cause the intention to join my students at the local pub ensures nothing about what I will in fact do. I can resist this rather strong inclination just as well as act upon it. The probability simply measures relative likelihood and serves to predict a distribution of outcomes were I to be similarly inclined in similar circumstances many times over (which of course I never am in actual practice). The reason that the alternative, causal indeterminist view is subject to the luck objection is not that it posits objective probabilities to possible outcomes but that it fails to posit a kind of single-case form of control by means of which the agent can determine what happens in each case. After all, were the causal indeterminist picture modified so that agents’ choices are caused but not determined by appropriate internal states whose propensities, while nondeterministic, lacked definite measure, the problem of luck or control would remain. Again, that problem concerns not prior influence but the ability to settle what occurs on the occasion of a causally undetermined outcome. The agent causationist’s solution is to posit a basic capacity of just that sort, while allowing that the capacity is not situated within an indifferent agent, but one with evolving preferences and beliefs. Surely having preferences does not undermine control!

7.3 Conclusion Causation is a primitive, yet fairly simple concept. Reflective theorizing, both philosophical and scientific, has yielded a variety of forms in which it can be coherently conceived. Absent convincing

 timothy o’connor reason to think one of these imagined forms is defective in some unobvious way, we ought to deem it possible. It has been the aim of the present essay to specify a coherent way we might think about the idea of agent-causal power, an idea that has guided some who theorize about freedom of the will and that is even deemed intuitively attractive by some who resist it. It may be metaphysically impossible that there be such a thing, but I have yet to encounter a convincing argument for it.

8 Structural Properties Revisited Alexander Bird

8.1 Dispositional monism and structural properties 8.1.1 Introduction Monistic dispositional essentialists (or dispositional monists) hold that all fundamental sparse (i.e. natural) universals have essences that are dispositional.¹ Thus all properties either have a dispositional essence or are not fundamental or are not natural. This view is motivated, for example, by the claim originating with Sydney Shoemaker (1980), that the identity of a property is given by its causal (or more generally dispositional and nomic) relations with ¹ I am assuming that natural properties are universals. But to a large degree my discussion is orthogonal to the issue of whether properties are universals or are better understood as classes of resembling tropes or in some other nominalistic fashion. Ann Whittle (‘Causal Nominalism’, this volume), for example, develops a nominalistic account of the kind of properties I am interested in here. For my part I have a preference for universals because I cannot see how a substantive or realist conception of the laws of nature can do without them. On any such view laws, or what they flow from, are supposed to provide a unified explanation of the behaviours of particulars. Without universals the explanation of the behaviours of things lacks the required unity. According to nominalism the interaction between electron a and positron b resembles the interaction between electron c and positron d, but there is no one interaction type that they both instantiate. Consequently it is difficult to see how a law, regarded as a single entity, can account for both.

 alexander bird other properties. An obvious extension of dispositional monism asserts that non-fundamental natural properties are also essentially dispositional or supervene on natural properties that are essentially dispositional. What one may call ‘structural’ properties seem to be potential counterexamples to dispositional monism. These are such properties as shape, possessing a certain spatial arrangement of parts, and relations such as spatial separation, or being n-wise distinct. These seem to be purely categorical, which is to say that they have no essential powers or dispositions. Instead their distinctive natures are wholly contingent, being dependent on the role they play in the contingent laws of nature. Faced with putative counterexamples, the dispositional monist has three strategies: (i) show that the property in question has a dispositional essence after all; (ii) deny that the property is natural; (iii) show that it supervenes on properties that do have dispositional essences. For example, the relation of being pairwise distinct does not seem to be a natural property. But even if it is, then it supervenes on other properties of material objects: if two objects have non-zero spatial displacement then they are pairwise distinct. The question then reduces to whether displacement has a dispositional essence. How are we to settle the question whether such properties are essentially dispositional or not? Traditionally it was thought that the following would provide a necessary and sufficient condition of a property P’s being dispositional: (CA) For all x, and for some S and M: x is P entails were x to be S, then x would be M.

Now it was also once thought that being dispositional was somehow disreputable, as shown by the above relationship with subjunctive conditionals, and that dispositional properties should somehow be reduced away to categorical ones. Hugh Mellor (1974) sought to show that dispositional properties were being traduced and that even allegedly respectable categorical properties had the

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same relationship to conditionals as dispositional ones. Mellor’s example was: x is triangular entails were one to count the corners of x, the answer would be three.

One possibility for settling the issue over the nature of structural properties is this. We can abstract away from the motivation of the ensuing debate between Mellor and Elizabeth Prior (1982) to use his argument to show that properties such as triangularity are after all essentially dispositional. I attempted this in ‘Structural properties’ (2003), but with what I now regard as only partial success. In this paper I revisit the question to propose a different and rather better way of making progress with the question. 8.1.2 Conditionals and dispositional essences The test for an essentially dispositional sparse property derived from (CA) would be: (D) ‘P’ denotes an essentially dispositional sparse property iff for all x, and for some S and M, x is P entails were x to be S, then x would be M.

There are various problems with (D). First of all, the right-hand side fails to provide a necessary condition on a property’s being dispositional. Finks (Martin 1994) and antidotes (Bird 1998) show that dispositions may fail to entail a subjunctive or counterfactual conditional. In the first case, the disposition may be removed momentarily after it receives its appropriate stimulus, but before the manifestation can come about. In the second case the normal operation of the disposition may be interfered with, preventing the manifestation from occurring. Furthermore, the test fails to provide a sufficient condition for being an essentially dispositional sparse property. There are three reasons why it fails to do so. 1. The right-hand side of (D) fails to ensure that ‘P’ denotes a sparse property. For example, one might think that the analysis

 alexander bird of the concept of fragility (ignoring finks and antidotes for the moment) is given by: x is fragile iff were x stressed, then x would break.

It looks as if according to our test, fragility will come out as an essentially dispositional sparse property. But we should not expect fragility to be a sparse property, let alone an essentially dispositional one. We may think that fragility is multiply realized—there are many underlying sparse properties or complexes of sparse properties that will make something fragile. Or fragility might be understood as a second order property, ‘having some sparse property or property complex such that when an object with the property is stressed, it breaks’. If that is correct then the test tells us that fragility is dispositional. But we wouldn’t want this second order property to be necessarily a sparse property. Some such second order properties might be sparse properties with dispositional essences, but not all. 2. For (D) to reflect the essences of sparse, natural universals, we want the entailment to hold de re whereas it may be true de dicto. Consider Armstrong’s view of dispositions, according to which it is a contingent law of nature that gives a categorical property its dispositional character at a given world. Thus different categorical properties might support the same dispositional character at different worlds, in virtue of the different laws at those worlds. So ‘x is P’ might be true in the actual world and is true in virtue of x having categorical property C0 governed by the law L 0 . Because of the analysis of ‘P’ it is the case that for some S and M, were x to be S then x would be M. Consider some other world w1 with different laws: at w1 x is P in virtue of possessing a different categorical property C1 governed by the law L 1 . Thus in each world where x is P it is true that were x to be S, then x would be M. But that is in virtue of a different categorical property in each case. Clearly it is the analysis of ‘P’ that is doing the work here. It is nothing to do with the nature of the actual property denoted

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by ‘P’, viz. C0 , which is distinct from C1 the property denoted by ‘P’ in w1 . 3. The entailment in the right-hand side of (D) might hold, not in virtue of the dispositionality of P, but instead in virtue of the dispositionality of S. Considering Mellor’s example, do we want to regard triangularity as supporting the conditional given above? Or does this instead reflect the dispositional character of being a counter? After all, we could hardly regard this anthropocentric conditional as reflecting the essence of a basic geometrical property. A naturalist should reject this as much as she rejects the anthropocentrism of the verification principle, and for the same reasons. These problems need not cause one to give up the project of using conditionals to test for dispositional essences. Rather they mean that one must be circumspect in employing the test. Consider the test as a necessary condition of being an essentially dispositional property: the failure of the entailment on the right-hand side shows that a property does not have a dispositional essence. On so using (D), one should exclude from proposed couterexamples cases where the failure of entailment is a consequence of finkishness or an antidote. Consider now the test as a sufficient condition of ‘P’ denoting an essentially dispositional sparse property. The test itself cannot guarantee sparseness, so we should ensure that there is independent reason to think that the property is sparse, e.g. that it is a natural property that plays a role in scientific explanation. Secondly, one should require that in using (D) to argue that some property has a dispositional essence it must be the case that the entailment is de re. That is, ‘x is P’ should be read as ‘x possesses that actual sparse property in virtue of which x is P’ rather than the de dicto reading ‘x possesses some property in virtue of which x is P’. That way the entailment is assessed considering the same sparse property at all worlds rather than different properties. Thirdly, that instead of Mellor’s conditional, one should employ a conditional that one may reasonably think could reflect the

 alexander bird essence of a fundamental natural property. The essence of property, kind, or thing records the core or fundamental features of the nature of that entity. For this reason the essence of X does not include just any necessary characteristic of X. Thus, as (Fine 1994) points out, it is a necessary truth that Socrates belongs to the set of which Socrates is the sole member. But it is no part of the essence of Socrates that he belongs to singleton Socrates. Likewise, it is no part of the essence of Socrates that 2 + 2 = 4, even though that is a necessary truth. I note that Fine regards essences as deriving from the identity of an entity whereas I have emphasized the nature of an entity as the source of its essence. While there may be subtle differences between these approaches, they are not germane to the current discussion.² Both the identity and the nature of an essentially dispositional property are determined by the relationship between the stimulus and manifestation. But neither identity nor nature include the necessary conditional ‘were x struck, then x would have been struck’ or ‘were x struck, then 2 + 2 = 4.’ So not every conditional entailed by ‘x is P’ is part of the essence of P. That goes also for Mellor’s conditional. Even though entailed by ‘x is triangular’, it seems to be a poor candidate for the essence of a property of a kind that one would expect to have a nature not specified in terms of humans and their counting abilities. The question then arises, in lieu of Mellor’s conditional, which conditional should we regard as characterizing the essence of, for example, triangularity (modulo the caveats articulated above). In what follows I shall discuss in general terms what sorts of conditional would be appropriate in characterizing the essences of geometrical and other, more general, spatial properties. The leading consideration will be that the conditionals should be expressed in terms that have a high degree of generality. This is because the essence (which I have identified with the nature) of a property ² Fine himself slips into talk of nature in more than one place, implying that identity and nature are either the same or closely related.

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should be the source of its explanatory power. Spatial properties are themselves highly general in their applicability and explanatory capacity. Although an anthropocentric essence for ‘triangular’ would not prevent its being applicable, even in worlds without humans, that essence would be powerless to explain anything in such worlds. (Perhaps such geometric properties explain little anyway. We shall in due course shift our attention away from them and onto more general spatial properties, principally spatial displacement, which do have general explanatory power.) For this reason, even Coulomb’s law fails to have sufficient generality to be the (sole) expression of the essence of spatial relations (for then such an essence would involve the widespread but still insufficiently general property of possessing charge). If one thinks that space and time are fundamental features of the world (which is not guaranteed) or close to fundamental, then one should expect the essence of spatial and hence geometrical properties to be specifiable with respect to other properties that feature in the fundamental laws. 8.1.3 Dispositional essences for structural properties—first attempt Sungho Choi has suggested to me that we could generalize the notion of counting corners. All we would need is a counting machine that can distinguish travelling along a geodesic from not doing so. If it did not do so at any point, then it would add one. Such a machine, travelling along a triangular path, starting at any non-apex point, would count to three on returning to its starting position. Even so, one might hope to find an essence constituted out of properties that one might expect to find in a fundamental theory. In my 2003, I suggested the following as a starting point: ( T ) The paths AB, BC, and AC form a triangle entails if a signal S travels along AB then immediately along BC, and a signal S∗ travels along AC, starting at the same time and traveling at the same speed, then S∗ will reach C before S.

 alexander bird N

A

B L

The problem I raised for this suggestion was that this is false for many non-Euclidean triangles. I therefore proposed that the following is true (again barring finks and antidotes): ( TE ) The paths AB, BC, and AC form an Euclidean triangle entails if a signal S travels along AB then immediately along BC, and a signal S∗ travels along AC, starting at the same time and travelling at the same speed, then S∗ will reach C before S.

One could then regard ‘triangle’ as ambiguous, or generic, across a range of triangle-properties, each for different kinds of geometry, and each of which has a different essence of this kind. I suggested triangles in Riemannian geometry or LobatchevskyBolyai geometry might have different (Ti ), although in fact (T) will do for many geometrical contexts. In spherical geometry one may consider the figure whose vertices are the north pole, N, and two nearby points, A and B, on the equator and whose sides are the longitudinal arcs NA and NB and the equatorial arc AB that goes the long way round the equator (see figure). AB is a little less than 2π × NA, and so the signal (such as a pulse of light) along AB will take longer to reach B than the signal passing from A to N and thence to B. Whether this counts as a counterexample to (T) rather depends on the definition of ‘straight

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line’ in the context of defining a triangle as a ‘figure with three vertices joined by straight lines’. For if a straight line is the shortest path between two points, the longer part of the great circle will not be a straight line and our figure is not a triangle, and so no counterexample to (T).³ On the other hand, if we remove from the sphere the points other than N on a line of longitude L that passes through the narrow gap between A and B, then our figure is a counterexample. On this view, there is no (sparse) property of triangularity in general. Triangularity is a portmanteau term covering different kinds of triangularity. The different kinds have dispositional essences relating to some variant on (T). It is (T) and its family of variants that define triangularity in general. One drawback for this approach is that it does not demonstrate that the dispositional monist is correct. For where the latter sees a specific and allegedly dispositional property (‘being an Euclidean triangle’) the categoricalist will see a conjunctive property consisting of a general categorical property plus a specification of the space it is in (‘being a triangle in Euclidean space’). The approach considered does not show that the former is correct, at most only that is it is an option. (That may be enough for the dispositional monist given that the properties in question are raised as counterexamples.) It is in any case far from clear that there is some clearly defined family of variants on (T) that will pick out all and only the triangles in various geometries. Furthermore, it seems a rather convoluted way of characterizing something that can be so easily defined in non-dispositional terms (‘a closed figure bounded by three straight line segments’). The Mellor–Prior debate was about whether being triangular entailed any subjunctive conditional, and happened to focus on one concerning the counting of vertices. But such a conditional would never have sufficed to characterize the essence of triangularity, if triangularity has an essence that is sufficient ³ But one could define a straight line as the set of points L = {a + tb; t ∈ S} where a and b are vectors and S is a closed segment of R. In which case both great circle paths are straight lines between A and B.

 alexander bird for something’s being a triangle, because many figures have three vertices that are not triangles (not having straight edges). Rather better than either Mellor’s suggestion or my (T) is the following: The straight line segments AB, BC, and AC form a triangle entails were a signal to pass along AB it would not pass through C (and similarly for the other two permutations of A, B, and C).⁴

Even so, I am inclined to think that such conditionals fail to get at the heart of the problem, for two reasons. First, it is difficult to see that anything like a causal or nomic role is being assigned to triangularity. In ‘Structural properties’ (2003) I claimed that the connection is causal, while admitting that this could be disputed. I am now less sure. The mere fact of (T) being a counterfactual may confer a spurious appearance of causality. I don’t take counterfactuals to be definitive (`a la Lewis (1973a, 2000)) of causality. A dispositional essentialist could accept a Lewisian account of causality and add that the counterfactuals arise because of the presence of dispositions. However, it would then seem to make sense to cut out the middle man, counterfactuals, and to regard causal relations as instances of dispositional relations. There is in any case good reason to do so, since both the counterfactual analysis of causation and the counterfactual analysis of dispositions have counterexamples. Perhaps both sets of counterexamples could be eliminated by bypassing counterfactuals altogether? Matters are, however, not quite so simple. The counterfactual analysis of the basic causal connection is: C causes E iff ¬C
¬E. However, the most obvious dispositional analysis of causation says that C causes E iff E is the manifestation of some disposition whose stimulus is C. If we apply the simple conditional analysis of dispositions to this, we have C causes E iff (C
E) ∧ C ∧ E.⁵ ⁴ This derives from a suggestion by Philip Welch. ⁵ Note that we need an analysis of counterfactuals for which C ∧ E does not suffice for C
E —which it does according to the centering condition of Lewis and Stalnaker. But we need this in any case if the counterfactual analysis of dispositions is to be acceptable. Nozick’s treatment of counterfactuals, for example, is such that C ∧ E does not entail for C
E.

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So we have this contrast, that the Lewis counterfactual analysis of causation focuses on (counterfactually) necessary conditions whereas the dispositional analysis identifies causation with sufficient conditions. This suggests that according to a dispositional account of causation, Lewis’s approach, along with Hume’s claim from which it originates, was misguided from the very start.⁶ Secondly, we should remember that ‘triangular’ is unlikely itself to name a fundamental structural property, and the dispositional essentialist is therefore not required to find a dispositional essence for it. The dispositional monist ought instead focus attention on the fundamental structural (primarily spatial and temporal) properties and argue that these have dispositional essences.

8.2 Dispositional essences for structural properties—second attempt: background-free physical theories I will now sketch an alternative view of how dispositional essentialism may be reconciled with structural properties at the fundamental level. I shall concentrate on spatial separation (displacement), but the argument carries over to temporal relations also. Our knowledge of the nature of space and time is in a state of flux and we do not know what the role of fundamental spatial and temporal properties will be in the final theory of everything—if indeed we ever get to such a theory. Note that it is not a priori that such a theory would refer to spatial and temporal properties at all, nor, if it does, that the fundamental ones neatly mirror the role of such properties in folk physics or even classical physics. Nonetheless, we can make some prognostications that suggest that a final theory would treat all fundamental properties ⁶ It is worth noting that some (Broadbent 2007) working within a conditional approach to causation have begun to adopt that very view. Jennifer McKitrick in ‘Dispositions, Causes, and Reduction’ (this volume) considers the possibility of a dispositional account of causation along the lines suggested above, and the problems that such an account would face.

 alexander bird dispositionally. I will first mention a brief response by Stephen Mumford (2004: 188) to the current problem. The gravitational force on an object is sensitive to both the masses of it and of other massy objects and its displacement from those other objects; lookGm1 m2 , the force F is a function of the ing at Newton’s law: F = r2 masses m1 and m2 and also of their displacement r. Mathematically speaking mass and displacement are on a par—there is no way for Newton’s law itself to distinguish between the two quantities as regards dispositional (causal or nomic) priority. In which case why should we not regard the force as a manifestation of the displacement, in which case displacement is characterized dispositionally: the displacement r between two points is the disposition whose manifestation, when masses m1 and m2 are located at the points, is Gm1 m2 ? a force between those masses with magnitude F = r2 While I think this is along the right lines, it needs supplementation. There are two issues to be addressed. First, we need some explanation as to why it seems so much more natural to regard the force as a manifestation of the masses rather than of their displacement. Speaking figuratively we are inclined to think of the force as being generated by the masses, not by their displacement. Secondly, displacement crops up not just in the law of gravitation, but also in Coulomb’s law and elsewhere. Thus it would appear that we could characterize displacement dispositionally with respect to a variety of different and seemingly independent manifestations. If so, then either (i) displacement is a multi-track disposition (one with more than one kind of manifestation); or (ii ) one of these manifestations (e.g. gravitational rather than electric force) is privileged over the others. 8.2.1 Multi-track dispositions The problem with regarding displacement as a multi-track disposition is that multi-track dispositions should not be regarded as fundamental. I shall here explain my reasons for thinking this. As we shall see, multi-track dispositions cannot have a pure dispositional

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essence. On the dispositional monist view of what properties are, that suffices to rule them out as fundamental. But there are more general reasons also. The intuitive idea is that if some property seems to be the conjunction of two dispositions, then that property does not look fundamental—since the conjuncts look more basic. Multi-track dispositions (Ryle 1949: 114) have more than one kind of manifestation or stimulus, or both. A common view is that mental dispositions are often multi-track. To use Ryle’s example, knowing French seems to be dispositional, but its manifestations may be various—talking French, writing French, obeying an order given in French, or even changing mental state when reading or hearing something in French. If we allow multiple manifestations, then we should allow multiple stimuli. For example, when discussing fragility it was clear that the manifestation is some kind of breaking, but it was less clear how to characterize the stimulus. One possibility is that fragility is a multi-track disposition with several different stimuli—striking, shaking, lateral stress (as would result in tearing). If we can have multiple manifestations and multiple stimuli, then we might have disposition-like properties with both multiple stimuli and multiple manifestations. Indeed the example of knowing French looks like this, since the stimuli are also various. They include not only external stimuli, such as hearing or reading something in French, but also internal stimuli, such as a desire to communicate with a Frenchman. It has been suggested that electric charge is a multi-track disposition. The manifestation of charge is a force on some other charge, its stimulus is the magnitude of that other charge. For different magnitudes of the other charge (viz. different stimuli) a different force (viz. a different manifestation) is exerted.⁷ Let us include among the multi-track dispositions all those which have multiple possible manifestations or multiple possible stimuli. Let us also call complex any disposition ⁷ And charge may also be regarded as multi-track for the perhaps more decisive reason that a charged body is disposed to experience a lateral force when moving through a magnetic field.

 alexander bird with either a logically complex stimulus or a logically complex manifestation. Our first question is whether all multi-track dispositions can be regarded as equivalent to complex single-track dispositions; i.e. can the multiplicity involved in a multi-track disposition be accounted for simply by the logical complexity of the stimulus or manifestation? In the case of a multi-track disposition with single stimulus but multiple possible manifestations, the manifestations can be regarded as one disjunctive manifestation, and so we can easily assimilate this to the single-track case; similarly for a multitrack disposition with a single manifestation but multiple stimuli. Matters are more complicated when it comes to multiple stimuli and multiple manifestations together. Typically these cannot be modelled by the single-track disposition with both a disjunctive stimulus and a disjunctive manifestation: D is the disposition to manifest (M 1 ∨ M 2 ∨ M 3 ∨ ...) in response to stimulus (S1 ∨ S2 ∨ S3 ∨ ...)

A disposition of which this characterization is true is one for which any of its possible stimuli could appropriately bring about any of its possible manifestations. That may hold for some multi-track dispositions, but it is clearly not correct for all. To the stimulus, ‘Comment allez-vous?’, the response, ‘La plume de ma tante est dans ma poche’ is not a manifestation of knowing French, although it might be in response to some other stimulus, such as ‘O`u se trouve la plume de votre tante?’. If charge is multi-track, then for a given stimulus (another charge at a certain distance) there is only one permitted manifestation. Let us call a pure disposition one which can, in principle, be characterized in the way that D is above, viz. as a relation between a stimulus and a manifestation, even if these may be logically complex, i.e. can be characterized as ‘the disposition to F when G’ for possibly complex F and G. Knowing French and charge (on the view proposed) are not pure dispositions. However, they do look like conjunctions of pure dispositions. Consider, for illustrative

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purposes, the case of charge. Let x be a real number that will act as an index, and let qx be a charge, rx a displacement, and Fx a force, such that, for a fixed value of Q: Qqx Fx =  2 rx Now consider, for some specific x the pure disposition Dx , whose stimulus is a charge qx at a displacement rx and whose manifestation is the exertion of a force Fx . Then an object with charge Q has this disposition. That object also has all the other parallel dispositions for other values of x. Let us assume that the indexing by x is such that all permissible combinations for values of q, r, and F are indexed by some x in the subset I of the reals. Then the impure disposition that the object has, its having the charge Q, will be
equivalent to the conjunction x ∈ I Dx , that is the conjunction of the Dx dispositions for all values of the index x.⁸ It should be noted that a conjunction of simple pure dispositions is not in general equivalent to some complex pure disposition. Let us accept the conditional analysis of dispositions for sake of argument. A conjunction of counterfactuals is not in general equivalent to some single but complex counterfactual. That is, if S1 and M 1 are counterfactually related, and S2 and M 2 are also counterfactually related, there are not always any S3 and M 3 satisfying: (S1
M 1 ) ∧ (S2
M 2 ) ⇔ S3
M 3 Consequently, if D(S1 ,M1 ) and D(S2 ,M2 ) are distinct dispositional essences, we cannot expect there to be a dispositional essence ⁸ It might be thought to be a disadvantageous departure from conventional wisdom (Armstrong, Lewis) to regard, for example, unit charge as a conjunction of properties rather than a single property. The disadvantage would be that this property is not a unity but a complex and so is less plausible as an inferred entity (assuming that inferred entities are inferred in part on the basis of their ability to provided a unified explanation). My response is that although the conjunctive ‘property’ is not a unity it is unified. It is not an arbitrary conjunction, but rather there is an explanation of the conjunction. In this regard the ‘property’ of possessing unit charge is akin to a natural kind, in that the extension of the natural kind is not an arbitrary collection but is one that has a unified explanation. I note in passing that even Armstrong (1983: 111–16) faces a similar problem in accounting for functional laws.

 alexander bird equivalent to their conjunction. So we are unable to characterize the nature of the property in question in terms of a dispositional essence. Thus if the conditional analysis were right, we typically cannot find a single pure disposition equivalent to a conjunction of pure dispositions.⁹ Impure multi-track dispositions are typically irreducibly multi-track. While it will be possible to gerrymander impure dispositions of all sorts, it is clear as regards the cases we are interested in, charge and knowing French, that the conjunctions are natural or non-accidental. It is my view that all impure dispositions are non-fundamental. Fundamental properties cannot be impure dispositions, since such dispositions are really conjunctions of pure dispositions, in which case it would be the conjuncts that are closer to being fundamental. However, pure dispositions may nonetheless be complex, and will include those pure multi-track dispositions with complex (disjunctive or conjunctive) manifestations. An interesting question is whether all complex dispositions, and multi-track dispositions in particular, are non-fundamental. I’ll consider four cases of complex dispositions: (i) simple (atomic) stimulus, conjunctive manifestation; (ii) disjunctive stimulus, simple manifestation; (iii) simple stimulus, disjunctive manifestation; (iv) conjunctive stimulus, simple manifestation. (i) A multi-track disposition with a simple stimulus but conjunctive manifestation is equivalent to the conjunction of dispositions each with the same stimulus but with different simple manifestations (each being one of the conjuncts in the original disposition). In which case it seems plausible to take the conjunctive disposition to be non-fundamental. (ii) Likewise, a disposition with a disjunctive stimulus is equivalent to a conjunction of dispositions each with a different ⁹ Although the conditional analysis is false there is nonetheless a sufficiently close relationship between dispositions and counterfactual conditionals that this argument remains decisive.

