Making a difference: essays on the philosophy of causation [First edition] 9780191809132, 0191809136

'Making a Difference' presents new essays on causation and counterfactuals by an international team of experts

679 45 3MB

English Pages 1 : Illustrationen (black and white) [349] Year 2017

Report DMCA / Copyright

DOWNLOAD FILE

Polecaj historie

Making a difference: essays on the philosophy of causation [First edition]
 9780191809132, 0191809136

Table of contents :
1: Helen Beebee, Christopher Hitchcock and Huw Price: Introduction2: Daniel Nolan: Causal Counterfactuals and Impossible Worlds3: Rachael Briggs: Two Interpretations of the Ramsey Test4: Cei Maslen: Pragmatic Explanations of the Proportionality Constraint on Causation5: Huw Price: Causation, Intervention, and Agency: Woodward on Menzies and Price6: David Braddon-Mitchell: The Glue of the Universe7: Christopher Hitchcock: Actual Causation: What's the Use?8: Nancy Cartwright: Can Structural Equations Explain How Mechanisms Explain?9: Peter Menzies: The Problem of Counterfactual Isomorphs10: Thomas Blanchard and Jonathan Schaffer: Cause without Default11: Brad Weslake: Difference-making, Closure and Exclusion12: Philip Pettit: The Program Model, Difference-makers, and the Exclusion Problem13: James Woodward: Intervening in the Exclusion Argument14: Christian List and Peter Menzies: My Brain Made Me Do It: The Exclusion Argument Against Free Will, and What's Wrong With It15: Helen Beebee: Epiphenomenalism for Functionalists16: Peter Menzies: The Consequence Argument Disarmed: an Interventionist Perspective

Citation preview

Making a Difference

Making a Difference Essays on the Philosophy of Causation

EDITED BY

Helen Beebee, Christopher Hitchcock, and Huw Price

1

OUP CORRECTED PROOF – FINAL, 10/5/2017, SPi

3

Great Clarendon Street, Oxford, OX2 6DP, United Kingdom 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. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © the several contributors 2017 The moral rights of the authors have been asserted First Edition published in 2017 Impression: 1 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, by licence 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 work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2016962739 ISBN 978–0–19–874691–1 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work.

In memory of Peter Menzies

Contents List of Illustrations List of Contributors 1. Introduction Helen Beebee, Christopher Hitchcock, and Huw Price

ix xi 1

2. Causal Counterfactuals and Impossible Worlds Daniel Nolan

14

3. Two Interpretations of the Ramsey Test R.A. Briggs

33

4. Pragmatic Explanations of the Proportionality Constraint on Causation Cei Maslen

58

5. Causation, Intervention, and Agency: Woodward on Menzies and Price Huw Price

73

6. The Glue of the Universe David Braddon-Mitchell

99

7. Actual Causation: What’s the Use? Christopher Hitchcock

116

8. Can Structural Equations Explain How Mechanisms Explain? Nancy Cartwright

132

9. The Problem of Counterfactual Isomorphs Peter Menzies

153

10. Cause without Default Thomas Blanchard and Jonathan Schaffer

175

11. Difference-making, Closure, and Exclusion Brad Weslake

215

12. The Program Model, Difference-makers, and the Exclusion Problem Philip Pettit 13. Intervening in the Exclusion Argument James Woodward

232 251

viii

CONTENTS

14. My Brain Made Me Do It: The Exclusion Argument Against Free Will, and What’s Wrong with It Christian List and Peter Menzies

269

15. Epiphenomenalism for Functionalists Helen Beebee

286

16. The Consequence Argument Disarmed: An Interventionist Perspective Peter Menzies

307

Index

331

List of Illustrations 7.1 Billy and Suzy throw rocks at a window

119

7.2 The effect of a bicycle helmet law

125

9.1 Causal graph for Backup

158

9.2 Causal graph for Window

161

9.3 Causal graph for Bottle

163

13.1 Kim’s diagram

252

13.2 The causal influence of HDL, LDL, and TC on HD

261

13.3 Kim-style causal diagram with additional assumptions

263

14.1 Realization-insensitive causation

283

16.1 A causal graph

311

16.2 A causal graph

312

16.3 A causal graph

315

16.4 A causal graph

317

16.5 Possible worlds

320

16.6 A causal graph

321

16.7 Logically possible trajectories

322

List of Contributors H ELEN B EEBEE , University of Manchester T HOMAS B LANCHARD , Illinois Wesleyan University D AVID B RADDON -M ITCHELL , University of Sydney R.A. B RIGGS , Stanford University N ANCY C ARTWRIGHT , University of Durham and University of California, San Diego C HRISTOPHER H ITCHCOCK , California Institute of Technology C HRISTIAN L IST , London School of Economics C EI M ASLEN , Victoria University of Wellington P ETER M ENZIES , formerly Macquarie University D ANIEL N OLAN , University of Notre Dame P HILIP P ETTIT , Princeton University and the Australian National University H UW P RICE , University of Cambridge J ONATHAN S CHAFFER , Rutgers University B RAD W ESLAKE , New York University Shanghai J AMES W OODWARD , University of Pittsburgh

1 Introduction Helen Beebee, Christopher Hitchcock, and Huw Price

When Peter Menzies died in February 2015 the philosophy of causation lost one of its clearest and most insightful voices, and many in philosophy generally lost a dear colleague, collaborator, and friend. Peter’s last illness was a long one, but when plans for this volume first took shape we were aware that it was likely to prove terminal; we wanted to do something to celebrate his contributions to our field, while we still had the opportunity. We had hoped to present Peter with the finished volume, but the past tense caught up with us; so instead we dedicate the collection to his memory, in warm appreciation of all that he did for our discipline. From the beginning, the volume named itself. Much of Peter’s work turns, as he puts it, on ‘the idea that a cause is something that makes a difference to its effects’ (2004b: 139). Our intention was to celebrate Peter’s own role—practising what he preached, as it were—in making a difference to our field. So we had our title and our central theme. Our contributors approach this theme from many different directions, and the essays here fall into two broad groups. Chapters 2–10 deal with a range of issues surrounding the analysis of causation, and Chapters 11–16 consider how analyses of causation and related notions can be brought to bear on two more general philosophical problems: particularly the exclusion problem in the philosophy of mind, and the problem of free will. We can orient the initial essays in the first group by noting that whether one prefers to analyse causation in terms of counterfactuals (along the lines of Lewis (1973a)), or counterfactuals in terms of causal structure (as Pearl (2009) recommends), there seems to be a tight connection between causation and counterfactuals. At the very least, most causal relationships have a corresponding ‘causal counterfactual’. The striking of the match caused it to light; if the match hadn’t been struck, it wouldn’t have lit. Daniel Nolan (Chapter 2) focuses on the issue of how we are to understand the counterfactuals that will need to figure in an account of causation, if causation is to be analysed in these terms. Following Stalnaker (1968) and Lewis (1973b), it has become common to understand counterfactuals in terms of possible worlds. The counterfactual



INTRODUCTION

‘if the match hadn’t been struck, it wouldn’t have lit’ is true in a world w just in case all of the closest possible worlds to w in which the match isn’t struck are worlds in which the match doesn’t light. To assess the counterfactual, then, we need to know what goes on in these closest worlds. The problem is that there are desiderata for what these closest worlds should be like that seem to be incompatible. On the one hand, the worlds that are closest to w should have the same laws of nature as w, and they should not contain any miracles (violations of those laws of nature). On the other hand, the worlds closest to w should also agree with w about what happens prior to the time at which the match is or isn’t struck. However, if the laws of w are deterministic, it seems that these desiderata can’t be jointly satisfied. If a world agrees with w about what happens prior to some time t, and has the same deterministic laws as w, then that world can’t disagree with w about whether a particular match is struck at time t. Even if the laws of w aren’t strictly deterministic, they may make the striking so probable that the absence of this event would be a semi-miracle, something else we might hope to avoid in the worlds closest to w. Nolan proposes that we augment the usual apparatus of possible worlds with impossible worlds. These are worlds in which incompatible things are true, but in which deductive closure fails. While this proposal sounds odd at first, Nolan draws on earlier work (Nolan 1997) to argue that impossible worlds are already needed to handle certain kinds of counterpossibles. For example, it seems natural to say that if 131 were equal to 27 times 4, then 131 would be composite. This has the same linguistic form as a counterfactual, but we cannot evaluate its truth by considering possible worlds in which the antecedent is true. Nolan discusses some drawbacks of this proposal, and stops short of giving it his full endorsement. However, he deflects a number of objections to this proposal and argues that it is worthy of further consideration. Rachael Briggs (Chapter 3) also focuses on a puzzle about conditionals, including counterfactual conditionals. She notes that various writers, including Peter Menzies, have been attracted to the idea that we should understand causation in terms of counterfactual conditionals. Yet, as she also notes at the beginning of her chapter, conditionals themselves are deeply puzzling. In part this is because two intuitively plausible avenues for making sense of them seem deeply in tension with one another. These avenues both begin with the so-called Ramsey test: as Briggs puts it, the thought that ‘[a]n individual should accept the conditional A ! B to the degree that she would accept B on the supposition that A, provided that Cr(A) > 0’ (this volume, 34) (where Cr is the individual’s credence, or subjective probability). One avenue interprets the Ramsey test in terms of Adams’ thesis, that credence in the conditional A ! B goes by the conditional credence Cr(B/A). The other interprets it in terms of Stalnaker semantics—as Briggs puts it, the thesis that ‘[t]he conditional A ! B is true at a possible world α just in case at the world most similar to α where A is true, B is true’ (this volume, 35). Yet as the triviality results of Lewis and others show, these two proposals are incompatible, at least as they stand.

HELEN BEEBEE, CHRISTOPHER HITCHCOCK, AND HUW PRICE



Briggs considers a proposed solution to the triviality problem, drawing on a revised version of Adams’ thesis proposed by Kaufmann. She shows, however, that when combined with Stalnaker semantics, Kaufmann’s proposal still leads to a kind of triviality result—local triviality, as she calls it—which ‘seems just as absurd as the original triviality results’ (this volume, 34). The solution, she argues, is to revise Stalnaker semantics too, replacing it with a generalized imaging semantics. Briggs argues that this ‘defangs’ the local triviality results, by explaining why they are not as counterintuitive as they initially seem—properly understood, they reflect an inevitable and manageable degree of context-sensitivity in our use of conditionals. Counterfactual conditionals and context-sensitivity are also major themes in Cei Maslen’s contribution to this volume (Chapter 4). Contextual accounts of causation have been proposed in recent years by a number of authors, including Peter Menzies and Maslen herself. One role that context is said to play, in many of these accounts, is that of picking out a contrast class which in turn plays a crucial role in determining precisely which counterfactuals are in play, in the causal judgements we make in the context in question. As Maslen puts it, the ‘idea of a contrastivist account of causation is that contrast cases for the cause and effect are determined by the context’. She notes that this idea ‘seems to fit particularly well with interventionist/causal modelling accounts of causation and other counterfactual accounts’ (this volume, 67). Maslen’s project in her chapter might itself be described as contrastive: she examines Yablo’s arguments for the need for a ‘proportionality constraint’ in an account of causation—roughly, the requirement that a specification of a cause be neither too specific nor too general—and compares Yablo’s approach to the contrastive approach. She argues that contrastive approach does a better job of explaining the examples that seem to motivate the proportionality constraint, and concludes by discussing the relevance of these factors to the metaphysics of causation. Contextuality has been thought by some to import an element of ‘subjectivity’ into an account of causation. After all, isn’t the determination of the relevant context or contrast class to some extent an anthropocentric matter, determined by the interests of the speakers in question? If there is subjectivity of this kind in a contextual account of causation, then it is a further question whether this should be counted a disadvantage; but many have felt that it would be an undesirable consequence, and that we should prefer an account that treats causation as fully ‘objective’. This issue—‘subjectivity’ versus ‘objectivity’ in an account of causation—is at the heart of Price’s contribution (Chapter 5). Price notes that in James Woodward’s influential book Making Things Happen (2003) and other places, Woodward has noted some affinities between his own account of causation and that proposed in Price’s joint paper with Peter Menzies (Menzies and Price 1993). However, Woodward has argued, precisely, that the Menzies and Price view is implausibly ‘subjective’. Price sets out to respond to Woodward’s objections. He argues that the Menzies and Price view is not as different from Woodward’s own account as Woodward



INTRODUCTION

believes, and that insofar as it is different, it has some advantages whose importance Woodward misses. However, he also concedes that the Menzies and Price view lacks some elements whose importance Woodward rightly stresses. But when properly characterized, Price argues, the ‘subjectivity’ of the Menzies and Price view survives unscathed, and turns out to be a feature rather than a bug: if Woodward’s view is interpreted so that it lacks it, it becomes vulnerable to a sceptical challenge that the Menzies and Price view can escape. Price stresses that in his view, the proper and fruitful target for a philosophical account of causation is not causation itself, but our concept of causation. In other words, as Price puts it, the project really belongs not in metaphysics but in what Price calls ‘anthropology’. The central task, as Price sees it, is to explain why creatures in our situation have a need for causal concepts—a task that needs to advert, above all, to the fact that we are agents. Price argues that Woodward is largely on the same page on this matter, but notes that Menzies has been more attracted to the metaphysical project. In one well-cited piece (Menzies 1996), Peter Menzies tackled the metaphysics of causation along the lines proposed by the so-called Canberra Plan. David BraddonMitchell’s contribution (Chapter 6) develops this project, raising the question of what causation might be, if it turns out that there is no single thing that meets all of the various desiderata. As Braddon-Mitchell notes, writers such as Hall (2004) have proposed a kind of pluralism about causation, according to which there may be no single thing that meets all the desiderata, but two or more things that each meet some of them. Two main desiderata have been proposed, in this context. One links to counterfactual reasoning, the other to the idea that causation has an intrinsic, productive nature. Braddon-Mitchell offers two extensions to this kind of pluralism. First, he argues that the latter of these intuitive desiderata might be met, if necessary, by something weaker than production: by a notion of ‘structural connectedness’, as Braddon-Mitchell puts it—‘the way the universe is glued together over time’ (this volume, 100). Second, drawing on earlier work, he offers a distinctive account of the way in which the weaker and stronger notions both play a role in settling what best deserves to be called ‘causation’. Roughly, the stronger notion takes precedence, if it turns out that there is actually something of the right sort to play that role; if not, then the concept defaults to the weaker notion. Braddon-Mitchell describes some early empirical evidence that our notion of causation does have this conditional, defaulting structure. At this point, several chapters draw on the machinery of one of the most influential developments in recent philosophy of causation. Following Pearl (2009), many philosophers became interested in the use of structural equation models (SEMs) to represent causal structures. More specifically, SEMs provide a useful tool for representing the types of non-backtracking counterfactuals (Lewis 1979) or intervention relations (Woodward 2003) that hold within a given system. These models allow for computations to calculate the effects of interventions or evaluate counterfactuals, and they admit heuristically powerful graphical representations.

HELEN BEEBEE, CHRISTOPHER HITCHCOCK, AND HUW PRICE



In chapter 10 of his book, Pearl offered an account of actual causation in terms of SEMs. Actual causation is a causal relation holding between particular events or states, and reported in ordinary claims like ‘Suzy’s throw caused the window to shatter’ and ‘the assassination of Archduke Ferdinand caused Austria-Hungary to declare war on Serbia’. This relation has also been called causation in fact in the law, as well as token causation and singular causation in philosophy. It has often been the target of philosophical analysis, for example in Lewis (1973a). Peter Menzies offered his own analysis of actual causation using SEMs in Menzies (2004a). A novel feature of this account was its use of the concept of default worlds. This new approach builds an on idea advocated in Menzies (2004b), that counterfactuals have a logic that differs from the familiar ones developed by Stalnaker (1968) and Lewis (1973b). In particular, Menzies rejected the centring condition, which says that counterfactuals having true antecedents are always evaluated at the actual world. Instead, Menzies argued that we often evaluate counterfactuals relative to default worlds, where various interfering conditions are removed and the situation is restored to a normal state. In the context of actual causation, Menzies’ proposal was motivated in part by the claim of Hart and Honoré that a cause involves a deviation from the normal state of things. Menzies developed these ideas further in Menzies (2007) and Menzies (2011). Several essays in this volume pursue these strands in Menzies’ work. Hitchcock’s project (Chapter 7) connects Menzies’ approach to actual causation with another strand in Menzies’ work, his interest in agency accounts of causation. By making this connection, Hitchcock aims to throw light on another issue: Why should we be interested in actual causation? As Hitchcock notes, the essence of the agency theory is that causes are ‘handles’ that we can use to achieve our ends—places where we can make a difference, in fact, and hence make some further difference, that matters in the light of our desires and goals. But if this is what causes are, what is the value of knowledge of actual causation, understood along the lines that Menzies has proposed? As Hitchcock puts it: ‘If causes are handles on the world, then actual causes are handles of a specific kind. What kind of handle are they?’ (this volume, 116). Hitchcock’s proposal is that actual causation has its home in contexts in complex goal-directed reasoning, in which we consider a series of intervention points. We thus become interested in the specific path by which an intervention may lead, several steps later, to a desired outcome. According to Hitchcock, this is the source of the path-specific character, that Menzies and others have associated with actual causation. As Hitchcock puts it, his ‘conjecture is that claims of actual causation identify the kinds of path-specific effects that can be exploited in this kind of [multi-step] goaldirected strategy’ (this volume, 128). Hitchcock argues that this proposal has a number of points in its favour. It makes it clear why actual causation does depend on pathspecific effects. It explains the role of normality, or default conditions. And it promises to explain why actual causation is crucial to attributions of moral and legal responsibility.