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simple stimulus corresponding to the disjuncts in the disjunctive stimulus. This is because the disjunctive stimulus says that the satisfaction of any of its disjuncts will bring about the manifestation, which is equivalent to possessing all of a set of dispositions with different simple stimuli. (iii) The case of a disjunctive manifestation cannot be regarded as equivalent to any compound of simpler dispositions. Nonetheless, we would never need to posit such a disposition. Let the stimulus be S and the manifestation be (M 1 ∨ M 2 ). Thus we find on certain occasions S yielding M 1 while on other occasions S yields M 2 . And so we would have no reason to posit the multi-track disposition rather than two single-track dispositions. For example, if striking glasses with a particular force sometimes leads to breaking and on other occasions leads to a bell-like ping, then we do not need to posit a single disposition whose manifestation is (breaking or pinging); instead some glasses have the disposition to break when struck with that force, and others have the disposition to ping. (In this example one might prefer the single multi-track disposition if one thought that there was a single causal basis. But if we are considering fundamental dispositions, there will not be a (distinct) causal basis.)¹⁰ ¹⁰ Where items of a single kind and which are otherwise identical can be divided into two classes on the basis of their different reactions to a single stimulus, and only on this basis, some might prefer to regard these items as sharing the same, disjunctive disposition. Might not kinds of subatomic particles be regarded as instances of this, where their probabilistic dispositions—propensities—may be regarded as single dispositions with a multiplicity of possible manifestations? Two possible responses to this suggestion would be as follows. First option: we need to distinguish between dispositions with chances as their manifestations, and the chances (or chancy properties) themselves. Particles of kind K are such that when bombarded with neutrons they acquire a certain half-life. The latter is a certain kind of property, a function of durations to probabilities of decay. However, this property is not itself dispositional property. So this approach would have to introduce certain non-dispositional fundamental properties, against the basic claim of this paper. Alternatively, one just accepts that in special cases there can be dispositions with more than one kind of manifestation, and that there is a chancy but fundamental relationship between the stimulus and the range of possible outcomes. Thus some fundamental dispositions, although pure, have logically complex, disjunctive, manifestations. This concession does not impinge on the conclusion that if spatial displacement is multi-track it is not fundamental.

 alexander bird (iv) In the case of a conjunctive stimulus, there is no option other than to regard this as irreducible. Thus in two of the four cases we can simply replace the disposition by a conjunction of single-track dispositions. In the third case, we can posit multiple single-dispositions in place of the multi-track disposition. Only in the fourth case must the logically complex disposition remain. This is the case of the conjunctive stimulus. And although I have included this among the multi-track dispositions on the grounds of complexity, it is certainly not the sort of case that one has in mind when talking of multi-track dispositions, where it is typically the multiplicity of manifestations that one has in mind. One would most naturally say that this is rather a case of a single-track disposition with a compound (conjunctive) stimulus. Some multi-track dispositions might have complex stimuli and manifestations. By putting the manifestation in conjunctive normal form and the stimulus into disjunctive normal form, we can use (i) and (ii) to break it into a conjunction of dispositions with disjunctive manifestations and conjunctive stimuli. Then (iii) allows us to posit instead just dispositions with conjunctive stimuli and simple manifestations. In conclusion, we do not need to posit fundamental dispositions with any greater complexity than conjunctive stimuli. Since a conjunctive stimulus requires all its components to be instantiated, a disposition of kind (iv) (unlike those of kind (ii)) cannot be regarded as having a multiplicity of possible stimuli. Thus we do not need to posit fundamental multi-track dispositions. Let us now return to the issue of whether spatio-temporal properties can be accommodated by the dispositional monist. The conclusion, that such properties, being multi-track, are not fundamental, is not itself inevitably problematic—it is not a priori that spatio-temporal properties and relations are fundamental. But it would mean that the debate is off. If they are not fundamental properties, then having dispositional essences or not does not directly bear on the truth of dispositional monism. As already

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remarked, it is the fundamental properties and relations that are held to be essentially dispositional. If it turns out that spatial separation is not a fundamental relation but supervenes on some other as yet unknown property or relation, then spatial separation provides no counterexample to dispositional monism and an investigation by inspection of whether the truly fundamental properties and relations are essentially dispositional must await further developments in physics. The alternative is to regard one of the dispositions as privileged in characterizing the essence of displacement, and given the general theory of relativity it is natural to see gravitational force as participating in the essence of spatial properties and relations. If we do take this view, the first question remains to be addressed. Why do we tend not to regard gravitational effects as equally the effect of displacement as of mass? This question is significant, because if we are right not to regard spatial displacement as causally efficacious (or more loosely as a potential agent) then displacement cannot be characterized with a dispositional essence. 8.2.2 Background structures and substantivalism versus relationalism In order to respond to that question, we must take a short detour via our conceptions of space and time, in particular the view of the nature of space (and time) associated with the conception of spatial properties as causally inert. The classical conception of spacetime has been that of a stage or container within which things and laws act, but which is not itself involved in the action. It is a mere background. As such, although space and time are a part of the natural world, they are certainly not patients, that is to say recipients of effects, in any cause-and-effect relation, or more generally subject to change according to natural law. Their status as causes or agents of law-governed change is ambivalent. On the one hand, terms for spatial and temporal dimensions appear in the laws. On the other hand, we do not classically regard these terms as indicating action on the part of space and time. One reason for

 alexander bird this is what Harvey Brown (Anandan and Brown 1995; Brown and Pooley 2006) among others calls the ‘action–reaction’ principle. Something can only be an agent if it is also a potential patient; something may only be a cause if is it also potentially the recipient of effects. Since on this view spacetime is a background entity, the displacement r between two objects is only indirectly a relation between them. It is primarily a relation between spacetime points. The objects inherit that relation by being located at spacetime points that are a distance r apart. On the classical view the structure of spacetime is fixed and unchanging. Since spacetime points do not change their relations with one another, it is difficult to see how they and their properties can contribute causally to the behaviour of objects located in spacetime. Thus the displacement r between spacetime points is inert, and so, in consequence, is the supervening displacement r between the objects. In view of this, the relationalist/non-substantivalist conception of spacetime ought to be more congenial to the dispositional monist. On the simplest version of this view, spatial relations are directly relations between objects (not between spacetime points). This reverses the absolutist/substantivalist view according to which relations between objects supervene on relations between spacetime points. The relationalist takes all the facts concerning space and time to supervene on facts about relations between objects. The laws of nature mention only spatial and temporal relations and these can be accounted for. They are at least in a position to obey the action–reaction principle, since spatial relations appear both as sources of change (e.g. in the gravitational law) and as objects of change (as in Newton’s second law). Since space and time just are the sum of spatial and temporal relations, and so there is nothing more to be explained than has been explained. While it hasn’t yet been shown that spatial relations really are agents of change, the possibility is now open that they are. The obvious problem with the simple relational view is that it fails to account for the full range of spatio-temporal possibility.

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There seem to be times and places where objects and events could be but are not. Hence Leibniz extends the set of relations to both actual and possible spatio-temporal relations. But then we must ask, what grounds such possibility? Furthermore the set of spatio-temporal relations is found to have a metric structure and we may ask for an explanation of that fact too. If spatial and temporal relations are fundamental, then we should expect them, according to a dispositional essentialist view of their essences, to generate the laws that underly the structure of spacetime, including facts about its metric. In classical physics understood in an absolutist, substantivalist sense, however, this seems not to be the case. We have discussed that fact that laws such as Newton’s law of gravitation and Coulomb’s law mention spatial relations. These laws cannot be serious candidates for expressions of the essence of spatial relations since they tell us nothing about the structure of space. They tell us how the magnitudes of forces of certain kinds depend on spatial relations. But they do not tell us what spatial relations are possible and they do not tell us what metric the set of points in space possesses. It is telling that one response to this is conventionalism about spacetime, a` la Poincar´e, Schlick, or Duhem for example. According to views of this sort, a choice of geometry and metric is conventional. We typically choose our geometry in such a way as to make the laws of physics expressible in a convenient form. The choice does not reflect some fact concerning the real structure of space and time, there being no facts of that sort. While one is not obliged by classical physics to be a conventionalist about the geometry of space and time, the fact that conventionalism is an option shows that no laws in classical physics determine that geometry. Either way, whether one prefers Newtonian substantivalism or conventionalism, there is no room for laws of the sort (ones telling us about the structure of spacetime) that the dispositional essentialist about spatial and temporal properties seeks.

 alexander bird In summary the dilemma is this. The general problem in classical physics is that relationalism posits too little structure, not enough to explain empirically revealed aspects of space and time, while substantivalism posits too much, and in particular makes spacetime a background structure. Scientifically, there is a problem in not having enough structure—excess structure is preferable. From the metaphysical point of view (that of the dispositional monist at least) matters are reversed. The thinner commitments of relationalism are prima facie acceptable. If space is nothing but the spatial relations between objects, then we do have a law telling us how space changes, Newton’s second law. On the other hand, if impelled by the requirements of physics to posit more structure, so that space is the fixed structure of spatial points, not the changeable structure of objects, then we have introduced a mere background that is not subject to any law. Such background structures of substantivalism, being inert, cannot be accommodated within the dispositional essentialist viewpoint. 8.2.3 Background-free physical theories In a dispute between physicists and metaphysicians, it would be wise to take the side of the physicists. And so the preceding discussion might seem to put dispositional monism at a disadvantage. Recently, however, physicists such as John Baez (2001); Lee Smolin (1991); and Carlo Rovelli (1997) have advocated the view that a good physical theory should be background-free (background-independent). Thus either space and time should be eliminated from our theories (although an unlikely prospect, this is not impossible). Or they should be shown not to be merely background. Either way the grounds for spatial and temporal properties and relations being clear exceptions to dispositional monism would be removed—in the first case because the properties no longer figure in fundamental science at all, and so are not fundamental, natural properties; and in the second case because space and time would no longer be mere background but instead are

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fully fledged agents, capable of acting and being acted upon. This would permit spatial and temporal properties to be understood dispositionally. It should be noted, however, that the motivation behind the drive for background-free physical theories is not exactly the same as that which seeks dispositional fundamental properties. In causal terms, the latter is concerned to show how space and time can be genuine causes. While spatial and temporal relations occur in physical laws, they seem, as presented classically, not to be entirely genuine causes. But the search for background-free theories is principally a matter of showing how space and time can be affected by other causes.¹¹ Let us put this a little more precisely. The dispositional essentialist wants the following to be true of any fundamental spatio-temporal property or relation P: P has a dispositional essence, viz. P can be characterized in terms of some stimulus and manifestation, S and M, such that it is essential to P that if Px, then (ceteris paribus) Sx
Mx.

The problem is that although we may be able to find an entailed counterfactual for certain spatio-temporal properties, not every such conditional will reflect the essence of those properties. We have seen the general reason for this above. As Fine tells us, not every necessary truth is part of every essence: it is not part of your essence that you are accompanied by the number two. A specific case in point relevant to conditionals arises because when the following is true: (A) Qx entails Sx
Mx ¹¹ Smolin (2003: 11–12) explains the motivations for the requirement of backgroundfreedom (background-independence) as being twofold: principle—a matter of philosophical debate going back to Newton and Leibniz and beyond; and experiment—as shown by the observational confirmation of Einstein’s prediction that gravitational radiation carries energy away from binary pulsars in two degrees of freedom of radiation, rather than five (this means that the gauge invariance of the laws of nature includes spacetime diffeomorphism invariance, which Einstein relates to background independence).

 alexander bird it is typically also true that:¹² (B) Sx entails Qx
Mx.

Thus if (A) shows us the essence of Q, it looks as if we have another entailment of a counterfactual, (B), which seems to indicate the essence of S. We should not exclude the possibility that (A) and (B) both characterize the essences of Q and S respectively, in which case they are what Charlie Martin (Armstrong, Martin, and Place 1996: 135–6) calls ‘reciprocal disposition partners’. Equally, for Fine’s reasons, we should not assume automatically that (A) and (B) do both characterize the essences of Q and S. And in certain cases there seems to be an asymmetry; our initial problem was that the relationships between the various sources of force (mass, charge, etc.) and displacement seem to be examples of such an asymmetry. I take it that something such as the following characterizes what is meant by a background: If K is a background structure in a theory T, then • K is not subject to change and is not affected by changes elsewhere; • the laws of T refer to properties and relations of elements of K or properties and relations defined on K.

It is the first clause, in particular the phrase ‘not affected by changes elsewhere’ that characterizes the ‘backness’, as it were of, the background. ¹² Typically, but not always. To see why consider this fallacious argument for the equivalence of ‘Qx entails Sx
Mx’ and ‘Sx entails Qx
Mx’. Assume that Qx entails Sx
Mx. If so, every Qx world is an Sx
Mx world, and so every Qx and Sx world is an Mx world. Now consider any Sx. We must show that such a world is also a Qx
Mx world. Consider the nearest Qx world. Such a world will be a world where both Sx and Qx. And we already have that all every Qx and Sx world is an Mx world. So this world is an Mx world. Hence every Sx world is a Qx
Mx world. The fallacy arises in assuming that the nearest Qx world to some Sx world is a world where Qx and Sx. But that need not be the case. In general it will not be the case where Qx and Sx are logically or metaphysically incompatible. Nor will it be true for Sx worlds where Sx and Qx are nomically incompatible. Such cases are, however, not pertinent to the issues currently under consideration.

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The claim therefore that theories should be background-free, or that there is no background, is tantamount to saying: (B-F) In a true theory, any structure appearing in the laws of that theory is subject to being affected by changes elsewhere.

Thus, if L is a structure in a true theory T, then for certain stimuli S, the following is true: (C) S
a change in L.

Does (C) help the dispositional monist, where L is spacetime? What the dispositional monist requires is a dispositional essence for spatial and temporal properties. If (C) provides that, then the essences of the spatio-temporal properties in question are such that under certain stimuli the structure of spacetime is itself changed. Now this is somewhat different from what we started looking for, which was spatio-temporal properties being responsible for changes rather than spacetime being the recipient of change. Nonetheless, (C) could do perfectly well in providing a dispositional essence. We may distinguish active and passive dispositions; active dispositions have manifestation in entities other than the possessor of the disposition, while passive dispositions have manifestations in the possessor of the disposition. Some favourite dispositions are passive, such as fragility. However, in general the manifestation of a disposition should be of a kind such that it can itself be responsible for changes. Otherwise we would find that the properties in question are merely epiphenomenal. In the case of (C) that means that changes in L (here spacetime) must themselves be capable of being responsible for changes of certain kinds. If so, those dispositions may be the ones most appropriately regarded as the essences of spatio-temporal properties. Nonetheless, (C), even if it does not constitute a solution to our problem, can show how our concerns may be addressed. One reason why it is difficult to see space and time as causes on a classical substantivalist conception, is that it is difficult to see them as in any way being effects. The background is unchanging. But if it

 alexander bird is unchanging how can it generate any effects? On the other hand, if it is subject to change, then it is easier to see how it might itself be a cause of change. According to the action–reaction principle, something is a potential cause only if it is a potential effect also. Thus (C), which reflects the requirement of background-freedom, (B-F), tells us that spacetime and its properties may be affected by changes elsewhere; and the action–reaction principle tells us that since spacetime and its properties may be the recipients of change they may also be causes of it. In dispositional essentialist terms, we can see that by being potential manifestations of dispositional essences, spatial and temporal properties may also have dispositional essences themselves. That perspective is precisely that endorsed by General Relativity. Each spacetime point is characterized by its dynamical properties, i.e. its disposition to affect the kinetic properties of an object at that point, captured in the gravitational field tensor at that point. The mass of each object is its disposition to change the curvature of spacetime, that is to change the dynamical properties of each spacetime point. Hence all the relevant explanatory properties in this set-up may be characterized dispositionally. And furthermore, this relationship helps address the second question raised above, by explaining why gravity is privileged over other forces in characterizing the essence of spatial relations.

8.3 Conclusion If spatial and temporal properties and relations are fundamental natural properties and relations, then the dispositional monist must provide reasons for thinking, contrary to a common intuition, that they too have dispositional essences. One approach is to take a familiar geometrical property (such as triangularity) and show that its instantiation entails some counterfactual. But ultimately this turns out to be indecisive. The dispositional monist will expect dispositional essences to be reflected in the laws of nature. And since triangularity is not a fundamental property of the kind that

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appears in the laws of nature, strictly speaking it is irrelevant to the dispositional monist’s argument, in that it is not the sort of example that would provide a counterexample to the claim that fundamental sparse properties are essentially dispositional.¹³ We looked therefore at the seemingly basic property of spatial separation and its relationship to the laws of nature. On a classical substantivalist conception of space, spatial separation is a relationship between points in an unchanging spatial background, and so incapable of acting as a cause, and so incapable of having a dispositional essence. A relationalist conception of space may seem more accommodating to dispositional monism, but was in the classical era scientifically problematic. Nonetheless contemporary physicists have resurrected relationalism in the form of the requirement that theories should be background-free. If that requirement is correct, then structures in true theories will not be mere backgrounds, but will be capable of being the recipients of effects. Add to that the action–reaction principle, then such structures, including spacetime, become potential causes also. In the light of the action–reaction principle it is the fact that in classical physics space is a mere background that prevents us from being able to regard it as having a causal role and so prevents us from seeing it as having a dispositional essence. Thus it is the requirement of background-freedom that makes room for dispositional essences for spatial (and likewise temporal) properties and relations. And that space is occupied by the relationship between spatiotemporal properties and mass in General Relativity.¹⁴ ¹³ On the other hand, a convincing argument that triangularity does have a dispositional essence would provide strong indirect evidence that the fundamental structural properties have dispositional essences also. ¹⁴ Research contributing to this paper was funded by the Arts and Humanities Research Council through the research project ‘Metaphysics of Science: causes, laws, kinds, and dispositions’. I would also like to thank audiences at the Universities of Leeds and Oxford for their comments, and likewise the editor of this volume and its referees.

9 Causal Nominalism Ann Whittle

If the causal theory of properties has a slogan, it is Shoemaker’s claim that ‘properties are causal powers’ (1980: 210). But this eyecatching statement has been apt to mislead, as it seems to promise a reduction of some sort. This impression has been reinforced by expositions of the view. Armstrong, for instance, identifies the core of the causal theory of properties with the claim that ‘properties are exhausted by their causal role’.¹ More recently, however, proponents of the causal theory have been quick to dispose of the whiff of reductionism. Shoemaker, for instance, is unequivocal about the matter: I would want to reject the formulation of the causal theory which says that a property is a cluster of conditional powers. That formulation has a reductionist flavour to it. And the reduction it seems to promise is a cheat. We must make use of the notion of a property in explaining the notion of a conditional power, so there is no question here of reducing properties to some more fundamental sort of entity. (1998: 64)

Causal theorists standardly distance themselves from statements that seem to propose a reduction of properties to causal powers, offering instead a more careful suggestion.² The essence of this is that ‘properties are individuated by the contribution they make ¹ Armstrong 1999: 26. See also Hawthorne 2001: 262. ² See, for instance, Shoemaker 1998; Elder 2001; Ellis 2001; and Chakravartty 2003.

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to the causal powers of their subjects’, so they provide transworld identity conditions for properties (Shoemaker 1998: 297). Why the seeming shift? The reason, I want to suggest, although it is never made explicit, is simple and well motivated. If we are realists about properties (or their instances), which I think all current causal theorists are, then properties are regarded as sui generis entities in their own right. In other words, they are basic, primitive items in our ontology. As a result, it is not at all clear what it could mean to say that these entities are exhausted by their effects, for there is an actual, existing primitive entity—a universal or trope—which is present in each bearer of the property. Consequently, we are left with the view that it is these universals or tropes which bestow powers onto their bearers. They are what make it true that these effects occur in such-and-such circumstances. What these causal theorists are offering us, then, is not a reduction, but rather a theory which locates the source of the world’s power in the properties of objects. But before we rest content with this non-reductive causal theory of properties, it is perhaps worth first considering whether there are any alternative, reductive readings of the slogan ‘properties are causal powers’. Can causal theorists Ockhamize our ontology by nurturing the reductive pretensions of the original statement? My suspicion is that there is a reductive strategy that can be pursued at this point: one which reduces properties to causal powers and so offers an analysis of causal powers which does not appeal to sui generis properties or property instances. Nobody, as far as I am aware, has laid claim to this nominalistic construal of the causal theory of properties. But two gestures towards such a view can be found. First, Chakravartty mentions the possibility of interpreting Shoemaker’s causal theory of properties as ‘a Rylean inference-ticket-type view’, which takes a ‘deflationary account’ of powers (Chakravartty 2003: 394). But this suggestion is quickly put to one side. Second, in a footnote, Hawthorne writes, I shall not be calling the existence of universals into question. I shall leave the reader to judge to what extent the issues [regarding the causal

 ann whittle theory of properties] are significantly affected by a shift to a set-theoretic conception of properties. (2001: 376–7)

My aim here is to explore these ideas. I think that there is an important connection between the two, for unless we embrace nominalism, we will be left with the distinctly unrylean claim that there are sui generis properties of objects grounding these causal powers. But more of that in part two. First, in part one, I shall attempt to do as Hawthorne suggests: consider whether a causal theory of properties could make do without an ontology of sui generis universals (or tropes). Despite the lack of nominalist causal theorists, I hope the rationale for this investigation is clear. If this view faces insurmountable difficulties, it would be good to know what these are so we can confidently conclude that the causal theory of properties requires sui generis properties or property instances. If, on the other hand, it escapes such objections, then we have another position whose merits and demerits should be considered.

I Setting Out Causal Nominalism 9.1 Introducing causal nominalism A nominalist causal theory of properties, as well as being an ungainly mouthful, may sound like an oxymoron. How could we have a causal theory of properties, if properties do not exist? This can be easily accounted for, however, by explaining what is meant by ‘nominalism’. In this paper, it is taken to be the conjunction of two theses. The first is the standard claim that everything that exists is particular, so there are no entities that exist in more than one place at the same time. The second asserts that there are no basic property instances or tropes. All the sui generis particulars are multi-faceted. In other words, the basic particulars are not instances of redness or roundness, but rather

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entities that exemplify a number of different features. Importantly, this characterization of nominalism does not commit one to an eliminative view of properties. Nominalists can say that there are such things as properties—they are real things that exist. It is just that properties aren’t among the basic entities of our ontology, as they are reducible to facts about particulars. So if properties could be reduced to facts about particulars and causation, the way is open for a nominalist causal theory of properties (or, for short, a brand of causal nominalism). Like all forms of the causal theory of properties, at the heart of causal nominalism lies the claim that the identity conditions for properties, and so facts about what properties objects exemplify, are determined by the causal powers of objects. But how can this be rendered consistent with nominalism? Take, for starters, the sentence that ‘a is F’: what is it that makes this sentence true? According to causal nominalism, a is F if and only if a has certain causal powers. Put another way, we can say that a is F if and only if a would stand in certain causal relations, given certain circumstances. For instance, the fact that the vase (a) is fragile (F) has certain causal ramifications. To take one, the vase would most likely break if a ten stone boulder were dropped upon it. Of course, the occurrence of this event (or the manifestation of this causal power) is not just conditional upon the fragility of the vase or the weight of the boulder. For the vase would not have broken in a gravity free zone or if there had been an obstacle shielding the vase from the boulder, and so on. But, the thought is, we can nevertheless characterize what it is for a to be F by all the complicated and particular causal relations F objects could contribute to. Another way of expressing this idea is via the familiar language of functional roles. To illustrate, suppose that the property of being 100◦ C is characterized by this very simple, toy theory: (T) For all substances, if that substance is water and is heated to 100◦ C, then this will cause that substance to boil and it will scald human skin on contact.

 ann whittle Despite not being expressed in the counterfactual form, the conditional nevertheless has counterfactual force since it implies that if this water were ever heated to 100◦ C (even if it never is) then it would have certain outputs. In addition, it is presumed that the conditional is not truth-functional, because there must be some causal connection(s) between the state of affairs described by the antecedent and the consequent. It may be possible to have some other functional dependence which is not causal (perhaps, for instance, if the dependence were underwritten by some non-causal law). But here I shall assume that the notion of a functional and causal role can be used interchangeably, since the dependences between the inputs and outputs are always causal.³ Our toy theory, (T), is obviously just a placeholder. The theories we are really interested in (although they may only exist ‘in the way never-to-be-written poems do’ (Lewis, 2001: 20)), are complete, substantive theories about what F, G, H, etc. objects can do. They are not conceptual analyses that characterize what we mean by ‘F-ness’ or ‘G-ness’. But the toy theory at least offers us a taster. According to this, a is 100◦ C just in case, if it is water and is heated to 100◦ C, it will cause boiling and scald human skin on contact. Causal nominalism then makes the further claim that this is all it is for the property of being 100◦ C to be true of a. In particular, there are not any sui generis tropes or universals that make it the case that a realises this functional role. So, generalizing, a is F if and only if the theory which charts out the functional role of F-particulars is true of a. In the philosophy of mind and elsewhere, Ramsey sentences are utilized to help clarify the analysis further. Following Block (1978), our theory for 100◦ C can be written as T(S1 ... Sn , I1 ... In , O1 ... On ), where S’s are various states, such as being water and being 100◦ C, I’s are the inputs, such as heating the water, and O’s are the causal outputs, such as boiling and scalding human skin. The ³ If this assumption is wrong, then the causal theory of properties will not be well-named. In order to accommodate these non-causal dependences, it would be better to refer to it as ‘a functionalist theory of properties’ or perhaps ‘a nomic theory of properties’.

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Ramsey sentence of this theory is then formulated by replacing the T-terms with variables and prefixing existential quantifiers to the theory. Suppose that F1 replaces the T-term ‘is 100◦ C’ in our theory, we can say that a is 100◦ C iff there is a set of entities, ∃F1... ∃Fn , that satisfies this formula: T(F1 ... Fn , I1 ... In , O1 ... On ) and a is F1 . The advantage of these Ramsey sentences is that, with them, we can avoid vicious circularity (Lewis 1970, 1972). Like all causal theories of properties, causal nominalism looks vulnerable to obvious circularities. For just as fragile particulars will be characterized in terms of ten stone particulars, ten stone particulars will be characterized in terms of fragile particulars. But Shoemaker and others have argued that by employing Ramsey sentences, we get round this problem, since the right-hand side of the bi-conditional contains no occurrences of the terms, S1 to Sn , we are analysing.⁴ The idea is that Ramsey sentences are like ‘equations’ that we ‘solve’ (Yablo 1993: 151). By formulating a mammoth theory, in which all the predicates of properties appear and Ramsifying that theory, all of its terms get their designations concurrently. But, it might be objected, surely causal nominalists cannot avail themselves of Ramsey sentences? For these quantify over properties—they say that there is a property F such that any object which instantiates F stands in such and such causal relations. This objection, however, fails to distinguish between those forms of nominalism which wish to eliminate properties and those which wish to reduce them. Causal nominalists, being in the latter category, can legitimately quantify over properties. For they are not denying the existence of properties, they are just claiming that they are not sui generis entities. Consequently, since Ramsey sentences do not presuppose any particular ontological analysis of properties, causal nominalists can utilize them just as other causal theorists can. At least, they can if they explain what a property is, granted it is not a sui generis universal or a set of tropes. ⁴ See, for instance, Lewis 1972 and Shoemaker 1981.

 ann whittle At this point, causal nominalists can respond by appealing to the aforementioned set-theoretic conception of properties, employed alike by trope theorists, resemblance nominalists and, of course, by set nominalists. The property of F-ness can be construed as the set of particulars all of which realize the functional role definitive of F-ness. The F-ness in the analysans is dispensable, as it is merely shorthand for the functional formula spelt out in the Ramsey sentence for F-ness. So it is abbreviating the claim that if a is F then it would do X in circumstance C1 , Y in circumstances C2 and so on. The property of F-ness can then be identified with all those objects which realize or satisfy this functional role. But what does it mean to say that an object realizes or satisfies a certain functional role? At this point, all a causal nominalist can say is that the object in question must do X in circumstance C1 , Y in circumstances C2 etc., as specified by the Ramsey sentence. There is no ‘real’ relation picked out by the predicate ‘realization’ or ‘satisfaction’. Rather, this is a primitive predicate which does not have a functional role of its own and so does not count as a property, according to the standards of the causal theory of properties. In this, causal nominalists, like other property theorists, find themselves on familiar territory. Trying to analyse away all predicates, such as a ‘instantiates’ F or a ‘participates’ in F, is a doomed project (see Lewis 1983b: 20–5). But whilst these predicates cannot be defined in terms of anything else, causal nominalists can plausibly maintain that we have a firm understanding of what this predication involves and when we can apply these terms. Although epistemological difficulties arise when trying to decipher whether a certain object satisfies a functional role, we nevertheless grasp that it satisfies this role if and only if it would do X in circumstance C1 , Y in circumstances C2 , and so on. We have, then, the bare bones of a nominalist theory. According to this, a is F if and only if a satisfies the functional role of Fness. Because different particulars can satisfy this functional role, many particulars can instantiate the very same property. Similarly, since one particular can realize more than one functional role, one

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particular can instantiate many different properties. So we get the causal nominalist’s solution to the one over many problem and the many over one problem.⁵ This view deserves the title ‘nominalism’ since it does not postulate any sui generis properties or tropes, just particulars that do things. But does it warrant being classified as a causal theory, in the tradition of Shoemaker et al.? I think it does because it preserves two related theses that are absolutely central to the causal theory of properties. The first of these is the claim that properties are individuated by their causal features. This is preserved by causal nominalism since, on this view, the property of F-ness is determined by what F-particulars can do. If an object instantiates F-ness then it must partake in the functional role specified by its Ramsey sentence, thus providing us with transworld identity conditions for F-ness. This commitment results in the second of the causal theorist’s theses. For, granted the laws are taken as charting these causal relations between properties,⁶ the metaphysical necessity of laws follows. Causal nominalism, therefore, is an anti-Humean form of nominalism. According to the doctrine of Humean Supervenience, a Humean property is one whose ‘instantiation requires no more than a spatiotemporal point and its instantiation at that point has no metaphysical implications concerning the instantiations of fundamental properties elsewhere and elsewhen’ (Loewer 1996: 102). The properties of causal nominalism certainly fail this requirement, since what property an object instantiates has consequences for what happens elsewhere. If, for instance, a is F and in circumstances C1 , then it will X, according to causal nominalism, because this is what it is for a to be F. As a result, I fear that causal nominalism will find few friends. For, recently at least, nominalists have tended to be of a Humean bent, while non-Humeans have been attracted to realism. This, of course, comes as no surprise, ⁵ For more details about these problems, see Rodriguez-Pereyra 2002. ⁶ Or non-causal relations, if a broader construal of the theory is embraced (see footnote 3, above).

 ann whittle for those attracted to the desert landscapes tend to err towards nominalism and Humeanism. But causal nominalism illustrates that we need not buy into this package.

9.2 How causal nominalism compares Causal nominalism clearly bears close affinities to resemblance and set nominalism. But it nevertheless should be regarded as a distinct position, as it avoids some of the objections that these other forms of nominalism are vulnerable to. Let us begin by considering causal nominalism’s relation to resemblance nominalism. According to resemblance nominalism, what makes a particular F is that it resembles all the F-particulars. So this dress is red because it resembles all the other red particulars.⁷ Causal nominalism endorses a seemingly similar thesis, since it claims that all F-particulars must bear certain causal resemblances to each other. But we should not draw too much from this point. For one thing, it should be a consequence of any analysis of properties that if two particulars instantiate the same property, then they resemble each other in a certain way. And, conversely, if two particulars resemble each other in some respect, then they have some property in common.⁸ More importantly, however, resemblance nominalists claim that what makes it the case that a is F is that a resembles all the other F-particulars. Whereas causal nominalists claim that a is F in virtue of the fact that a occupies such and such a functional role. So, unlike resemblance nominalism, causal nominalism does not claim that a is F because a resembles other F particulars. This is just a consequence of its analysis of what makes ‘a is F’ true. Rather, all F-particulars bear certain causal resemblances to each other, ⁷ An alternative formulation, which Rodriguez-Pereyra calls ‘Aristocratic resemblance nominalism’, states that what makes a particular F is that it resembles some paradigms of F. As Rodriguez-Pereyra persuasively argues that there is nothing to be gained except problems from this formulation of resemblance nominalism, I shall compare causal nominalism to what he calls the ‘Egalitarian’ form of resemblance nominalism (see 2002: chapter 7). ⁸ At least that is the case if we are dealing with sparse, rather than abundant, properties. See Lewis 1983b.

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because a particular is F if and only if it realizes such and such a functional role. This difference between the two views is significant, as it enables causal nominalists to answer objections that have plagued resemblance nominalism.⁹ Take, for instance, the claim that it is possible for a particular to exist alone in a possible world, so a particular is not F in virtue of resembling other F-particulars. Although there are ways of dealing with this, causal nominalism is not subject to such a difficulty. For, on this view, a is F if and only if a satisfies such-and-such a functional role. Bearing causal resemblances to other particulars is not part of what makes it the case that this a is F. So the question of whether there are any other particulars in the world that also satisfy this functional role is irrelevant. Because of this, causal nominalism escapes Goodman’s more serious imperfect community objection (1966: 162–4). A resemblance nominalist cannot say that a set of particulars all resemble each other because they share a common property. Rather, the reverse must be the case—they share a common property because they all resemble each other. But we can have a set of particulars whose members all resemble each other, which fail to have a property in common. For instance, suppose that we have a set of particulars, a, b, and c. a is F, G, and H, b is F, J, and K and c is G, J and L. All of these particulars resemble each other, but they do not have any property in common. So if resemblance is what makes these particulars share a property, why do these particulars not share one? Causal nominalists have this response to make: a, b, and c do not form a property set (i.e. there is no one property which all these particulars have), as they do not satisfy the functional role of any one property. In other words, although a and b would do ⁹ I do not wish to claim that these objections are unanswerable, as Rodriguez-Pereyra (2002) has provided us with a thorough defence of this view. However, I do think that causal nominalism is at least worth considering as a possible alternative to resemblance nominalism.

 ann whittle X in circumstances C1 and Y in circumstances C2 , etc. c would not. And although b and c would do U in circumstances C3 , V in circumstances C4 , etc. a would not, and so on.¹⁰ It might be objected that this is circular. To say that the set {a, b, c} does not form a property set because its members fail to satisfy the functional role of any one property is making a blatant appeal to properties. But, as I mentioned earlier, the claim that a is F iff a satisfies the functional role of F-ness is merely shorthand for saying that a would do X in circumstances C1 , Y in circumstances C2 etc. Moreover, the talk of other properties which would inevitably arise when spelling out the circumstances, can, in principle, be dispensed with by employing a gigantic Ramsey sentence. The ease with which causal nominalists escape Goodman’s objection makes it a worthy rival of resemblance nominalism. But causal nominalism arguably has another advantage over its rival, as it seems to offer a more perspicuous account of what resemblance between objects involves. Resemblance nominalists, in order to deal with such difficulties as one-off instances, need to appeal to possible particulars (Rodriguez-Pereyra 2002: §§4.10, 5.3). So an F particular must resemble all possible as well as actual F particulars. But, we might wonder, in what way will these actual and possible F-particulars resemble each other? Suppose that F is a fundamental property of physics. In the actual world, all the F-particulars will resemble each other because they X in circumstances C1 , Y in circumstances C2 , and so on. But in worlds with different laws, granted the laws are contingent, this will not occur. So in what way will these F-particulars resemble each other? Given that this is a nominalist theory, the F-particulars cannot be said to resemble each other due to some quiddity, be that a universal’s or a trope’s. Moreover, the example was limited to fundamental properties to exclude those properties of particulars ¹⁰ This also answers Goodman’s similar companionship difficulty, a case in which all the F-particulars are G-particulars but the reverse is not the case (see Rodriguez-Pereyra 2002: chapter 10). For a is F not because it resembles a certain set of particulars, but rather because it satisfies a specific functional role.

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that can be thought of as composed of further parts of the particular. For this might give content to the claim that all actual and possible F-particulars have resembling ‘natures’. Finally, if all actual and possible F-particulars are said to resemble each other in that they all dispose their particulars to X in circumstances C1 , Y in circumstances C2 , etc., this conflicts with the assumption that the laws of nature are contingent. For a particular would not be F if it failed to act in the way specified by the laws. So any law stating the behaviour of F-particulars will be metaphysically necessary. Unless a resemblance nominalist is willing to embrace the metaphysical necessity of these laws, then, it looks like they will have to say that F-particulars all resemble each other in that they will all act in such and such a way in worlds with laws of type 1, in such and such a way in worlds with laws of type 2, and so on. But what is it that binds these sets together now? How do these F-particulars resemble the F-particulars in our world? Resemblance nominalists can fairly point out that they are taking resemblance to be a primitive. So it is not incumbent upon them to offer an explanation of what the resemblance between these actual F-particulars and these possible F-particulars amounts to. They just do resemble each other and that is all that can be said about the matter. But whilst I accept this point, I think that the query raised still undermines much of the intuitive force of resemblance nominalism. For resemblance nominalists, such as RodriguezPereyra, claim that this view is preferable to set nominalism because there is something about the set which accounts for the fact that it is a property set, namely, the fact that all the particulars resemble each other. This idea seems strikingly intuitive, for we imagine a set of red particulars that all resemble each other and so which share a property. But once we are dealing with possible individuals in worlds with different laws, our homely grasp of what this notion of resemblance consists in (for instance, when and where the notion can be used) disintegrates. Why does this matter? Unless we can give some account of how these F-particulars across

 ann whittle possible worlds resemble each other, the suspicion is that we are left with just another version of set nominalism. For we lack an understanding of what it is about these particulars that makes them members of the F-set, so their being F just seems to amount to their being members of the F set. In contrast, causal nominalism offers a very clear idea of what it means to say that all the F-particulars resemble each other. Whilst it requires embracing the metaphysical necessity of laws, this commitment is integral to causal nominalism, rather than an optional, ad hoc addition to resemblance nominalism. Moreover, although the notion of resemblance is still needed, since causal nominalism appeals to the idea that particulars behave in similar ways in similar circumstances, we are given a firm grasp of what resemblance between the F-particulars consists of. According to causal nominalists, all the F-particulars resemble each other in certain, functional respects. In other words, they all belong to the set of F particulars because they would do X in circumstances C1 , Y in circumstances C2 , and so on. This analysis coheres with our everyday conception of resemblance, and thus, in this respect, the account seems to have the edge over resemblance nominalism. This feature of the analysis is also what makes causal nominalism a more intuitive form of nominalism than set nominalism. Set nominalists state that a is F iff a is a member of the set of Fparticulars. So the property of being F is identified with the set of all and only F-particulars. But this seems to put the cart before the horse. For, as Armstrong comments, it seems intuitively clear that the relation between a and the set of Fs ‘does not constitute a’s being F but rather depends upon a’s being F’ (1978: 36). Set nominalism renders a’s membership in the F-set a primitive and unanalysable fact—it is unaccounted for in terms of anything else. But this strikes many as an unsatisfactory stopping point—surely some explanation should be offered of why these particulars constitute the F-set? This is what causal nominalism provides. a’s belonging to a certain set is not taken to be a primitive fact on this view. It is accounted for in terms of what its members—the particulars—can

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do. a, b and c are all members of the F-set because they all satisfy a certain functional role. So causal nominalism gets the order of explanation the right way round. These particulars are not F because they are part of the F-set. Rather, they are members of the F-set because they stand in certain causal relations, and thus bear important functional similarities to each other. Causal nominalism, therefore, warrants consideration, since it avoids some significant difficulties that other forms of nominalism are subject to. But why might causal theorists, with realist tendencies, be interested in it? The most obvious reason for preferring causal nominalism is that it promises to offer a sparser ontology. Moreover, the entities which it endorses are familiar. They are the concrete particulars which we are greeted with everyday: the dog, the TV, the tree, etc. Even those of us who are not particularly concerned with inhabiting a barren landscape might still be disinclined towards the weird world of tropes or universals. Whilst Mackie’s ‘queer entities’ (1977: 38) consideration is not an argument against realism, it is a powerful motivating factor underlying philosophers’ choices. Recently, for instance, this motivation has been seen at work in discussions concerning the ‘intrinsic natures’ or ‘quiddities’ of properties.¹¹ In addition to ontological qualms regarding these strange metaphysical posits, Langton (1998) and Lewis (2001) have argued that we can have no knowledge of these intrinsic natures or quiddities. Elsewhere (2006) I have argued that a realist form of the causal theory of properties eases these sceptical worries. But they are not eradicated completely, since concerns remain regarding our lack of knowledge of the intrinsic nature of the entity bestowing these causal powers—the quiddity of the universal or trope if you will. Causal nominalism neatly eradicates such misgivings by simply denying that there are sui generis universals or tropes that bestow these causal powers. The real battle between realist and nominalist versions of the causal theory of properties, however, is to be found elsewhere—in ¹¹ See, for instance, Robinson (1993) and Black (2000).

 ann whittle the causality debate. Right at the start, I suggested that only nominalist causal theories of properties could avoid commitment to the irreducibility of causal powers.¹² This commitment brings with it the irreducibility of causality more generally, for causal relations depend upon the powers of their relata.¹³ Many think that theories which postulate irreducible facts of any kind should be employed only as a last resort. So causal nominalism is attractive in that it keeps these reductive hopes alive. Whether or not this will transpire into a substantial benefit, depends upon the success of these reductive accounts—an issue which I shall only begin to scratch in part two. But the carrot, for the causal theorist, is clear: we can have the transworld criterion of identity for properties, the metaphysical necessity of laws and all the advantages these commitments (arguably) bring, combined with a reductive analysis of causality. Now, however, it is time for the bad news.

9.3 Difficulties for causal nominalism? Whilst escaping some of the objections that other forms of nominalism are subject to, causal nominalism does not dodge them all. Two objections, in particular, loom large. The first concerns the issue of naturalness. Causal nominalism does not result in such ‘gerrymandered’ and ‘undiscriminating’ properties as set nominalism (Lewis 1983b: 12–13), for not just any old set is a property. A set of particulars only constitutes a property if (1) every particular in that set satisfies a particular functional role, and (2) all particulars that satisfy that functional role are members of that set. But, still, it is extremely implausible to claim that this criterion fixes upon those natural properties which ‘comprise a minimal basis for characterising the world completely’ (Lewis 1983b: 12). ¹² For more on this, see Part 2: §1. ¹³ A realist causal theorist could argue that our concept of causation is analysable in terms that do not make reference to causation. For instance, they may argue that a causes b just in case a raises the probability of b. However, given their view of properties, it is still the case that irreducible causal facts make it true that a raises the probability of b. So we can separate claims about conceptual and ontological reduction.

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Given this analysis, sets such as {pencil, table, flower, rainbow, axe, skirt ...}, (if we keep extending it indefinitely) will constitute a property, since they have a shared functional role, namely that of all being visible to the naked eye. Similarly, predicates such as ‘being poisonous’ and ‘being fragile’ will designate properties, even though it seems unlikely that such properties ‘carve nature at its joints’.¹⁴ So how do we distinguish between causal nominalism’s more abundant properties and those natural properties which, in Lewis’s (1983b: 12) words, ‘ground the objective resemblances and the causal powers of things’? In the absence of an elite band of tropes or universals, causal nominalists are left with a familiar set of choices. If they appeal to the primitive relation of objective resemblance, and say that a set is natural if and only if all its members exactly resemble each other, causal nominalism collapses into resemblance nominalism. Alternatively, causal nominalists could make Quinton’s move (1957), and help themselves to a primitive distinction between those sets of particulars that are natural properties and those that are not. But this seems to get things backwards, for causal nominalists do not claim that particulars instantiate certain (special) properties because they are members of certain (privileged) sets. The reason that a particular instantiates a property is because it satisfies a particular functional role, so it is certain functional roles, not sets, that should be privileged. How should this privileging be done? A natural way of dealing with this problem, especially given that this is a causal theory, is to privilege certain properties or functional roles via reference to scientific laws.¹⁵ The rationale for this is aptly captured by Lewis: Scientific theorizing and the discovery of fundamental properties have gone hand in hand. For instance, the discovery of the phenomena of electromagnetism and the laws governing them was inseparable from the ¹⁴ This famous saying is inspired by Plato, who in Phaedrus writes, ‘The second principle is that of division into species according to natural formation, where the joint is, not breaking any part as a bad carver might’ (265d–266a). ¹⁵ Fodor (1974) and Mellor (1991) both adopt this strategy.

 ann whittle discovery of previously unknown, and very likely fundamental properties of positive and negative charge. So if we had a true and complete ‘final theory’, it ought to deliver a true and complete inventory of those fundamental properties that play an active role in the actual workings of nature. (2001: 3).

So if, in Mellor’s words ‘we stated all the laws there are in a single Ramsey sentence ’ (i.e. all those laws which appear in the ‘final theory’) then ‘the properties  would quantify over all the properties there are’ (1991: 175). Or, alternatively, we can say that  would quantify over all the natural properties. On this proposal, then, the natural properties are those whose predicates appear in the ideal ‘final’ theory. Particular a instantiates the natural property F if and only if it satisfies the functional role set out in that complete and final theory. This way of demarcating natural from non-natural properties is very much in keeping with causal theories of properties. Certain functional roles are privileged because they play an essential role in accounting for the behaviour of particulars in the complete description of the universe. Moreover, natural properties are rendered independent of our present theories and us, for this final theory is something that awaits our discovery and exists whether or not we are lucky enough to happen upon it.¹⁶ The second of the problems that causal nominalism faces is, unfortunately, far more serious. The formulation of causal nominalism, like set and resemblance nominalism, appeals to sets. This makes the view vulnerable to the notorious co-extension problem. The problem is this: if a property is a set of particulars, then two properties that are co-extensional, i.e. instantiated by exactly ¹⁶ There may be a problem on the horizon if an account of laws has to invoke natural properties, in the manner of Lewis (1983b: 41–3). But it is far from clear that this need be the case and, even if it were, I suspect that this would not damage the causal nominalist’s ontological aspirations, it would only dash reductive hopes for a conceptual analysis of laws and natural properties. This is not the place, however, for a discussion of the deep and far-ranging issues that a comprehensive analysis of natural properties raises.