INTRODUCTION

Nancy Cartwright’s contribution (Chapter 8) explores the limitations of structural equation models. Machamer, Darden, and Craver (2000) have influentially argued that much causal explanation, especially in the biological sciences, involves the elucidation of mechanisms. Mechanisms are comprised of entities, which have characteristic activities, which work together to regularly produce effects. Menzies (2012) argued that the notion of an activity is too imprecise, and is used to group together a heterogeneous collection of processes. He challenged defenders of mechanistic explanation to specify the common features of activities that warranted their grouping under a common label. Following Craver (2007), Menzies suggested that activities corresponded to interventionist counterfactuals, and that they can be represented by structural equations in a SEM. Cartwright criticizes Menzies’ proposal. Structural equations can usefully represent the pattern of dependence between inputs and outputs in a mechanism or submechanism, but these dependence patterns only emerge once the parts of the mechanism are appropriately configured. The structural equations cannot give us insight into the more basic capacities of the entities that make the construction of the mechanism possible in the first place. As an alternate picture, Cartwright proposes that causation is what Neurath called a ‘Ballung’ concept. It is a complicated assortment of loosely affiliated notions that only gains a more precise definition in the context of a specific application. Thus she maintains that Menzies’ demand for a feature common to all activities is inappropriate. For scientific purposes it is often necessary to replace the messy ‘Ballung’ with a tidier concept. SEMs are one such replacement, and they are useful for guiding predictions. But such sanitized concepts hide the richness and complexity of our concept of causation, and they will not be suitable for all purposes. The next contribution (Chapter 9) is from Peter Menzies himself, and builds on his earlier work on the concept of actual causation. Here, he tackles the problem of counterfactual isomorphs. Counterfactual isomorphs pose a problem for any counterfactual theory of causation, including theories that make use of SEMs. The problem is that there can be pairs of cases that exhibit isomorphic patterns of counterfactual dependence, and hence can be represented by isomorphic SEMs, but where our intuitive judgements of actual causation are different. This problem has led a number of authors, starting with Menzies himself (2004a), to propose that judgements of actual causation are also sensitive to what we regard as the default states of a system. Menzies makes use of a similar idea in his chapter, but he deploys it in a very different way. Instead of contributing to the evaluation of the counterfactuals, certain states of a system form ideal conditions for specific causal relations. While causation is still to be understood in terms of counterfactuals, the counterfactuals that underwrite a causal relationship must obtain under ideal conditions. Thus, there can be causation without counterfactual dependence (as in cases of pre-emption and overdetermination) when conditions are not ideal. Menzies then uses this proposal to address the problem of counterfactual isomorphs. Although two cases may have isomorphic patterns of counterfactual dependence, the isomorphism

HELEN BEEBEE, CHRISTOPHER HITCHCOCK, AND HUW PRICE



may not map ideal conditions for one causal relationship onto ideal conditions for the other. In this case, the patterns of counterfactual dependence that obtain under ideal conditions may be different for the two causal systems. Thomas Blanchard and Jonathan Schaffer, in their contribution (Chapter 10), defend one aspect of Menzies’ approach to actual causation while challenging another. They endorse the use of SEMs to model causal systems, and give an elegant presentation of the formalism. However, they criticize the idea that an account of actual causation must appeal to a distinction between default and deviant states of a causal system. For one thing, supplementing a SEM with an assignment of default and deviant states adds complexity to the model. Furthermore, it requires an evaluation of states that is guided by imprecise and potentially conflicting criteria. In some very simple systems, there may be no reasonable grounds to declare one state the default. For instance, there is no default outcome when a fair coin is tossed, but the outcome can still cause one team to start the game with the football. Blanchard and Schaffer argue that the problem cases that have led Menzies and others to appeal to a distinction between default and deviant states can be better handled by consideration of aptness conditions on causal models. (Some of these problem cases are closely connected to the problem of counterfactual isomorphs discussed in Menzies’ chapter.) Suppose that we have a SEM, M, of a particular causal system. Applying a definition of actual causation to M yields the result that X = x is a cause of Y = y in that model. Are we then entitled to conclude that the event represented by X = x is in fact a cause of Y = y? No, because there may be another model, M’, in which the same definition yields a different answer. For example, suppose that Billy and Suzy throw rocks at a window. Suzy’s rock hits the window first, shattering it; Billy’s rock then sails through the hole in the window. If we model this system with three variables—corresponding to Suzy’s throw, Billy’s throw, and the window shattering—then the model will be symmetric in its treatment of Suzy’s throw and Billy’s throw. No definition of actual causation, applied to such a model, could yield the result that Suzy’s throw is a cause, while Billy’s is not. However, if we add additional variables to the model, representing whether Suzy’s rock and Billy’s rock hit the window, we can distinguish the causal role of the two throws. In order to conclude that Suzy’s throw was the cause of the window’s shattering, while Billy’s wasn’t, we must have a reason to judge the second model apt, and the first model inapt. Blanchard and Schaffer canvas a number of criteria that have been proposed for the aptness of models. They then argue that rigorous application of these criteria will eliminate problematic causal models that seemed to give rise to the need for a default/deviant distinction. Turning now to the essays in the second group (Chapters 11–16), we can orient them with respect to an influential paper by Christian List and Peter Menzies (2009). In this paper, List and Menzies claim to solve the ‘exclusion problem’ facing nonreductive physicalists. According to physicalism, any purported mental cause supervenes on some sufficient physical cause; however, the existence of a sufficient



INTRODUCTION

physical cause would seem to exclude the existence of any supervening cause (except in relatively rare cases of overdetermination, such as firing-squad cases) (see e.g. Kim 1998). The reason why the exclusion problem is a problem for non-reductive physicalists in particular is that non-reductive physicalists take mental properties to be multiply realizable: when one is in a given mental state (in pain, say), there are in principle various different physical states—various different neural configurations, say—that might realize this mental state. By contrast, reductive physicalists hold that mental properties just are physical properties. If mental property M = physical property P, then the fact that P is a sufficient physical cause guarantees that M is, since M and P are the very same property. List and Menzies (hereafter LM) argue that the exclusion principle is false. They appeal to the idea—one that has already loomed large in earlier chapters of this collection—that a cause is something that makes a difference to whether or not the effect in question occurs. Thus (to use a standard example, from Yablo 1992), suppose that Sophie the pigeon is trained to peck at crimson things. Then a button’s being crimson makes a difference to her pecking: give Sophie a crimson button and she’ll peck, but give her a non-crimson button and she won’t. Whether or not a given button is red supervenes on its specific shade, such as crimson, scarlet, or aqua. However, if you give Sophie a red button she may not peck—it might be scarlet, after all, and she’s not trained to peck at those. So whether or not the button is red makes no difference to whether or not she’ll peck; it’s whether or not it’s crimson that matters. So far, no disagreement with Kim: the subvening property excludes the supervening property. (So this is a case of ‘upward exclusion’.) But what if Sophie is trained to peck at red things? Then give her a red button and she’ll peck; give her a non-red button and she won’t. But being crimson, in this case, doesn’t make a difference: if it’s crimson, she’ll peck—but if it’s another shade of red, she’ll also peck. So in this case it is the button’s being red that causes Sophie to peck, and not its being crimson; as Yablo puts it, being red is proportional to the effect in question, viz., Sophie’s pecking. And so, according to LM, this is a case of downward exclusion. Subvening and supervening properties do (by and large at any rate—except when the relation between the supervening cause and the effect is ‘realization-sensitive’) exclude one another, just as Kim says. Kim, however, assumes that there is only upward exclusion. But, since causes must make a difference to their effects, and sometimes it is the supervening property rather than the subvening one that makes a difference, there can be downward exclusion too. And, we can assume, if nonreductive physicalism is true, then it will sometimes be multiply-realizable mental states, and not their physical realizers, that make a difference. If I’m in pain, it’s that that makes a difference to my saying ‘ouch’, and not the physical state that realizes my mental state. Against this background, Brad Weslake (Chapter 11) argues that LM’s solution to the exclusion problem fails. The central issue here is whether we should endorse LM’s

HELEN BEEBEE, CHRISTOPHER HITCHCOCK, AND HUW PRICE



claims about upward and downward exclusion. Weslake argues that there are good reasons not to. He motivates an alternative conception of what it is for one property to make a difference to another, within an interventionist framework, which delivers different—and, Weslake argues, better—results than LM’s account. In particular, Weslake’s account upholds a principle that LM are forced to reject, namely that if F is causally sufficient for G, then F is a cause of G. It is this principle that LM need to reject in order to deliver the possibility of upward and downward exclusion, since such cases are, precisely, cases where a property that is causally sufficient for G (e.g. the button that Sophie is pecking being crimson) is nonetheless not a cause of G. Finally, Weslake offers an alternative explanation for our tendency to assert claims like ‘Sophie pecked because the button was red’ in preference to ‘Sophie pecked because the button was crimson’—LM’s explanation being that the first claim is true and (because of downward exclusion) the second is false. Weslake appeals instead to the explanatory superiority of the first claim over the second—an appeal that is consistent with holding that the second claim is true. Philip Pettit’s contribution (Chapter 12) offers a comprehensive comparison of the merits of LM’s approach and those of the ‘program model’ of explanation—a model that Pettit developed in a series of earlier publications with Frank Jackson. While, as Pettit notes, there are some natural affinities between the two views (LM’s differencemakers can be thought of as ‘super-programmers’ according to Pettit’s view), they differ significantly in their attitude to the connection between difference-making and causation. Pettit acknowledges that, qua response to the exclusion problem, LM’s account fares better than Jackson and Pettit’s (hereafter ‘JP’). By agreeing with Kim that exclusion is a genuine threat to causal status but using it to argue for the existence of downwards, as well as upwards, exclusion, LM, as Pettit puts it, ‘turn the tables on Kim’s exclusion claim, [rather than] just denying it’ (this volume, 239). By contrast, on JP’s account, the causal relevance of supervening, programming properties remains hostage to the causal efficacy of the underlying supervenience base. On the other hand, Pettit, like Weslake, in effect takes issue with LM’s claim that causal sufficiency does not entail causation. He argues that it is absurd to think that, while difference-maker M (my intending to move my hand, say) causes effect E (my moving my hand) because M has some neural realizer, neural realizer P itself has no genuine causal status whatsoever with respect to E. After all, M’s causing E depends upon its neural realizer in a way that it does not depend, in turn, on M’s realizing some still higher-order property—the property of having some intention or other, for example. Pettit’s conclusion is that LM should embrace JP’s claim that all programmers, and not just super-programmers, are bearers of causal relevance, and hence that P, as well as M, is causally relevant to E. Were they to do so, Pettit claims, then the accounts offered by JP and LM would, in a sense, be of a piece: they would differ only insofar as LM would still insist that talk of causation proper, as opposed to causal relevance, is appropriate only for super-programming properties.



INTRODUCTION

James Woodward’s contribution (Chapter 13), like Weslake’s, takes an interventionist approach to solving the exclusion problem. He claims that from an interventionist point of view there is no problem with according mental properties causal status, except for the fact that supervenient properties are not distinct from the properties on which they supervene. If the value of variable M supervenes on the value of variable P, M and P stand in a relation of non-causal dependence: changing the value of M guarantees a change in the value of P. This creates a problem because in order for something to constitute an intervention I on variable X (with respect to Y), there must be no causal route from I to Y that doesn’t itself go via X. But— prima facie at least—since any intervention on mental property M will guarantee a change in its realizer P, this condition on I is not met in the case of purported mental causation; after all, the causal route from P to E does not proceed via M. Woodward argues—on general grounds that appeal to kinds of non-causal dependency that do not involve multiple realization—that in assessing the causal role of supervenient properties we should not, in fact, control for those properties’ supervenience bases. In the final section of his chapter, Woodward compares his own interventionist solution to the exclusion problem with that of LM. As both Weslake and Pettit do, he denies both upward and downward exclusion, but argues, along lines similar to Weslake’s, that the problem with claims such as ‘Sophie’s pecking was caused by the button being scarlet’ is that they are less informative than alternative claims that respect proportionality, and not that they are false. In their contribution (Chapter 14), List and Menzies tackle a well-known argument from neuroscience that we lack free will because our conscious mental states do not cause our decisions. (Versions of this argument have been widely dismissed by philosophers, but generally on grounds that are largely independent of the grounds adduced by List and Menzies.) List and Menzies formulate the argument as an exclusion argument: our lack of free will follows from the fact that conscious mental states do not cause our actions—thanks to the existence of a causally sufficient supervenience base—and hence, since acting freely requires that it be caused by the agent’s mental states, nobody ever acts freely. The basic gist of List and Menzies’ response to the argument should be unsurprising, given the foregoing: they reject the exclusion principle on which the argument depends and hence avoid what they call ‘neuroscientific scepticism’ with respect to free will. In the light of the above discussion, one interesting feature of List and Menzies’ chapter is what it says about the disputed principle that causal sufficiency implies causation. In footnote 11 (this volume, 272), they say that they ‘use the term “sufficient cause” as shorthand for “causally sufficient condition” ’. This might suggest that they do endorse the principle that causally sufficient conditions are indeed causes, since one might expect something’s being a sufficient cause to automatically qualify as a cause simpliciter. However, a later footnote (fn. 19, this volume, 278) seems to undermine this expectation: ‘since a man (under standard assumptions) can never become pregnant’, they say, ‘his taking a contraceptive pill cannot change that fact and

HELEN BEEBEE, CHRISTOPHER HITCHCOCK, AND HUW PRICE



hence will qualify as a sufficient cause for his not becoming pregnant, no matter whether we interpret causal sufficiency in nomological terms, counterfactual terms, or probabilistic terms’. While they might in principle be right that the man’s taking a contraceptive pill qualifies as a causally sufficient condition for his failure to get pregnant, presumably they do not think that his doing so is a cause of his not getting pregnant. So they really do seem to think that being a sufficient cause does not suffice for being a cause simpliciter, and hence (as they also suggest explicitly in the same footnote) they remain committed to rejecting the principle that causal sufficiency implies causation. Helen Beebee’s contribution (Chapter 15) focuses on an assumption implicitly made by most recent attempts to solve the exclusion problem for mental causation— and briefly discussed by Pettit in }1 of his chapter—including those of LM, Weslake, and Woodward. The assumption is that mental (and so multiply realized) properties are ‘distinct existences’ from their alleged effects. (By contrast, Woodward’s concern in his chapter is with the lack of distinctness of mental properties from their physical realizers.) Without that assumption, no such solution can work, since we have excellent grounds for thinking that there is no causation between entities that are not distinct from one another. But, assuming functionalism—which, after all, constitutes the grounds for thinking that mental properties are multiply realized in the first place—mental properties are not distinct from the effects to which they are alleged to bear causal relevance, since functional properties are defined in terms of the causal roles of their realizers. Beebee argues that the natural consequence— epiphenomenalism with respect to mental properties—is not as problematic as many philosophers tend to assume. The final chapter of this collection (Chapter 16) is a paper that Peter Menzies was working on before he died. It has been lightly edited by Christian List, with all editorial changes flagged in the footnotes. The chapter argues that Peter van Inwagen’s well-known Consequence Argument for incompatibilism fails. In fact, the bulk of the chapter constitutes an argument for the falsity of determinism, and hence an argument against a slightly different argument that starts from the assumption that determinism is true and—by the same method as the Consequence Argument itself—reaches the conclusion that there is no free will. (The consequences of this argument for the Consequence Argument proper are discussed by List in }6, an editorial addition to the chapter.) Menzies argues, on the basis of an interventionist framework, that determinism is, in fact, false. Roughly, we should abandon what we might call ‘strict’ determinism in favour of what List calls ‘qualified’ determinism. This is because the structural equations governing local deterministic systems implicitly include a ‘no interventions’ proviso: the structural equation for an endogenous variable can be disrupted by an intervention. Menzies goes on to argue that considering the whole universe as a single causal system—as van Inwagen’s conception of determinism effectively does—does not undermine his argument. While the notion of an intervention makes no sense when the system under consideration is the whole



INTRODUCTION

universe, we can redefine an intervention—in a way that has obvious commonalities with Lewis’s conception of a miracle—so that an ‘intervention’, thus defined, is simply an uncaused disruption to the system rather than a disruption caused by an external influence. Crucially, however, a Menzies-style ‘miracle’ involves no violation of the laws, since the laws come with a ‘no interventions’ proviso. Menzies’ proposal connects with Daniel Nolan’s proposal in Chapter 2 that we conceive of the closest world w at which the antecedent of a given counterfactual is true as one with the same past and the same laws as the actual world—and hence (assuming determinism) as impossible worlds. On Menzies’ view, by contrast, we can turn roughly the same trick without resorting to impossible worlds: given that we should endorse qualified rather than strict determinism, there is no contradiction involved in taking w to have both the same past and the same (qualified-deterministic) laws as the actual world. We are very grateful to several people for their assistance with this project: to Peter Momtchiloff, of Oxford University Press, for his support and patience, at all stages; to Christian List, for his assistance in preparing Peter Menzies’ last paper for inclusion; to Professor Catriona Mackenzie, for her kind permission to include that paper in the volume; and most of all, of course, to Peter himself. Our gratitude to Peter reaches well beyond his own contributions to this volume, or indeed his own writings as a whole. Like many in our field, we also owe him a great debt for his role as a collaborator, colleague, and teacher, over thirty years. Those of us who were fortunate enough to work with Peter find it easy to understand why he was such a successful teacher and supervisor, held in such grateful regard by generations of students. He combined patience, equanimity, generosity, and unfailing good humour, with insight, exceptional clarity, and an almost encyclopaedic acquaintance with relevant parts of the literature. In effect, he made it impossible for his students, and his collaborators, not to learn, and not to enjoy the process. As Dr Lise Marie Andersen (Aarhus), one of Peter’s last PhD students, puts it: ‘As a supervisor Peter was patient, warm and extremely generous with his time and knowledge. As a philosopher he was an inspiration.’ He is sadly missed.

References Collins, J., Hall, E. J., and Paul, L. A. (eds). 2004. Causation and Counterfactuals. Cambridge, MA: MIT Press. Craver, C. 2007. Explaining the Brain. New York: Oxford University Press. Hall, E. J. 2004. ‘Two Concepts of Causation’, in Collins, Hall, and Paul 2004: 225–76. Kim, J. 1998. Mind in a Physical World: An Essay on the Mind-Body Problem and Mental Causation. Cambridge, MA: MIT Press. Lewis, D. 1973a. ‘Causation’, Journal of Philosophy, 70: 556–67. Reprinted in Lewis 1986: 159–72. Lewis, D. 1973b. Counterfactuals. Oxford: Basil Blackwell.

HELEN BEEBEE, CHRISTOPHER HITCHCOCK, AND HUW PRICE



Lewis, D. 1979. ‘Counterfactual Dependence and Time’s Arrow’, Noûs, 13: 455–76. Reprinted in Lewis 1986: 32–52. Lewis, D. 1986. Philosophical Papers, Volume II. Oxford: Oxford University Press. List, C. and Menzies, P. 2009. ‘Non-reductive Physicalism and the Limits of the Exclusion Principle’, The Journal of Philosophy, 106: 475–502. Machamer, P., Darden, L., and Craver, C. 2000. ‘Thinking about Mechanisms’, Philosophy of Science, 67: 1–25. Menzies, P. 1996. ‘Probabilistic Causation and the Pre-emption Problem’, Mind, 104: 85–117. Menzies, P. 2004a. ‘Causal Models, Token Causation, and Processes’, Philosophy of Science, 71: 820–32. Menzies, P. 2004b. ‘Difference-making in Context’, in Collins, Hall, and Paul 2004: 139–80. Menzies, P. 2007. ‘Causation in Context’, in H. Price and R. Corry (eds), Causation, Physics, and the Constitution of Reality. Oxford: Oxford University Press, 191–223. Menzies, P. 2011. ‘The Role of Counterfactual Dependence in Causal Judgements’, in S. Beck, C. Hoerl, and T. McCormack (eds), Understanding Counterfactuals, Understanding Causation. Oxford: Oxford University Press, 186–207. Menzies, P. 2012. ‘The Causal Structure of Mechanisms’, Studies in History and Philosophy of Biological and Biomedical Sciences, 43(4): 796–805. Menzies, P. and Price, H. 1993. ‘Causation as a Secondary Quality’, British Journal for the Philosophy of Science, 44: 187–203. Nolan, D. 1997. ‘Impossible Worlds: A Modest Approach’, Notre Dame Journal of Formal Logic, 38: 535–72. Pearl, J. 2009. Causality: Models, Reasoning, and Inference, Second Edition. Cambridge: Cambridge University Press. Stalnaker, R. 1968. ‘A Theory of Conditionals’, in N. Rescher (ed.), Studies in Logical Theory. Oxford: Basil Blackwell, 98–112. Woodward, J. 2003. Making Things Happen: A Theory of Causal Explanation. Oxford: Oxford University Press. Yablo, S. 1992. ‘Mental Causation’, The Philosophical Review, 101: 245–80.

2 Causal Counterfactuals and Impossible Worlds Daniel Nolan

There seem to be tight connections between claims about what caused what, and many claims about what would have happened if things had been otherwise.1 A special, but important, case of these are the connections between causal structure and what would have been different had things been different. A lot of careful and ingenious work has gone into trying to articulate the connections between the two, though it is probably safe to say that no completely satisfactory account has yet emerged: or at the very least, those who are completely satisfied with an account of the connection between causation and counterfactuals are few, and disagree with each other about which is the completely satisfactory account. This chapter is not directly in the service of either of the ambitious analytic projects of analysing causation in terms of the holding of certain counterfactuals, nor of analysing counterfactuals in terms of causal matters. It focuses instead on one of the traditional puzzles that connect the two that arise almost whatever one takes the connection between counterfactuals and causation to be. The puzzle has no neat label that I am aware of, but it arises in its clearest form when we consider counterfactuals involving antecedent states that involve a difference from the actual course of events at a particular time, and a consequent, at least in part involving a state somewhat later than the time of the antecedent difference. In the possible worlds framework, the puzzle is often put in terms of what other differences there are in the relevant possible worlds where the antecedent is true. Do those worlds match ours with respect to nearly all their pasts until the time relevant to the antecedent? Do they require ‘small miracles’ relative to the laws of the actual

1

This research was supported by the Australian Research Council’s Discovery Projects funding scheme (project number DP130104665). Thanks to the audience at the Doing Philosophy: From Metaphysics to Ethics Workshop at Bundanoon, NSW and to Arif Ahmed, Helen Beebee, Rachael Briggs, Adam Elga, Alan Hájek, and Peter Menzies for discussion. Especial thanks, also, to the late Peter Menzies for his role in introducing me to the topics I have been grappling with in this chapter: he will be sorely missed.

DANIEL NOLAN



world? Is their causal structure the same except for an ‘intervention’ on a state associated with the antecedent?...and so on. Let me label this problem the ‘deviation problem’ to suggest that it concerns what deviations from actuality would be required for the antecedent to be true, in the class of counterfactuals of interest. In this chapter I will propose a novel solution to the deviation problem. This solution will have several signal advantages over a number of the better-known proposed solutions to this problem, though it also incurs some distinctive costs. I am not sure, then, whether something like it will turn out to be the best solution, though I am sure it deserves a run for its money alongside its better-known cousins. I will do so by presenting the puzzle and solution in a closest-worlds framework of the Stalnaker– Lewis variety: those familiar with alternative systems will likely be able to see easily enough how to fit the kind of positive proposal I offer into those approaches. After some remarks about the problem my solution is intended to solve, and the kinds of resources I will deploy to construct my version of the solution, I will argue for a number of desiderata for a solution that traditional approaches compromise, before presenting my solution and displaying that it can satisfy those desiderata. Finally, I will discuss some of the vices of the particular solution I offer, and while I do not intend to suggest this solution is without costs, I will have some things to say about why those vices may not be as great drawbacks as they might initially appear.

1 The Target The problem I wish to address in this chapter is more specific than the general problem of the truth conditions of counterfactuals. It is the narrower problem of offering a story about the truth conditions of what I am calling causal counterfactuals. So it would be good to begin by being a bit more specific about which counterfactuals I have in mind. The counterfactuals I will pay attention to are those whose antecedents concern a specific one-off event or state, and their consequents deal with what happens after that event or state (or as a consequence of a failure of the antecedent event to influence the consequent). Furthermore, they are the non-backtracking counterfactuals of this sort. A backtracker, intuitively, is a counterfactual that invites us to consider what would have had to be different in the causal ancestry of an event if it were to have come about. How exactly to demarcate which counterfactuals are backtrackers is controversial, but see Lewis 1979 (33–4) for the locus classicus of a characterization of back-tracking conditionals. The causal counterfactuals that are my focus here all come with an antecedent time.2 Some counterfactual conditionals have antecedents that are about a relatively particular event: ‘if I had set the fire alarm off at 11.00 this morning, the fire service would have been here by 11.30’. In such cases, we can talk about a particular time associated with Lewis 1979 introduces the idea of an antecedent time TA, though he characterizes it as ‘the time the antecedent is about’, which is not quite how I will characterize the notion I wish to use. 2



CAUSAL COUNTERFACTUALS AND IMPOSSIBLE WORLDS

the antecedent: roughly, the time at which the situation described by the antecedent would have obtained. In the example, that time would be some period around 11 a.m. Many other antecedents suggest a time in a much less explicit way. ‘If I had skipped breakfast, I would have had more to eat at lunch’ suggests a time around my normal breakfast time, or perhaps my actual breakfast time. Not every counterfactual is associated in this way with a time, and it would be natural to extend the account given to cases where there are a number of salient times associated with an antecedent of a causal counterfactual, but I will restrict my discussion for tractability. For the purposes I want to use the notion, the ‘antecedent time’ associated with a counterfactual will not always be the exact time that the event associated with the antecedent would take place. It will often need to extend some relatively short time before that event. The motivating idea is that the antecedent time is the time at which a world where the antecedent occurs would have to rapidly become quite different from the actual world, so will typically involve difference from the actual world some time immediately before as the ‘run-up’. (Were I to have turned off on the previous exit ramp, it would not be by a last-minute swerve or by teleportation, but rather may well have been by getting into the correct lane, signalling a turn, etc.) So it seems better to say that the antecedent time can include some period before the time of the event explicitly invoked by the antecedent. A tricky and unsolved problem is exactly how much of the run-up to the relevant event is best to include in the ‘antecedent time’. The puzzle about setting an antecedent time is unfinished business, but the details should not matter for current purposes.3 The target problem, then, is the deviation problem for causal counterfactuals. What would be different were the antecedent of a causal counterfactual true? Or, to put it in the world terminology introduced in §2, what are the most relevantly similar worlds where the antecedent of such a counterfactual is true? The proposal to be offered will be straightforwardly generalizable in a number of ways, including to cases where antecedents have a number of natural antecedent times associated with them, to some counterfactuals with general antecedents, and even to counterfactuals where the states associated with the antecedent and consequent are non-causally related. But the interested reader can chart for herself how the proposal in this chapter can be generalized, as even the relatively narrow range of counterfactuals I have picked out will give us quite enough fish to fry.

2 Resources The most salient commitment of the approach to be used is to an apparatus of worlds, possible and impossible. Relying on accounts of counterfactual conditionals 3 A general account will also need to say when an antecedent time ends, and may want to derive the fact that we treat the past differently from the future in causal counterfactual contexts from some more basic principle.

DANIEL NOLAN



in terms of possible worlds has, by now, a long history, with the important papers of Stalnaker 1968; Stalnaker and Thomason 1970; and Lewis’s influential 1973 book helping to make this approach to counterfactuals close to orthodox. I will adopt some of the details of Lewis’s specific proposal. For the counterfactual A □➞B to be true at a possible world w, B must be true at all the ‘nearest’ worlds to w where A is true (and A □➞B is false otherwise). Lewis explains nearness in terms of similarity, and holds that which aspects of similarity are relevant is set by the context in which the sentence expressing A □➞B is produced (I will have more to say about context, below). In Lewis’s framework a lot of the work in determining the truth value of a counterfactual is done by the similarity measure on worlds. The dimensions of relevant similarity are not a matter of all-things-considered similarity (whatever that would be), but are rather a matter of similarity in relevant respects. Which are the relevant respects, and how they are weighted against each other, is then a central question for this account (and, given that the account says that relevant similarity is determined by context, a question that must be re-asked for each context of utterance). Lewis 1979 is his account of what he takes the relevant dimensions of similarity to be for causal counterfactuals, and while I will not be endorsing that account, it is an example of the kind of account that is needed. This chapter will follow Lewis in appealing to comparisons of relevant similarity as part of the machinery for delivering truth conditions of counterfactuals. Both Lewis’s and Stalnaker’s systems were constructed so that when the antecedent of a counterfactual was impossible, the counterfactual was automatically true. However, it does seem very natural to not treat counterfactuals with impossible antecedents all in the same way: these so-called counterpossible counterfactual conditionals seem to be usefully employed in logic, mathematics, metaphysics, and in many other areas (Nolan 1997). For convenience, I will refer to these conditionals simply as ‘counterpossibles’, though that label often has a wider application to all sorts of conditionals with impossible antecedents (including indicative conditionals, for example). The easiest way to incorporate counterpossibles into a world’s framework is to include impossible worlds as well as possible worlds in the account of truth conditions of counterfactuals. Consider the conditional ‘If 27x4 were 131, then 131 would be composite’. Plausibly, of the impossibilities where 27x4=131, the most relevantly similar to actuality are those where being the product of two whole numbers other than 1 or 0 is sufficient for being composite, and will treat that consequent as true. On the other hand, when evaluating ‘If 27x4 were equal to 131, then 27x4 would be equal to 1310’, then the same, or a very similar, 27x4=131 worlds seem most relevantly similar: and in none of those will 27x4=1310. That would be a gratuitous departure from actual mathematical truth, so the second counterpossible mentioned is false. A full account requires a story about what makes for relevant similarity between a possible and impossible world, of course. The particular example above may not strike everyone as convincing. But what is important is to notice that treating some impossible worlds as more relevantly similar



CAUSAL COUNTERFACTUALS AND IMPOSSIBLE WORLDS

to actuality than others is a natural way to extend the basic Lewis/Stalnaker semantics for counterfactuals. If we do so, we face a number of choices about how to understand these impossible worlds. One straightforward way to do so is to model them as sets of propositions: but to not insist that these sets are closed under logical consequence. Modelling worlds as arbitrary sets of propositions will give us possible worlds as well as impossible ones, but it should not matter exactly where we draw the possible/ impossible line, except that I will assume that sets of propositions which are jointly inconsistent are associated with impossibilities. One distinction is particularly important to keep in mind when employing impossible worlds: the distinction between what is true according to an impossible world and what is true about an impossible world. (Something like this distinction is sometimes characterized as the distinction between what is true in a world versus what is true of a world, but that terminology can be more confusing.) An impossible world may not have true according to it that what happens is impossible, for example: it might represent that everything that happens in it is possible. It may not have true according to it that a contradiction is true, even if the proposition that roses are red, and also the proposition that roses are not red, are both true according to it. Suppose we model impossible worlds with sets of propositions, as above. One set can contain the proposition that there is a round square cupola, while also containing the proposition that everything which exists is possible. One set can contain the following three propositions: that roses are red, that roses are not red, and that no contradictions are true. Even though the first set contains a proposition that there is a round square cupola, and so it is true about that set that it represents that there is an impossible object, it is not true according to the set. The second set contains a contradiction, so it is true about the set that it is contradictory, but the proposition that a contradiction obtains is not true according to the set, understood as an impossible world (or a fragment of one). Alternative theories of impossible worlds will offer different ways of accounting for the according to/about distinction, but the illustration should suffice to indicate the distinction I have in mind. As well as worlds, possible and impossible, ordered by similarity in relevant respects, the account of causal counterfactuals I will develop shares with many such accounts a commitment to laws of nature rich enough to impose constraints on the evolution of the world in the respects we care about. I will try to stay relatively neutral on how to understand these laws of nature: in particular, as mentioned above, I will not take a stand here on whether some kind of Humean regularity account of laws of nature is sufficient, or whether something more metaphysically heavy-duty is required. I will presuppose for the rest of the chapter that laws of nature are contingent, in the sense that they can vary from possible world to possible world. I do this in a concessive spirit, however: appeals to impossible worlds to evaluate causal counterfactuals are much more appealing if any rival laws of nature are impossible, and hold in no possible worlds at all.

DANIEL NOLAN



A resource that will be lurking in the background is the view that counterfactuals exhibit a certain amount of context sensitivity, here implemented by allowing that which standard of relevant similarity can vary from one context of utterance to another. This context variability of counterfactuals also makes a difference to how I am conceiving of this project. It is not the task of providing the truth conditions of all counterfactuals whatsoever, nor of isolating some semantic ambiguity in conditional locutions so that one disambiguation is the ‘causal’ one. It is to explain the truth conditions of some uses of counterfactuals: perhaps many typical counterfactual utterances. I take it this context-sensitive approach to counterfactuals is in the spirit of Lewis’s (1979: 33–5), but not in the spirit of everyone who offers closest-world analyses of counterfactual conditionals: Bennett 2003 does not allow for contextual variability, for example.

3 Desiderata for a Solution Given a closest-world approach to counterfactual conditionals, a solution to the deviation problem will be the specification of some conditions on relevant similarity. This specification will ensure the most relevantly similar worlds when evaluating a causal counterfactual are ones that are not gratuitously different from ours, and line up with correct counterfactual judgements. That is, when the causal counterfactual ‘A □➞B’ is true, the most relevantly similar worlds according to which A is true are ones that have B true according to them as well; and when ‘A □➞B’ is false, this condition will not obtain. There are three plausible desiderata for this solution that are each supported by plausible arguments. They appear to be jointly inconsistent if we want to get the intuitive truth values for ordinary causal counterfactuals, and so solutions to the deviation problem in the literature give up on one or more of them. In this section I will outline and defend each of these desiderata, before explaining in the next section how we can maintain all three in a solution to the deviation problem.

3.1 The Same Laws of Nature, and No Counterfactual Miracles When considering a counterfactual situation, we initially assume the same fundamental principles of nature are at work. There are at least two reasons to think that we do this: one is that we freely employ stable generalizations about what leads to what when reasoning about whether things being a certain way at the antecedent time leads to the consequent obtaining. (Hmm, the weight would have been here, so the scales would have moved to here, so that would have tripped the lever...) The second reason is that, for the kind of antecedents found in causal counterfactuals, ‘if it had been that A then the laws of nature would have been different to the actual laws of nature’ rarely sounds like an appealing counterfactual. That suggests that for most of these antecedents, the relevantly similar worlds where they are true are not ones where the laws of nature differ from the actual laws. For that matter, ‘even if it had



CAUSAL COUNTERFACTUALS AND IMPOSSIBLE WORLDS

been that A, the laws of nature would have been the same’ also normally sounds fine, if a little odd to utter—we tend to take for granted that various differences would not have resulted in different laws of nature. Perhaps despite these observations, the laws of nature at such counterfactual worlds need not be exactly the same. Even if they are not exactly the same, presumably they should not be too arbitrarily different—that would violate the motivating idea of similarity in relevant respects, at least insofar as we are concerned with laws that affect the influence (or not) of the antecedent event on the state associated with the consequent. Despite this initial appeal, a number of authors have endorsed the option that the nearby worlds where the antecedent obtains vary with respect to the laws. Terminology for these deviations from actual laws of nature introduced by Lewis labels them as ‘miracles’.4 Let me now say in some more detail why we should not be happy with a theory that invokes miracles for standard causal counterfactuals. Had things been different in various ordinary ways, that would not have taken a miracle, or so we think. My having lunch at a different cafe, or Everest being found twenty metres closer to K2 than it in fact is, or there being half a tank of petrol in a car instead of a full tank, would not require violations of the actual laws of nature. Or so we ordinarily think. Of course, we could be radically wrong about the actual laws of nature: perhaps everything that happens, happens as a matter of nomic necessity, for example. And I do not mean to say that no counterfactual whose antecedent is about specific causal processes could have a consequent saying there were miracles and still be true: if I were to cause a miracle worker to perform miracles, there would be a miracle. In ‘Are We Free to Break the Laws?’ (Lewis 1981) Lewis defends the view that some possible agents in deterministic worlds are free to perform acts such that, if they perform them, a miracle would occur. And in Lewis 1979, he defends the view that in deterministic worlds, often the nearest world in which standard antecedents for causal counterfactuals are true are ones with miracles: ‘small miracles’, that do not make for too much distance between worlds. Lunching at a different cafe, Everest being a little closer to K2, cars having different levels of petrol in their tank, and so on are all compatible with the actual laws of nature. We are inclined to think that were any of these things the case, we would not need to have different laws of nature, but just differences in ordinary matters of fact. Nobody trying to change the level of petrol in a car ever tries to do this by changing the laws themselves. Very few people who regret they did something that was under their control blame the laws of nature rather than their particular actions. I do not think those who are led to suppose that leaving a chip uneaten, or putting on a

4 Well, strictly speaking, the definition should make no mention of the actual world: an event in w1 counts as a miracle according to a possible world w2 provided the event is against the laws of w2, and I intend this general definition to be the one in force: but the more general definition is unnecessary to get the idea.

DANIEL NOLAN



different shirt in the morning, would have taken a miracle, do so because that strikes them as the pre-theoretically compelling view: rather, they seem pushed there by the apparent lack of a feasible theoretical alternative that has other features they want. If quotidian things could be otherwise without requiring miracles, that would seem preferable. For one thing, miracles cannot happen. (That is, events that in fact violate our laws are nomically impossible—though they are possible in a more generous sense, and are nomically possible in the worlds where they occur.) But wearing a different shirt or not eating a chip are things that can happen, we ordinarily think. On the face of it, were they to happen, nothing impossible would need happen. The case for requiring miracles in the nearby worlds relevant for ordinary causal counterfactuals often requires some other assumptions: that those worlds share a lot of other truths with ours, and that the laws tightly constrain how things can be at the antecedent time given those other truths, or at least that we should have an account flexible enough that it delivers similar results even when the laws restrict the possible outcomes in this way. Let us, then, turn to the other two desirable features the nearby (i.e. relevantly similar) worlds should have when evaluating causal counterfactuals.

3.2 Common Past The first two constraints suggest a picture: that we consider the closest worlds where what happens at some time associated with the antecedent varies from what in fact happens, but are otherwise as similar as feasible, in respect of what happens at that time, to the actual world; and which obey the actual laws of nature at all the times in those worlds (and perhaps shares the actual laws of nature to boot). One feature that this approach would have is that it may well result in some of the closest worlds having quite different pasts from the actual world. It is a familiar point that in a world that is deterministic and chaotic (in the technical sense of chaotic), very small changes at one time can result in very great differences in the future: one butterfly flaps its wings in one place, and a tornado, that would not have otherwise happened, happens on the other side of the world a year later.5 In such deterministic and chaotic worlds, fixing the physical state at a time and determining what follows, given that state and the laws, for earlier times can produce equally extravagant differences. An extra butterfly flapping its wings now, plus the laws, might entail tornadoes in the years before that are absent from the actual world. The oddness of these counterfactual worlds diverging in their pasts (and in some cases, more and more radically as times considered are earlier and earlier than the antecedent) may only seem a curiosity so long as we consider causal counterfactuals with consequents only about the future. But they give incorrect results about a range of counterfactuals which have consequents that are partly about the future and partly 5 I am not aware of any meteorological model that is this sensitive to slight air movements, and the case that the weather is this sensitive has not been made, to my knowledge: but the illustration of the principle is useful enough, perhaps as a convenient fiction, even if actual weather systems do not behave like this.



CAUSAL COUNTERFACTUALS AND IMPOSSIBLE WORLDS

about the past. Cases like this have been presented by Lewis (1979: 33) and by Bennett (2003: 202, 214). Let me present two, very ordinary, cases of this sort. Suppose I have just come home and looked through my bag, worried about my umbrella, and located it. I say ‘if I had left my umbrella in the bar, that would have been the third umbrella I’d have lost this month’: and let us suppose that counterfactual is true in the envisaged case. For that to be true, the nearest umbrella-in-thebar worlds have to be worlds that do not just have to resemble ours with respect to laws or how the world unrolls from the incident in the bar, but must also agree with ours in how many umbrellas I had lost earlier in the month. Examples like this can be multiplied indefinitely: it is very natural to utter counterfactuals with consequents that require all sorts of matches with the actual past to be true. The natural thing to think, here, is that our practice of uttering causal counterfactuals takes for granted that the past before the antecedent time would be as it in fact is. Counterfactuals like these also count against theories that consider situations with no past before the antecedent time: see Paul and Hall 2013 (47–8) for a proposal of this variety.

3.3 Compatibility with Determinism, and Near-Determinism If determinism is true, then necessarily if the laws are as they actually are and some complete time slice of the past is as it actually is, then every other event will be as it actually is. So given determinism, keeping both the laws and the past the same is a challenge if we are looking for a relevantly similar world W where some antecedent which is actually false is true according to W. A theory that is compatible with determinism is one that allows that even when an antecedent of a causal counterfactual is false at a deterministic world, still there will typically be worlds relevantly similar to that world in which that antecedent is true. Indeed, the past and the laws will be able to rule out some antecedent times varying from what actually happened even if determinism is not true. Having indeterministic laws is not the same as saying that anything goes: it just means that there can be some variation in worlds that share some common past and the same laws. If our laws were indeterministic about some phenomena but not others, or some stages of the evolution of the universe but not others, they might still have the result that the past before an antecedent time, plus those laws, guarantee that the antecedent will not occur at the antecedent time. Call such cases cases of ‘near-determinism’. Some philosophers’ reactions will be that this is so much the worse for determinism, and near-determinism. Some are inclined not to worry about how an account of counterfactuals deals with determinism and near-determinism, since the kind of indeterministic world we inhabit seems to be one where almost any event permitted by the laws at all could happen after almost any history, albeit often with a vanishingly small chance of in fact doing so. However, I think there are several reasons to prefer an account that can vindicate many of our ordinary causal counterfactuals even if determinism were true, and one reason to like the style of account that can

DANIEL NOLAN



accommodate determinism even if our focus is only to produce an account fit for the sort of indeterministic world many take us to in fact be in. One reason to look for a theory compatible with determinism is our tendency to, at least sometimes, treat determinism as irrelevant for causal counterfactuals. ‘Okay, I wouldn’t have left my umbrella behind, given the past and the laws. But if I had, would I have been able to get it back?’ Since we are (presumptively) competent users of counterfactual expressions, that suggests that determinism would not by itself render all causal counterfactuals vacuous or otherwise defective. Another, related, reason is that apparently competent users did not eschew the construction when determinism was widely believed (at least among the Newtonian intelligentsia). This chapter will remain of some interest even for those unconvinced of these motives to have an account compatible with determinism. After all, the issue of whether determinism would have serious consequences for the truth values of causal counterfactuals can be of interest (perhaps relatively academic interest) even to those convinced of indeterminism: and so the prospects of theories that yield the normal truth values for causal counterfactuals even in deterministic worlds otherwise rather like our own (superficially, at least), should be of interest in weighing up different verdicts about what impact determinism would have on causal counterfactual propositions. One reason why it is instructive to consider options for counterfactuals under determinism is that some of the pressures on theories of counterfactuals under indeterminism are similar. Some indeterministic frameworks, including the ones that most plausibly describe the actual world, can produce variation from actuality at the antecedent time, while keeping the laws and past fixed, only at the cost of strange and mind-bogglingly unlikely chance events: quantum tunnelling, massive spontaneous decay, and the like. Call an incredibly unlikely quantum event that would mimic a Lewisian miracle a ‘semi-miracle’. (Note I do not mean a ‘quasimiracle’ in Lewis’s sense (1986: 60), which is its own can of worms.) Solving the deviation problem by keeping the past and laws fixed and postulating a semimiracle to bring about an antecedent looks only a little less bad to many than postulating Lewisian miracles. If you think that semi-miracles should not be needed in an account of counterfactuals under the sort of indeterminism we probably have in this world, then you have a similar dilemma to the determinist. Just as same laws (and no miracles), same past, and a contrary-to-fact event at the antecedent time form an inconsistent triad, same laws, same past, a typical contrary-to-fact event at the antecedent time and no semi-miracles at the antecedent time will often be an inconsistent tetrad, when ‘semimiracle’ is understood in the appropriate way. The solution I will offer those who wish to allow for determinism will be straightforwardly adaptable for those who wish to endorse typical causal counterfactuals under indeterminism without its being true according to relevantly similar worlds that semi-miracles occur.