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the same particulars, are the same property. For instance, if the functional role of F is only satisfied by particulars a, b, c and d, and the functional role of G is only satisfied by particulars a, b, c and d, then the F-set = the G-set, because they have exactly the same members. Consequently, on the assumption that properties are to be identified with sets, property F = property G. Following Lewis, the standard solution to this problem is to appeal to possible, as well as actual, particulars. Even if all actual creatures with hearts also have kidneys, the response goes, this does not matter because there are some possible creatures which have hearts but lack kidneys and vice versa. So the property of having a kidney is identified with the set of all actual and possible creatures with kidneys. But whilst this solves the problem of accidentally co-extensive properties for set nominalists like Lewis and resemblance nominalists like Rodriguez-Pereyra, causal nominalists cannot appeal to this standard response. The reason for this is simple. According to causal nominalists, the functional role of a property is essential to it. So if it is a law that all Fs are Gs and it is a law that all Gs are Fs, properties F and G will be necessarily co-extensive. For instance, given the WiedemannFranz Law, electrical and thermal conductivity are co-extensive in metals. So, if the laws are metaphysically necessary, the property of thermal conductivity-in-metals is necessarily co-extensive with the property of electrical conductivity-in-metals, and hence (ignoring non-metals or the purpose of illustration) they are one and the same property. This makes the prospects of combining nominalism with a causal theory of properties look very bleak indeed. If we endorse a causal theory of properties, and so with it the metaphysical necessity of laws, we must reject the principle of recombination. This states that ‘anything can coexist with anything else, at least provided they occupy distinct spatiotemporal positions. Likewise, anything can fail to coexist with anything else’ (Lewis 1986b: 88). The result of denying this principle, for all causal theorists, is a proliferation of necessarily co-extensive properties. This poses no problem for

 ann whittle those forms of the causal theory which distinguish the property from the set of particulars that instantiate it. But once we try to combine nominalism with a rejection of this recombination principle, we get stuck with a virulent strain of the co-extension problem. Is there any way of defending causal nominalism which preserves its causal and nominalist credentials? One possibility would be to modify the position slightly. Rodriguez-Pereyra, in his defence of resemblance nominalism, suggests that there is no need for resemblance nominalists to identify properties with sets of resembling particulars (2002: §4.2). Unlike set nominalism, a’s membership of the F-set is no part of the truthmaker for ‘a is F’, as a is F just in case a resembles all the other F particulars. Consequently, granted ‘property’ is used in a way that does not commit one to anything over and above the particulars that have them, resemblance nominalists do not require an ontology of sets. Causal nominalists seem to be in a similar position. According to them, an object is F in virtue of a particular functional role being true of it. In the formulation of causal nominalism offered earlier, property F was then identified with the set of particulars which satisfy this functional role. But, as with resemblance nominalism, this looks like an optional extra. For causal nominalists do not make a’s membership of the F-set part of the truthmaker for ‘a is F’. Its truthmaker is just the fact that a satisfies a certain functional formula. So perhaps causal nominalists can avoid the co-extension problem by dispensing with this optional, very troublesome, extra? This seems a promising line of response. However, RodriguezPereyra argues that resemblance nominalists cannot solve the coextension problem in this way. He writes, the co-extension difficulty goes deeper, since it does not depend on identifying properties with classes. The root of the problem is this: Resemblance Nominalism says that a particular that is F and G, is F in virtue of its resembling all the F-particulars and G in virtue of resembling all the G-particulars. But if all F-particulars are G and all G-particulars

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are F, then how can a particular have two different properties in virtue of resembling the very same particulars? (2002: 96).

Do similar considerations preclude causal nominalists making headway on the co-extension problem by identifying properties with sets? I doubt it, because causal and resemblance nominalists appeal to different truthmakers. Resemblance nominalism runs into problems because ‘a is F’ must have a different truthmaker from ‘a is G’—a desideratum which is not met if a qua F resembles exactly the same particulars as a qua G. But on the causal nominalist’s analysis, ‘a is F’ and ‘a is G’ do have different truthmakers, even if F-ness and G-ness are co-extensional. For a is F if and only if it satisfies such and such a functional role, whilst a is G if and only if it satisfies a different functional role. But, it may be objected, if all the particulars that satisfy the functional role of F also satisfy the functional role of G, surely there is no telling these properties apart, since the functional roles of F and G can simply be combined? In other words, in the case of co-extensional properties, why suppose that there are two distinctive functional roles, F and G, which characterize two different properties, rather than just one functional role and property (F&G)? In response, causal nominalists can say that if we are talking about non-natural properties, then it is permissible to say that there is a conjunctive property of (F&G). But if we are dealing with natural properties the matter is different. Given that their characterizations are drawn from the ideal scientific theory, it may be the case that the function that predicate F plays in the theory differs significantly from the function that predicate G performs. So it would be a mistake to simply combine the functional roles of F and G, even if the very same particulars do instantiate them. Another difficulty for this modified causal nominalism is this: if we refuse to identify properties with sets of particulars, what are our Ramsey sentences, which characterize the functional roles of

 ann whittle properties, quantifying over? Ramsey sentences state that there is a property F such that any object which is F stands in such and such causal relations. But if properties are not sets of particulars, sets of tropes or universals, then there is nothing that these sentences can quantify over. One possible response to this problem is simply to reinterpret the Ramsey-Lewis sentences. Instead of adopting the standard objectual reading of the quantifier, causal nominalists could opt for a substitutional reading.¹⁷ In other words, rather than saying that there is some entity F such that anything which is F will ..., we say that at least one substitution instance of ‘F’ is true.¹⁸ So a makes it true that ‘∃F(Fx)’ iff a satisfies such and such a functional role. Here, granted the substitutional reading, the second-order quantification over F does not commit us to the existence of F-ness. So as long as causal nominalists are prepared to adopt these substitutional quantifiers, they can still employ Ramsey sentences in the formulation of their theory.¹⁹ The final difficulty is one that infects all causal theories of properties. The scope of causal theories of properties is usually taken to be very broad. Shoemaker, for instance, claims that his theory holds of all ‘genuine properties’ (1980: 297). But most causal theorists have recognized the need to place some restrictions on the properties within its domain. Proponents, for instance, do not want to say that properties of mathematical entities, such as being even or ¹⁷ Or, alternatively, see A. N. Prior’s non-nominal quantifiers (1971: chapter 3). ¹⁸ For more on these substitutional quantifiers, see Haack 1978: chapter 4. ¹⁹ Another possibility is to identify properties, not with sets, but with groups or collections of individuals whose identity conditions goes with the conditions of entry. These, of course, would not be extensional entities, but we have an intuitive grasp on them nevertheless. McTaggart, for instance, argues that the intuitive notion of a class is ‘determined by a class-concept’. He writes, ‘the content of two different classes may be co-extensive. Cambridge colleges in which, in the year 1919, the Headship is not in the gift of the fellows are a class. Cambridge colleges founded between the years 1515 and 1550 are another class. Each class contains only the same two members—Magdalene College and Trinity College. But the classes are different’ (1921: 131–2). Whilst McTaggart’s talk of class is now misleading, Simons makes a similar claim for groups (see 1987: 146, 168). Perhaps, then, causal nominalists could explore the idea of identifying properties with something like McTaggart’s classes or Simons’ groups.

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being prime, are subject to their analysis, as these properties receive their characterizations from mathematical theories. Similarly, it is unwise to include properties and relations which characterize ‘the form of the world’,²⁰ such as identity and causation, into the domain of the causal theory. For the prospect of defining these relations in terms of their causal features seems, at best, unpromising. The difficulty, then, is this: if causal nominalism does not offer a theory of all properties, then we have to endorse another kind of theory, such as realism or set nominalism, for these properties. But if we employ one of these analyses to deal with properties outside the scope of causal nominalism, we are stuck with all of its problems and so we might as well embrace one of these analyses for all properties. Causal nominalists can respond by arguing that this difficulty is not unique to them. It seems unlikely, as Lewis (1983b) and Oliver (1996) have argued, that any one analysis can satisfy the different roles assigned to properties. Lewis, for instance, points out that unadorned set nominalism cannot deal with natural properties, whilst Armstrong and Rodriguez-Pereyra state that their realist and nominalist theories respectively are not concerned with abundant properties. Similarly, both set and resemblance nominalism leave untreated necessary co-extensive properties. Causal nominalists can push their defence further by arguing that it is plausible to treat mathematical properties (and other structural properties, such as identity and mereological properties) differently. Although the property of being even and having charge, for instance, are grouped together under the heading ‘property’, it is far from clear that they bear anything more than a superficial resemblance to each other. In any case, since the properties of the former category, unlike the latter, do not make a causal contribution to the world, it would be pointless to attempt to utilize the causal theory for these sorts of properties. The properties of space-time pose a more serious challenge to all causal theorists. ²⁰ Hawthorne 2001: 373.

 ann whittle It may be that these relations can be brought under the causal nominalist’s umbrella. Bird, for instance, writes: The lesson of general relativity is just that we may see the components of this set-up as dispositional. Each space-time point is characterised by its dynamic properties, i.e. its disposition to affect the kinetic properties of an object of that point, captured in the gravitational field tensor at that point. (2003: 165)

But, of course, the jury is still out on this. Even if they cannot be dealt with in this way, however, there are still grounds for claiming that it is not arbitrary or ad hoc to say that these relations are part of the ‘structure’ or ‘form’ of the world, and thus warrant separate treatment from, what Hawthorne calls ‘the nodes in the structure (the ‘matter’ of the world)’ (2001: 373). Unfortunately, this fails to adequately dispense with the objection, for while we might be justified in dealing with these properties differently, we still need some account of how they should be treated and why that analysis would not serve equally well for all properties. But there is increasing recognition that, due to the different roles theories of properties play, this will be a challenge that most, if not all, analyses of properties will have to meet. So this objection certainly is not decisive against causal nominalism. In light of the discussion here, then, I think that it is worth pursing this position further, by considering causal nominalism’s ramifications for an analysis of causal powers.

II Ryling away Causal Powers 9.4 Reduction, Ryle, and causal nominalism Shoemaker’s claim that ‘properties are causal powers’, I argued earlier, cannot be understood reductively if a realist causal theory of properties is embraced. Properties cannot be reduced to causal powers, for if we are realists about properties (or their instances),

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then these are sui generis entities in their own right. Similarly, causal powers cannot be reduced to non-powerful properties for the simple reason that properties are conceived of as powerful entities. According to causal theorists, properties are the entities which bestow power onto the world. They do not do this when amalgamated with laws (be those Humean or non-Humean); they are themselves dynamic. So causal powers are not reduced to a different kind of entity—there is no getting rid of them for something else. This account of properties and causal powers has important consequences for causality. Whilst it does not bear on the issue of whether we can offer a reductive analysis of our concept of cause, what is excluded is reductionism about causation: the view that causal facts can be reduced to non-causal facts about the world.²¹ Any suggested reductive base for the causal facts will have to include facts about properties. According to causal theorists, these properties are fundamentally powerful entities, and so facts about them count as causal facts. Consequently, if we turn to Tooley’s definition of causal reductionism, which states that ‘any two worlds that agree with respect to all of the non-causal properties of, and relations between, particular events or states of affairs, must also agree with respect to all of the causal relations between states of affairs’ (1993: 173), we find that realist causal theories fall on the other side. For if properties are themselves powerful entities, holding fixed all the ‘non-causal properties’ (which for causal theorists will only include a very small number, perhaps only the mathematical and structural properties mentioned earlier) will certainly not fix the causal relations across possible worlds. Causal nominalism looks in a similar position. On this view, a’s being F has certain causal implications—a is only F if it does X in circumstances C1 , Y in circumstances C2 , etc. Once again, ²¹ By ‘causal fact’ here, I mean a true proposition about what causes what, or what could cause what—what causal powers a thing has.

 ann whittle then, it looks like holding fixed all the non-causal facts will not fix all the causal facts, since the non-causal properties are very few in number. There is, however, a substantial difference between the two positions here. Those who embrace a realist causal theory of properties claim that there are sui generis powerful properties that are absolutely fundamental—they cannot be accounted for in terms of anything else. Causal nominalists, in contrast, do not assert this. Whilst a’s being F entails certain causal counterfactuals, the question of whether these causal counterfactuals are irreducible or not is left open. Perhaps facts about what a can and does cause can be reduced to non-causal facts about the world, such as patterns of regularity in this world, our best scientific theories, psychological facts, etc. If this is the case, then whilst the reductive base for causal facts will, of course, appeal to the properties of objects, the causal counterfactuals that these entail may then themselves be reducible to further non-causal facts.²² So although causal nominalists are committed to rejecting Humean supervenience, the denial of causal reductionism does not automatically follow. In addition to this, causal nominalism reverses the ontological priority found in realist accounts. A realist causal theory of properties gives ontological priority to the persisting powers of objects over the causal relations that happen. On this view, whilst it might be correct to analyse our concept of poison in terms of what would happen, that this causal relation occurs depends upon the persisting, powerful properties of the particulars involved. If sugar did not have certain properties which were the source of its solubility, if, for instance, it did not have the ability to form hydrogen bonds, then this lump of sugar would not have dissolved in water. In contrast, causal nominalism makes facts about the causal powers of objects dependent upon facts about what causal relations objects would enter into. There are no sui generis properties of the objects bestowing irreducible powers. Rather what we have are particulars and facts about what they would do. So every causal power, on this ²² I shall say a little more about this in §3, part 2.

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view, is identical to some complex of would-be causal relations. In other words, causal powers are reducible to facts about what an object would do. It is because of this, that causal nominalism can offer a reductive rendering of Shoemaker’s claim that ‘properties are causal powers’. In broad outline, the story goes as follows: first, following Shoemaker (1980: 212), we should distinguish between macro-powers of particulars and the property (or complex of properties) that supports that power. For instance, two substances may both display the macro power of being poisonous, but the substances are different, so their diverse properties are responsible for their damaging effects. While the properties of methyl mercury achieve their deadly effect by killing neurons in the nervous system, for example, hydrogen cyanide works by inhibiting our metal-containing enzymes. These properties of the substances should not just be identified with the causal powers of particulars, since they have different identity conditions. If, for instance, properties F1 , F2 and F3 , which are responsible for the object’s property or power of being poisonous, change, then these properties will form a different set of properties or, what I will call, ‘a property complex’. However, whilst the property complex may change, if the complex functional role that is definitive of the property of being poisonous remains true of the object, the object’s property or power of being poisonous will nevertheless persist. This distinction between macro causal powers and property complexes of objects can and should be maintained by causal nominalists, because we want to allow that there are interesting things to be said about the differing powers of particulars. The properties that are responsible for mercury’s being poisonous no doubt differ from those that make cyanide poisonous, but they both satisfy the functional role definitive of being poisonous—a functional role which will differ from the functional roles of its property complexes that make it the case that this substance is poisonous. So causal theorists, be they nominalists or realists, can say something more about the power/property, even though the

 ann whittle identity conditions for that property are given by facts about what that object would do. But whilst macro-powers of objects can be thought of as being made true by property complexes of objects (or their parts), this does not exclude the possibility of a reduction of properties to causal powers. In the second stage of the analysis comes the main claim, namely that for some properties, the natural properties which ‘ground ... the causal powers of things’ (Lewis 1983b: 12), all it is for the object to instantiate that property is for a certain functional formula to be true of it. There is nothing else about the particular, no sui generis tropes or universals, which make this functional formula true of the object. So macro-powers or properties are constituted by (though not identical to) property complexes of objects, each of which might in turn be constituted by (though again not identical to) further property complexes. But as the natural properties, which are not constituted by any other properties, are themselves just complexes of facts about how the particular would behave, all the properties ultimately get reduced to Rylean causal powers. They are, in Armstrong’s colourful language, just ‘congealed hypothetical facts or states of affairs’ (1997: 79). Causal nominalism, then, in Chakravartty’s words, can be thought of as ‘a Rylean inference-ticket-type view’, since it offers us a ‘deflationary account’ of powers (2003: 394). It is similar, at least in spirit, to Ryle’s account of dispositions, because the powers of objects ultimately get reduced to facts about what would and could happen to objects.²³ To instantiate a property—which macro-powers are complexes of—is not for the object to instantiate a universal or trope, rather it is for that object, in Ryle’s words, ‘to be bound or liable to be in a particular state, or to undergo a particular change, when a particular condition is realised’ ²³ Although Ryle tends to talk of dispositions rather than powers, I shall continue talking of powers because, following Shoemaker (1980) and Mellor (2000), I think that the distinction between the dispositional and the categorical is best understood as a distinction between predicates rather than properties.

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(1949: 117). So although we can talk about property complexes of objects making different macro-powers or dispositional properties true of them, because what it is to have a property is just for the object to behave in certain ways, macro-powers and properties are reduced to facts about the causal relations objects do and can stand in. Despite preserving the spirit of a Rylean view, however, the differences allow causal nominalists to escape some of the criticisms this position has given rise to. For instance, one frequently cited objection is this: if we allow for the possibility, as Ryle’s account does, that one object can have a power to X, while its duplicate has a power to not-X, then it looks as if dispositions are randomly imposed upon the object, as they have no grounding in the object’s nature. But this, as Geach remarks, seems to go against both ‘scientific investigation’ and ‘a very deep rooted way of thinking’ (1957: 5). He writes: A physicist would be merely impatient if somebody said to him: ‘Why look for, or postulate, any actual difference between a magnetized and an unmagnetized bit of iron? Why not just say that if certain things are done to a bit of iron certain hypotheticals become true of it? (1957: 6).

These worries, I think, are dodged by causal nominalism. It rejects the claim that ‘two items could be alike in all their causally relevant properties and one item possess a particular disposition—D—but the other item not possess that disposition’.²⁴ Causal nominalism, just like other forms of the causal theory, claims that the identity conditions of properties are determined by what objects can do. If two particulars act in just the same ways, they have all the same properties. So this view does not hinder the search for more advanced explanations. We can appeal to the properties of objects to explain the differences between magnetized and unmagnetized ²⁴ Elizabeth Prior (1985: 31) thinks that this is one of the essential theses of Ryle’s phenomenalism. If this is correct, then causal nominalism certainly should not be regarded as a form of phenomenalism. Nevertheless, the parallels between the two positions are clear.

 ann whittle objects, and we can say more about the properties of objects by investigating their basis in the object (and its surroundings). Consequently, causal nominalism is not vulnerable to Geach’s worries. But whilst causal nominalists can happily talk with the realists, and claim that there are persisting properties of objects which make these causal conditionals true, in essence they side with Ryle. For all it is for the (natural) properties to be had by particulars is for certain functional roles to be satisfied by them. So philosophers who discuss analyses of dispositions or powers often present us with a false dichotomy. Mumford, for instance, writes: Are we intending to ascribe properties, as the realist claims, or are we saying that some events are possible, as Ryle and Dummett would have it? (1998: 63)

Causal nominalism illustrates that we need not make this choice: we could be both ascribing properties to an object and just saying something about what that object can do, since properties can be reduced to facts about the actual and possible behaviour of objects. This middle way between Ryle’s phenomenalism and the realism of Armstrong and others deserves consideration for, as we have just seen, the extent to which it is vulnerable to the objections targeted at Ryle’s position is unclear. In the next two sections, I shall begin this task. In order to make it manageable, I shall focus on two objections that are commonly regarded as the most serious. Indeed, I think it is fair to say that they account (rightly or not) for the demise of Ryle’s position from the philosophical scene. The aim of this discussion will be to see whether well-known difficulties raised against Ryle’s account, render a nominalist form of the causal theory of properties untenable.

9.5 Finks and antidotes The so-called simple conditional analysis, which is standardly attributed to Ryle, has come in for some tough criticism. The

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analysis states that dispositional predicates or concepts can be reductively analysed in terms of conditional statements. So, roughly speaking, statements concerning dispositional expressions can be translated into statements lacking them by employing the following formula: Something x is disposed at time t to give response r to stimulus s iff, if x were to undergo stimulus s at time t, x would give response r.

But now take this analysis of the dispositional predicate ‘is fragile’: x is fragile iff if x is dropped or struck, x breaks. This glass could be fragile, but nevertheless fail to break when dropped, because a sorcerer protects it. This protection might come in one of two forms: first, at the time the glass is dropped, the sorcerer may cast a spell so that the glass ceases to be fragile (a finkish disposition, see Martin 1994 and Lewis 1997). Alternatively, as the glass is dropped, the sorcerer may find some way of protecting the glass—an antidote to its breaking (Bird 1998). Perhaps, for instance, she magically makes it the case that a soft duvet always appears for it to land upon. Consequently, the objection goes, dispositional predicates cannot be eliminated in favour of conditional statements. We should, I think, be careful about attributing this simple conditional analysis to Ryle, since he writes: There are many dispositions the actualisations of which can take a wide and perhaps unlimited variety of shapes ... If we wish to unpack all that is conveyed in describing an animal as gregarious, we should similarly have to produce an infinite series of different hypothetical propositions. (1949: 43–4).

This suggests that Ryle is not offering a conceptual analysis of what dispositional terms mean. For it is unclear in what sense an infinite series of different hypothetical propositions could provide a conceptual analysis of ‘gregarious’, as such an analysis would be far too unwieldy for us to employ. Given the stated aims of causal nominalism, however, it is doubtful whether this, or the failure of the simple conditional analysis, should concern its proponents. For causal nominalists are not purporting to offer a conceptual analysis

 ann whittle of dispositional (or any other) predicates—they are not in that business. It might well be the case that the meaning of fragility cannot be given a non-circular analysis in terms of conditionals. Perhaps the best we can do is something like ‘if x were stressed without ceasing to be fragile, it would break’ (Mellor 2000: 763). But, as Molnar (1999: 8) points out, a conceptual reduction is not necessary or sufficient for an ontological reduction. So whilst the functional formula an object must satisfy in order to be fragile may be far too complex to be graspable by us, and so not give the meaning of the concept of fragility, it might still be the case that ‘what in reality’ fragility is,²⁵ can be reduced to facts about what objects would and could cause. We may object, however, that this fails to get to the heart of the matter. If Ryle is right and there are cases (or, worse, all cases) that require an infinite series of hypothetical propositions, then the functional role of the property would not be specifiable even in principle. This is certainly the view of some; Mumford, for instance, writes: The possible interfering background conditions cannot be excluded in a finite list that is appended to the conditional. This is because there is no finite list that could name all such possible conditions in which the manifestation is prevented. (1998: 88).

If this were the case, then the functional roles, central to the ontological reductions, would be open-ended. It would be impossible to specify the entire of the functional role definitive of some, if not all, properties. But surely this is unacceptable? Just as we should not identify a mental property with an infinite disjunction of physical properties, because the latter is shapeless with respect to the former and thus cannot offer any explanation of the pattern of dependences found at the mental level, similarly, an infinitely complex functional role excludes any reduction of properties to ²⁵ Mellor 2000: 758.

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facts about the causal behaviour of objects. So we need to postulate some property, a sui generis universal or trope, which is the source of this open-ended behaviour. In response to this, two lines of defence are open to the causal nominalist. One possibility would be to challenge the claim that infinitely complex functional roles are required. I think that the best way of pursuing this line is by utilizing the distinction between the functional roles of natural and less than perfectly natural properties. Although non-natural properties or powers, such as fragility, are given by a particular functional role, they are nevertheless made true by further properties of the objects. This licenses the use of ceteris paribus clauses because, at this level, causal nominalists do not require an ontological reduction of fragility to a precise set of facts about how fragile objects do and could behave. So we can avoid infinitely complex functional roles by saying something like this: Other things being equal (there are, for instance, no fragility antidotes, finks etc.) this glass is fragile iff it breaks when dropped or knocked.

Causal nominalists can make sense of this because they can talk like a realist and appeal to the underlying property complexes which support the power. For example, they can say that, in this instance, the fragility of the glass can be identified with such and such a property complex (although not generally because they have different extensions). So we can understand the ceteris paribus clause in terms of whether there is a suitable property base that continues to support the attribution of the property in tricky finkish or antidote cases.²⁶ But this tactic, of course, cannot be employed when dealing with the natural properties, for ex hypothesi there are no property bases making them true of objects. So surely we have only delayed, ²⁶ But if, for instance, the sorcerer always changed the properties of the glass when dropped, so that it broke due to another complex of properties, we would still want to say that the glass was fragile. This again supports the claim that the individuation of the property of fragility goes with what the object does, not directly with the property complexes that support it.

 ann whittle not solved, the problem, because infinitely complex functional roles will reappear at the level of natural properties? No argument, however, has been offered which shows that complex functional roles are required at this level. Not surprisingly, then, philosophers have been far less confident of this claim. As Mumford, for instance, writes. Is there some condition ... available to defeat every disposition manifestation? Possibly not. Some dispositions of basic particles may manifest indefeasibly whenever their stimulus conditions are realised. (2001: 376).

Bird strengthens the causal nominalist’s hand here by arguing that the existence of ‘fundamentally finkish dispositions can be excluded fairly straightforwardly’ and ‘fundamental antidotes may be eliminable’.²⁷ The argument for the latter claim draws upon the difference between natural and non-natural properties. Nonnatural properties, such as being poisonous, are multiply-realizable, so a number of different property complexes can make its functional role true of the object. This makes it difficult to envisage how we could rid ourselves of antidotes, since we have to list all the antidotes to every different property base. Even if this is possible in principle, Bird argues, the resulting property will lack the explanatory power of the original, so the ‘antidote-free’ dispositions should not be replaced with ‘antidote-sensitive’ ones (2004: 7). In the case of natural properties, however, there are no property complexes making the functional role true of the object. So whilst there may well be some antidotes that stop the natural properties manifesting their powers, there is no reason to think that these would be, in principle, unspecifiable. We could thus replace the antidote-free functional roles with antidote-sensitive ones. Given the aims of causal nominalists, this would suffice to solve the current problem, ²⁷ Bird 2004: 1. Although I refer the reader to the details of Bird’s argument, in the case of finkish dispositions, the basic idea is that we need some time delay between the stimulus that the object with disposition D receives and the manifestation of D. But in the case of fundamental properties, i.e. ones with no supporting property complexes or causal bases, that there should be any such time gap is mysterious.

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since it does not matter if the antidotes are many in number, so long as they are not infinite in number. This defence, however, makes the success of the reduction depend upon an empirical matter—if it turns out that there are an infinite number of antidotes at the fundamental level, then no reduction is possible. The next response does not require such a commitment, since it simply denies that infinitely complex functional roles would preclude a reduction of properties to facts about what objects can do. Causal nominalists can argue that the analogy with the philosophy of mind which motivates this objection is not a good one. Whilst it seems extremely plausible to say that a mental property is not identical to an infinite disjunction of physical properties, for such a disjunction lacks theoretical unity, and so does not appear to form a natural kind, such considerations do not apply here. For the functional formula in question, even if it were infinitely long, may not be shapeless or lack theoretical unity. There may be a good scientific rationale behind the various kinds of causal interactions F-particulars can stand in, even if they cannot in principle be specified. The model we should be thinking of here is not Nagel’s, or the functionalist’s, model of reduction,²⁸ but rather ontological reductions of metaphysical categories, such as that offered by set or resemblance nominalists. What, then, is required for a reduction of these metaphysical categories? This is admittedly a difficult (and under-discussed) issue. But since opponents claim that an infinite number of facts about the possible behaviour of objects would preclude a reduction, the onus is on them to provide desiderata for such reductions that warrant this conclusion. This, I suspect, will prove difficult. The success of a metaphysical reduction depends largely upon whether the explanatory work done by the metaphysical category targeted ²⁸ Ernest Nagel’s (1974) model of reduction requires a derivation of the laws of the reduced theory from those of the reducing theory, when this is taken in conjunction with bridge laws that connect the predicates of the two theories. The functionalist model, in contrast, depends upon the functionalizability of the target property to be reduced (see Kim 1998).

 ann whittle for reduction can be executed as well by the category doing the reducing. So, in this context, the key question is: can the explanatory role performed by sui generis universals or tropes (for instance, the part they play in an analysis of resemblance, of laws, causation, etc.) be carried out by facts about objects and how they behave? If it turns out that causal nominalism can only perform this explanatory role if its functional definitions are, in principle, specifiable, then these open-ended definitions will pose a problem for the proposed metaphysical reduction. But I see no reason why this must be the case. So, in the absence of further argument, it is open to causal nominalists to deny that specifiability in principle is a necessary requirement for reduction. But, it may be objected, surely there is such an argument in the offing here, namely the one gestured at earlier? If the functional definition of F-objects is open-ended, so it cannot be encapsulated by a finite number of causal facts, there must be some entity, a sui generis universal or trope, which is the ‘source’ of this behaviour. For this entity is what explains or accounts for the fact that these particular truths form a cohesive, although open-ended, cluster of causal facts. So, by postulating this sui generis entity, we provide an explanation of this open-ended, causal behaviour—an explanation which is fatally lacking from the causal nominalist’s account. This line of reasoning, however, whilst admittedly seductive, is resistible. Talk of ‘F-ness’ leads us to think that there is some thing or entity in the object which is making all these causal counterfactuals true. But whilst we can posit these sui generis entities as truthmakers, it is not clear that the explanatory advantage claimed by the realist over the causal nominalist at this juncture is significant.²⁹ Causal nominalists can respond by saying that the causal counterfactuals are unified into cohesive clusters by scientific laws. It is these laws, possibly in combination with other scientific facts, that explain why, when an object is F, it can engage in such and such (perhaps open-ended) behaviour. Realists, one suspects, will ²⁹ I shall say more about this, and the issues raised in this paragraph, in the next section.

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also appeal to the laws and detailed scientific explanations to explain why such and such behaviour is definitive of the universal of F-ness rather than the universal of G-ness, for instance. So one might question whether postulating a sui generis universal or trope, which is the ‘source’ of this open-ended behaviour, really does amount to an explanatory advance. Does their metaphysical explanation add anything to our understanding of F-ness or the causal facts in question? Or, is it just an unnecessary metaphysical postulation, which brings with it added ontological costs and epistemological worries?³⁰ The fink-antidote objection, therefore, does not render causal nominalism defunct. This position does not claim to offer a conceptual analysis of our predicates, so there is no requirement that our concept of fragility be substitutable for some simple, conditional formula. Moreover, even if the functional roles definitive of natural properties were infinitely complex, an eventuality which seems unlikely, it remains to be seen whether this would damage the kind of reduction on offer here. Ramsey sentences could still be employed—‘if the postulate of T was an infinite set, we must introduce devices for infinite conjunction—to do so would be bothersome, but not problematic’.³¹ And causal nominalism would still be presenting a clear conception of which of the metaphysical categories are basic. If causal nominalists are right, macro causal powers can be reduced to complexes of properties which themselves can be reduced to (a finite or infinite number of) facts about what objects can do. Of course, all this is still very problematic, but infinitely complex functional roles do not obviously undermine this account of which ontological items are sui generis.

9.6 Truthmakers The most influential of the objections to Ryle’s analysis, however, has been saved until last. Armstrong (1968); Lewis (1992); Mumford ³⁰ See earlier, p. 255. ³¹ Lewis 1970: 80. For more details, see Berent 1973 and H. E. Hendry 1975.

 ann whittle (1998); and Heil (2003), amongst many others, have all argued that Ryle’s view is unacceptable because it violates the demand for truthmakers. Heil, for instance, writes: Nowadays, few philosophers would be willing to endorse Ryle’s conception of dispositionality. A large measure of the resistance issues from an implicit commitment to a truthmaker principle: if a statement concerning the world is true, there must be something about the world in virtue of which it is true. (2003: 62).

Ryle’s account is accused of failing to meet this demand because, again in Heil’s words, certain descriptions could hold true of objects without there being anything about those objects in virtue of which the descriptions held ... Such statements do not answer to features of the world, but instead function as ‘inference tickets’ to license inferences. (2003: 61)

The question I shall address here is whether, given that causal nominalism is similar in spirit to Ryle’s view, it is subject to the same complaint. It is not clear that it is, although the issue is complicated by the fact that there are numerous formulations of the truthmaker principle. If we look at Heil’s statement of the objection, however, it is doubtful whether it has any weight against causal nominalism. For, according to this, the powers of objects do ‘answer to features of the world’. The fact that a is fragile is made true by property complexes or further features of the object. So there is something that makes the counterfactual ‘if this glass were dropped, then it would break’ true. Even when we get to the natural properties, a causal nominalist can still claim that this object would do X in circumstances Y because a is F, since that is part of what it is for a to be F. So causal nominalism does not seem to fall foul of this formulation of the truthmaker objection.

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Even if we beef up the truthmaker principle and say, with Parsons, that, To say that a certain class of sentences (in our case, sentences asserting dispositions) are made true is to say that those sentences supervene for their truth on the qualitative properties of something in the world. ‘Qualitative’ is here used to contrast with ‘dispositional’, but it is equally intended to cover something of what is meant by ‘intrinsic’. (1999: 2)

There is still an issue about whether causal nominalism would fail this test. For, first, causal nominalists can claim that natural properties are not dispositional, since they are not referred to by dispositional predicates whose meanings are given by something like the simple conditional analysis. Second, they can claim that their properties are intrinsic, because they pass the duplication test. If a would X in circumstances C since a is F, then all duplicates of a (i.e. those which have exactly the same perfectly natural properties), will also be F and so do X in circumstances C. Of course, there are other usages of the word ‘dispositional’ and ‘intrinsic’ according to which the properties of causal nominalism would not count as dispositional or intrinsic,³² but the case is certainly not cut and dry. A feeling, however, will no doubt persist that causal nominalism does somehow fall foul of the truthmaker principle. We can home in on this worry by turning our attention to the unmanifested powers of particulars. According to causal nominalists, a could be F even if a never manifested any part of the functional role which made it the case that a is F, since the circumstances never arise which render a’s F-ness apparent. But even if some of F’s functional role is made manifest, in most instances, a will only exemplify a ³² For such usages of the word ‘dispositional’ see, for instance, Armstrong 1997: 69 and Ellis 2001: 119. On such usages of the word ‘intrinsic’ see, for instance, Dunn 1990: 178 and Humberstone 1996: 242. Kim’s (1982) well-known (though flawed) definition of intrinsic could be incompatible with some of the properties postulated by causal nominalism—those properties whose functional role demands the existence of something independent of the property, whatever the circumstances—but this kind of case will not be standard.

 ann whittle small fraction of the functional role definitive of F-ness. Given this, although causal nominalists can say that a is F iff a satisfies the functional role definitive of F and, conversely, that a does Y in circumstances C etc. because it is F, they cannot say that how the object actually behaves is what makes a F. So what, then, are the truthmakers of the sentence, ‘a satisfies the functional role of F’? What is it about the universe in virtue of which this sentence is true? According to causal nominalists, the truth of ‘a is F’, as well as requiring the existence of a, also requires certain facts concerning what a would do in this and nearby possible worlds. For what makes it true that a satisfies the functional formula of F is that a would X in circumstances C1 , Y in circumstances C2 , etc. So even if those circumstances are never actualized in this world, there are still counterfactual truths concerning what would happen to that object in such and such circumstances. But this is just to restate the problem, since we do not know what it is about the world that makes it the case that these counterfactuals are true of the object. Why is it that if this object had been in circumstances C1 it would have X-ed? When talking about the macro causal powers of an object, such as its fragility or solubility, causal nominalists can respond by saying that the counterfactuals definitive of such powers are made true by property complexes of the object. Even when we get to the level of natural properties, causal nominalists can still talk with the realist and say that this particular would have done such and such because it is F. But this will not satisfy the realist’s intuitions for, at this level, all there is to a’s being F is that a particular cluster of causal conditionals holds true of the object. The claim that ‘a is F’ functions as an ‘inference ticket’; it allows us to infer that if a were in such and such circumstances then it would X etc. But there are no non-spatiotemporal parts or constituents of the objects—its universals or tropes—which make this counterfactual true of a. Consequently, realists might argue, the demand for truthmakers is violated.

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But just because causal nominalists refuse to postulate sui generis entities, such as universals or tropes, which are responsible for such and such a functional role being true of an object, does not automatically mean that the view violates a (sensible) demand for truthmakers. It is open to the causal nominalists to say more here about why it is that a satisfies the functional formula of F-ness, and hence why the counterfactual ‘if a is in circumstances C1 then a Xs’ is true. Broadly speaking, at least three kinds of analyses are open to causal nominalists. First, causal nominalists could argue that a satisfies the functional role of F because of a’s possible, as well as actual, behaviour. Even if a is never in the right circumstances and so never Xs, still, a satisfies the functional role of F because a counterpart of a, in nearby possible worlds, is in those circumstances and Xs. On this view, then, it is not just actual world entities that makes it case that a is F and thus satisfies such and such a functional role. The truth of this statement also supervenes upon events across possible worlds. In light of the co-extension problem, many nominalists have embraced modal realism.³³ Causal nominalism, as stated in part one, avoided commitment to such a view, but now qualms about truthmaking once again push us in that direction. This is unfortunate, since modal realism is a hard view to believe. Its heavy ontological cost makes an ontology of universals or tropes look far less extravagant. Moreover, resorting to other possible worlds rides roughshod over intrinsicality intuitions. For what a’s counterpart does in some other possible world seems to have very little to do with a’s causal powers in this world. However, it is doubtful whether this sort of consideration should sway nominalists, since they have to violate at least some of our intrinsicality intuitions anyway. If, for instance, properties are construed as sets of particulars, or resembling particulars, properties cannot be thought of as ‘in’ or ‘interior to’ the spatiotemporal boundaries of their object.³⁴ ³³ See, for instance, Lewis 1986b and Rodriguez-Pereyra 2002. ³⁴ See Dunn (1990) and Humberstone’s (1996) notion of an intrinsic or interior property. The intuitive idea is that an intrinsic property is one whose existence and nature has been,

 ann whittle Similarly with causal nominalism, whether or not a particular has a certain property depends upon that object’s relations with other things, so intrinsicality intuitions have already been largely contravened. A second kind of response attempts to eschew talk of real possible worlds in favour of quasi ones. Granted that causal nominalists are trying to propose a reductive analysis of what it is to say that a could cause it to be the case that X, this makes their job a lot harder. For if we do not construe possible worlds and the events that happen in them as real entities which simply make these counterfactuals true, we are still left with the question of what makes it the case that if a was in such and such circumstances, it would bring X about. Causal nominalists, however, may be able to develop a satisfactory, reductive account of this—one which does not postulate any sui generis causal facts, and so by holding fixed all the non-causal facts, the causal facts are thereby fixed. For instance, causal nominalists could analyse what it is for a to satisfy the functional role definitive of F via its causal behaviour in this and nearby possible worlds (perhaps construing these worlds as sets of propositions or sentences), and then analyse this talk of nearby possible worlds in terms of widespread facts about the actual world, such as similarity of particular matters of fact, nomic axioms of the best system, and so on. Whether or not such a project could be successfully carried out is, of course, a question that stretches far beyond the boundaries of this paper. But if it could be done, causal nominalists would have a response to the realists. For they could say that a is F iff a satisfies such and such a functional role, and then plug in their reductive analysis of what it is that makes these causal counterfactuals true. It would, however, be better if the success of causal nominalism did not depend upon such a contentious issue as the viability of a reductive analysis. So it is fortunate that there is a third way that in Humberstone’s words, ‘entirely determined by what is the case within the confines of the would-be possessor’ (1996: 242).

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causal nominalists could take, which is less ambitious but which does not require modal realism. This simply accepts that there are irreducible functional facts about what particulars can do. In other words, at the level of natural properties, a is F iff it could do X in circumstances C1 , etc.—there is nothing further we can appeal to which accounts for the behaviour of the particulars in question. It is just a brute primitive fact which (whilst perhaps susceptible to conceptual analysis) cannot be accounted for in terms of other, non-causal facts. Realists might interject that this violates the truthmaking principle, since there is nothing that makes this counterfactual true of its object. But at this level, it is not clear how seriously causal nominalists need take the complaint. After all, realists such as Armstrong or Shoemaker also posit irreducible facts. Realist causal theorists, for instance, claim that what makes it true that a Xs in circumstances C1 is that a instantiates an irreducibly powerful universal or trope. Once we have reached the level of natural properties, upon whose powers all the others depend, there is nothing more that can be said about why the counterfactual holds true, it just does because the particular instantiates this property. Causal nominalists, then, can respond to these objectors by turning the tables and fairly questioning the explanatory value of such metaphysical posits. They can argue that appealing to sui generis powerful universals or tropes, as the realist causal theorist does, or powerful laws and causally inert universals, as Armstrong does, offers us no real advancement. For, either way, we still have to make do with irreducible causal facts. All in all then, it is very unclear whether an account of truthmaking could be offered which would disallow the causal nominalist’s appeal to irreducible causal facts about the objects, without thereby also rendering illegitimate analyses offered by realists who endorse the principle of truthmaking. It might, however, be objected that this third response strips causal nominalism of all its potential interest to causal theorists, since one of its aims was to leave open the possibility of adopting a causal theory of properties and a reductive analysis of causation. I

 ann whittle agree that this is a reason for pursuing the position but, as we have seen, the truthmaking objection does not foreclose this option. Here, all I wish to draw our attention to is the fact that it looks like causal nominalists can wriggle out of the truthmaker objection by endorsing a non-reductive account of causality. If this route is taken, then causal nominalism would remain an interesting, informative position, since we would still get a reduction of properties and causal powers to facts about particulars and what causal relations they stand in. None of this would be lost, all causal nominalists would be claiming is that we can go no further—there are irreducible causal facts about how objects behave.

9.7 Conclusion I have argued that issues regarding the ontology of properties have a significant impact upon what kinds of analyses of powers causal theorists can offer. If you hold a realist causal theory of properties, then persisting causal powers are privileged over facts about the causal relation. For these causal theorists claim that universals (or tropes) are the ground of irreducible power in the world, and so because what causal relations occur depends upon the powers of the entities concerned, these irreducible powerful properties play an essential role in the analysis of causation. Even if standard conditional analyses of causal power concepts could be made to work, therefore, this would not reflect the underlying ontological priority of causal relations over causal powers. Nominalist causal theories of properties, on the other hand, reverse this order of ontological priority. Powerful sui generis properties are exchanged for basic concrete particulars and facts about what causal relations these particulars can enter into. Unlike realist causal theories, this leaves open the possibility of a reduction of these causal facts about the actual and possible behaviour of objects, but certainly no such account is in the offing here. What has been offered, however, is a reductive reading of Shoemaker’s claim that ‘properties are causal powers’. We have

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seen that the resulting form of nominalism has a number of significant advantages over rival accounts. Moreover, although its analysis of causal powers has much in common with Ryle’s ‘inference-ticket-type view’, it cannot be easily dismissed.³⁵ ³⁵ Many thanks to Toby Handfield, Joel Smith, Keith Allen, and Tom Smith for all their helpful comments. Thanks also to the participants of the ‘Dispositions and Causation’ conference, Bristol and HPS’s Departmental Seminar, Cambridge.

10 Why do the Laws Explain Why? Marc Lange

What exactly is this criterion, that laws must explain the phenomena? ... What makes laws so well suited to secure us this good? When laws give us ‘satisfying’ explanations, in what does this warm feeling of satisfaction consist? There are indeed philosophical accounts of explanation, and some mention laws very prominently; but they disagree with one another, and in any case I have not found that they go very far toward answering these questions. Bas van Fraassen (1989: 31) To tell a physicist that the laws of nature are not explanations of natural phenomena is like telling a Tiger stalking prey that all flesh is grass. Steven Weinberg (1992: 28–9)

10.1 From where do the laws derive their explanatory power? Long before Hempel and Oppenheim formulated their deductivenomological model of scientific explanation in 1948, laws of nature were explicitly recognized as possessing distinctive explanatory power. For example, in his 1841 anatomy textbook, Jacob

why do the laws explain why?  Henle (the founder of modern histology) wrote, ‘To explain a physiological fact means in a word to deduce its necessity from the physical and chemical laws of Nature.’¹ What gives the natural laws their special power to explain? This question can be sharpened. Henle refers to deducing a phenomenon’s ‘necessity’ from the laws. Presumably, for a phenomenon to derive necessity from the laws, the laws themselves must possess necessity. However, the laws are widely held to be contingent facts.² How, then, can they possess necessity? Of course, we might say that they possess ‘nomic’ (a.k.a. ‘natural’, ‘physical’) necessity even though they are not logically, conceptually, mathematically, or metaphysically necessary. But if ‘p possesses nomic necessity’ just means that p follows logically from the laws, then why does ‘nomic necessity’ count as a variety of necessity? It must deserve to be so designated, or else we could just as well say that there is a variety of ‘necessity’ possessed by all and only the logical consequences of, for example, ‘George Washington was the first President of the United States.’ To explain why the laws explain why, one might assert that all scientific explanations are causal and that laws explain by connecting causes to effects. We would then need an account of causation to understand how laws contribute to creating causal connections. However, we do not need to wait for an account of causation in order to investigate why the laws explain why, because not all scientific explanations are causal. Some laws explain others, for example, and those explanations are not causal. Indeed, that p is a law ¹ T. H. Huxley found this passage memorable enough to place atop his student notepad in 1845 (Morris 1997: 28). ² This view is disputed by scientific essentialists (such as Bird (2005b); Collier (1996); Ellis and Lierse (1994); Ellis (2001); Fales (1993); Harr´e and Madden (1975); T. Nagel (1979: 186); Sankey (1997); Shoemaker (1998); Q. Smith (1996–7); Swoyer (1982); and Tweedale (1984)), who ascribe metaphysical necessity to the laws. See Lange 2004b, 2005b criticizing the essentialists’s account of the relation between laws and counterfactuals. Nevertheless, one motivation for essentialism is easily understood: how can the laws possess the necessity requisite for their explanatory power if they are contingent? Essentialists argue that their view can account nicely for the laws’ necessity and explanatory power. My project in this paper is to see whether an account of laws as contingent truths can do so.

 marc lange explains why p is the case, and this explanation is not causal. For instance, suppose it is a fundamental law of nature that between any two point bodies that carry Q and Q statcoulombs (respectively) of positive electric charge and have been at rest, R centimeters apart, for at least R/c seconds, there is a mutual electrostatic repulsion of QQ /R2 dynes, for any values of Q, Q , and R. This law (‘Coulomb’s law’) explains why there is in fact such a force between the bodies in every such pair, throughout the universe’s entire history. It is no accident or coincidence that in every such case, there is such a force; it does not reflect some special condition that just happened to prevail in each actual case. The reason for this regularity p is that p is required by law; even if pairs had existed under different conditions, it would still have been the case that p. If Coulomb’s law is fundamental, then the law requiring p is none other than that p is a law; there is no other explanation. And this explanation is not causal, since it would be a category mistake to regard a law of nature as a cause. (For instance, a law has no specific spatiotemporal location, unlike a cause.) A law is a ‘because’ but not a cause. As I mentioned, the laws’ explanatory power is puzzling. The laws explain by virtue of their necessity. For example, Coulomb’s law explains why there is in fact such a force between the bodies in every such pair, throughout the universe’s entire history: there had to be, so there was. But the laws of nature are contingent facts. How, then, can they be necessary so as to be empowered to make other facts necessary, thereby explaining them? The laws have a paradoxical-sounding status: necessary and contingent. The laws’ explanatory power is especially puzzling in the case of the most fundamental laws, whatever they really are. Suppose Coulomb’s law to be one of them. A derivative law (such as the law concerning the electrostatic forces exerted by uniformly charged spheres) may derive its necessity from the fundamental laws (in this case, Coulomb’s law). But the fundamental laws possess their necessity without inheriting it from any other law. So consider the facts in virtue of which Coulomb’s law is a law—the facts that make it a law: its ‘lawmakers’. If the lawmakers are necessary, then what

why do the laws explain why?  makes them necessary? If their necessity is an ontological primitive, then why is it a kind of necessity? Why does it deserve to be so called? (If it does not merit the title, then it cannot endow the laws with their explanatory power.) If, on the other hand, the lawmakers’s necessity is constituted by other facts, then are those facts necessary or not? If they are necessary, then the regress continues as we turn our attention to what makes those facts necessary. But if the lawmakers are not necessary, or if their ‘necessity’ is constituted by facts that are not themselves necessary, then once again, the laws’ ‘necessity’ is bogus; a law has no necessity to bestow upon what it is supposed to explain. Inevitability cannot be inherited from what isn’t inevitable; what is thereby endowed would then be mere ‘conditional inevitability’.³ In order for q’s obtaining to help make it the case that p had to obtain, it must be that q had to obtain. ³ Of course, I use the word ‘inevitable’ advisedly, since a statistical explanation cannot make its explanandum inevitable. But I am concerned with p’s lawhood explaining p, which is not a statistical explanation. (However, the laws’ modal force makes itself felt in statistical explanations as well. Whether there is a single sense of scientific explanation or several senses, some vaguely derivative from others, is something that I cannot address here. Likewise, I shall not consider whether explanations that cite initial conditions are derivative from those citing none by taking the form ‘p because it is a law that p’.) Some philosophers deny that there is any modal force behind scientific explanations, and so would presumably deny that the laws have to possess a variety of necessity in order for them to possess their characteristic explanatory power. Such philosophers would presumably reject my use of ‘inevitable’, even as an intuition pump. Salmon (1985) famously distinguishes the modal conception of scientific explanation from the ontic and the epistemic conceptions. By rejecting the modal conception of scientific explanation, one might seem to make it easier to account for the laws’ explanatory power (since the laws’ modality is no longer at issue). But perhaps one makes it too easy: if the laws’ modality is not responsible for their explanatory power, then why can’t accidents function as laws do in scientific explanations? My goal is to see what laws would have to be like in order for them to possess explanatory power within the constraints of a roughly modal conception of scientific explanation. That such a conception would have to be stretched somehow to accommodate statistical explanations is a familiar problem. My concern is that the origin of the laws’ explanatory power remains mysterious even on a modal conception of scientific explanation. Furthermore, as I mentioned in note 2, essentialists have attacked Lewis’s and Armstrong’s accounts of law as failing to supply laws with the modal force required for laws to possess their explanatory power. Essentialists issue the same challenge to any account of laws as contingent truths. The essentialists’ critique plainly presupposes a modal conception of scientific explanation. My aim here is to develop an alternative to essentialism about laws that accounts for the laws’ explanatory power and directly takes on the essentialists’ challenge rather than dodging it by arguing that significantly less modal force suffices for explanation than essentialists believe.

 marc lange This is the sort of regress that ought to bother us. In epistemology, for instance, it is easy to get a regress started by pointing out that the belief that p cannot be justified by the belief that q unless the belief that q is justified in some manner prior to the belief that p. The belief that p cannot ‘inherit’ positive justificatory status from the belief that q unless the latter belief has ‘earned’ this status already. How this regress comes to an end is the question that has vexed foundationalists, coherentists, infinitists, and others who populate the epistemological menagerie. A similar regress ought to bother theorists of natural law and scientific explanation. Presumably, the fact that q cannot render necessary the fact that p unless the fact that q has necessity to lend; otherwise, p’s deriving from q gives p only a ‘conditional’ necessity—a condition that, in the case of the fundamental laws, is undischarged by other laws. As Blackburn (1993: 53) remarks: if p’s necessity is constituted by F and ‘F just cites that something is so [but F] does not have to be so, then there is strong pressure to feel that the original necessity has not been explained or identified, so much as undermined.’ Van Fraassen (1980: 213), who is more concerned than Blackburn with scientific explanation, expresses the same problem thus: To posit a micro-structure exhibiting underlying regularities, is only to posit a new cosmic coincidence. That galvanometers and cloud chambers behave as they do, is still surprising if there are electrons, etc., for it is surprising that there should be such regularity in the behavior of electrons, etc.