CAUSAL COUNTERFACTUALS AND IMPOSSIBLE WORLDS

3.4 Theorists Often Compromise on These Desiderata Given the above desiderata, it is easy to see why many theorists have thought one or more of them has to go. There is apparently a tension. If world W is deterministic, then the past of W plus the laws of W entail all the other propositions true according to W. (All the other propositions about events subject to the laws of nature, in any case.) So if the antecedent of a counterfactual, A, is true according to a world with the same laws and same past as W, it looks like A would have to be entailed by W’s laws and the past. So when we want to consider some counterfactual world which disagrees with W— when we want to consider a counterfactual with an antecedent A that is false according to W—it seems that something has to give, out of the laws and the past. Different attempts to solve the deviation problem give up one or more of the desiderata listed above. For example, Lewis (1979) offers two accounts that address the deviation problem, and settles on the second. (Both presuppose determinism for purposes of tractability, though he offers some remarks about how to extend them to indeterminism in Lewis 1986.) Lewis’s first account is not presented as a closestworlds account, though it is easily paraphrased into one. Both options Lewis considers violate one or more of the desiderata, above. The first permits violations of the actual laws during ‘a transition period beginning shortly before tA’ (Lewis 1979: 39) (in my jargon, violations of actual law during the ‘antecedent time’). Lewis’s second proposal in principle allows for violation of both the desideratum about laws and the one about a common past (and indeed for cases where both are violated): but in practice it lends itself to violations of the principle about laws in deterministic worlds. Typically, the relevantly similar worlds are ones that contain miracles relative to the deterministic worlds. Jonathan Bennett (2003) talks of ‘forks’, which occur in relevantly similar worlds when the world first diverges from the actual world in a significant way. He talks of forks happening not long before what he calls the antecedent time TA. In my usage, Bennett’s whole fork happens within what I call the antecedent time. Bennett allows that forks can happen in one of three ways in the relevantly most similar worlds. One is through indeterministic variation. The second is through a miracle in Lewis’s sense. The third way does not require any changes in laws, even in deterministic worlds, but only ‘tiny imperceptible’ differences in great stretches of the past (Bennett 2003: 217–18). This violates the ‘common past’ desideratum in a comparatively lowcost way, at least in worlds that have laws kind enough to permit it, since while worlds differing in this way do not have common pasts, they have pasts that are the same in a number of respects we care about. Bennett wishes to allow that all three of these methods of forking can occur in the relevantly similar worlds (Bennett 2003: 218). Only the second two will be available in deterministic worlds (and in some indeterministic ones): so in effect, Bennett compromises both the desideratum about laws and the desideratum about the common past.

DANIEL NOLAN



One increasingly popular style of analysis of causal counterfactuals is to invoke the sort of causal models popularized by Pearl (2000). Different theorists have used these models in different ways to offer semantics for causal counterfactuals, but these approaches either compromise on the desiderata listed above or fall silent about the semantics of relevant counterfactuals, or often both. Woodward (2003), for example, both adopts a story of ‘interventions’ for evaluating interventionist counterfactuals that, in effect, asks us to consider setups where there are breaches of actual laws (see Woodward 2003 (136) where he compares his interventions to Lewis’s ‘small miracles’), and in effect only offers a way of understanding only a narrow range of counterfactuals: those whose antecedents and consequents only concern values of variables in causal models, or counterfactuals related to these. (Counterfactuals with consequents about law violations or miracles are not treated.) Menzies (2002: 828) gives a closest-world account of the truth conditions of a wide variety of ‘causally relevant counterfactuals’, albeit truth conditions relative to causal models rather than guidance about which counterfactual claims are true or false simpliciter. I take it the best way to understand Menzies here is in light of Menzies 2004 where he describes his view as a contextualist one: context fixes one or more causal models, and a counterfactual in a context is true provided it is true relative to the contextually relevant model(s). While Menzies’ account is broad enough to evaluate counterfactuals with any propositions in their antecedents and consequents (as a result of using complete worlds in the semantics), on the face of it this view also compromises the desideratum that there are no law violations. In systems that are comprehensive enough so that the initial conditions and the laws guarantee the falsehood of the antecedent, ‘miracles’, in the Lewisian sense, occur in the closest worlds where the antecedent obtains (Menzies 2004: 164). Menzies also allows other law violations and differences in initial conditions for some counterfactuals, but says these are not the typical case for the sort of conditionals we are presently considering, as opposed, for example, to explicit counterlegals or backtrackers (2004: 163–5). Menzies’ version of a causal models theory of counterfactuals does have some signal advantages over others in dealing with the present puzzle. The ‘laws’ of one of Menzies’ causal models do not need to be the really-and-truly laws of nature, even when a causal model is one of the appropriate ones given a context. When an ‘interfering factor’ is not ruled out by the laws of a causal model, the nearest worlds where the laws of the model and the initial conditions obtain may have interferers, even if the model is a deterministic one. Menzies also does not insist that a contextually salient causal model need be actually instantiated: the actual world may contain interferers the model is silent about. So the laws of a contextually appropriate causal model need not even be true universal generalizations. While Menzies himself is willing to employ miracles, a Menzies-style view that used enough of these other resources could be developed to preserve all of the desiderata I mentioned in most cases. In some special contexts and worlds, however, when



CAUSAL COUNTERFACTUALS AND IMPOSSIBLE WORLDS

the contextually salient causal models are (i) instantiated at the world of utterance, (ii) comprehensive enough to rule out interferers, and (iii) deterministic, even a Menzies-style view will have few options but to violate one of our desiderata. There are, of course, many revisionist options for assigning truth conditionals to counterfactuals, including taking their truth-conditions to be those of the material conditional, offering a non-truth-apt account, or endorsing the claim that they are nearly all false (for the last see Hájek unpublished). I will assume, for the purposes of this chapter at least, that we should prefer a theory of the truth conditions of causal counterfactuals that more closely tracks our reflective assent and dissent: classifying counterfactuals as true when we take them to be true in good conditions, and false when we take them to be false in good conditions. (And where our guide to which conditions are ‘good’, in this sense, is our ordinary standards for counterfactual evaluation, not our standards ‘enlightened’ by much philosophical theorizing.)

4 The New Option The option I wish to propose satisfies all of the desiderata discussed above. For a causal counterfactual to be true at a world W, it must be that all the nearest worlds according to which the antecedent is true, and which meet certain other conditions, are worlds according to which the consequent is true as well. The conditions on the worlds W* nearest to W are: first, that the laws of nature true at W are true according to W*. Second, that for the antecedent time t, claims entirely about the goings on in W* before t are true according to W* if, and only if, they are true according to W. Third, no proposition is true according to W* which says that a violation of the laws of nature occurs.6 Let us in addition require that there will be some worlds among the W*s where the antecedent is true, and the nearest of the worlds in W* where the antecedent is true are worlds where the time after t is constrained to evolve by the goings-on at t and the laws of nature in the natural way (however it is best to spell that out). What this proposal does not insist on, however, is that the closest worlds to actuality where the two conditions are satisfied and the antecedent is true are possible worlds. It might well be that a certain past, together with things being a certain way at an ‘antecedent time’, is strictly inconsistent with a certain body of laws of nature. There is an important respect in which these worlds do not give rise to miracles: even if there is a proposition true according to them about what happens that in fact is inconsistent with the propositions true according to them about the laws, or indeed about what mere universal generalizations hold in these worlds, still the world may not have true according to it that there are any law violations, and may have no contradictions true according to these worlds. What is true according to possible worlds is closed under logical consequence, but this is not in general the case for 6

When considering the indeterministic case, we may also wish to insist that no proposition to the effect that a semi-miracle occurs at W* occurs, or something more sophisticated along those lines.

DANIEL NOLAN



impossible worlds. This respect in which they do not give rise to miracles is important, because the truth value of counterfactuals such as ‘if I had skipped lunch, something ruled out by the actual laws of nature would have occurred’ depends on whether ‘something ruled out by the actual laws of nature occurred’ is true according to the relevantly most similar lunch-skipping world. And even if the conjunction of the actual past, the actual laws, and my skipping lunch is inconsistent, impossible worlds representing all three need not have true according to them that there is a law violation, either of their own laws or the actual laws. There would be more to say about relevant similarity in a complete account. For example, I have not tried to spell out explicitly what conjunctions of information about the past before the antecedent time plus the future of the antecedent time are true according to such closest worlds. There must be plenty of the usual ones, on pain of not vindicating the right counterfactuals that have consequents partly about the past and partly about the future, like the examples in §3.2. It is not necessary to spell out all of the details exactly in order to evaluate this style of proposal, however: nor, indeed, would an exact specification of any sort be very plausible, since there is likely to be some semantic indeterminacy as to exactly which counterfactual conditionals are true in which contexts. Still, enough has been said to make clear why, once we appeal to impossible worlds, we can retain the laws and past of W together with the antecedent, while holding on to many of the ordinary verdicts about the truth values of different causal counterfactuals: and can do this even if determinism, or something like it, is true in our world, or a world like ours. The compromises explored by Lewis, Bennett, and others are not needed after all. Furthermore, we can see why the quick argument in Lewis 1981 fails: he suggests that we can discount worlds where contradictory propositions are each as true as relevantly nearest, ‘for if I had raised my hand, there would still have been no true contradictions’ (Lewis 1981: 292). But ‘there still are no true contradictions’ (or however else we should extract the consequent) need not fail to be true according to any of the impossible worlds that are relevantly nearest in such a case: Lewis’s objection fails to touch the proposal in this chapter. There is at least one intuitive motivation for appealing to impossible worlds as a principled way out of our puzzle, and not just a technical fix. The thought is that when we evaluate a causal counterfactual, we neglect some features of counterfactual scenarios, including, to some extent, the gritty detail of how the goings-on specified in the antecedent emerged from the past of the world under consideration. (Consideration of the gritty details tends to put us more in a frame of mind to evaluate backtracking counterfactuals: had A happened, how would it have come about?) Furthermore, this neglect is not just due to our ignorance about the exact processes that our past and laws permit. It may be that the rules of the practice itself are insensitive to some of the details here. If the principles of the practice are somewhat insensitive to these details, then even if the practice is primarily concerned with imposing constraints that it is individually possible to satisfy (sameness of laws,



CAUSAL COUNTERFACTUALS AND IMPOSSIBLE WORLDS

sameness of past, sameness of the kind of dependence the future displays on the laws plus the arrangement of the antecedent time), philosophers may well be over-idealizing if they look for scenarios that are possible all-things-considered, rather than just matching possibilities in a number of respects, respects which conflict in an area with which the practice is not particularly concerned. If this picture is the right way of thinking about the counterfactual scenarios relevant to causal counterfactuals, then the discovery that these scenarios are all-things-considered impossible no longer seems particularly objectionable, nor even particularly surprising once we see how the competing demands of actual laws, actual past, and counterfactual antecedent can be inconsistent given determinism, or something close to determinism. The new option I have proposed satisfies all the desiderata listed above, and if that is all we were concerned about it might at this point look ideal. Before reaching that conclusion, however, it would be well to look at the apparent costs of the theory. Others may disagree with me about what weight we should give each of these considerations, but I hope at least to touch on the ones most likely to occur to critics.

5 Counting the Costs The first feature that some will take to be a cost is that the account requires impossible worlds as well as possible ones: and even those happy with possible worlds sometimes balk at ways things couldn’t be. (See e.g. Stalnaker 2002.) Positing impossible worlds, and using them in the theory of counterfactuals, seems to me eminently worth doing for reasons entirely independent of puzzles about causal counterfactuals: see Nolan 1997 for arguments to this effect. Employing impossible worlds is not a reason per se to be suspicious of this account. A second potentially objectionable feature of this theory is that it yields the result that many counterfactuals with possibly true antecedents and possibly true consequents nevertheless require evaluations of those propositions at impossible worlds to yield their truth-values. Or, to put it a different way, the theory holds that the nearest worlds where certain possible antecedents are true are impossible worlds: they manage to be closer than all of the possible worlds where those antecedents obtain. This violates a plausible principle I have labelled the ‘Strangeness of Impossibility Condition’ (SIC) (Nolan 1997: 550): the principle that every possible world is closer to every other possible world than any impossible world is to any possible world. This principle is plausible for at least two reasons. One is that it captures the idea that if something A could obtain, its obtaining wouldn’t be impossible: a natural way to try to capture this thought formally would be that, for possible A and impossible I, no case of ‘if A then I’ is true. Another is that if SIC is true, then something like the usual possible-worlds semantics for counterfactuals can hold in the vast range of ordinary cases when the antecedents of the conditionals that concern us are possible. Impossible worlds need only make a difference to truth-conditions when impossible antecedents are in play.

DANIEL NOLAN



Despite these advantages of the SIC, I think there are good enough independent reasons to reject it. I had already expressed some reservations about it in Nolan 1997 (550, 569 fn. 21), and more counterexamples can be found in Vander Laan 2004. In some contexts at least, relevant similarity seems to require that we count some impossible worlds as closer than some possible worlds. Here is a relatively everyday example. Suppose I have been playing a game with a boy called Oliver, where we arrange balls into a square grid, then tip the balls into a bag, then count the balls that come out. Sometimes the total is 4, sometimes 9, sometimes 49...and so on. While playing it, I introduce Oliver to the idea of a square number, in the obvious way. On a particular occasion, we come up with a count of 63 balls from the bag. ‘If the bag had 63 balls in it, 63 would have been a square number’ seems like an appropriate thing for me to say in explaining why I think we miscounted: and I think a true thing to say, in that context. But of course it is possible for that bag to contain 63 balls, and impossible for 63 to be square. So at least in some contexts of utterance of counterfactuals, SIC fails. Even if we reject the SIC in full generality, however, there remains a problem. Many counterexamples to SIC involve relatively unusual cases, or at least unusual contexts of utterance. But the violations of SIC suggested by the theory in this chapter are potentially far more widespread, and infect many more everyday conditionals. In deterministic worlds, almost all false antecedents in causal counterfactuals will invoke impossible worlds: and in indeterministic worlds where the laws put strict limits on what is permitted in the future given the past, many false antecedents will produce SIC violations. If we are to use the strategy of this chapter to avoid semimiracles, even cases where the past and the laws are co-possible with the antecedent may still be ones where the relevantly nearest world may be an impossible one that lacks semi-miracles rather than possible worlds containing semi-miracles. Even those suspicious of the SIC may be inclined to raise their eyebrows at the claim that goings-on in impossible worlds are relevant to the truth value of mundane causal counterfactuals. There are some ways to sugar this pill. If we think of people putting together beliefs about how things typically work, with beliefs about what happened before the relevant time, with beliefs about ordinary ways for the antecedent to be true at the antecedent time, and then roll the situation forward in thought, it might not be so surprising after all that the first three parts of that process might answer to standards that can come into conflict. It is agreed on all hands that we lack an a priori guarantee that the actual laws and the actual past will permit the antecedent to be the case, or permit it to be the case in a non-miracle-like way. Finding some possible situation that meets the demands well enough in a non-obvious way is a sensible thing to try: but when we discover that these worlds are unsatisfactory in various respects (containing miracles, containing different pasts, etc.), then involving an impossible situation that meets all the constraints our practice answers to does, after all, seem like an option that is not so unintuitive.



CAUSAL COUNTERFACTUALS AND IMPOSSIBLE WORLDS

A third dubious commitment of this theory is that it requires a particular account of which worlds are most similar, in relevant respects, to the world at which the causal counterfactuals are being evaluated. Some will find the judgement of relevant similarity straightforwardly implausible. Let us suppose that a world is deterministic, and a strong man is standing, holding a hammer, next to a thin glass vase—and at that world he stands still. Why, apart from the demands of the theory, should we suppose that the most relevantly similar world where that man (or his counterpart) swings the hammer at the vase (or its counterpart) is a strange, inconsistent world, where even though the laws plus the past dictate that he stands still he nevertheless swings the hammer and the glass flies into pieces, and furthermore that according to this world, everything happens in accordance with its laws? We may be able to make some surrealist sense of such an impossibility, but surely a possibility where the laws are slightly different, or the past was different enough to produce a man ready to swing, should be counted as a more similar situation to the world we began with? It is important to remember that not any old similarity judgement can be relied upon when evaluating these theories, and even though it is easy to provoke similarity judgements according to which the impossible worlds invoked in this theory are very dissimilar from worlds like ours, when we focus on the desiderata as giving us our standard, there will not always be a relevantly similar possible world that meets that standard, whatever else might be said for possible worlds that compromise those standards. A fourth and final feature of this account which will make it unattractive to some is that it might sit uncomfortably with analyses of causation in terms of counterfactuals. It seems odd to hold that what causes what depends on how things are in inconsistent and impossible worlds: though which causal counterfactuals are true does seem to depend on how things are in those worlds. Of course, many who favour counterfactual analyses of causation have made their peace with the charge that their view seems to commit them to thinking that what actually causes what depends on the goings-on in different possible worlds, so many of the strategies for dealing with that challenge will be available to this view as well. It can also be protested that, in the important sense of dependence, the causal facts do not depend on the facts about the contents of other possible worlds. Perhaps, instead, both the causal facts and the facts about worlds depend on some deeper actual matter, or it can be pointed out that closeness of another possible world supervenes on what this world is like, so causal matters depend ultimately on actual matters of fact. (David Lewis’s theory has this structure, for example.) Or perhaps the analysis is not one that shows that the truth of one side of the analysis depends on the truth of the other side: it could be claimed that it is a non-reductive analysis, or an important equivalence without one side being ‘deeper’ than the other. My own view is that counterfactual analyses of causation, and other nomic phenomena like laws, chance, dispositions, difference-making, and the rest are

DANIEL NOLAN



unlikely to succeed, and not just because of the technical troubles they have often faced. Still, insofar as they are plausible at all, they would seem to still be in contention even if the suggestion of this chapter about how to account for causal conditionals were adopted.

6 Conclusion We learn very easily how to use and evaluate causal counterfactuals, but it has been frustratingly difficult to capture the truth conditions of these counterfactuals in other terms. While there is something very appealing in closest-world analyses of these conditionals, none of the standard attempts to account for them in that framework have been entirely satisfactory. The attempt presented in this chapter is unlikely to bring our disagreements to a conclusion either. At best, it will be added as yet another option with distinctive benefits, but also distinctive costs. If my diagnosis of the problem we face is correct, the desiderata for a theory of causal counterfactuals appear to be in tension if we restrict ourselves only to possible worlds, so perhaps no ideal solution will be forthcoming. If there is no ideal solution in the offing, then the option set out in this chapter deserves to be in the running for being the best of a group of less-than-ideal options.