If the vaunted explanatory power of the laws is merely the power to render various facts inevitable given the laws, then it remains unclear why the laws are more fit to explain than other facts are; for example, the fact that George Washington was the first President of the United States can render various other facts ‘inevitable’ given itself. Of course, all explanations come to an end somewhere—that is to say, all explanations that we actually offer in practice. You do not have to know why it is that q obtains in order for q to answer

why do the laws explain why?  your question ‘Why p?’ Likewise, by citing my belief that q, I may succeed in justifying my belief that p without having to go on and justify my belief that q; every justification that we give comes to an end somewhere. But although my belief that q need not ever have been the target of an act of justifying in order for me to use it in another such act (to answer your question ‘How do you know that p?’), my belief that q must have the status of being justified in order for it to help contribute to another belief’s having that status. Likewise, the facts constituting p’s lawhood must have the status of being necessary in order for them to help make p necessary (i.e., a law) and thereby explain why p obtains.⁴ That every explanation given in practice comes to an end somewhere does not entail that there is an end to the regress consisting of (i) the regularity involving the electrostatic forces between pairs of point charges at rest, (ii) the fact that this regularity is necessary (i.e., Coulomb’s law, which thereby explains the regularity), (iii) some fact that helps to make Coulomb’s law necessary, (iv) some fact that in turn helps to constitute the necessity of the previous fact, and so on. I shall suggest that each of these facts possesses a species of necessity full stop, not merely necessity conditional on some fact appearing later in the regress. Consequently, each fact in the regress can help to constitute the necessity of its predecessor in the regress. Thus, none of these necessities is primitive. Each fact in the regress is necessary in virtue of facts at the next step in the regress—which, being themselves necessary, are able to constitute its necessity. In the following section, I shall examine some accounts of what laws are in virtue of which they possess their characteristic explanatory power. Perhaps one of these accounts can explain why the fact that p is a law deserves to count as explaining why p obtains. For the moment, I wish only to emphasize that we ⁴ That a belief ’s ‘justification’ (or a fact’s ‘explanation’) may refer either to the act of justifying (explaining) it or to its status of being justified (having an explanation), a status that it can possess even if it has never been the target of such an act, is a case of the ‘notorious ‘‘ing–ed’’ ambiguity’ (Sellars 1963: 154).

 marc lange cannot dodge this question simply by responding that laws are appropriate ‘givens’ because scientific explanation just is derivation from the laws. Hempel (2001: 337) rightly points out that if the facts cited by p’s explanation must themselves have explanations in order for them to explain why p obtains, then an infinite regress beckons. I agree. Hempel says that the infinite regress would be unacceptable because ‘we will normally require of an explanation that it be expressed in a finite number of statements’. Although finitude seems appropriate to require of p’s ‘explanation’ in the sense of some (known or unknown) description of various facts that is sufficiently complete or relevant to satisfy certain concerns, finitude does not seem mandatory for p’s ‘explanation’ in the sense of the facts in virtue of which p had to obtain. The threat of a regress is no reason for denying that the facts that constitute p’s lawhood (that make p necessary) must themselves have explanations rendering them necessary in order for them to be capable of making p necessary—any more than (most) epistemologists are motivated by the threat of a regress to reject the view that the belief that q must already have the status of being justified in order for it to justify the belief that p. Epistemologists try to deal somehow with the threat rather than suggest that the status of being justified means merely ‘given certain premises’. I shall try to deal with the analogous threat for the case of scientific explanation. There are no further laws to make the fundamental laws necessary. Rather, the fundamental laws seem to be explanatorily self-sufficient: Coulomb’s law is able to explain (to render certain regularities necessary) without in turn deriving its explanatory power (its necessity) from other laws. But if there is nothing in virtue of which it is necessary, then it seems to ‘explain’ merely by rendering certain facts necessary given itself. Even if a scientific explanation is precisely a derivation from the laws (and perhaps certain initial conditions), it remains unclear why we should be interested in scientific explanations—why the lawhood of Coulomb’s law deserves to be taken as a given. Henle himself seems

why do the laws explain why? 

sensitive to this puzzle about scientific explanation. Immediately after identifying laws as powering explanations, he admits, ‘It is true, even these laws offer no explanation as to the ultimate grounds.’ (Nordenskiold 1936: 398) But then how do they explain?⁵ I shall propose a conception of natural laws that accounts for their necessity (and hence their explanatory power) while recognizing their status as contingent facts. I will explain what gives the laws their distinctive variety of necessity, being careful not merely to stipulate that the laws merit being characterized as necessary. I will suggest that the laws are laws in virtue of certain contingent facts, that each of these facts possesses a certain species of necessity, that it derives its necessity from other contingent facts that are likewise necessary, and so on endlessly, without circularity—since a fact cannot help to explain itself. All of these facts are among the facts in virtue of which the laws are laws. That is why the fundamental laws appear to be explanatorily self-sufficient: able to explain without having explanations themselves. Each of the lawmakers is necessary in virtue of other lawmakers. Throughout I will avoid any conception of what scientific explanations are that is tailored in an ad hoc manner to an antecedent metaphysical account of what laws of nature are. To better appreciate these various desiderata, I will now look briefly at whether some other proposals in the literature are able to account for the laws’ explanatory power.

10.2 Some answers on the market Let’s look briefly at some answers to our title question that others have given. Here is how Hempel explains why the laws explain why: A D-N explanation answers the question ‘Why did the explanandumphenomenon occur?’ by showing that the phenomenon resulted from ⁵ Parfit (1992: 5) writes, ‘We should not claim that, if an explanation rests on a brute fact, it is not an explanation.’ However, he immediately concedes, ‘But we might claim something less. Any such explanation may, in the end, be merely a better description.’

 marc lange certain particular circumstances, specified in C1 , C2 , ... , Ck , in accordance with the laws L1 , L2 , ... , Lr . By pointing this out, the argument shows that, given the particular circumstances and the laws in question, the occurrence of the phenomenon was to be expected; and it is in this sense that the explanation enables us to understand why the phenomenon occurred. (Hempel 1965: 337)

Here we have a characteristically positivist attempt to analyze a metaphysical notion (explanation) in epistemological terms (expectation). I take this strategy to be a non-starter. Armstrong (1978, 1983, 1997) analyzes laws as contingent relations of nomic necessitation N holding among universals: N(F,G) makes it a law that all F’s are G. Although such a relation could have failed to hold, there is (at least in the case of a fundamental law) no reason why it holds. How, then, can it explain? Armstrong says that the law that p makes it the case that p. But this ‘making’ is merely stipulated to be a consequence of ‘nomic necessitation’. Lewis is correct in criticizing Armstrong for this ad hoc device: [H]ow can the alleged lawmaker impose a regularity? ... Don’t try defining N in terms of there being a law and hence a regularity—we’re trying to explain lawhood. And it’s no good just giving the lawmaker a name that presupposes that somehow it does its stuff, as when Armstrong calls it ‘necessitation’. If you find it hard to ask why there can’t be F ’s that are not G’s when F ‘necessitates’ G, you should ask instead how any N can do what it must do to deserve that name. (Lewis 1986c: xii; cf. Lewis 1983b: 366; van Fraassen 1989: 98)

Without an account of why N(F,G) qualifies as a variety of ‘necessity’, it remains mysterious how p is rendered necessary, and thereby explained, by the fact that it is a law that p. We could, of course, simply stipulate that scientific explanation of p involves p’s derivation from nomic-necessitation relations. But this move seems just as unsatisfactory as the ordinary-language ‘dissolution’ of the problem of justifying induction. If ‘justification’ of a prediction in science simply means ‘by induction’ and if ‘explanation’ of a

why do the laws explain why?  fact in science simply means ‘by law’, then although it is pointless to ask why inductive arguments justify and why laws explain, we can still ask why we should care about giving ‘justifications’ and ‘explanations’. However, Lewis’s criticism of Armstrong’s account as ad hoc may boomerang against his own account (Lewis 1973b, 1983b, 1986c, 1994a) of laws as roughly the generalizations in the deductive system of truths possessing the best combination of simplicity and strength. The question ‘Granted that p follows from the generalizations in the best deductive system, why does p obtain?’ remains an open question. It is unclear why p’s derivation from laws so understood deserves to be called a scientific explanation—a reason why p holds. Lewis himself seems to downplay the need to explain why the laws explain: If you’re prepared to grant that theorems of the best system are rightly called laws, presumably you’ll also want to say that they underlie causal explanations; that they support counterfactuals; that they are not mere coincidences; that they and their consequences are in some good sense necessary; and that they may be confirmed by their instances. If not, not. It’s a standoff—spoils to the victor. (Lewis 1994a: 232)

Yet it seems ad hoc to say that laws are necessary (and so make their consequences necessary, thereby explaining them) in virtue of belonging to the best system. Of course, Lewis is satisfied with Humean stand-ins for genuine necessity. On Lewis’s picture, events are metaphysically prior to laws, and so laws cannot genuinely explain events. Lewis suggests that we reconstrue explanation so that it does not require any such metaphysical priority. Lewis (1986c: xv–xvi) insists that whatever entities a philosopher construes chances to be, those entities have got to deserve to be called ‘chances’. They can’t merely be stipulated to be chances; beliefs about them must rationally constrain our opinions in the way that beliefs about chances do (namely, in accordance with the Principal Principle). But the same principled stand Lewis takes

 marc lange regarding a satisfactory account of chances should also be taken regarding a satisfactory account of laws. Generalizations in the best system cannot merely be stipulated to be laws. They must deserve to be called ‘laws’ by (among other things) explaining. Lewis might have thought that generalizations in the best system explain because to explain p is to unify p with other facts, and the greatest unification is achieved by integrating p with the deductive system of truths possessing the optimal combination of simplicity and strength. On the other hand, it seems question-begging to construe ‘unification’ in exactly this way, as van Fraassen (1989: 48–51) has argued, and so it remains ad hoc to say that explanatory power derives from membership in the Lewisian best system. That explanations unify is an idea that has been developed in different ways by different philosophers: in terms of explanations reducing the number (of types) of unexplained facts, for instance, or in terms of explanations deriving many facts through arguments taking the same form (see, e.g., Kitcher 1989). Let’s consider briefly what it would take for the unificationist picture to account for the laws’ explanatory power. Henle seems to have thought that although laws are contingent, their capacity to unify gives them the capacity to explain. The full passage from Henle’s textbook is as follows: To explain a physiological fact means in a word to deduce its necessity from the physical and chemical laws of Nature. It is true, even these laws offer no explanation as to the ultimate grounds, but they make it possible to combine a mass of details under one point of view. (Nordenskiold 1936: 398)

Of course, there are many ways to ‘combine’ a mass of details. One might simply conjoin them, for instance. But a mere conjunction is not explanatorily prior to its conjuncts. If a ‘point of view’ somehow captures the mass of details in a more orderly or compact form (e.g., integrates them with the ‘best system’, or derives them from very few facts using very few kinds of arguments), then although such a thing may be convenient or elegant, it is not

why do the laws explain why?  yet clear why it thereby counts as explanatory—that is, why it counts as a reason why those details hold, why it counts as prior to those details in some sense that is not ad hoc. A unificationist picture must include some account of why a law captures a mass of details so as to explain them. If p’s lawhood unifies various facts by showing how they are all inevitable given p’s lawhood, then once again, those facts are not thereby made inevitable unless p’s lawhood is inevitable. For that matter, if p has many, diverse consequences, and p unifies and hence explains those facts, then it is not clear how p’s lawhood, in explaining p, thereby increases the unity; no additional facts are integrated by this explanation that weren’t already unified by p. On the other hand, if the bare fact that p cannot explain its various consequences, but only p’s lawhood can explain them, then we need some account of why this is so. Merely to define ‘unification’ as ‘under law’ remains unilluminating. I shall now look more closely at one final, recent proposal. Woodward and Hitchcock (2003a, 2003b) have suggested that an explanatory generalization ‘can be used to answer a range of whatif-things-had-been-different questions’ (2003a: 4) and thereby ‘tells us what [the explanandum] depends on’, explaining it. This approach has several advantages over some of its predecessors. First, it avoids the charge of ad-hocness because answering whatif-things-had-been-different questions seems intuitively to have something to do with explaining (and in this respect differs from a fact’s deriving from nomic-necessitation relations or from generalizations in the best system). That Coulomb’s law helps to explain why there is a certain force between two bodies seems plausibly bound up with the fact that Coulomb’s law correctly specifies how that force would have been different, had the two bodies’ charges and separation been different in various ways. Secondly, the capacity of Coulomb’s law to specify correctly what would have happened under these conditions reflects a characteristic feature of laws that has long been recognized: their intimate relation to counterfactuals. In scientific practice, the natural laws are called

 marc lange upon to tell us what would have been the case, had things been different in some nomically possible way. For example, were Uranus’s axis not so nearly aligned with its orbital plane, then conditions on Uranus would have been different, but the laws of nature would have been just the same (which is why conditions on Uranus would have been different). Scientific practice thereby suggests a principle that I shall call ‘nomic preservation’ (NP). NP: For any counterfactual supposition q, it is true that had q been the case, the natural laws would have been no different—as long as q is nomically possible, i.e., logically consistent with all of the m’s (taken together) where it is a law that m⁶ where I shall henceforth reserve lower-case letters m, q, etc. for sentences purporting to state facts entirely governed by laws rather than concerning which facts are laws. (Therefore, NP does not cover counterfactual suppositions such as ‘Had it been a law that ...’ or ‘Had it been an accident that ...’.) Although the truth-values of counterfactual conditionals are notoriously context-sensitive, NP is intended by its advocates to hold in all contexts, since it purports to capture the logical relation between laws and counterfactuals, and logic is not context-sensitive. Principles roughly like NP have been defended by Bennett (1984); Carroll (1994); Chisholm (1946); Goodman (1983); Horwich (1987); Jackson (1977); Mackie (1962); Pollock (1976); Strawson (1952), and many others.⁷ Woodward ⁶ Advocates of principles like NP must intend to include (e .g.) the logical, mathematical, conceptual, and metaphysical necessities among the natural laws. This seems reasonable; if p possesses a higher grade of necessity, then it possesses all lower varieties ‘by courtesy’. ⁷ In Lange 2000: 58–82, I examine various sorts of challenges to NP, including eccentric contexts where counterfactuals seemingly in violation of NP are properly held to be true. Notably, Lewis (1986c: 171) rejects NP (even though NP appears to reflect scientific practice). Lewis’s argument is that if we insist that the laws would have been no different, had Jones missed his bus to work this morning, then apparently, we must say (if the world is deterministic) that the world’s state billions of years ago would have been different, had Jones missed his bus. That sounds counterintuitive. Although I cannot discuss this issue adequately here, I am inclined to think that q
m (‘Had q been the case, then m would have been the case’) says not that m is true in the closest q-world, but rather that (roughly speaking) m is true in a non-maximal situation that consists just of the relevant

why do the laws explain why?  and Hitchcock exploit the fact (ensured by NP) that Coulomb’s law would still have held, had the bodies’ charges or separation been different, and so that Coulomb’s law correctly specifies the forces that those bodies would have experienced under those circumstances. I shall return to NP in the next section. However, let me mention four difficulties encountered by the Woodward–Hitchcock account of why the laws explain why. First, Woodward and Hitchcock emphasize that for a generalization to be explanatory, it suffices that there exist a range of what-if-thingshad-been-different questions that it can correctly answer. (Roughly speaking, the broader the range, the deeper the explanations that the generalization supplies. Woodward and Hitchcock do not regard the ‘laws’ as uniquely explanatory; they regard any generalization for which there exists such a range as explanatory.) Consider, then, a generalization (g) that is the same as Coulomb’s law except that it predicts a vastly different force for a single combination of Q, Q , and R—a combination that happens to go forever uninstantiated. So g is true, since it departs from Coulomb’s law only in a circumstance that is never realized. Moreover, there exists a range of what-if-things-had-been-different questions that g correctly answers—nearly the same range as Coulomb’s law does. Yet g is not nearly as explanatorily potent as Coulomb’s law. In fact, I don’t think that g has any explanatory power at all (at least in fundamental physics).⁸ A given actual case conforms to g fragment of the closest q-world. In a context where we should not ‘backtrack’ in assessing counterfactuals, the relevant fragment does not concern the events responsible for bringing q about (Lewis’s ‘small miracle’). Therefore, an actual law would still have been true, had q, since the miracle (which violates the actual law) is ‘offstage’. The world’s state billions of years ago likewise stands outside of the relevant fragment of the closest q-world. So when we occupy a non-backtracking context and consider what would have happened, had Jones missed his bus, we are not interested in whether the world’s state billions of years ago would have been different. If we focus our attention upon q’s past light cone (e .g., in discussing how remarkable a deterministic world would be), then we enter a (backtracking) context where it is true that the world’s state billions of years ago would have been different, had Jones missed his bus. In neither context is a counterfactual of the form (q
a violation of the actual laws) true. ⁸ Here’s why I said ‘at least in fundamental physics’. Some sub-field of physics might be interested only in a limited range of the conditions allowed by the fundamental laws

 marc lange not because all cases have to do so, but rather because all cases have to obey Coulomb’s law, and the demands of Coulomb’s law happily coincide with g’s demands in the given case. Likewise, all actual cases conform to g not because g must be obeyed, but merely as an accidental byproduct of their complying with Coulomb’s law—accidental in that g would not have resulted from Coulomb’s law, had a certain combination of Q, Q , and R happened to be instantiated. Here is a second, closely related difficulty. Consider the generalization that whenever the gas pedal of a certain car is depressed by x inches and the car is on a dry, flat road, then the car’s acceleration is f(x). According to Woodward and Hitchcock, this generalization can help to explain the car’s acceleration on a given occasion because (following Haavelmo 1944: 29) had the pedal on that occasion been depressed to a greater or lesser degree, then the car’s acceleration would still have been correctly specified by the above generalization. However, these counterfactuals would themselves not still have held, had the car’s engine been modified in various ways. (Here we have our first example of a nested counterfactual.) It is difficult to regard the above counterfactuals as exhibiting the generalization’s explanatory power considering that their holding is something of a fluke—so precariously resulting from prevailing conditions. (Those conditions, rather than the generalization, should presumably be part of the explanation.) The generalization’s correctly answering various what-if-thingswould-have-been-different questions seems too accidental to give the generalization explanatory power. We thus return to one of our original questions: if the truths supposedly responsible for a given generalization’s explanatory power are not themselves necessary, then how can that generalization render facts necessary so as to explain them? of physics. If the uninstantiated circumstance in which the alternative to Coulomb’s law diverges from Coulomb’s law involves conditions outside of the limited range of interest to the sub-field, then the alternative to Coulomb’s law might have explanatory power in that field.

why do the laws explain why?  Here is another example where a generalization’s capacity to answer a certain range of what-if-things-had-been-different questions is itself too fragile to supply the generalization with explanatory power. Suppose I am asked why all U.S. Presidents have (as of this writing) been male, and I answer that the reason is that all persons nominated for President by major U.S. parties have been male, so no matter which candidate had won the election, all Presidents would have been male. This generalization specifies that the explanandum would still have held under certain unrealized conditions (e.g., had the Republican candidate won in the election of 1912).⁹ However, it is really the conditions that are responsible for this generalization about nominees that explain why all U.S. Presidents have been male. Had these conditions been different, then perhaps a woman would have been President if the Republican candidate had won in the 1912 election. (That was another nested counterfactual.) Now for a third difficulty with the Woodward–Hitchcock proposal. The range of what-if-things-had-been-different questions that p answers seems to be the same as the range of what-if-thingshad-been-different questions that ‘It is a law that p’ answers. However, it might be argued that ‘It is a law that p’ has explanatory power, whereas the bare fact that p does not. For example, there is a given force between two bodies not because Coulomb’s law is true, but because it is a law. Of course, the mere fact that Coulomb’s law is true suffices to entail that any two such bodies do feel such a force. But that they must feel such a force requires that the equation hold as a matter of law. ⁹ I am not suggesting that this regularity is explanatory according to Woodward and Hitchcock. It is not, on their view, because it does not answer questions about what would have happened, had the quantities in the regularity taken on different values. I do not see why they privilege those sorts of counterfactual suppositions; an ecological law concerning the relation between an island’s biodiversity and its area, for example, presumably derives some of its explanatory force from the fact that the same relation would still have held even if different species had evolved (and even if matter had been a continuous rigid substance rather than corpuscular), though the law’s equation contains no such variables, but merely relates biodiversity to area. (See Lange 2002, 2004a.) But this is not my concern here.

 marc lange There is a fourth, related difficulty. Woodward and Hitchcock purport to explain how a law explains a regularity, as when Newton’s gravitational-force law (and the Earth’s mass) explain the regularity that all bodies in free fall near the Earth’s surface accelerate at approximately 9.8 m/s2 . According to Woodward and Hitchcock, the gravitational-force law explains the regularity concerning free fall because the law specifies correctly what alternative regularity would have obtained, had (say) the Earth’s mass taken on some other value. Because the law includes variables that the regularity does not, the law specifies what the new regularity would have been, under other values of those variables. However, ‘It is a law that p’ includes no variables that are absent from p. So ‘It is a law that p’ cannot specify the extent to which events would have departed from p under other conditions. (For instance, Newton’s gravitational-force law obviously does not specify by how much the gravitational force would have departed from being inversely proportional to the square of the separation, had certain nomically impossible conditions obtained—whereas Newton’s gravitational-force law does specify by how much freefall acceleration would have departed from 9.8 m/s2 had Earth’s mass been twice as great.) Hence, the Woodward–Hitchcock account cannot explain why p is explained by the fact that it is a law that p.¹⁰ I shall offer an account of the laws’ explanatory power that also focuses on counterfactual conditionals. But unlike Woodward and Hitchcock, I shall draw a sharp distinction between laws and accidents, and I shall try to account for why ‘It is a law that p’ explains p. Furthermore, I shall argue that a generalization’s answering some range or other of what-if-things-had-been-different questions is insufficient to give it explanatory power. A particular ¹⁰ Woodward and Hitchcock regard many generalizations as explanatory despite not being traditionally considered ‘laws’; Woodward and Hitchcock do not believe that there exists a sharp, important distinction between laws of nature and accidental generalizations. Therefore, I believe, they would not be bothered by the third or fourth objections I have raised. In addition, I believe that they would regard as oversimplified an ‘explanation’ of the form ‘p because it is a law that p’.

why do the laws explain why? 

kind of range of invariance under counterfactual suppositions is required for a generalization to qualify as necessary. Furthermore, the generalization’s invariance across that range of counterfactual suppositions cannot itself be precarious; its invariance must be invariant, and so forth all the way down, in order to generate explanatory power.

10.3 Laws: necessary yet contingent NP entails that if it is a law that p, then p would still have been true, had q been the case—for any q that is ‘nomically possible’: logically consistent with all of the m’s (taken together) where it is a law that m. Obviously, no accident would still have been true under every q that is nomically possible, since ∼p is nomically possible if p is an accident. But the range of counterfactual suppositions being considered here (every nomically possible q) is designed expressly to suit the laws. What if we allowed any logically closed set of truths to pick out for itself a convenient range of counterfactual suppositions: those with which all of the members of that set (taken together) are logically consistent? Let’s call the set ‘stable’ exactly when (whatever the conversational context) the set’s members would all still have held, under every such counterfactual supposition—even under however many such suppositions are nested. (Nested counterfactuals are important. Recall that my second objection to the Woodward–Hitchcock proposal was that the relation f(x) between the gas pedal and the car’s acceleration seems too accidental to be explanatory. Nested counterfactuals help to cash out this thought: although there obtain various counterfactuals of the form ‘Had the gas pedal been depressed by x inches with the car on a dry, flat road, then the car’s acceleration would have been f(x)’, there fail to obtain various nested counterfactuals of the form ‘Had the car’s engine been modified ..., then had the gas pedal been depressed by x inches with the car on a dry, flat road, the car’s acceleration would have been f(x).’)

 marc lange More precisely: Consider a non-empty, logically closed set  of truths p. Then I define  is ‘stable’ exactly when for any member p of  and any claims q, r, s... each of which is logically consistent with all of the members of  taken together (e.g.,  ∪ {q} is logically consistent), the subjunctive conditionals (which will be counterfactuals if q, r, s... are false) q
p, r
(q
p), s
(r
(q
p)), etc. hold in any context.¹¹

The intuitions behind NP (which are manifested in scientific practice) suggest that the laws (together with the logical, mathematical, conceptual, and metaphysical necessities—and all of the logical consequences thereof) form a stable set. In contrast, the analogous closure of Reichenbach’s (1954: 10) favorite accident, ‘All solid gold cubes are smaller than a cubic mile’, is unstable, since had Bill Gates wanted to build a gold cube exceeding a cubic mile, then I dare say there would have been such a cube. Likewise, the gas-pedal generalization that I mentioned in the previous section does not belong to a stable set unless that set also includes a description of the car’s engine (since had the engine contained six cylinders instead of four, the gas-pedal generalization might have failed to hold). Having fortified the set with a description of the car’s engine, we find the supposition that the engine contains six cylinders to be logically inconsistent with the set, and so the gas-pedal generalization’s failure to be preserved under this counterfactual supposition is no obstacle to the set’s stability. But now the set, to be stable, must also include a description of the factory that manufactured the engine (since had that factory been different, the engine might have been ¹¹ Strictly speaking, it is redundant to include the requirement that the members of a stable set be true. If p is false, then if q is a logical truth, (q
p) is false, and so no set to which p belongs is stable. (I have just asserted that if q is a logical truth, then (q
p) is true only if p is true. I have doubts about the if direction; see note 25.)

why do the laws explain why? 

different). For that matter, suppose that I am not wearing an orange shirt, and consider the counterfactual ‘Had either I been wearing an orange shirt or the gas-pedal generalization failed to hold.’ Is ‘... then the gas-pedal generalization would still have held’ true in all contexts? I think not. Therefore, to be stable and include the gas-pedal generalization, the set must also include the fact that I am not wearing an orange shirt. I conclude that the only stable set containing the gas-pedal generalization is the set containing all truths p. Accordingly, I suggest that stability distinguishes the laws from the accidents in that no set  containing an accidental truth is stable (except for the set of all facts p, which is trivially stable since no counterfactual supposition q is logically consistent with all such facts).¹² The sort of argument I have just made could presumably be made regarding any logically closed set of truths p that includes some of the accidents but not all of them.¹³ I have suggested that the closure of the laws forms a stable set and that no set containing an accident is stable (except for the trivial case where the set contains all of the facts m). Are there any other stable sets? Stability possesses an interesting formal property: for any two stable sets, one must be a proper subset of the other. In other words, the stable sets come in a natural hierarchy; there is a total ordering. ¹² I have argued elsewhere (2000, 2002, 2004a) that the laws of an inexact (a.k.a. special) science need not be stable simpliciter, as long as they form a set that is stable ‘for that field’s purposes’. Thus I agree with Woodward and Hitchcock that the explanatory generalizations include some facts that are not laws of physics and that philosophers do not traditionally consider to be laws. ¹³ Actually, I am willing to acknowledge the possibility in principle of a logically closed set  of truths, containing some but not all of the accidents, where each member m of  would still have held under any q with which every member is logically compatible. But if such a set were to exist, I claim, its invariance would be a fluke; although q
m holds, there is some r that is logically consistent with every member of  for which r
(q
m) does not hold, or there is some more highly nested counterfactual under which m fails to be preserved. In contrast, it is the case not only that had we tried to break the laws, we would have failed, but also that had we had access to 23rd-century technology, then had we tried to break the laws, we would have failed. This is one reason why we need nested counterfactuals in the definition of ‘stability’. Shortly we will see one nice consequence of including those nested counterfactuals.

 marc lange Here is the proof: Show: If  and  are distinct stable sets, then one must be a proper subset of the other. Proof by reductio: Suppose that sets  and  are stable, t is a member of  but not of , and s is a member of  but not of . Then (∼s or ∼t) is logically consistent with . Since  is stable, every member of  would still have been true, had it been the case that (∼s or ∼t). In particular, then, t would still have been true, had it been the case that (∼s or ∼t). That is, (∼s or ∼t)
t. Since t and (∼s or ∼t) would have held, had (∼s or ∼t), it follows that ∼s would have held, had (∼s or ∼t). Of course, this does not mean that ∼s is a member of , merely that ’s stability demands that (∼s or ∼t)
∼ s. Now let’s apply similar reasoning to . Since (∼s or ∼t) is logically consistent with , and  is stable, every member of  would still have been true, had it been the case that (∼s or ∼t). In particular, then, s would still have been true, had it been the case that (∼s or ∼t). That is, (∼s or ∼t)
s. But we have now reached an impossible conclusion: (∼s or ∼t)
(s & ∼s)!

This last would be for something logically impossible to occur in the ‘closest world’ where a given logical possibility is realized. (I shall return to this idea in a moment.) That the laws’ closure is stable does not preclude certain of its proper subsets from being stable. For instance, perhaps the logical closure of the basic laws of motion qualifies as stable, since its members would still have held, even if the force laws had been different (e.g., even if electromagnetic forces had been somewhat stronger). With a hierarchy of non-trivially stable sets, there would be various grades of nomic necessity.

why do the laws explain why?  Since there may be a hierarchy of stable sets, I propose that m is a law if and only if m belongs to some (or, equivalently, the largest) nonmaximal stable set.¹⁴ We have here a way to draw a sharp distinction between the laws and the accidents. On this view, what makes the laws special, as far as their range of invariance is concerned, is that they are stable: collectively, taken as a set, the laws are as resilient as they could logically possibly be. Because each law helps to delimit the range of invariance that each other law must possess, in order for the whole set of laws to be stable, the laws form a unified, integrated whole. That is, lawhood is a collective affair, not an individual achievement, since p is a law exactly when p belongs to a nontrivially stable set.¹⁵ All of the laws would together still have held under every counterfactual supposition under which they could logically possibly all together still have held—that is, under every supposition with which they are all together logically consistent. No set containing an accident can make that boast non-trivially. A stable set is maximally resilient under counterfactual perturbations; it has as much invariance under counterfactual suppositions as it could logically possibly have. In this way, the relation between lawhood and membership in a nontrivially stable set ties nicely into the laws’ necessity. Intuitively, ‘necessity’ is an especially strong sort of persistence under counterfactual perturbations. But not all facts that would still have held, under even a wide range of counterfactual perturbations, qualify as ‘necessary’ in any sense. Being ‘necessary’ is supposed to be qualitatively different from merely being invariant under a wide range of counterfactual suppositions. The set of laws is maximally resilient—as resilient as it could logically possibly be. ¹⁴ By this definition, the logical, mathematical, conceptual, and metaphysical necessities also qualify as laws. For some purposes, however, we might want to construe the ‘laws’ more narrowly as the truths belonging to some nonmaximal stable set and not possessing any of these other varieties of necessity. ¹⁵ There is, then, a sense in which the laws’ unity is bound up with their lawhood, though my take on this idea obviously differs from Lewis’s as well as from the interpretation offered by those who identify the laws’ explanatory power as deriving from the unification they bring.

 marc lange For every set that is maximally resilient, I suggest, there is a variety of necessity that is possessed by all and only its members. No flavor of necessity is possessed by an accident, even by one that would still have held under many counterfactual suppositions (such as the gas-pedal generalization).¹⁶ Here is another argument that stability is associated with a variety of necessity. Suppose that q is possible and that p would have held, had q been the case. Then intuitively, p must be possible: whatever would have happened, had something possible happened, must also qualify as possible.¹⁷ Now what must the set containing exactly the necessities of some particular variety be like in order to respect the above principle? It says that if q is possible—that is to say, logically consistent with the relevant set—and if p would have held, had q been the case, then p must be possible—that is, logically consistent with that set. That is immediately guaranteed if the set is stable. (If q is logically consistent with a given stable set, then under the counterfactual supposition that q holds, every member of that set would still have held, and so anything else that would also have been the case must join the members of that set and therefore must be logically consistent with them.) On the other hand, look what happens if a logically closed but unstable set of truths contains exactly the necessities in some sense. Because the set is unstable, there is a counterfactual supposition q that is logically consistent with the set but where some member m of the set would not still have held under this supposition.¹⁸ That is to say, m’s negation might have held. But m, being a ¹⁶ Of course, the set of all truths p is stable. But I don’t see its ‘maximal resilience’ as giving it a corresponding flavor of necessity, since its stability arises from the fact that there are no counterfactual suppositions with which all of its members are consistent. We could, I suppose, take the set of all truths as corresponding to the zeroth grade of necessity, the degenerate case. (We could likewise weaken the notion of ‘stability’ so that the null set possesses stability, though again trivially.) ¹⁷ This is the same as the ‘possibility’ principle that Williamson (2005) endorses and deems ‘pretheoretically plausible’. ¹⁸ For simplicity, I have temporarily ignored the nested counterfactuals in the definition of ‘stability’. To accommodate them, we would have to add nested counterfactuals to ‘whatever would have happened, had something possible happened, must also qualify as possible’. For instance, we would have to add ‘had something possible happened, then

why do the laws explain why?  member of the set, is supposed to be necessary, so m’s negation is an impossibility. Therefore, if an unstable set contains exactly the necessities in some sense, then had a certain possibility (in that sense) come to pass, something impossible (in that sense) might have happened. This conflicts with an intuition slightly broader than the one we were looking at: namely, that whatever might have happened, had something possible happened, must also qualify as possible. Here is still another, perhaps more picturesque way to put this: If an unstable set contains exactly the necessities in some sense, then though some q-world is possible (in that sense), the closest q-world—or, at least, one of the optimally close q-worlds—is impossible (in that sense). This conflicts with the intuition that any possible q-world is closer to the actual world than is every impossible q-world. Hence, if a logically closed set of truths contains exactly the necessities in some sense, then that set must be stable. It seems plausible and fruitful to connect necessity to stability. What makes the set of logical truths and the set of natural laws alike is that they are both nontrivially stable sets. It is this commonality that makes both sorts of truths ‘necessary’. Stability allows different varieties of necessity to be given a unified treatment, but without suggesting that for every logically closed set of truths, there is a corresponding variety of necessity. As we have seen, the stable sets are not plentiful. (The logical consequences of ‘George Washington was the first President of the United States’, for example, do not form a stable set.) The hierarchy of stable sets explains how the laws could be necessary and yet contingent. Interestingly, this view takes a fact’s necessity not to be an individual achievement, but rather as a collective affair, since p possesses some flavor of necessity exactly when p belongs to a nontrivially stable set. Notice also that ‘stability’ is not defined in terms of law. Whereas NP uses laws to pick out the relevant range of counterfactual whatever would have happened, had something possible happened, must also qualify as possible’. In other words, if r is possible, q is possible, and r
(q
m), then m must be possible.

 marc lange suppositions, stability allows the set in question to do so. Thus, the notion of stability lets us break out of the notorious circle that results from specifying the nomic necessities as the truths that would still have held under every counterfactual supposition that is logically consistent with the nomic necessities. The laws’ stability accounts not only for their necessity and for their sharp difference from the accidents, but also for another important feature of lawhood: that the laws would all still have been laws, had q been the case, for any q that expresses a nomic possibility. Suppose m is a member of , a stable set, and q, r, s... are all logically consistent with . Then q
(r
m), q
(s
m), q
(r
(s
m)), etc. So in the closest q-world, these counterfactuals hold: r
m, s
m, r
(s
m), etc., which are just the counterfactuals needed for  to remain stable in the closest q-world. Therefore, if the laws (and their logical consequences) are exactly the members of a non-trivially stable set, then automatically the laws remain laws in the closest q-world, as long as q is nomically possible. We thereby save the intuition that were Uranus’s axis not so nearly aligned with its orbital plane, then although conditions on Uranus would have been different, the laws of nature would have been just the same—which is why conditions on Uranus would have been so different. Many features of lawhood can thus be explained by the connection between lawhood and stability. Let’s now consider how this approach could account for the laws’ explanatory power.

10.4 The lawmakers are explanatorily self-sufficient Presumably, the laws’ explanatory power derives from their necessity. In virtue of what do the laws possess a species of necessity? We saw in the previous section that lawhood is associated with membership in a nonmaximal stable set. What accounts for this association? Is one relatum responsible for the other, or do they have a common origin in some third fact? I propose that the laws

why do the laws explain why?  are necessary in virtue of forming such a set and that their necessity is what makes them laws. In other words, rather than holding that the lawhood of p, q, ... is responsible for various subjunctive facts (namely, those that make stable the set spanned by p, q, ...), I suggest the opposite order of ontological priority: those subjunctive facts¹⁹ make it a law that p, a law that q, etc. Admittedly, this proposal reverses the standard picture of laws as ‘supporting’ or ‘underwriting’ counterfactuals. It also runs counter to the familiar view that typical subjunctive facts are not ontologically primitive, but rather have as their truthmakers the laws together with various non-subjunctive (‘categorical’) facts.²⁰ I cannot do justice here to the difficult metaphysical issues raised by this proposal. But let me mention briefly four of its attractive features. ¹⁹ Of course, counterfactuals are notoriously context sensitive. Accordingly, the subjunctive fact that makes ‘Had I jumped from the ledge, I would have hurt myself badly’ true in one conversational context is distinct from the subjunctive fact that makes it false in another conversational context. The same counterfactual expresses different propositions on different occasions of use. From the context sensitivity of such counterfactuals, van Fraassen has argued that ‘science by itself does not imply’ them (1989: 35) since ‘scientific propositions are not context-dependent in any essential way’ (1980: 118). But doesn’t science tell us in a given context whether some counterfactual conditional is true? (How close Jones’s height must be to exactly six feet, in order for ‘Jones is six feet tall’ to be true, differs in different contexts, but that does not prevent the truth of the claim about Jones’s height from being ascertained scientifically in a given context.) Van Fraassen’s modus ponens becomes my modus tollens: since science plainly does reveal the truth (in a given context) of various counterfactuals, some scientific claims do express different propositions in different contexts. I think that we discover what color the emeralds in my pocket would have been, had there been any, in just the same way as we discover the colors of the actual emeralds forever unobserved deep underground. ²⁰ However, my proposal is compatible with our discovering (or justifying our belief in) a given counterfactual conditional’s truth by consulting (or appealing to) what we already know about the laws (and perhaps also about various categorical facts). The order of knowing (or justifying) may differ from the order of being. It might be objected that ‘Had p obtained, then q would have obtained’ just means ‘Had p obtained, then q would have to have obtained’ where q’s necessitation arises from law—so laws must be ontologically prior to subjunctive facts. However, even if we may be tempted to think laws partly responsible for the truth of ‘Had the match been struck, it would have lit’, are we equally tempted to think laws partly responsible for the truth of ‘Had the match been struck, it would still have been dry’? Goodman famously revealed the difficulties involved in trying to understand a counterfactual as having truth-conditions involving only laws and non-subjunctive facts, without primitive subjunctive facts. Furthermore, ‘... then q would have obtained’ is not equivalent to ‘... then q would have to have obtained’. For example, had I gone out to lunch, I would have eaten Chinese food, but I wouldn’t have to have; there are plenty of other restaurants around.

 marc lange 1. If we take the subjunctive truths as responsible for the laws, then as we saw in the previous section, we can give a nice account of what makes the laws necessary despite being contingent. That account has no need to posit some novel, question-begging notion of ‘necessity’. A stable set’s members are collectively as resilient under counterfactual perturbations as they could collectively be. This fits nicely with our pretheoretic conception of what it takes to deserve to be called ‘necessary’: If there be any meaning which confessedly belongs to the term necessity, it is unconditionalness. That which is necessary, that which must be, means that which will be whatever supposition we make with regard to other things. ( J. S. Mill, A System of Logic, Book III, ch. 5, §4)

When the question is whether the members of a certain set  possess a distinctive variety of necessity, then the answer is determined by whether the set’s members would together all still have held ‘whatever supposition we make with regard to other things’, which I have interpreted as requiring that the supposition be logically consistent with . Perhaps this is what Mill meant by restricting the relevant suppositions to those with regard to other things. Stalnaker (1968) and Williamson (2005) omit Mill’s restriction; they suggest that p is necessary exactly when ∼p
p (or, equivalently, exactly when q
p for any q). This biconditional presumes that counterfactuals with impossible antecedents are (vacuously) true. This presumption is commonly enshrined in formal logics of counterfactuals. (If there are no possible q-worlds, then trivially, p holds in every possible q-world.) However, this presumption is not motivated by scientific practice or by any ordinary counterfactual reasoning (since counterfactuals of the form ‘If p hadn’t been the case, then p would still have been the case’ are not in ordinary or scientific use). Consequently, I am reluctant to make this presumption. Indeed, it seems to me that counterlogicals (like counterlegals) are not trivial, but are much like other counterfactuals. For example, a counterlogical such as ‘Had there been a

why do the laws explain why?  violation of the principle of double negation, then G¨odel would probably have discovered it’ is true in certain contexts, whereas ‘... then I would probably have discovered it’ is false in those contexts, and neither is trivial. (The same applies to counterarithmeticals: Had Fermat’s last theorem been false, then a computer program searching for exceptions to it might well have discovered one, but it is not true that had Fermat’s last theorem been false, then I would have discovered an exception to it.) Furthermore, notice that the biconditional ‘p is necessary exactly when ∼p
p’ depicts p’s necessity as p’s individual achievement rather than a collective affair bound up with p’s belonging to some integrated whole (as I explained in the previous section). Likewise, even if counterlogicals are trivially true, the biconditional ‘p is necessary exactly when ∼p
p’ does not generalize to any variety of necessity other than the strongest kind; unless the laws of nature are metaphysically necessary²¹, the biconditional cannot account for the natural laws’ necessity. All of these difficulties are avoided on the account involving stability. For example, it identifies something as common to necessities of all varieties in virtue of which they qualify as necessary, without collapsing all varieties of necessity into one. 2. Similarly, by holding that ’s stability is what makes laws out of ’s members, I avoid having to give some ad hoc account of why the facts that make p a law also succeed in making p invariant under precisely those counterfactual suppositions that are logically consistent with all of the m’s (taken together) where it is a law that m. It is difficult to imagine how a metaphysical account of the lawmaking facts that is not given in terms of subjunctive truths could have as a consequence that the laws form a stable set, unless this consequence were built into the analysis artificially—inserted, as it were, ‘by hand’.²² 3. Consider instantaneous rates of change, such as a body’s velocity or the strengthening of the electric field at a given location. I ²¹ As some have held—see notes 2, 3, and 22. ²² In my (2004b, 2005b) I deploy this sort of argument against Ellis’s (2001) ‘scientific essentialism’.

 marc lange have argued (2005a) that in order for a quantity Q(t)’s instantaneous rate of change at time t0 to be a cause of (and to help explain) Q(t)’s values at later moments, the instantaneous rate of change cannot be reduced to some mathematical function of Q(t)’s actual values at various moments in t0 ’s neighborhood (as Russell famously maintained it could). Rather, Q’s instantaneous rate of change at t0 should be understood in terms of a subjunctive fact having no ‘categorical ground’. For example, what it is for a body’s instantaneous velocity at t0 to equal 5 cm/s is for the body to exist at t0 and for it to be true at t0 that were the body to exist after t0 , the body’s trajectory would have a time-derivative from above at t0 equal to 5 cm/s. Any motivation for this view also amounts to an argument, independent of puzzles about natural law, that some subjunctive facts supply fundamental physical magnitudes. 4. If lawhood is associated with being contingent but belonging to a nonmaximal stable set, then it appears to be metaphysically possible for a world to contain no laws at all. I see no reason why the subjunctive truths holding in a given possible world must fit together to make stable at least one of the nonmaximal sets containing contingent truths there. It could be that for each such set , there is some p that is logically consistent with ’s members (taken together) but where (p
m) is false, for some m in . Nevertheless, presumably various contingent subjunctive facts hold in a possible world lacking laws. Here is a way to imagine one such world. To begin with, it contains objects with various capacities, such as matches with the capacity to light when struck. By this, I mean merely that various contingent subjunctive facts hold there, such as (p
m): had a given match been struck, then it would (still) have been true that all struck matches light. However, every such capacity has a potential defeater so as to preclude the stability of any nonmaximal set containing contingent truths. For example, the set generated by m (that all struck matches light) is logically consistent with q (that some matches are wet when struck), but it is false that q
m, so the set generated by m is unstable. Furthermore, if we

why do the laws explain why?  now also include ∼q in the set, there is a further defeater—e.g., an r that is logically consistent with the set such that it is false that r
m, or perhaps false that r
(p
m). In this way, no non-maximal set containing contingent truths manages to be stable. The metaphysical possibility of a world with contingent subjunctive facts but no laws sustaining them suggests that in the actual world, the subjunctive facts are ontologically prior to the laws.²³ My claim that subjunctive facts are ontologically prior to the laws sounds roughly like claims made by Cartwright (1989, 1999) and Mumford (2004), among others, that assign ontological priority to capacities over laws. Both Cartwright and Mumford believe that (roughly speaking) properties come modally loaded because a property just is the cluster of capacities it bestows on its bearers, and these capacities do the work traditionally assigned to laws. Cartwright says that laws, as exceptionless regularities, are restricted to ideal cases or to the highly controlled conditions of ‘nomological machines’; Mumford says that there are no laws because nothing needs to be added to property instantiations to ‘govern’ them. In contrast, I defend the ontological priority of subjunctive facts over laws without accepting an analysis of properties in terms of capacities or accepting that actual laws cover only ideal or artificial cases.²⁴ On my view, the metaphysical possibility of a world without laws (to which I alluded in the previous paragraph) arises neither from the existence of capacities that make laws dispensable nor from the possibility that there exists no patch of the universe ²³ Admittedly, this argument is not much more than an intuition pump, and others (e.g., Carroll 1994: 10) have invoked the opposite intuition: that without laws, there are no nontrivially true counterfactuals. However, even those who have asserted that all contingent subjunctive facts are sustained by laws and categorical facts should, I think, revise their view to allow that some contingent subjunctive facts in the actual world are sustained by no laws, such as the fact that had I worn a red shirt today, then Lincoln would still have been assassinated in 1865. This counterfactual may not be true in every context, since sometimes we ‘backtrack’. But in those contexts where backtracking is disallowed, I see no laws that have a hand in making this counterfactual true. ²⁴ For discussion of what a law of an inexact science would be, and how the concept of a ‘stable’ set can be extended to include sets containing ceteris-paribus generalizations that are accurate enough for certain purposes, see my 2000, 2002, 2004a.