References Bennett, J. 2003. A Philosophical Guide to Conditionals. Oxford: Oxford University Press. Hájek, A. unpublished. ‘Most Counterfactuals are False’. Lewis, D. 1973. Counterfactuals. Oxford: Basil Blackwell. Lewis, D. 1979. ‘Counterfactual Dependence and Time’s Arrow’, Noûs, 13: 455–76. Reprinted in Lewis 1986: 32–52. Lewis, D. 1981. ‘Are We Free to Break the Laws?’, Theoria, 47: 113–21. Reprinted in Lewis 1986: 291–8. Lewis, D. 1986. Philosophical Papers, Volume II. Oxford: Oxford University Press. Menzies, P. 2002. ‘Causal Models, Token Causation, and Processes’, Philosophy of Science, 71(5): 820–32. Menzies, P. 2004. ‘Difference-making in Context’, in J. Collins, N. Hall, and L. A. Paul (eds), Causation and Counterfactuals. Cambridge, MA: MIT Press, 139–80. Nolan, D. 1997. ‘Impossible Worlds: A Modest Approach’, Notre Dame Journal of Formal Logic, 38(4): 535–72. Paul, L. A., and Hall, N. 2013. Causation: A User’s Guide. Oxford: Oxford University Press. Pearl, J. 2000. Causality. Cambridge: Cambridge University Press. Stalnaker, R. 1968. ‘A Theory of Conditionals’, in N. Rescher (ed.), Studies in Logical Theory. Oxford: Basil Blackwell, 98–112. Stalnaker, R. 2002. ‘Impossibilities’, in R. Stalnaker, Ways a World Might Be: Metaphysical and Anti-Metaphysical Essays. Oxford: Oxford University Press, 55–67.



CAUSAL COUNTERFACTUALS AND IMPOSSIBLE WORLDS

Stalnaker, R., and Thomason, R. 1970. ‘A Semantic Analysis of Conditional Logic’, Theoria, 36(1): 23–42. Vander Laan, D. 2004. ‘Counterpossibles and Similarity’, in F. Jackson and G. Priest (eds), Lewisian Themes. Oxford: Oxford University Press, 258–75. Woodward, J. 2003. Making Things Happen: A Theory of Causal Explanation. Oxford: Oxford University Press.

3 Two Interpretations of the Ramsey Test R.A. Briggs

One recurring theme in the work of Peter Menzies is that many causal ideas are best understood in probabilistic and counterfactual terms.1 Counterfactual conditionals play a key role in Menzies’ account of negative causation (Menzies 2006), as well as his solution to the exclusion problem (List and Menzies 2009; Menzies and List 2010). While he ultimately rejects the probabilistic counterfactual analysis of causation proposed in Menzies 1989, he maintains that causation is connected to probabilities and counterfactual conditionals through the platitudes used to characterize causation (Menzies 1996), and proposes some reasons for optimism about sophisticated counterfactual analyses of counterfactuals (Menzies 2011). If Menzies is right, then to understand causation, it is important to have an account of when conditionals obtain, what relationships they bear to probabilities, and the conditions under which it is reasonable to believe them. (Below, I will drop the restriction to counterfactual conditionals, though much of what I say bears on counterfactuals rather than indicatives.) An idea called the Ramsey test addresses all three questions about conditionals. According to the Ramsey test, a person should accept a conditional to the extent that she would accept the consequent on the supposition that the antecedent holds—this is an account of the conditions under which it is reasonable to believe a conditional. There are two attractive ways of interpreting the Ramsey test. Adams’ thesis states that the probability of a conditional is the conditional probability of the consequent given the antecedent—in other words, a conditional is probable to the extent that its consequent is probable, if one supposes its antecedent by conditionalizing on it. Stalnaker semantics states that a conditional is true at a world α just in case its consequent is true at all closest antecedent worlds to α—in other words, a conditional

1

Thanks to Albert Atkin, Mark Colyvan, Al Hájek, Christopher Hitchcock, Mark Jago, Peter Menzies, and Robbie Williams for helpful comments on earlier drafts of this chapter.



TWO INTERPRETATIONS OF THE RAMSEY TEST

is true just in case its consequent is true at the world as it would be, if it were minimally modified with the supposition that the antecedent is true. Unfortunately, a well-known class of triviality theorems shows that when the two interpretations of the Ramsey test are combined, they entail seemingly absurd triviality results. Stefan Kaufmann has proposed (for reasons largely independent of the triviality theorems) a revised version of Adams’ thesis, which I call Kaufmann’s thesis. I prove that combining Kaufmann’s thesis with Stalnaker semantics leads to ‘local triviality’ results, which seem just as absurd as the original triviality results. Luckily, Stalnaker semantics can be revised too; it can be replaced with a generalized imaging semantics. I argue that combining Kaufmann’s thesis with generalized imaging semantics provides a way of defanging the local triviality results, not by undercutting the arguments for them, but by explaining why the results are not as philosophically problematic as they seem.

1 Introducing the Ramsey Test Ramsey (1978: 143n.) famously characterized conditionals in the following way: If two people are arguing ‘If p, then q?’ and are both in doubt as to p, they are adding p hypothetically to their stock of knowledge and arguing on that basis about q; so that in a sense ‘If p, q’ and ‘If p, :q’ are contradictories. We can say that they are fixing their degree of belief in q given p. If p turns out false, these degrees of belief are rendered void. If either party believes not p for certain, the question ceases to mean anything to him except as a question about what follows from certain laws or hypotheses.

Where the arrow ! stands for a generic conditional, Ramsey’s claim can be paraphrased as the Ramsey test An individual should accept the conditional A ! B to the degree that she would accept B on the supposition that A, provided that CrðAÞ>0. In order to make sense of the Ramsey test, we must know what it is to suppose the antecedent of a conditional—to add it hypothetically to one’s stock of knowledge. Roughly, to suppose that A is to imagine revising one’s view of the world so that one is committed to A, but to make the revision as small as possible. To evaluate the acceptability of a conditional A ! B, one imagines minimally revising one’s view of the world to accommodate the information that A, and evaluates B’s acceptability subsequent to the supposed revision. There are two popular interpretations of the Ramsey test that differ as to exactly what object is revised, and what constitutes a minimal revision. According to the first interpretation, the object of a minimal revision is an individual’s credence function, and one minimally revises one’s credence function to accommodate A by conditionalizing on A. Thus, the Ramsey test can be interpreted as the claim that every suitable credence function Cr satisfies

R . A . BRIGGS

Adams’ thesis CrðAÞ>0



For all propositions A and B, CrðA ! BÞ ¼ CrðBjAÞ, provided

(The qualifier ‘suitable’ will receive more attention in section 2.2.) According to a second interpretation of the Ramsey test, the object of minimal revisions is a possible world, and one minimally revises a possible world to accommodate the information that A by moving to the possible world where A holds (henceforth ‘the A world’) that is most similar to the original world. Thus, the Ramsey test can be understood in terms of Stalnaker semantics The conditional A ! B is true at a possible world α just in case at the world most similar to α where A is true, B is true. More formally, where vα is a valuation function taking each proposition A to a value of 0 or 1 (the truth value of A at the possible world α), and f is a selection function taking each proposition A and ‘base’ world α to a ‘selected’ world (the ‘closest’A world to α), vα ðA ! BÞ ¼ vf ðA;αÞ ðBÞ. The selection function is governed by the following rules (Stalnaker 1981b: 46): S1.

For all antecedents A and base worlds α, vf ðA;αÞ ðAÞ ¼ 1.

S2. For all antecedents A and base worlds α, f ðA;αÞ = Λ iff there is no world β possible with respect to α such that vβ ðAÞ ¼ 1. (Λ is a conventional ‘absurd’ world at which all propositions are true.) S3.

For all base worlds α and antecedents A, if vα ðAÞ ¼ 1, then f ðA;αÞ ¼ α. 0

S4. For all base worlds α and antecedents B and B , if vf ðB0 ;αÞ ðBÞ ¼ 1 and 0 0 vf ðB;αÞ ðB Þ ¼ 1, then f ðB;αÞ ¼ f ðB ;αÞ. Gibbard (1981) proves that for conditionals without conditional subsentences, an inference is probabilistically valid according to Adams’ thesis if and only if it is valid according to Stalnaker semantics. (The definition of probabilistic validity, from Adams (1975), says that an inference is probabilistically valid iff necessarily, as the probabilities of the premises approach 1, the probability of the conclusion approaches 1 too.) Given this striking logical resemblance, it seems only natural to try combining the probabilistic features of Adams’ thesis with the semantic features of Stalnaker semantics. One might claim that Stalnaker semantics characterizes the truth conditions of conditionals, while Adams’ thesis characterizes the relationship between credences in conditionals and conditional credences. Unfortunately, any attempt to combine Adams’ thesis (as it stands) with Stalnaker semantics (as it stands) is bound to end in failure.

2 Triviality A growing literature of triviality theorems, beginning with an article by Lewis (1976) and helpfully surveyed by Hajek and Hall (1994), shows that Adams’ thesis and



TWO INTERPRETATIONS OF THE RAMSEY TEST

Stalnaker semantics jointly entail absurd results. To explain how these triviality theorems work in more detail, I will need to introduce a few new terms. Call a probability function P nontrivial if it assigns positive probability to at least three pairwise incompatible propositions, and trivial otherwise. Say that a connective ∘ is a function from a pair of propositions hA;Bi to a third proposition A∘B. Then the basic upshot of the triviality theorems is this: Given a connective ! and a set of probability functions P such that ! and each P 2 P jointly satisfy Adams’ thesis, and given some additional background assumptions, one can show that each P 2 P is trivial. (The background assumptions vary from theorem to theorem.) These results raise trouble for Adams’ thesis when P is interpreted as the set of credence functions (or more generally, when the set of credence functions can be expressed as a union of sets satisfying the background assumptions about P). For then the triviality theorems show that Adams’ thesis, together with the appropriate background assumptions, entails the absurd conclusion that all credence functions are trivial. I will consider particular triviality results in more detail, beginning with the original result by Lewis (1976).

2.1 Lewis’s Triviality Theorem The key premise in Lewis’s argument is 1. For any propositions A and B such that PðA ∧ BÞ>0, PðA ! CjBÞ ¼ PðCjA ∧ BÞ From premise 1, Lewis argues that where A and C are two propositions such that PðA∧CÞ and PðA∧:CÞ are both greater than 0, A and C are probabilistically independent. 2. PðA ! CjCÞ ¼ PðCjA∧CÞ ¼ 1 (by premise 1) 3. PðA ! Cj:CÞ ¼ PðCjA∧:CÞ ¼ 0 (by premise 1) 4. PðCjAÞ ¼ PðA ! CÞ (by Adams’ thesis) 5. PðCjAÞ ¼ PðA ! CjCÞPðCÞ þ PðA ! Cj:CÞPðCÞ (by 4 and the probability calculus) 6. PðCjAÞ ¼ 1  PðCÞ þ 0  Pð:CÞ ¼ PðCÞ (by 2, 3, and substitution into 5). The conclusion, 6, has been proved for arbitrary A and C such that PðA ∧ CÞ and PðA∧:CÞ are both greater than 0, but can only hold for arbitrary such A and C if P is trivial.

R . A . BRIGGS



The argument for premise 1 relies on two assumptions. The first is that Adams’ thesis holds not just for P, but also for the probability function P* obtained by conditionalizing P on the proposition A. This gives us the result that P* ðA ! CÞ =P* ðCjAÞ The second assumption is that ! expresses the same propositional connective in every context, so that conditionalizing P on B does not affect the truth conditions of PðA ! CÞ. This lets us substitute PðA ! CjBÞ for P* ðA ! CÞ and PðCjA ∧ BÞ for P* ðCjAÞ in the above equation to obtain premise 1. Each assumption can be challenged. Perhaps Adams’ thesis holds for P, but fails for P* ; perhaps the set of suitable credence functions is not closed under conditionalization. The objection is supported by the following observation: there are propositions to which one can rationally assign nonzero credence, but on which one cannot rationally conditionalize—for instance, the proposition that the standard kilogram contains an even number of gold atoms, but no one will ever be certain that it does. (To assign this proposition nonzero credence is fine, but to conditionalize on it is Moore-paradoxical!) A person who started out rational, and then conditionalized on such a proposition, would not end up rational. Second, defenders of Adams’ thesis might claim that ! expresses different connectives in different contexts. A number of authors, including Harper (1976), Gibbard (1981), and van Rooij (2006), have suggested for independent reasons that the meaning of a conditional varies with context. Perhaps we can deploy their insights to defend Adams’ thesis. Unfortunately, both strategies face serious formal and philosophical obstacles.

2.2 Closure Under Conditionalization Suppose the defender of Adams’ thesis takes the first strategy, and claims that Adams’ thesis holds only for rational credence functions. Although the set of rational credence functions is not closed under conditionalization, it should be closed under some more suitable belief updating rule (one that forbids conditionalizing on Moore-paradoxical propositions). A person who starts with a rational credence function and updates using the right rule should end with a rational credence function. The question is then: what is the right rule? Hall (1994), strengthening earlier results by Lewis (1986a), shows that the only available updating rules are highly unappealing. Say that two probability functions P and P* are orthogonal iff there is a proposition A such that PðAÞ ¼ 1 and P* ðAÞ ¼ 0, and say that they are non-orthogonal iff they have the same domain and are not orthogonal. Hall shows that if P is a set of probability functions satisfying Adams’ thesis, P contains two non-orthogonal probability functions, and ! expresses the same propositional connective in every context, then every P 2 P is trivial. The first strategy, then, commits the defender of Adams’ thesis to the following claim: a good belief updating rule can never lead from a suitably rational (and



TWO INTERPRETATIONS OF THE RAMSEY TEST

nontrivial) credence function to a second credence function which is non-orthogonal to the first. But this claim is highly implausible. It would mean that any suitably rational individual who started out with a nontrivial credence function, and learned something new, would need to reject as certainly false propositions they previously accepted as certainly true. Intuitively, learning should be compatible with adding to one’s stock of knowledge, rather than merely revising it. From a philosophical standpoint, the problem is this: if Adams’ thesis is restricted to suitably rational credence functions, then we need some principled way of determining which credence functions are suitably rational, and some principled explanation of what’s wrong with the irrational ones. Hall’s results show that whatever property we choose to play the role of rationality, it cannot be preserved by any appealing updating rule. And why should such a property deserve the honorific ‘rationality’, or any interesting normative status?

2.3 Context-Dependence The defender of Adams’ thesis might opt instead for the second strategy, claiming that ! expresses different connectives in different contexts. Then another set of triviality theorems looms. These theorems show that for many individual probability functions P, there is no connective ! such that P and ! jointly satisfy Adams’ thesis. Until now, the triviality theorems have required no background assumptions about the logic of the connective !. Many of the theorems in this section will appeal to the following three constraints on ! (all valid in the Stalnaker semantics): Modus Ponens For all propositions A and B, A∧ðA ! BÞ ‘ B Entailment Within the Consequent For all propositions A, B, and C, ðA ! BÞ∧ðA ! CÞ ‘ ðA ! ðB∧CÞÞ Weakened Transitivity For all propositions A,B, and C, ðA ! BÞ∧ðB ! AÞ∧ðB ! CÞ ‘ ðA ! CÞ The first result, by Hajek (1994), is that if P is nontrivial and finite-ranged, then there is no connective ! such that P and ! jointly satisfy Adams’ thesis. The second result, by Hall (1994) is this: Let a proposition A be a P-atom just in case PðAÞ>0 and for all B, either PðA ∧ BÞ ¼ PðAÞ or PðA ∧ BÞ ¼ 0. If P is nontrivial and there is a P-atom, and ! validates Modus Ponens, then P and ! cannot jointly satisfy Adams’ thesis. The third result, by Hajek and Hall (1994) (drawing on Stalnaker (1976)) is that if ! validates Modus Ponens, Entailment Within the Consequent, and Weakened Transitivity, then there is no nontrivial probability function P such that P and ! jointly satisfy Adams’ thesis. In addition to these technical worries, there are philosophical worries. If the meanings of conditionals are so radically context-dependent, how can we use them

R . A . BRIGGS



to communicate? When an informant tells me ‘If A, then C’, I should be able to understand her utterance without knowing anything in particular about her credence function. How is this possible if what she means by ‘if ’ depends in subtle and sensitive ways on unknown features of her credence function? Moreover, radical context-dependence makes a mystery of disagreement. Suppose I assert, and you deny, the conditional ‘If it rains in September, then the corn will grow high’. We appear to genuinely disagree. It is not as though you had said ‘My credence function has property ϕ’ and I had said ‘My credence function lacks property ϕ’; this is not a situation where both of us can be right. How is disagreement possible unless we mean the same thing by conditional, different though our credence functions may be? So to sum up the situation: There are persuasive formal and philosophical reasons to think Adams’ thesis (at least as it stands) is irreconcilable with Stalnaker semantics (at least as it stands). Fortunately, there are good reasons for rejecting both Adams’ thesis (as it stands) and Stalnaker semantics (as it stands). Suitably adjusted versions of these two theories form a unified view of conditionals that incorporates both probabilistic and semantic elements.

3 Refining Adams’ Thesis Kaufmann (2004) denies that Adams’ thesis can fully capture the relationship between an agent’s credences and the credences she assigns to conditionals. He points to examples by McGee (2000) and Pollock (1981) in which common intuitions about the probabilities of conditionals seem to conflict with Adams’ thesis.2 These examples, argues Kaufmann, admit of a simple explanation: we need to replace Adams’ thesis with a more sophisticated probabilistic version of the Ramsey test. We might hope that Kaufmann’s replacement thesis, in addition to explaining some puzzling examples, will provide a way around the triviality results. In fact, Kaufmann (2004: 597–9) briefly conjectures that his proposal may avoid the most worrisome consequences of Lewis’s original triviality theorem. I will illustrate Kaufmann’s proposal using an example from Kaufmann (2004: 584–5), which he attributes to Dorothy Edgington. You are about to choose a ball from a bag. It could be one of two bags, X or Y. Bag X contains ten red balls, nine of them with a black spot, and two white balls. Bag Y contains ten red balls, one of them with a black spot, and fifty white balls. By virtue of additional evidence—say, the bag in front of you looks big—you are 75 percent sure that it is bag Y. For ease of reference, the relevant facts are summarized in the table below.

2

Similar cases can be found in Skyrms 1981 and Morton 2004.



TWO INTERPRETATIONS OF THE RAMSEY TEST

Cr (Bag X) = 1/4

Cr (Bag Y) = 3/4

10 red balls 9 of them with a black spot 2 white balls

10 red balls 1 of them with a black spot 50 white balls

Kaufmann asks how acceptable the following conditional is: (1)

If I pick a red ball, it will have a black spot.

Intuitively, Kaufmann suggests, the probability of (1) is low—less than 1/2. But the conditional probability of drawing a ball with a black spot given that the ball is red is 0.6—greater than 1/2. This can be verified by a quick calculation:

CrðBjRÞ

= = =

CrðBRÞ CrðRÞ CrðBRXÞþCrðBRYÞ CrðRÞ CrðBjRXÞCrðXjRÞCrðRÞþCrðBjRYÞCrðYjRÞCrðRÞ CrðR

= CrðBjRXÞCrðXjRÞ þ CrðBjRYÞCrðYjRÞ = 9=10  5=8 þ 1=10  3=8 ¼ 0:6

Kaufmann’s diagnosis is that the conditional admits of a ‘local’ reading, on which one’s beliefs about a background variable X—representing, in this case, the identity of the bag the ball is drawn from—are held constant. He holds that for local conditionals, every suitable credence function Cr satisfies Kaufmann’s thesis For any propositions A and B, the probability of a conditional A ! B, relative to a background partition X ¼ fX1 ;X2 ;...g, is X CrðBjA ∧ Xi ÞCrðXi Þ. i (More about what ‘suitable’ means in section 6.1.) In other words, the probability of a local conditional can be computed in two steps. First, for each of a set of background hypotheses, take the conditional probability of the consequent given the conjunction of the antecedent with that hypothesis. Second, take the average of the results from the first step weighted by the initial probabilities of the background hypotheses. Kaufmann’s thesis yields the intuitive result that the probability of (1) is low.