 marc lange that is so ideal or isolated that only a single kind of capacity is expressed there. Rather, the metaphysical possibility of a world without laws arises from the possible failure of the subjunctive facts to fit together so as to make stable a nonmaximal set containing contingent truths. Whereas Cartwright and Mumford place capacities (a.k.a. causal powers, ‘natures’) at the bottom of the world, I locate subjunctive facts there. Just as Cartwright and Mumford see little or no work for laws to do, once capacities are admitted, I see no work for capacities to do once primitive subjunctive facts are admitted. I ask Cartwright and Mumford: Are capacities supposed to be ontologically distinct from subjunctive facts? If so, then how do capacities make the subjunctive facts turn out a certain way? If not, then a capacity cannot scientifically explain subjunctive facts, since a capacity just is a collection of subjunctive facts. Cartwright seems to struggle with the problem of characterizing a capacity as distinct from the subjunctive facts for which it is partly responsible. She concludes that the ‘nature’ associated with possessing (say) one statcoulomb of positive electric charge is to make a certain ‘contribution’ to the resultant force—the same contribution whatever other influences are present (1999: 82). But on her view, that contribution is not a piece of the world’s furniture. Rather, the contribution is specified by the difference it would make to the outcome in various circumstances. The nature of charge would seem, then, to be fully captured by a large collection of subjunctive facts. My suggestion that subjunctive facts are ontologically primitive (and so ungrounded by laws and non-subjunctive facts) does not entail that all ontologically primitive facts are subjunctive. The latter view has sometimes been motivated by the idea that all fundamental physical properties are nothing but collections of causal powers. That view, which Whittle proposes in her contribution to this collection, encounters a familiar regress problem: A given property is individuated by the effects that its instantiation would produce in various circumstances, but those effects and circumstances are themselves individuated by their own effects in various

why do the laws explain why?  circumstances, and so forth endlessly. Mumford is sensitive to the objection that a property’s relations to other properties can individuate it only if those other properties have already been individuated. He suggests (2004: 187) that ‘we can break into the circle of interdefinability’ because some properties have effects on us: their ‘phenomenal appearances’. But the issue is not how we know a given property, but what makes it the property that it is. That question is not addressed by turning to some other property that we are caused to possess by interacting with instances of the given property, unless that other property is itself individuated somehow other than by its relations. In contrast, Whittle responds to the regress problem by suggesting that all of the properties get individuated together as collectively forming the satisfier of a gigantic Ramsey sentence. However, I see no reason to believe that the Ramsey sentence will have a unique actual satisfier. When Ramsey sentences are used to implicitly define theoretical terms in the philosophy of mind and elsewhere, the Ramsey sentences contain some O-predicates (‘O’ for ‘old’ or ‘original’—in the olden days, for ‘observational’) that are understood independently of the Ramsified theory. But if all properties are to be individuated by their causal roles, then we have no O-predicates. We are left with just bare causal nodes and branches. Nothing obliges this austere causal network to be actually realized in only one way. If having one statcoulomb of positive electric charge is supposed to be the property standing in a certain causal relation to the property standing in a certain causal relation to the property standing ..., but this system of simultaneous equations has no unique solution, then it fails to individuate properties. Let me return from this digression, which (ironically!) aimed to elaborate my suggestion by sketching its relations to various suggestions made by others. Having briefly looked at four attractive features of construing subjunctive facts as ontologically primitive, let’s consider how this picture might allow us to make sense of the laws’ explanatory power. On this view, p is a law in virtue of p’s invariance under a certain range of subjunctive suppositions—that

 marc lange is, in virtue of various subjunctive facts q
p, r
p, and so forth. So when p’s lawhood explains the fact that p, it is these subjunctive facts that do the explaining. They explain p by entailing that p is inevitable, is no fluke, is not the result of some accidental circumstance, but rather would still have been the case no matter what, i.e., under any possible circumstances. Of course, p would not have been the case under certain logically, metaphysically, mathematically, and conceptually possible (but nomically impossible) circumstances, such as had ∼p been the case. But the circumstances q, r, ... —the ‘nomically possible’ circumstances—do not constitute an arbitrary, gerrymandered range (as we saw suffices for explanatory power on the Woodward–Hitchcock account; recall my first objection to that proposal). This range deserves to be called ‘any possible circumstances’ because these circumstances are exactly those that are logically consistent with the laws, and the laws’ stability (as we have just seen) invests the laws with a variety of necessity. Therefore, even though ∼p is logically, mathematically, metaphysically, and conceptually possible, p would still have been the case ‘no matter what’. The subjunctive truths (not merely q
p, r
p, and the others explaining p, but all of the subjunctive facts that make stable the set containing p and the other laws, thereby making them laws) carve out a genuine variety of possibility where p would still have been the case in any possible circumstance. Since the subjunctive facts q
p, r
p, and so forth are (on this picture) ontologically primitive, they are not made true by p, and so when they explain why p is the case, p is not helping to explain itself. Having used the laws’ stability to account for the laws’ paradoxical-sounding status (necessary yet contingent), I now return to the key question I pressed at the start of the paper: how do p’s lawmakers manage to constitute p’s necessity unless they are necessary themselves? But if they are necessary, then what constitutes their necessity? A fundamental law’s necessity cannot derive from the necessity of other laws, so it must come from its lawmakers. If they, in turn, are not necessary, then the law cannot be necessary and so cannot supply necessity to what it

why do the laws explain why?  explains. To say that the fundamental laws explain by fiat (because a ‘scientific explanation’ just is subsumption under the laws) leaves it unclear why we should care about such ‘explanation’. How does the regress of necessity come to an end? I am now, at last, prepared to give my answer to this question. On the picture I am sketching, p is a law in virtue of various subjunctive facts. So when p’s lawhood explains why p is the case, what must really be doing the explaining are various subjunctive facts q
p, r
p, and so forth (which make p a law). Whence do they derive their necessity, without which they could not make p necessary? Although they are ontologically primitive (rather than having various categorical facts and laws as their truthmakers²⁵), these subjunctive facts are not explanatorily primitive. Like other contingent facts, they have explanations. Just as p is explained by q
p, r
p, and so forth (which ensure that p would still have obtained no matter what), so q
p is explained by r
(q
p), s
(q
p), and so forth. These nested subjunctive truths ensure that (q
p) would still have obtained under all possible circumstances (for the relevant flavor of possibility, which is carved out by these and ²⁵ So on my view, p does not help to make it the case that q
p, even when q obtains. Indeed, I think there may well be contexts in which q and p obtain, but q
p does not obtain—contrary to ‘Centering’ in the Stalnaker–Lewis possible-worlds account of counterfactuals. (I mentioned this in passing in note 11.) For instance, suppose that a given radioactive particle that now exists has a half-life of 100 years. (I assume that its decay is an irreducibly statistical process; the half-life does not reflect our ignorance of some ‘hidden variable’ that determines when it will decay.) Then in the next 100 years, it may decay, but then again, it may not. Were I to wear a red shirt today, then the particle might decay in the next 100 years, but then again, it might not; it is not the case that it would decay, and it is not the case that it would not decay, in the next 100 years. (Here we have the widely accepted failure of conditional excluded middle for subjunctive conditionals.) I take it that this is the case today even if, in fact, I do wear a red shirt today. Here then (whether the particle decays or not) we have an example where q and p obtain, but (in a given context) q
p does not obtain. (In another context, however, we properly say that the particle would still have decayed whether or not I had worn a red shirt today.) Setting this controversial argument aside (and for a different view of counterfactuals involving events governed by statistical laws, see Edgington 2004), I have suggested that subjunctive facts are ontologically basic—that p does not help to make it the case that q
p, even when q obtains. Hence, given my view that various subjunctive facts (such as q
p) are responsible for p’s qualifying as a law, p does not help to make it the case that p is a law. Hence p does not help to explain itself when p’s lawhood explains the fact that p.

 marc lange other subjunctive facts)—the very same ‘all possible circumstances’ under which p would still have held. In other words, these nested subjunctive truths render (q
p) necessary just like p. Like the non-nested subjunctive facts explaining p, these nested subjunctive facts are required (according to the definition of ‘stability’) in order for p and its colleagues to form a stable set—that is, to be laws. Moreover, these nested subjunctive facts also have explanations, in terms of twice-nested subjunctive facts, and so forth all the way down. Each of these multiply nested subjunctive facts is likewise required (according to the definition of ‘stability’) in order for the laws to be laws. (Recall that my second objection to the Woodward–Hitchcock proposal arose from its not requiring that an explanatory generalization’s invariance be invariant. That is ensured, on my proposal, by the multiply nested subjunctives required for stability.) Thus, the subjunctive facts that explain p are able to make p inevitable since they, in turn, are inevitable, and the subjunctive facts making them inevitable are inevitable, and so forth infinitely. Our puzzle was that the fundamental laws have no explanations among the laws, making the source of their necessity (and hence their explanatory power) mysterious. How can p’s lawhood involve p’s inevitability if nothing makes the lawmakers inevitable? My answer is that the lawhood of a fundamental law is constituted by various subjunctive truths, and each of these truths is necessary in virtue of other subjunctive truths from among those that constitute the law’s lawhood, and so forth infinitely. Since there are no primitive necessities ending this regress, its members do not have mere conditional inevitability. When p’s lawhood explains why p is the case, each of the subjunctive facts that helps to constitute p’s necessity is itself necessary, its necessity constituted by other subjunctive facts that help to constitute p’s necessity. The structure is ‘self-contained’; its members depend on no outside facts to constitute their necessity. This structure (in which every fact that helps to make it a law that p is explained by other facts that help to make it a law that p)

why do the laws explain why?  gives a fundamental law the appearance of being explanatorily self-sufficient: able to render certain regularities necessary without in turn deriving its necessity from anywhere else. But if there is nothing in virtue of which it is necessary, then it seems to ‘explain’ merely by rendering certain facts necessary given itself—that is, conditionally necessary, not necessary full stop. Now we have seen that each of the facts that makes p a law has an explanation. But since the facts that make it inevitable are drawn exclusively from among the other facts that make p a law, the fundamental laws are explanatorily self-sufficient: their lawmakers depend on no outside facts to constitute their necessity.²⁶ ²⁶ For comments on previous drafts, thanks to Toby Handfield, Ram Neta, and John Roberts.

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Index analytic method, in science 159–61 grounded in behaviour 162–3 grounded in capacities (irreducible dispositions) 170–9 grounded in dispositions 167–9 grounded in laws 163–7 antidotes, see conditional analysis of dispositions, counterexamples to Aristotle 192, 194 Armstrong, D. M. 13–15, 22–3, 25, 189, 190 n., 191, 254, 263, 268, 270, 283, 294–5 see also laws, Dretske–Tooley– Armstrong theory of; properties, as universals or tropes background freedom (independence) 236–40 Baez, John 236 Bayes’ Theorem 106 Bayesian networks 130–1 Bechtel, William 148 Bennett, J. 298 Bird, Alexander 69, 72, 77, 84–5, 97, 264, 274 Block, Ned 246 Broad, C. D. 201–2 Brodbeck, M. 184 Brown, Harvey 234 capacities, see dispositions; dispositions, as distinct from capacities Carroll, J. W. 298 Cartwright, Nancy 79, 81 n., 126, 165–7, 169, 172–6, 179–83, 209, 315–6 causal influence 9–10 see also dispositions, non-occurrent exercise of causal powers, see dispositions causal processes 18, 108, 119, 130, 192

causal structuralism 65–99, 242–85 see also dispositionalism causal theory of action 196–9 causation: by absence 107 agent 193, 201–3, 207–13 see also dispositions, agent-causal backwards in time 102–4 see also chance, backwards-directed chance-lowering 206 counterfactual analysis of 3, 7–8, 9–10, 19, 111–13, 119, 122, 138, 224 dependent upon laws 12, 15 emergent 185–6 see also causation, agent and essential properties 51–4 grounded in chance 101–22 as intrinsic relation 20, 24–7 and INUS conditions 128 and manifestation of dispositions 10, 15, 17–18, 34–5, 59 and necessary connections 19–20 and persistence 49–51 involving pre-emption 7–9, 105, 118–21 primitive concept of 20, 213–14 probabilistic, see chance reduction of 256, 265 singular 15 n., 58, 101–2, 129, 132 and spontaneous events 107, 208 spurious (bogus) 106, 141–3, 224 temporally discontinuous 102 transitivity of 121–2 n. versus non-causal connection 115–16 see also causal processes; ontology, substance versus event ceteris paribus clauses 84–8 as primitive 94–5 see also conditional analysis of dispositions, counterexamples to

 index Chakravartty, A. 243, 268 chance: backwards-directed (past-directed) 102–4, 105–6, 110–11 in causal explanations 103–7, 192–3 determined by potential causes 108–11, 205–13 infinitesimal 104 inverse 106 knowledge of 121, 295 processes 102, 118–21 in quantum mechanics 96, 123, 205 see also causation and spontaneous events; dispositions, probabilistic Choi, Sungho 221 Chisholm, R. 298 Churchill, John 207 Clarke, Randolph (Randy) 202–3, 205–8, 210 conditional analysis of dispositions 3, 7, 37–8, 122–3, 167, 175, 216, 219, 230 involving chance 123–4 counterexamples to 6–9, 38–42, 44, 77–8, 217, 270–7 Lewis’s 10, 40–4 conditionals: counterfactual, see counterfactuals counterlogical 312–3 Corry, Richard 126, 188 counterfactual dependence 76 counterfactuals: and centreing assumption in semantics 224 n., 319 n. and ceteris paribus operators 86–7 and failure of strengthening the antecedent 75–6 as primitive 92–5, 282–3, 315–17 grounded by dispositions 71–2, 77 semantics of 11, 41–2, 73, 75–80, 298 n. see also causation, counterfactual analysis of; conditional analysis of dispositions Creary, L. G. 183–4, 188 dispositional actualism 65–99 dispositional essentialism, see dispositionalism

dispositionalism 15–20, 23–4, 25–7, 69, 171, 189–91, 215–41 see also dispositions, fundamental; laws, dispositionalist account of; properties, as causal powers dispositions 68 agent-causal 191–201, 203–7 see also causation, agent; causation, emergent; properties, emergent as basis of laws, see laws, dispositionalist account of; laws, grounded in capacities and causal bases 10, 42, 43, 49 conditional analysis, see conditional analysis of dispositions dependent on laws 12, 14–15, 37, 47–9 as distinct from capacities 144–6, 173 fundamental (irreducible) 16, 43, 56–7, 170, 180, 189–91, 226–33 intrinsic versus extrinsic 22–5, 42–3, 69–71, 279, 281–2 knowledge of their presence 145–7, 171–3 manifestation of 10, 44, 57, 151–5, 173, 174–9 see also causation and manifestation of dispositions multi-track 168–9, 173, 226–33 non-occurrent exercise of 144–5, 151–5, 174–84 probabilistic 61, 123–5, 190 without stimulus conditions 125, 144, 205 ungrounded 43, 47, 49 Dowe, Phil 18, 108–11, 119 Dretske, Fred 13 n. see also laws, Dretske–Tooley– Armstrong theory of Duhem, Pierre 235 Dummett, Michael 270 Einstein, Albert 237 n. Ellis, Brian 15–16, 69, 77, 78, 92–4, 97, 169–72, 173, 175 Elster, Jon 148 emergence, see causation, emergent; properties, emergent

index  essential properties: contrasted with necessary properties 219–20 see also causal structuralism; causation and essential properties; dispositionalism Euclidean geometry 222–3 explanation 159–61, 184–5, 200–1, 207–10, 287–8 deductive nomological 293–4 see also laws, explanatory role of events, individuation of 52–3, 54–5 Fara, Michael 23 n., 86, 90 Fetzer, J. 106 Fine, Kit 74–5, 220, 237 finks, see conditional analysis of dispositions, counterexamples to flukes, see laws, invariance under intervention; laws, modal status of Fodor, Jerry 257 n. forces 79–82, 151–5, 179–83, 207, 226 freedom of the will 191–214 Friedman, M. 159 Geach, Peter 268–9 General Relativity 233, 240–1, 264 generic sentences 88–9 Goodman, Nelson 251–2, 298, 311 n. habitual sentences 89–92, 97, 98 Haji, I. 211 n. Handfield, Toby 18 Harr´e, Rom 169 Hawthorne, John 67, 243–4, 264 Heil, John 278 Hempel, Carl 164–5, 286, 292–4 Hendry, David 135, 137–9, 156–7 Henle, Jacob 286–7, 292–3, 296–7 Hiddleston, Eric 207–10 Hitchcock, Chris 297–303, 305 n. Holland, P. W. 133 Hoover, Kevin 138–9, 141, 143 Horwich, P. 298 Hume, David 24–5, 65–6, 128, 151–2, 156, 225 see also ontology, Humean versus anti-Humean accounts of; Humean supervenience

Humean supervenience 45–6, 74, 249–50, 266 Humphreys, P. 106 Invariance, see analytic method; laws, invariance under intervention Jackson, F. 298 Johnston, Mark 38–9 Kane, Robert 192 Kim, Jaegwon 20 n., 279 n. Kitcher, P. 159 Kratzer, A. 90 n. Kripke, Saul 2 n. Lange, Marc 87, 125–6 Langton, Rae 255 law of large numbers 113–4 laws (of nature): and Bayesian networks, see Bayesian networks best-systems analysis of 12–13, 22, 295–6 causal 93, 128–50, 156–7 conservation 17 content of 129–34, 181 n. Coulomb’s 177–8, 181, 221, 229, 235, 288, 297, 299–301 dispositionalist account of 5, 16–17, 48, 62–3, 82, 93 Dretske–Tooley–Armstrong theory of 13–14, 22–3, 131, 294–5 explanatory role of 13, 257–8, 286–321 gravitational 151–3, 162, 166, 177–8, 181, 226, 234–5, 302 see also General Relativity grounded in capacities 144–7, 156, 315–7 invariance under intervention 135–47, 163–7, 299–301 knowledge of 133, 147–50 modal status of 13, 14, 17, 82–3, 98, 130, 252–4, 256, 286–321 Newton’s second (F = ma) 165, 234–6 population relativity of 129 primitivist accounts of 5, 58 probabilistic 63

 index laws (of nature): (cont.) see also Bayesian networks stability of 134–5, 149–50, 156, 303–10 see also laws, invariance under intervention Leibniz 235 Lewis, David 9–13, 20 n., 21 n., 22, 25, 39, 65, 69, 70 n., 103–4, 191, 225, 255, 257–9, 263, 295–6, 298 n., 307 n. see also causation, counterfactual analysis of; conditional analysis of dispositions, Lewis’s; counterfactuals, semantics of; Humean supervenience; laws, best-systems analysis of; recombination Lierse, C. 169–72, 173, 175 Lucas, Robert 134, 156 Mackie, J. L. 128, 255, 298 McKitrick, Jennifer 69, 225 n. see also dispositions, intrinsic versus extrinsic McTaggart, J. 262 n. Martin, C. B. 38, 72, 189, 196, 238 see also conditional analysis of dispositions, counterexamples to masks, see conditional analysis of dispositions, counterexamples to Maudlin, Tim 70 n. Mele, A. 211 n. Mellor, D. H. 170 n., 216–17, 219–20, 223–4, 257–8, 268 n. Menzies, Peter 25 Mill, J. S. 134, 163 n., 182–3, 312 miracles (hypothetical anomalous interventions) 114, 136, 137 see also laws, invariance under intervention Mitchell, Sandra 156 modal realism 11 n., 281, 283 modality 31, 72–5, 83, 98–9 Humean analysis of 87, 97 Molnar, George 6 n., 43, 69, 74, 77, 97, 169, 174, 183–4, 272 Mumford, Stephen 43, 49 n., 69, 74, 77, 84, 85–6, 97, 125, 226, 269, 270, 272, 274

natural properties, see properties necessary connections 5–6, 25, 46 n., 85 see also recombination necessity, natural 4, 73, 82, 91, 287 see also laws, modal status of Neurath, Otto 133 Newton, Isaac 190, 237 n. Newtonian physics, see forces; laws, gravitational; laws, Newton’s second nomological machines 142–3, 144, 147–50, 156 Noordhof, Paul 112–13 n. Nottelmann, Nikolaj 199 n. Nozick, Robert 224 n. Nute, D. 106 object separability 70–1, 96 O’Connor, Timothy 160, 169 n. Oliver, Alex 262 ontological free lunch 188, 190 n. ontology: Humean versus non–Humean 5–6, 12–13, 19, 65–6, 92, 97, 151–6, 169, 174–6, 183–4, 191, 204, 209 substance versus event 201–3, 210 see also substance dualism; properties; quiddities; dispositionalism Oppenheim, P. 33 n. Parfit, D. 293 n. Parsons, Josh 93 n., 279 Pearl, Judea 130–1 Pereboom, Derk 211–13 Plato 257 n. Poincar´e, Henri 235 Pollock, J. 298 Popper, Karl 96 Prior, A. N. 262 Prior, Elizabeth (E. W.) 217, 223, 269 n. properties (including natural properties): as causal powers (essentially characterised by causal role) 5–6, 16, 68, 215 see also causal structuralism; dispositionalism

index  categorical (non–dispositional) 37, 47, 49, 67–8, 216 disjunctive, see multiply realizable dispositional, see dispositions dispositional theory of, see dispositionalism emergent 160, 185–6, 193–5 as entities 97–8 individuated by causal role 65 intrinsicness of 20–1, 69, 77 multiply-realizable 16–17, 191, 218, 271–7 nominalist theories of 244–85 non-natural, see multiply-realizable Platonism about 55 and quiddities, see quiddities structural 190–1, 193–5, 204 n., 216–41 as universals or tropes 189, 204, 215 n., 243, 246–7, 255 Putnam, Hilary 33 n. quantification, substitutional 262 quantum mechanics 6, 70–1 n., 96, 103, 120 n., 144–5, 190, 200–1 see also chance, in quantum mechanics quiddities 66–7, 95, 97, 189, 252, 255 Quine, W. V. 45 n. Quinton, A. 257 Ramsey sentences 246–8, 252, 258, 261–2, 277, 317 recombination (ban on necessary connections) 18 n., 65–6, 259–60 reduction 32–4 Reid, Thomas 196 Reichenbach, Hans 304 relations: intrinsic versus extrinsic 21, 70 n., 76–7 see also properties, structural; spacetime Rodriguez-Pereyra, Gonzalo 250 n., 251 n., 253, 259–61, 263 Rovelli, Carlo 236 Rubin, D. B. 133 Russell, Bertrand 1, 18, 188, 314

Ryle, Gilbert 153, 173, 227, 268–72, 277–8 Salmon, Wesley C. 18, 289 n. Schaffer, Jonathan 21 n. Schlick, Moritz 235 Shoemaker, Sydney 68, 215, 242–3, 249, 262, 264, 267, 283 Simons, Peter 262 n. Smolin, Lee 236–7 spacetime 204 n., 225, 233–6, 239–41, 263–4 conventionalism regarding 235 Spohn, Wolfgang 131 Spurrett, D. 188 Stalnaker, Robert 224 n., 312 see also counterfactuals, semantics of Strawson, P. F. 298 subjunctive conditionals, see counterfactuals substance dualism 193 Taylor, Richard 198 Tooley, Michael 13 n., 169, 191, 265 see also laws, Dretske–Tooley– Armstrong theory of tropes, see properties, as universals or tropes Trout, J. D. 33 n. truthmakers 24–6, 43, 73–4, 76–7, 260–1, 276–84, 311, 319 universals, see properties, as universals or tropes van Fraassen, Bas 290, 296, 311 n. van Inwagen, Peter 192 n. velocity, instantaneous 152, 313–4 Wegner, Daniel 210 Welch, Philip 224 Whittle, Ann 19, 35–6, 98 n., 126, 316–7 Williamson, Timothy 83, 308 n., 312 Woodward, James 87, 136–8, 140–2, 148 n., 156, 297–303, 305 n. Yablo, Stephen 8 n.