CrðR ! BÞ

¼ CrðBjRXÞCrðXÞ þ CrðBjRYÞCrðYÞ = 9=10  1=4 þ 1=10  3=4 ¼ 0:3

R . A . BRIGGS



Kaufmann’s thesis gets this case and similar cases right. Another source of support for Kaufmann’s thesis comes from causal decision theory. According to evidential decision theory, the expected value of an action A is X CrðV ¼ vjAÞv: v

If Adams’ thesis is right, this quantity is equal to X CrðA ! ðV ¼ vÞÞv v

According to causal decision theory, on the other hand, the expected value of an action A is XX CrðV ¼ vjA ∧ Xi ÞCrðXi Þv: v

i

If Kaufmann’s thesis is right, this quantity is equal to X CrðA ! ðV ¼ vÞÞv: v

One way of spelling out the debate between evidential and causal X decision theorists, then, is to see them as agreeing that it is rational to maximize CrðA ! ðV ¼ vÞÞv, v but disagreeing about whether the conditional should be interpreted in accordance with Adams’ thesis or Kaufmann’s thesis. Insofar as one finds causal decision theory plausible, one should find Kaufmann’s thesis plausible too. Furthermore, Kaufmann’s thesis inherits some plausibility from examples that support Adams’ thesis. The two theses coincide in the special case where the antecedent A of a conditional is independent of the value of the background variable X. Many of the examples invoked in support of Adams’ thesis (e.g. ‘If I roll a die, it will land on an even number’) are instances of this special case; therefore, they lend equal support to Kaufmann’s thesis. So Kaufmann’s thesis inherits much of the evidential weight of Adams’ thesis, together with the additional weight provided by the anomalous examples and its relationship to causal decision theory. Note that although Kaufmann’s and Adams’ thesis coincide in special cases, they are fundamentally incompatible—at least if we assume that the conditional has a single, uniform reading. In the example given above, Kaufmann’s thesis entails that CrðR ! BÞ ¼ 0:3, while Adams’ thesis entails that CrðR ! BÞ ¼ 0:6. Since one cannot coherently assign two different credences to the same conditional at the same time, it looks like if ! is univocal, either Adams’ thesis or Kaufmann’s thesis will have to go. Kaufmann suggests that ! is not univocal. Instead, there are two kinds of conditionals: one characterized by Kaufmann’s thesis (roughly corresponding to the class of subjunctive conditionals), and the other characterized by Adams’ thesis



TWO INTERPRETATIONS OF THE RAMSEY TEST

(roughly corresponding to the class of indicative conditionals). We know that Adams’ thesis is incompatible with Stalnaker semantics, so let us leave Adams’ thesis and the corresponding conditionals aside for now. Can we combine Kaufmann’s thesis with Stalnaker semantics instead?

4 Local Triviality Unfortunately, Kaufmann’s thesis fares no better than Adams’ thesis. There is a straightforward way of transforming triviality results into what I will call local triviality results. Before explaining these local triviality results, it will be useful to introduce a few new terms, which closely parallel the ones introduced in section 2. Call a probability function P locally nontrivial for a proposition A iff P assigns positive probability to at least three pairwise incompatible propositions that entail A. Say that P is locally nontrivial for a partition X ¼ fX1 ;:::Xn g iff there is some Xi 2 X for which it is locally nontrivial. Say that P is locally trivial (for a proposition or a partition) iff it is not locally nontrivial (for that proposition or partition). Then the basic upshot of the local triviality theorems is this: Given a connective !, a partition X ¼ fXi ;:::Xn g, and a set of probability functions P such that !, X, and each P 2 P jointly satisfy Kaufmann’s thesis, and given some additional background assumptions, one can show that each P 2 P is locally trivial relative to X. Thus by universal generalization, Kaufmann’s thesis together with the appropriate background assumptions entails that all credence functions are locally trivial for every suitable background partition. Local triviality is not as obviously worrisome as triviality. Still, it is worrisome enough. Local triviality requires that every member of the background partition answer every question (save perhaps one) that an agent is uncertain about. But members of the background partition need not be that informative. In Edgington’s example, there are many disjoint propositions compatible with the proposition that a ball is drawn from Bag X, rather than Bag Y: it might be red with a black dot, red with no black dot, or white. All these propositions should receive nonzero credence. Therefore, we must reject local triviality, along with anything that entails it.

5 A General Strategy for Local Triviality Proofs My strategy for proving the local triviality theorems is as follows. First, I will introduce an important assumption. Then, using this assumption, I will show that for every partition X, probability function P, and connective ! jointly satisfying Kaufmann’s thesis, each Xi 2 X can be used to generate a probability function Pi which, together with !, satisfies Adams’ thesis. As a corollary, where P is a set of probability functions such that !, X, and each P 2 P jointly satisfy Kaufmann’s

R . A . BRIGGS



thesis, it is possible to generate a set P* ¼ fPi : P 2 P; Xi 2 Xg, such that each P* 2 P* satisfies Adams’ thesis. Next, I will map assumptions about X, !, P, and P onto assumptions about !, Pi , and P* . This will let me establish that if there were a connective !, partition X, and set of probability functions P with at least one locally nontrivial member, such that !, X, and each P 2 P jointly satisfied Kaufmann’s thesis (along with the appropriate background assumptions), then we would have a procedure for constructing a set of probability functions P* with at least one nontrivial member, such that ! and each P* 2 P* jointly satisfied Adams’ thesis (along with the corresponding background assumptions). The triviality theorems tell us that (given certain background assumptions) we cannot construct such a P* . Therefore, by modus tollens, we cannot construct an X, P, and ! such that P has at least one nontrivial member, and !, X, and each P 2 P jointly satisfy Kaufmann’s thesis (together with the corresponding background assumptions).

5.1 The Details My important assumption is: The Big Assumption Suppose that a partition X, probability function P, and connective ! satisfy Kaufmann’s thesis. Let Pi be the probability function that results from conditionalizing P on Xi . Then X, Pi , and ! satisfy Kaufmann’s thesis. The Big Assumption is intuitively appealing. The unconditional probability of A ! B is the expected conditional probability of B given A, where this expectation is computed using the partition X. Therefore, the conditional probability of A ! B, given any Xi 2 X, should be the probability of B given A subsequent to conditionalizing on Xi . Moreover, the Big Assumption follows from other appealing commitments. First A ! B ought to express a context-independent proposition—or at the very least, conditionalizing on a member of the relevant background partition X ought not to change which proposition it expresses. Second, since Kaufmann’s thesis is meant to capture something important about the meaning of the conditional, there should be a connective ! such that for every probability function P, there is some background partition X which (together with P and !) satisfies Kaufmann’s thesis. Third, simply conditionalizing on a member of the background partition X should not change which background partition is relevant. These three commitments together entail the Big Assumption. Where X, P, and ! satisfy Kaufmann’s thesis, the Big Assumption tells us that Pi and ! satisfy Adams’ thesis. By the definition of Pi , Pi ðXi Þ ¼ 1. Therefore, X Pi ðBjA ∧ Xj ÞPi ðXj Þ ¼ PðBjAÞ: PðA ! BÞ ¼ j



TWO INTERPRETATIONS OF THE RAMSEY TEST

The next step is to map constraints on X, P, and ! onto corresponding constraints on Pi and !. Fact 1 If P 2 P is locally nontrivial for Xi , then Pi is nontrivial. (Proof: Suppose P is locally nontrivial for Xi . Then by the definition of local nontriviality for Xi , P assigns positive probability to at least three pairwise incompatible propositions that entail Xi (call them B1 , B2 , and B3 ). By the probability calculus, PðB1 jXi Þ, PðB2 jXi Þ, and PðB3 jXi Þ are all nonzero. Since Pi ¼ PðjXi Þ, Pi ðB1 Þ, Pi ðB2 Þ, and Pi ðB3 Þ are all nonzero. And since by our original hypothesis, B1 , B2 , and B3 were pairwise incompatible, Pi is nontrivial. (Other proofs involve similarly straightforward plugging and chugging, and are left to the reader.) Corollary: if P contains at least one probability function P locally nontrivial for X, then P* contains at least one nontrivial probability function, namely Pi . Fact 2 If P is closed under conditionalization, then P* is closed under conditionalization. 0

Fact 3 Say that two probability functions P and P are Xi -orthogonal iff there is a 0 0 proposition A such that PðAjXi Þ ¼ 1 and P ðAjXi Þ ¼ 0. Say that P and P are Xi -non-orthogonal iff both of them assign positive probability to Xi , they have the 0 same domain, and they are not Xi -orthogonal. Then if P and P are Xi -nonorthogonal, Pi and Pi0 are non-orthogonal. Fact 4 If P is finite-ranged, then Pi is finite-ranged. Fact 5 If there is a P-atom that entails Xi , then there is a Pi -atom. Facts 1–3 raise trouble for Kaufmann’s thesis, on the background assumption that X and ! are context-independent. From Facts 1 and 2, together with Lewis’s original triviality result, we can conclude that if both X and ! receive the same interpretation in all contexts, then there is no set P of probability functions such that each member of P satisfies Kaufmann’s thesis, P contains at least one locally nontrivial member, and P is closed under conditionalization. This is worrisome: the set of rational credence functions ought to include at least one locally nontrivial function, and ought (it seems) to be closed under conditionalization. Weakening the ‘closure under conditionalization’ assumption will not solve the problem. One should at least be able to update on one’s evidence in multiple ways without ruling out any member of the background partition. (In the Edgington example, one can draw a white ball, a red ball without a black dot, or a red ball with a black dot without learning whether one has drawn from Bag X or Bag Y.) But Facts 1 and 3 entail that this is impossible, at least if X and ! receive the same interpretation in all contexts. Kaufmann’s thesis also leads to trouble when X is held fixed, but the meaning of ! is allowed to vary according to context. For some probability functions P, there is no

R . A . BRIGGS



connective ! such that P and ! jointly satisfy Kaufmann’s thesis, as Facts 1 and 4 attest. Once again, the context-dependence strategy can be combined with the strategy of restricting Kaufmann’s thesis to a range of suitable credence functions, but once again, doom lurks. Fact 1 shows that where ! satisfies Modus Ponens, Weakened Transitivity, and Entailment Within the Consequent, there is no probability function P such that P and ! jointly satisfy Kaufmann’s thesis. Since the conditionals characterized by Stalnaker semantics satisfy all these principles, the game is nearly up. There are still some avenues of escape: one might allow the partition X to vary with context, in a way that permitted violations of the Big Assumption. And indeed, my ultimate solution to the problem will allow for contextual variation in X. I will now turn away from Adams’ thesis, and back to Stalnaker semantics, to find a solution to the local triviality worries.

6 Refining Stalnaker Semantics Stalnaker semantics, as it stands, is not quite right. For some worlds α and propositions A, there is no unique closest world to α where A is true—rather, there are multiple worlds tied for closest.3 Suppose you have a fair coin which you do not toss. Among the closest worlds where you do toss the coin, there are some where it lands heads and others where it lands tails, with none uniquely closest. The example does not turn on indeterminism: even if the universe is deterministic, there need be no precise way you would have tossed the coin, had you tossed it. We can begin to address these difficulties by replacing Stalnaker’s selection function with a set selection function s. Whereas f ðA;αÞ was a single world, sðA;αÞ is a set of worlds. If we take this approach, then we can let vα ðA ! BÞ ¼ 1 if vβ ðAÞ ¼ 1 for every β 2 sðA;αÞ, and vα ðA ! BÞ ¼ 0 if vβ ðAÞ ¼ 0 for every β 2 sðA;αÞ. What 0 happens if there exist both a β 2 sðA;αÞ such that vβ ðAÞ ¼ 1, and a β 2 sðA;αÞ such that vβ0 ðAÞ ¼ 0? Lewis (1981) suggests that such cases, vαðA ! BÞ ¼ 0, while Stalnaker (1981a) suggests that vα ðA ! BÞ is neither 0 nor 1. I will adopt a version of Stalnaker’s approach. Set selection functions don’t encode probabilistic information—they will not tell you that if you were to toss a particular fair coin, the probability of its landing heads would be exactly 1/2. But we can enrich them. Let us define a class of generalized imaging functions, which map each proposition A and world α to a probability space sðA;αÞ; FðA;αÞ; PAα , where sðA;αÞ is a set of worlds, FðA;αÞ is a Borel field on sðA;αÞ, and PAα is a probability function defined over propositions in FðA;αÞ.4 (Henceforth,

3 I set aside violations of the so-called ‘Limit Assumption’; see Stalnaker (1981a) for a proposal about how to resolve them. 4 See Sobel (1979) and Gärdenfors (1982) for similar proposals.



TWO INTERPRETATIONS OF THE RAMSEY TEST

I will shorten ‘generalized imaging function’ to ‘imaging function’; I do not intend to suggest that PAα must concentrate all its probability on one world.) Stalnaker’s rules governing selection functions can be extended to imaging functions. I1 For all antecedents A and base worlds α, vβ ðAÞ ¼ 1 for every β 2 sðA;αÞ. I2 For all antecedents A and base worlds α, sðA;αÞ ¼ ∅ iff there is no world β possible with respect to α such that vβ ðAÞ ¼ 1. (Where sðA;αÞ ¼ ∅, FðA;αÞ and PAα are undefined.) I3

For all base worlds α and antecedents A, if vα ðAÞ ¼ 1, then sðA;αÞ ¼ fαg. 0

0

0

0

I4 For all base worlds α and antecedents B and B such that B  B , if B overlaps 0 0 0 0 sðB;αÞ, then sðB ;αÞ ¼ sðB;αÞ \ B ; FðB ;αÞ ¼ fA [ B : A 2 FðB;αÞg; and where 0 0 PBα ðjB Þ is well defined, PB0 α ¼ PBα ðjB Þ. (These are the constraints on set selection functions given by Lewis (1973), except that I2 and I4 have been strengthened to constrain the Borel field and probabilistic parts of the imaging function.) I have followed Stalnaker’s suggestion that where sðA;αÞ contains both B worlds and :B worlds, A ! B is neither true nor false at α. A generalized imaging function lets us say more: it lets us assign an intermediate truth value to A ! B. Let vα ðA ! BÞ ¼ PAα ðBÞ whenever PAα is defined. (I mean this rule as an addition to, rather than a replacement for, the rule which says that vα ðA ! BÞ ¼ 1 if vβ ðAÞ ¼ 1 in every β 2 sðA;αÞ, and vα ðA ! BÞ ¼ 1 if vβ ðAÞ ¼ 0 in every β 2 sðA;αÞ. The two rules can never give contradictory answers: whenever all the worlds in sðA;αÞ agree that B is true, then PAα ðBÞ must be 1 if defined at all; likewise, whenever all the worlds in sðA;αÞ agree that B is false, then PAα ðBÞ must be 0 if defined at all.) On the picture that emerges, conditionals are a sort of quasi-propositions (see Stalnaker and Jeffrey 1994). An ordinary proposition can be understood as a function from possible worlds to the truth values 0 and 1, or (equivalently) as the set of worlds in which the function takes value 1. Conditionals can be understood as functions from possible worlds to truth values between 0 and 1, but unlike ordinary propositions, they cannot be completely captured by a single set of possible worlds. Following Stalnaker and Jeffrey (1994), let us say that ϕ’s probability is its expected truth value.5 Probability for nonconditional propositions (which always take on value 0 or 1) then emerges as a special case of probability in general. Once the truth values of conditionals are settled, truth values can be assigned to compounds using the methods of van Fraassen (1976), McGee (1989), and Stalnaker and Jeffrey (1994). Let us now consider the nature of the imaging function, and its relationship to Kaufmann’s thesis.

5

Along similar lines, Smith (2009) suggests that in degree-theoretic treatments of vagueness, probability should be identified with expected truth value.

R . A . BRIGGS



6.1 Interpreting the Imaging Function Edgington (1991) and Kaufmann (2005) suggest that conditionals should receive intermediate truth values, and that these truth values should be determined (insofar as possible) by the objective chances. Chances exhibit a type of context-dependence: they vary from time to time, as well as from world to world. So we will need to relativize PAα and vα to a time parameter t. (Where A is a nonconditional proposition vtα ðAÞ ¼ vα ðAÞ.) As a first pass, we might claim that where chtα is the objective chance function, the imaging function is characterized by Chancy Imaging

If vtα ðAÞ ¼ 0, then PtAα ¼ chtα ðjAÞ.

Both Edgington (2004) and Kaufmann (2005) discuss examples which suggest that Chancy Imaging is not exactly right. Consider the following two hypothetical situations. Situation 1 A particular fair coin will be tossed at t2 . At an earlier time t1 , you will bet on either heads or tails; your bet has no effect whatsoever on the coin-tossing setup. At a still earlier time t0 , I tell you, ‘If you bet on heads, you’ll win’. You bet on tails; the coin lands heads. What I told you was unjustified, but completely true. (‘If only you had bet heads’, I might truly say afterwards, ‘you would have won!’) Situation 2 Some fair coin or other will be tossed at t2 . But this time, exactly which fair coin it is will depend on how you bet at t1 . If you bet on heads, I will toss the coin in my pocket; if you bet on tails, you will toss the coin in your pocket. At t0 , I tell you, ‘If you bet on heads, you will lose’. You bet on tails and I toss the coin in my pocket; it lands heads. What I told you was, if not outright false, at least not true. (Here, it is wrong for me to say afterwards, ‘If only you had bet heads, you would have won!’ If you had bet on heads, it would have been a completely different coin toss, and that toss might well have landed tails.) In both Situation 1 and Situation 2, your conditional chance of winning given that you bet on heads is 1/2 at t0 , 1/2 at t1 , and undefined at t2 . Yet the truth value of the conditional ‘If you bet on heads, then you will win’ differs between the two situations. Edgington suggests that when we consider the closest worlds at which a proposition A is true, we must hold fixed not just the past, but future events that do not depend causally on A. Kaufmann proposes a concrete way of cashing this suggestion out. He represents relations of causal dependency among events using what I will call causal structures, where each causal structure consists of a set of binary variables together with a strict partial ordering on these variables. I will write A>α B just in case in α, the value of variable A causally depends (directly or indirectly) on the value of variable B. Kaufmann assumes that at each world α, there is a single correct causal structure. Let the proposition Sα be a complete description of the correct causal structure at α— a proposition that either implies or is incompatible with any other proposition about



TWO INTERPRETATIONS OF THE RAMSEY TEST

which causal structure is correct, and that is true at α. Kaufmann assumes that each factual sentence A can be matched to a variable A, that takes value 1 if and only if the sentence does. (For example, where A is the proposition that a particular coin is tossed, A is the binary variable that takes value 1 if the coin is tossed, and value 0 otherwise.) Let NAα be a proposition that specifies the values of all variables B such that B ≯ A. Kaufmann’s suggestion then amounts to the suggestion that where vtα ðAÞ ¼ 0, the imaging function is characterized by Causal-Chancy Imaging PtAα ¼ chtα ðjA ∧ NAα ∧ Sα Þ. (Chancy Imaging does not tell us how to compute vtα ðAÞ when the relevant conditional chances are undefined. I propose Chancy Imaging as a constraint on the imaging function, but allow that the imaging function may be well defined even when Chancy Imaging doesn’t tell us what it is.) Causal-Chancy Imaging does a better job of handling the examples than Chancy Imaging. In Situation 1, the outcome of the coin toss is causally independent of your choosing to bet on heads (or tails). Therefore, at all closest worlds where you bet on heads, we hold the actual outcome of the coin toss fixed. Therefore, if you had bet on heads, the coin would still have landed heads, and so you would have won. In Situation 2, on the other hand, the outcome of the coin toss is causally dependent on how you bet (albeit in an inscrutable and perhaps chancy way). Therefore, we let the outcome of the coin toss vary among closest worlds where you bet on heads. Since the chance of heads at t0 is 1/2, then as of t0 , only half the closest worlds where you bet on heads are worlds where you win. Although it handles the examples nicely, Causal-Chancy Imaging has hidden costs. Kaufmann assumes that every nonconditional proposition can be uniquely matched to a single variable. But this is not feasible: the structure of propositions does not match the structure of variables. In the causal modeling literature that serves as Kaufmann’s inspiration, variables are assumed to be logically independent of one another. If there are variables A and B that correspond to the propositions A and B, there is no variable corresponding to A∧B or A∨B. Although Causal-Chancy Imaging works well when A is a proposition that corresponds to a variable, it falls silent when A is a conjunction, disjunction, or other Boolean combination of such propositions. In what follows, I will remain neutral as to whether Chancy Imaging or CausalChancy Imaging is correct.

6.2 Recovering Kaufmann’s Thesis Using my characterization of the imaging function, along with some machinery developed by Lewis (1986b), I can prove a restricted version of Kaufmann’s thesis. It’s now time to introduce Lewis’s machinery, beginning with the concept of historyto-chance conditionals, Lewis (1986b: 95) defined as conditionals with the following three features:

R . A . BRIGGS



(1) The consequent is a proposition about chance at a certain time. (2) The antecedent is a proposition about history up to that time; and further, it is a complete proposition about history up to that time, so that it either implies or else is incompatible with any other proposition about history up to that time. It fully specifies a segment, up to the given time, of some possible course of history. (3) The conditional is made from its consequent and antecedent not truthfunctionally, but rather by means of a strong conditional operation of some sort. This might well be the counterfactual conditional of Lewis (1973), but various rival versions would serve as well, since many differences do not matter for the case at hand. One feature of my treatment will be needed, however: If the antecedent of a conditional holds at a world, then both or neither of the conditional and its consequent hold there. I’ll need to make one slight amendment to Lewis’s definition of a history-to-chance conditional. The ‘strong conditional operation’ in (3) cannot be Lewis’s counterfactual connective, which is characterized by a version of Stalnaker semantics, because this would introduce a vicious circularity into my attempt to provide a semantics for conditionals. I will treat the strong conditional operator as a strict conditional instead. In other words, I will assume that where Htα is a complete description history up to time t, a history-to-chance conditional of the form ‘If Htα then ϕ’ can be rewritten as WðHtα ⊃ϕÞ, where W is a nomological necessity operator. This interpretation ensures that the conditional is suitably strong, but avoids the circularity associated with Lewis’s interpretation. My history-to-chance conditionals can be defined purely in terms of disjunction, negation, and nomological necessity. My change is perfectly compatible with Lewis’s requirement that if the antecedent of a conditional holds at a world, then both or neither of the conditional and its consequent hold there. The chances at a time, whatever they are, should obtain at every world that shares the same history as a matter of law. Therefore if the antecedent and consequent of a history-to-chance conditional are true, then the conditional must be true as well. And since every world is nomologically possible with respect to itself, at every world where the antecedent holds and the consequent does not, the history-to-chance conditional must be false. Lewis says that the correct theory of chance at a world α is the conjunction of all history-to chance conditionals that are true at α. I’ll make one more amendment: I will treat the correct theory of chance at α as the conjunction of all history-tochance conditionals that are true at α, and whose consequents say all there is to say about the chance function. In other words, the consequents of conditionals in the correct theory must take the form cht ¼ p, where cht is a variable denoting the objective chance function at time t, and p rigidly designates some probability function. This amendment is harmless: the history-to-chance conditionals in my special class will entail all other history-to-chance conditionals that are true at α.



TWO INTERPRETATIONS OF THE RAMSEY TEST

To fix chtα , one needs only the correct theory of chance at α (call it Tα ), and a complete description of α’s history up to t (call it Htα ). One then finds the conjunct of Tα whose antecedent is Htα . Where that conditional has the consequent cht ¼ p, one can conclude that chtα ¼ p. The next crucial piece of the puzzle is the Principal Principle (Lewis 1986b: 97), which states that where A is any proposition, t is any time, Htα is a complete description of the history of world α up to t, Tα is a complete theory of chance at α, and chtα is the objective chance function at t in α, a rational agent’s credences should conform to the following principle, provided she has no inadmissible information with respect to A and t.6 PP

CrðAjHtα ∧Tα Þ ¼ chtα ðAÞ

(Information is admissible for an agent with respect to a proposition A, and a time t just in case its impact on the agent’s credence about A comes entirely by way of the agent’s credence about A’s chance at t (Lewis 1986b: 92).) In addition to the unconditional Principal Principle, we might adopt a Conditional Principle, which governs conditional credences. Let us introduce a concept of conditional admissibility: say that information is admissible for an agent with respect to one proposition A, conditional on another proposition B, at a time t just in case its impact on the agent’s conditional credence in A given B comes entirely by way of the agent’s credence about the chance of B at t and the conditional chance of A given B at t. Then where A and B are any propositions, t is any time, Htα is a complete description of the history of world α up to t, Tα is a complete theory of chance at α, and chtα is the objective chance function at t in α, a rational agent’s conditional credences should conform to the following principle, provided she has no inadmissible information with respect to A given B at t. CP

CrðAjB∧Htα ∧Tα Þ ¼ chtα ðAjBÞ

PP and CP are closely related: PP is the special case of CP where B ¼ Τ, and PP entails the special case of CP where CrðB ∧ Htα ∧Tα Þ>0 (on the assumption that if the agent has no inadmissible information with respect to either A∧B or B, then she has no inadmissible information with respect to A conditional on B). So I suggest that if we are justified in accepting PP, we are justified in accepting CP too. We can use CP in conjunction with either Chancy Imaging or Causal-Chancy Imaging to derive Kaufmann’s thesis, provided we choose the appropriate partition and make a few assumptions about the agent’s credence function. Let us begin with Chancy Imaging. Let us partition logical space into propositions of the form Hti ∧ Ti .

6 My formulation differs slightly from Lewis’s: I omit the appeal to ‘initial credence functions’ which Lewis supposes are held prior to absolutely all evidence. On the assumption that a rational agent’s credences come from her initial credence function by conditionalization on her total evidence, Lewis’s formulation entails mine, but not vice versa.

R . A . BRIGGS



(I relativize Ht , and T to indices, rather than to worlds. I assume that two worlds α and β have the same index iff Htα ¼ Htβ , and Tα ¼ Tβ .) The probability of a conditional is its expected truth value. X CrðA ! BÞ ¼ vα ðA ! BÞCrðαÞ α

By Chancy Imaging, CrðA ! BÞ ¼

X

vα ðBÞCrðαÞ þ

α2A

X

chtα ðBjAÞCrðαÞ

α2:A

Assuming that the agent has no inadmissible information (with respect to B conditional on A), we can make use of CP. X X CrðA ! BÞ ¼ vα ðBÞCrðαÞ þ CrðBjA∧Htα ∧Tα ÞCrðαÞ α2A

α2:A

We can group the worlds into equivalence classes and rewrite CrðA ! BÞ as a sum over these equivalence classes. X CrðA ! BÞ ¼ ðCrðBjA∧Hti ∧Ti ÞCrðA∧Hti ∧Ti Þ i

þCrðBjA∧Hti ∧Ti ÞCrð:A∧Hti ∧Ti ÞÞ Simplifying, we have CrðA ! BÞ ¼

X ðCrðBjA∧Hti ∧Ti Þ i

Letting Xi ¼ ðHti ∧Ti Þ, we have CrðA ! BÞ ¼

X

CrðBjA∧Xi ÞCrðXi Þ

i

But this is just Kaufmann’s thesis, with a partition given by conjunctions of the form Hi ∧Ti . We can do exactly the same thing with Causal-Chancy Imaging. This time, we partition logical space into propositions of the form NAi ∧Si ∧Hti ∧Ti . (Once again, NA , S, Ht , and T are relativized to indices rather than worlds, and two worlds share an index iff they agree about NA , S, Ht , and T.) The probability of a conditional is its expected truth value. X CrðA ! BÞ ¼ vα ðA ! BÞCrðαÞ α

By the Causal-Chancy Imaging, X X CrðA ! BÞ ¼ vα ðBÞCrðαÞ þ chtα ðBjA∧NAα ∧Sα ÞCrðαÞ α2A

α2:A



TWO INTERPRETATIONS OF THE RAMSEY TEST

Assuming that the agent has no inadmissible information (with respect to B conditional on A∧NAα ∧Sα ), we can make use of CP. X X vα ðBÞCrðαÞ þ CrðBjA∧NAα ∧Sα ∧Htα ∧Tα ÞCrðαÞ CrðA ! BÞ ¼ α2A

α2:A

We can group the worlds into equivalence classes and rewrite CrðA ! BÞ as a sum over these equivalence classes. X CrðA ! BÞ ¼ CrðBjA∧NAi ∧Si ∧Hti ∧Ti ÞCrðA∧NAi ∧Si ∧Hti ∧Ti Þ i

þCrðBjA∧NAi ∧Si ∧Hti ∧Ti ÞCrð:A∧NAi ∧Si ∧Hti ∧Ti Þ Simplifying, we have CrðA ! BÞ ¼

X CrðBjA∧NAi ∧Si ∧Hti ∧Ti Þ i

Letting Xi ¼ ðNAi ∧Si ∧Hti ∧Ti Þ, we have X CrðBjA∧Xi ÞCrðXi Þ CrðA ! BÞ ¼ i

This is Kaufmann’s thesis, with a partition given by conjunctions of the form NAi ∧Si ∧Hi ∧Ti . To illustrate the proposal a little more concretely, let us return to the example from section 3, in which you draw a ball from either bag X or bag Y. At the time of your drawing (call this time t), the chance of B conditional on R is determined by which bag is in front of you: if it’s bag X, the conditional chance is 9/10; if it’s bag Y, the conditional chance is 1/10. I will assume, for the sake of simplicity, that the world has whatever causal structure it has with chance 1. Furthermore, I will assume that, given the facts about the chance (which fix whether you draw from bag X or bag Y), the truth value of B does not depend causally or constitutively on any events independent of R. In fact, I will assume that you know this—i.e. you are certain that from the perspective of the chance function, R screens B off from all information about these events. Thus, in each of your epistemically possible worlds α, chtα ðBjR∧NAα ∧Sα Þ ¼ chtα ðBjRÞ. Therefore, it makes no difference whether you subscribe to Chancy Imaging or Causal-Chancy Imaging: the two proposals assign the same truth value to R ! B in each epistemically possible world α. So in every world α where bag X stands before you, vtα ðR ! BÞ ¼ 9=10, while in every world β where bag Y stands before you, vtβ ðR ! BÞ ¼ 1=10. Your credence in R ! B is your expected truth value for R ! B, i.e., X CrðR ! BÞ ¼ vtα ðR ! BÞCrðαÞ α

R . A . BRIGGS



Since the X worlds all agree with each other, and the Y worlds all agree with each other, about the truth value of R ! B, we can rewrite the sum as follows: CrðR ! BÞ ¼ ð9=10ÞCrðXÞ þ ð1=10ÞCrðYÞ ¼ 9=10  5=8 þ 1=10  3=8 ¼ 0:6 This is exactly what Kaufmann’s thesis predicts. So CP guarantees that every suitable credence function satisfies Kaufmann’s thesis. Furthermore, I am now in a position to say exactly what ‘suitable’ amounts to. A credence function Cr is suitable just in case it satisfies CP, and the two other assumptions we used to derive Kaufmann’s thesis, namely: 1. An agent whose credence function is Cr has no inadmissible information. (More particularly, if we use Chancy Imaging, she has no inadmissible information about the consequent conditional on the antecedent, and if we use Causal-Chancy Imaging, she has no inadmissible information about the consequent conditional on the conjunction of the antecedent, a complete specification of which events depend causally on the antecedent, and a complete description of the events that are causally independent of the antecedent.) 2. chðBjA∧NAα ∧Sα Þ is well defined for all worlds α 2 :A that the agent considers epistemically possible. When are these two assumptions satisfied? Assumption 1 is typically satisfied when the agent is located at or before t, since historical information is typically admissible. When a conditional contains no past tense markers and its antecedent describes events wholly in the agent’s future, we should expect t to be either the time of the agent or the time of the events described in the antecedent. In either case, the agent is unlikely to possess inadmissible information. So even modulo assumption 1, Kaufmann’s thesis is likely to hold in a wide variety of cases. Assumption 2 might fail for one of two reasons. First, A and B may be outside the domain of the chance function. In these cases, my characterization of the imaging function leaves PtAα undefined at :A worlds. It may still be possible to determine vtα ðA ! BÞ, either by extending PtAα to recalcitrant cases, or by falling back on a well-defined set selection function, but neither of these moves can be used together with CP to guarantee Kaufmann’s thesis. Second, assumption 2 might fail because cht ðAÞ ¼ 0 in the case of Chancy Imaging, or because chtα ðA∧NAα ∧Sα Þ ¼ 0 in the case of Causal-Chancy Imaging. According to the ratio definition of conditional probability, chtα ðBjϕÞ is equal to chtα ðB∧ϕÞ chtα ðϕÞ , and must be undefined when the denominator of this fraction is 0. We could reject the ratio definition of conditional probability and claim that chtα ðBjϕÞ is well defined even when chtα ðϕÞ ¼ 0. (For a recent account of conditional probability along these lines, see Hajek (2003).) If worked out in detail, this proposal would let us extend the scope of Kaufmann’s thesis.



TWO INTERPRETATIONS OF THE RAMSEY TEST

At the moment, however, 2 does constitute a genuine restriction on the strength of my result. This restriction is closely analogous to the clause that limits Adams’ thesis to cases where the agent’s credence in the antecedent is greater than 0—or more generally, where the agent’s credence in the consequent given the antecedent is well defined. In the case of Kaufmann’s thesis, the agent herself needs to be certain that the chance of the consequent given the antecedent (together with some background information) is well defined. So on the generalized imaging semantics, Kaufmann’s thesis holds, if not for all credence functions, at least for a significant class of ‘suitable’ ones. It looks as though a version of Adams’ thesis and a version of Stalnaker semantics can be reconciled after all. I will conclude with an explanation of how this account circumvents the triviality results. But first, I must address some unfinished business. I must say something about how to assign truth values to complex sentences containing conditionals, and about what constitutes a valid inference in the resulting logical system.

6.3 Handling Local Triviality How exactly does the move from selection functions to generalized imaging functions avoid the troubles raised by the local triviality theorems? This move combines the two strategies discussed in section 2: it restricts Kaufmann’s thesis to suitably rational credence functions, and it makes the meaning of the conditional contextdependent. But it also furnishes an account of why neither move is as philosophically problematic as it looks at first glance. I deny that the set of credence functions that satisfy Kaufmann’s thesis is closed under conditionalization. Or more precisely, given any fixed interpretation of the conditional, I deny that the set of such credence functions is closed under conditionalization, or under any other plausible updating rule. But this is not as bad as it seems. Updating is apt to change the context by providing inadmissible information (relative to the original contextually determined chance function). The only way to avoid changing the context altogether is to update on propositions that had chance 1 at the contextually salient time t—that is, propositions about the laws of nature and history before t. One may still conditionalize at will—provided one changes one’s interpretation of the conditional when necessary. Nor is all this context-sensitivity as drastic as it might seem. It’s true that conditionalizing on information about what happens after the contextually salient time t always changes the meaning you give to some conditional. But given any conditional, there are many propositions on which you can conditionalize without changing the meaning you assign to it. One major philosophical problem for the context-dependence strategy involved communication: if what each person means by a conditional depends on idiosyncratic and possibly unknown features of her credence function, then how can two individuals use a conditional to communicate? But on the account I’ve given, the

R . A . BRIGGS



contextual parameter is simply a time. And it is easy enough for all participants in a conversation to know which time is contextually salient. There were also several technical problems for the context-dependence proposal. We saw that no locally nontrivial but finite-ranged probability function could satisfy Kaufmann’s thesis, and that no Xi -nontrivial probability function with Xi -atoms could satisfy Kaufmann’s thesis. We could have retreated by deeming such credence functions irrational—and therefore not subject to Kaufmann’s thesis—unless they were sufficiently rich. But it was not clear why rationality required this richness. The move from selection functions to generalized imaging functions does not remove the demand for richness. But it does help to explain why richness is rationally required. If conditionals expressed ordinary two-valued propositions, we would have to interpret the richness as involving infinitely fine-grained distinctions between possibilities. It is not clear why rationality should require anyone to draw such fine distinctions. But since conditionals express many-valued propositions, we can interpret the richness as involving many functions from the same (possibly finite) set of worlds to truth values between 0 and 1. Begin with ordinary, two-valued propositions and simple conditional quasi-propositions, and you get the rest of the propositions for free. The last technical problem was this: no conditional that validated three principles—Modus Ponens, Entailment Within the Consequent, and Weakened Transitivity—was capable of satisfying Kaufmann’s thesis. It seemed as though any conditional whose truth conditions accorded with Stalnaker semantics had to validate all three principles. The generalized imaging semantics gives us a sort of compromise: it has been shown to validate all three principles and Kaufmann’s thesis, but only for conditionals with nonconditional antecedents and consequents.

References Adams, E. 1975. The Logic of Conditionals. Dordrecht: D. Reidel. Edgington, D. 1991. ‘The Mystery of the Missing Matter of Fact’, Proceedings of the Aristotelian Society, Supplementary Volume 65: 185–209. Edgington, D. 2004. ‘Counterfactuals and the Benefit of Hindsight’, in Cause and Chance: Causation in an Indeterministic World, ed. P. Dowe and P. Noordhof. London: Routledge, 12–27. Gärdenfors, P. 1982. ‘Imaging and Conditionalization’, The Journal of Philosophy, 79: 747–60. Gibbard, A. 1981. ‘Two Recent Theories of Conditionals’, in Ifs, ed. W. Harper, R. Stalnaker, and G. Pierce. London: D. Reidel, 211–47. Hajek, A. 1994. ‘Triviality on the Cheap?’, in Probability and Conditionals, ed. E. Eells and B. Skyrms. Cambridge: Cambridge University Press, 113–40. Hajek, A. 2003. ‘What Conditional Probabilities Could Not Be’, Synthese, 137: 273–323. Hajek, A., and Hall, N. 1994. ‘The Hypothesis of the Conditional Construal of Conditional Probability’, in Probability and Conditionals, ed. E. Eells and B. Skyrms. Cambridge: Cambridge University Press, 75–112.



TWO INTERPRETATIONS OF THE RAMSEY TEST

Hall, N. 1994. ‘Back in the CCCP’, in Probability and Conditionals, ed. E. Eells and B. Skyrms. Cambridge: Cambridge University Press, 141–60. Harper, W. 1976. ‘Rational Belief Change, Popper Functions, and Counterfactuals’, in Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, ed. W. Harper and C.A. Hooker, volume I. London: D. Reidel, 76–300. Kaufmann, S. 2004. ‘Conditioning Against the Grain’, Journal of Philosophical Logic, 33: 583–606. Kaufmann, S. 2005. ‘Conditional Predictions: A Probabilistic Account’, Linguistics and Philosophy, 28: 181–231. Lewis, D. 1976. ‘Probabilities of Conditionals and Conditional Probabilities’, Philosophical Review, 85: 297–315. Lewis, D. 1981. ‘Counterfactuals and Comparative Possibility’, in Ifs, ed. W. Harper, R. Stalnaker, and G. Pierce. London: D. Reidel, 57–86. Lewis, D. 1986a. ‘Probabilities of Conditionals and Conditional Probabilities II’, Philosophical Review, 95: 581–9. Lewis, D. 1986b. ‘A Subjectivist’s Guide to Objective Chance’, in Philosophical Papers, volume 2. Oxford: Oxford University Press, 83–113. Lewis, D. K. 1973. Counterfactuals. Cambridge, MA: Harvard University Press. List, C., and Menzies, P. 2009. ‘Nonreductive Physicalism and the Limits of the Exclusion Principle’, Journal of Philosophy, 106: 475–502. McGee, V. 1989. ‘Conditional Probabilities and Compounds of Conditionals’, Philosophical Review, 98: 485–541. McGee, V. 2000. ‘To Tell the Truth About Conditionals’, Analysis, 60: 107–11. Menzies, P. 1989. ‘Probabilistic Causation and Causal Processes: A Critique of Lewis’, Philosophy of Science, 56: 642–63. Menzies, P. 1996. ‘Probabilistic Causation and the Pre-Emption Problem’, Mind, 105: 85–117. Menzies, P. 2006. ‘A Structural Equations Account of Negative Causation’, in Contributed Papers of the Philosophy of Science Association 20th Biennial Meeting. http://philsci-archive. pitt.edu/2962/. Menzies, P. 2011. ‘The Role of Counterfactual Dependence in Causal Judgements’, in Understanding Counterfactuals/Understanding Causation, ed. C. Hoerl. Oxford: Oxford University Press. Menzies, P., and List, C. 2010. ‘The Causal Autonomy of the Special Sciences’, in Emergence and Causation, ed. C. Macdonald and G. Macdonald. Oxford: Oxford University Press. Morton, A. 2004. ‘Against the Ramsey Test’, Analysis, 64: 294–9. Pollock, J. 1981. ‘Indicative Conditionals and Conditional Probability’, in Ifs, ed. W. Harper, R. Stalnaker, and G. Pierce. London: D. Reidel, 249–52. Ramsey, F. 1978. ‘Law and Causality’, in Foundations, ed. D. Mellor. London: Routledge, 128–51. Skyrms, B. 1981. ‘The Prior Propensity Account of Subjunctive Conditionals’, in Ifs, ed. W. Harper, R. Stalnaker, and G. Pierce. London: D. Reidel, 259–65. Smith, N. J. 2009. ‘Degree of Belief is Expected Truth Value’, in Cuts and Clouds: Essays on the Nature and Logic of Vagueness, ed. R. Dietz and S. Moruzzi. Oxford: Oxford University Press, 491–508. Sobel, J. H. 1979. ‘Probability, Chance, and Choice: A Theory of Rational Agency’. Unpublished manuscript.

R . A . BRIGGS



Stalnaker, R. 1976. ‘Letter to van Fraassen’, in Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, ed. W. Harper and C. A. Hooker, volume 1. London: D. Reidel, 302–6. Stalnaker, R. 1981a. ‘A Defense of Conditional Excluded Middle’, in Ifs, ed. W. Harper, R. Stalnaker, and G. Pierce. London: D. Reidel, 87–104. Stalnaker, R. 1981b. ‘A Theory of Conditionals’, in Ifs, ed. W. Harper, R. Stalnaker, and G. Pierce. London: D. Reidel, 41–55. Stalnaker, R., and Jeffrey, R. 1994. ‘Conditionals as Random Variables’, in Probability and Conditionals, ed. E. Eells and B. Skyrms. Cambridge: Cambridge University Press, 31–46. van Fraassen, B. 1976. ‘Probabilities of Conditionals’, in Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, ed. W. Harper and C. A. Hooker, volume I. London: D. Reidel, 261–300. van Rooij, R. 2006. Attitudes and Changing Contexts. Dordrecht: Springer.

4 Pragmatic Explanations of the Proportionality Constraint on Causation Cei Maslen

1 Introduction In a number of papers, Stephen Yablo has argued for a proportionality constraint on causes. This idea is unusual in the causation literature, though recently Williamson and Shoemaker have adopted similar restrictions.1 The basic idea is that causes need to be at an appropriate level of specificity. The cause needs to be specific enough but at the same time general enough to be fully relevant to the effect. So when faced with a range of causal descriptions of determinates and determinables, Yablo advises that we should keep on subtracting details until we find the true cause. Continuing to subtract details after that takes us away from the true cause. The case for this proportionality constraint mainly rests on some examples. Suppose we are searching for the cause of an injury: ‘being hit by a red bus’ is too detailed, ‘being hit’ isn’t detailed enough, but ‘being hit by a bus’ is about right.2 This sort of example has undeniable intuitive appeal. However, I think that the intuitive appeal needs to be examined with more care, before jumping to conclusions about the metaphysics of causation and the mereology of causal relata. This chapter re-examines the case for a proportionality constraint on causation and investigates and compares some alternative pictures and interpretations of Yablo’s examples that involve different pragmatic features. I find a contrastivist approach to causation gives the best explanation of the proportionality examples. This also turns out to have some interesting consequences for causal claims at different levels.

1

See Shoemaker 2001, 2007 and Williamson 2000. ‘A little generality is causally speaking a good thing: being hit by a bus, Williamson notes, is a better candidate for cause of death then being hit by a red bus. But there are limits. The pursuit of greater and greater generality eventually takes one away from the cause’ (Yablo 2003: 319). 2

CEI MASLEN



2 Introducing Proportionality Yablo’s proportionality constraint applies to determinables and their determinates. The determinable/determinate relation is a relation between properties that is often introduced by example. Scarlet is a determinate of the determinable red, and being hit by a bus is a determinate of being hit. One way of understanding this relation is that having a determinate property is a specific way of having the determinable property.3 For example, scarlet is a specific way of being red, and being hit by a bus is a specific way of being hit. Sometimes determinable properties are specified by a range of determinate properties. For example, the determinable property of travelling at between 50 and 60 km/hr is specified by a range of determinate properties. According to Yablo, determinables and determinates always compete to be causes. That is, only one property in a determinable/determinate pair may be a cause of a given effect. If a property is a cause of an effect then none of its determinables or determinates may also be causes of that effect. This idea is captured in his definition of proportionality. His definition involves the notion of screening off: a screens b off from e iff, had a occurred without b, then e would still have occurred. For example, being hit by a bus screens off being hit by a red bus from the death, because if the victim had been hit by a non-red bus, then he would still have died. Roughly speaking, a screens off b when a improves on b by removing unneeded detail. Then Yablo’s proportionality constraint on causation is as follows: c is a cause of e only if c is proportional to e, and c is proportional to e iff it is required (none of its determinables screen it off), and it is enough (it screens off all of its determinates).

As Bontly puts it, the proportionality constraint implies that causation is just plain fussy. He refers to Yablo’s proportionality constraint as the ‘Goldilocks Principle’ (2005: 332). Just as Goldilocks only eats porridge that is ‘just right’, and rejects porridge that is too hot or too cold, we must only accept causes that are ‘just right’ and we must reject those that are not required or not enough. Yablo motivates his requirement with some examples. These are striking examples. Whether or not Yablo’s proportionality constraint is correct, his proportionality examples certainly show something of interest. Pigeon. ‘Imagine a pigeon Sophie trained to peck at red shapes...’4 She sees a scarlet triangle and pecks at it. Let’s ask ourselves which of the following causal claims are correct: The triangle’s being scarlet is a cause of Sophie’s pecking. The triangle’s being red is a cause of Sophie’s pecking. The triangle’s being coloured is a cause of Sophie’s pecking.

3

For example, see Funkhouser 2006. ‘Imagine a pigeon Sophie trained to peck at red shapes. No one would call the triangle’s redness irrelevant to her pecking on the grounds that the effect was already provided for by its specific shade of red’ (1997: 256). 4



PROPORTIONALITY CONSTRAINT ON CAUSATION

Applying Yablo’s proportionality constraint, the triangle’s scarletness is not a cause of Sophie’s pecking, because it was not required. The scarletness is screened off by its determinable, redness: if the triangle had been red, but not scarlet, Sophie would still have pecked. On the other hand, the triangle’s colouredness is not a cause of the pecking because it was not enough. The colouredness does not screen off one of its determinates—redness. If the triangle had been coloured, but not red, then the pigeon would not have pecked. The redness of the triangle is proportional to the effect, and so, according to Yablo it is the only one of these three candidates that counts as a cause of the pecking.5 Here are three further well-known examples: Platform. Woodward supposes that a platform will collapse if and only if a weight more than 1000 kg is placed on it. He then asks which of the following claims are true: the weight on the platform being more than 1000 kg caused it to collapse, the weight on the platform being 1600 kg caused it to collapse (or both). According to the proportionality constraint, weighing more than 1000 kg is a cause in this case, but weighing 1600 kg is not because it was not required. Socrates. Suppose that Socrates was a sloppy eater, and he did not sip the hemlock, but rather guzzled it quickly. Yablo argues that his guzzling the hemlock was not a cause of his death, because it was not required. One of its determinables screens it off—Socrates’ drinking the hemlock screens it off. Mind-Body. Yablo argues that mental events (like the desire for a chocolate bar) may be causes of behaviour (like reaching for a chocolate bar), for they may be proportional to behaviour. However, the underlying physical realizations of those mental events are never causes of behaviour according to Yablo, as they are never proportional to behaviour—they are not required. (The Mind-Body example is such a contested case that we will postpone discussion of it insofar as we can until we are done with our analysis of proportionality rather than designing an analysis of proportionality to fit our preconceived ideas of that central example.) The first part of Yablo’s definition of proportionality, required, rules out overspecific causes, while the second part of the definition, enough, rules out overgeneral causes. The motivation for required seems to be to ensure that the cause contains no irrelevant details. The motivation for enough seems to be to restrain the action of required—to avoid pointless or irrelevant generality. So for example, the triangle’s 5

Note that Yablo also comments on this example that both scarletness and redness can be causally relevant. Although determinates do compete with their determinables for causation, according to Yablo, they do not compete for causal relevance: causal relevance is a more permissive relation than causation. I am reluctant to postulate a relation of causal relevance in addition to a relation of causation, and I avoid the topic in this chapter. I don’t think we need two separate causal notions once we have a correct analysis. (In this I agree with Woodward: ‘Put slightly differently, if we understand causal (ir)relevance in the manner just suggested...there is no such thing as a cause of Y that is not causally relevant to Y. Equally, if X is causally relevant to Y, then X causes Y. Bona fide causal claims always have relevance built into them’ (Woodward 2008: 227).)

CEI MASLEN



colouredness is not a cause of the pecking because it was not enough. Although colouredness is more general than redness, this is irrelevant or pointless generality because colouredness does not improve on redness. If the triangle had been coloured, but not red, then the pigeon would not have pecked. Yablo’s examples do have intuitive power—they seem to show that we are somewhat fussy about causes, at least when we are encouraged to be fussy. But I don’t think that the proportionality constraint does full justice to our intuitions about the examples. Suppose that I initially say that the collapse of the platform was caused by the weight’s being 1600 kg. Although I may acknowledge that it is an improvement to say that it was caused by the weight’s being greater than 1000 kg, I am reluctant to say that my initial statement was incorrect. It seems inappropriate to retract my earlier statement, yet the proportionality constraint implies that I should retract this statement, as determinables and determinates cannot both be causes. Moreover, the main motivation for the proportionality constraint seems to be to find the most relevant cause, and this suggests that our preference for proportional causes has a pragmatic or contextual explanation of some sort. A number of different philosophers have suggested this recently—and in the rest of the chapter I want to consider the nature of this pragmatic explanation. I should also say here that I am not in the least moved to reject overgeneral causes (i.e. to accept the part of his definition Yablo calls ‘enough’). If our goal were to analyse the concept of being a sufficient cause then it would make sense to insist that a sufficient cause is enough for the effect to come about. But our goal is to analyse the concept of being one of the causes of the event, not the concept of being a sufficient cause, so it seems wrong to insist that each cause is enough for the effect to come about. (I also personally do not feel moved by the examples to accept this part of Yablo’s definition. For example, I am happy to accept that being coloured is one of the causes of Sophie the pigeon pecking. After all if the triangle had not been coloured, Sophie would not have seen it.6)

3 Bontly’s Pragmatic Explanation of our Preference for Proportionality Bontly claims that ‘Proportionality is...a pragmatic feature of our use of causal language, derived from general principles of language use’ (2005: 332). He argues that it is generated by conversational implicature. For example, he claims that ‘Socrates’ guzzling the hemlock’ and ‘Socrates’ drinking the hemlock’ are both causes of his death, but that we wouldn’t normally call ‘Socrates’ guzzling the hemlock’ a cause, because the less specific event—‘Socrates’ drinking the hemlock’ is preferable 6 The ‘required’ part of Yablo’s proportionality constraint turns out to be primary in Yablo’s response to the causal exclusion problem, as his crucial claim is that mental events are required while their underlying physical realizations are not.



PROPORTIONALITY CONSTRAINT ON CAUSATION

on pragmatic grounds. He argues that when I use the more specific cause I falsely conversationally implicate that the more specific cause is required and that the less specific cause was not enough. He appeals to the Gricean Maxim of Quantity: ‘Make your utterance as informative as necessary for the purposes of the conversation but no more so.’7 If we grant Bontly his starting assumption—that Socrates’ guzzling the hemlock and Socrates’ drinking the hemlock are both causes of his death, then Bontly’s appeal to Grice’s Maxim of Quantity seems to work in this case: citing Socrates’ guzzling the hemlock as a cause may falsely conversationally implicate that Socrates’ drinking the hemlock is not a cause, for we may reason that if Socrates’ drinking the hemlock were also a cause, then extra information about guzzling need not have been included.8 (But I think it is important to note that this conversational implicature will not be generated if ‘guzzling’ is relevant for other reasons. For example, suppose Xanthippe wanted to convey information about Socrates’ impolite manners at the same time as conveying information about the cause of his death. Then in this particular case, citing Socrates’ guzzling the hemlock as a cause of death is no more informative than is required for the purposes of the conversation and there would be no false conversational implicature that Socrates’ drinking the hemlock is not a cause of death.) Given his assumptions, Bontly’s explanation does seem to work to explain why it is inappropriate to say that Socrates’ guzzling the hemlock caused his death.9 In fact it may seem to work too well. If Socrates’ guzzling the hemlock on a Tuesday were also a cause of his death then Grice’s maxims could also be used to explain why it is inappropriate to mention Socrates’ guzzling the hemlock on a Tuesday as a cause! My point at this stage is just that Bontly’s explanation is only successful if his starting assumptions are true. That is, his explanation is only successful if Socrates’ guzzling the hemlock and Socrates’ drinking the hemlock are both treated as causes of his death. Bontly’s argument for this is less than convincing—he simply appeals to the fact that Socrates’ guzzling the hemlock has some influence on the time and manner

7 He says, ‘Thus, in explaining E by a lower-level cause, I conversationally implicate that this subvenient event was required and the higher-level, supervenient event not enough’ (Bontly 2005: 342). 8 Although it is obvious why the claim that Socrates guzzled the hemlock is more informative than the claim that Socrates drank the hemlock—the first entails the second and not vice versa—it is actually not obvious that the claim that Socrates’ guzzling the hemlock caused his death is more informative than the claim that Socrates’ drinking the hemlock caused his death. After all, each of these causal claims only gives information about one causal link. I presume that Bontly’s reason for saying that the claim that Socrates’ guzzling the hemlock caused his death is more informative than the claim that Socrates’ drinking the hemlock caused his death is simply that the first claim presupposes the additional information that Socrates guzzled it, and will grant him this for the time being. However, I explain below why the parallel claim is problematic for the platform example. 9 Also note that Bontly does not explain other features of the proportionality cases, for example why it is preferable to state the triangle’s being red rather than the triangle’s being coloured as a cause of the pigeon’s pecking. But as I said at the outset, I too do not see the appeal of rejecting causes as overgeneral.

CEI MASLEN



of Socrates’ death. I am not convinced by this; merely influencing the time and manner of an effect is not the same as causing it.10 In case this just seems like a quibble with one example, let us apply Bontly’s explanation to the platform example. Using the Socrates example as a model, Bontly would say that both the platform’s weighing more than 1000 kg and the platform’s weighing 1600 kg are causes of the collapse, but that it is not appropriate to mention the platform’s weighing 1600 kg as a cause for that would falsely implicate that the less informative claim (the platform’s weighing more than 1000 kg) is false. In this case, I do find it plausible that both the platform’s weighing more than 1000 kg and the platform’s weighing 1600 kg are causes of the collapse. However, there are still some major problems with Bontly’s explanation. One problem is that it doesn’t account for a subtle feature of our reactions to the example. It doesn’t account for our sense that if we begin by saying that the platform’s weighing 1600 kg is a cause of the collapse then it subsequently seems like an improvement to add that the platform’s weighing more than 1000 kg is a cause of the collapse. On Bontly’s explanation, both of these are true, and it is mysterious how adding what he sees as a less informative claim would be an improvement. A second problem with Bontly’s explanation here is that the claim about informativeness he needs is false in this case! It is simply not true that the claim that the platform’s weighing more than 1000 kg caused the collapse (call it Statement>1000kg) is less informative than the claim that the platform’s weighing 1600 kg caused the collapse (call it Statement1600kg). Admittedly it is true that there is one little piece of information presupposed by Statement1600kg that is not implied by Statement>1000kg, and that is just that the platform does weigh 1600 kg. However if you think about it further, more information is implied by stating a precise weight limit for a platform (that is, stating that the platform will collapse if and only if this precise weight is exceeded) than by stating that one particular weight was too much for that platform. In support of this claim, let us compare the sets of counterfactuals that are implied by Statement>1000kg and Statement1600kg. Statement>1000kg implies a lot of different counterfactuals: if the platform had been 1001 kg the collapse would still have happened, if the platform had been 1002 kg the collapse would still have 10

In assuming that both the determinable and its determinate—Socrates’ drinking the hemlock and Socrates’ guzzling the hemlock—are causes of his death, Bontly may have had in mind the conclusion he wanted to reach on the Mind-Body example. One of Bontly’s main goals in his paper is to defeat Yablo’s response to the Causal Exclusion problem by arguing that even if it seems that physical realizers of mental events are not proportional to behaviour, this only implies that they are not conversationally appropriate, not that they are not causes of behaviour. Bontly also argues that Yablo’s conclusion that physical realizers of mental events are not causes of behaviour because they are not proportional to behaviour conflicts with the principle of the Causal Completeness of Physics in an unacceptable way (e.g. Bontly 2005: 339, ‘There is an irremediable tension between the proportionality requirement and the completeness of physics’). However, as we shall see later, there are other pragmatic explanations of the proportionality intuitions that do not conflict with the Causal Completeness of Physics in an unacceptable way. Let me repeat here that we should postpone discussion of the contested Mind-Body example until we are done with our analysis of proportionality.



PROPORTIONALITY CONSTRAINT ON CAUSATION

happened,...if the platform had been more than 1600 kg the collapse would still have happened, if the platform had been more than 1601 kg the collapse would still have happened...In contrast, Statement1600kg (together with background knowledge in the context, that increasing weight increases likelihood of collapse) implies just a subset of these counterfactuals: {if the platform had been more than 1600 kg the collapse would still have happened, if the platform had been more than 1601 kg the collapse would still have happened...} Statement>1000kg also implies that if the platform had been 999 kg the collapse would not have happened, if the platform had been 998 kg the collapse would not have happened...Statement1600kg, on the other hand, does not also imply that if the platform had been 999 kg the collapse would not have happened, if the platform had been 998 kg the collapse would not have happened...(It seems to me that Statement1600kg does imply some counterfactuals of the form ‘If the platform had not been 1600 kg, then the platform would not have collapsed’, but it is vague exactly which these are.)11

4 Explanations in Terms of the Pragmatics of Naming Causal Relata A different kind of pragmatic explanation of the proportionality examples relies on the claims that causal relata are fine-grained, and that there is a lot of flexibility and context-dependence involved in naming them. (These are very plausible claims. Although I accept these claims myself and think this explanation of the proportionality examples is worth considering, I will later argue that it is not an adequate explanation of the examples.) Then we may say that when we prefer some causal statements to others on the grounds of proportionality, these are only preferred on the grounds of explicitness: the statements in the examples are all equivalent in meaning, but the preferred statements are more explicit. Looking at the Platform example, initially it seems acceptable to say that the collapse of the platform was caused by the weight’s being 1600 kg (Statement1600kg), but it seems an improvement to say that it was caused by the weight’s being greater than 1000 kg (Statement1600kg). If I initially claim that the platform’s weighing 1600 kg caused the collapse, and you ask me, ‘Do you mean the platform's weighing exactly 1600 kg?’ this will prompt me to clarify by saying ‘No, it was actually the platform's weighing more than 1000 kg that was a cause.’ The second statement is making the same claim as the first, only more explicitly. Looking at the Pigeon example, initially it seems acceptable to say that the triangle’s being coloured is a cause of Sophie’s pecking, yet it seems an improvement to say that it is the triangle’s being red that is a cause

11 As Christopher Hitchcock has suggested to me, perhaps it could be understood as implying an existential claim: there is some n < 1600, such that if the platform weighed  n kg, then the platform would not have collapsed.

CEI MASLEN



of Sophie’s pecking. The second statement is making the same claim as the first, only more explicitly. This is a pragmatic explanation of the phenomena in the sense that the disproportionate statements (e.g. ‘The platform’s weighing 1600 kg caused the collapse’, ‘the triangle’s being coloured is a cause of Sophie’s pecking’) are not claimed to be false, but merely to be unassertible in certain contexts—in contexts where we are offered a choice between accepting these claims and more explicit claims (‘the platform’s weighing more than 1000 kg caused the collapse’, ‘the triangle’s being red is a cause of Sophie’s pecking’). This explanation in terms of the pragmatics of naming causal relata has some strengths as compared to Yablo’s picture. Yablo owes us an explanation of why we so often mistakenly make disproportionate causal statements. We frequently say things like ‘the platform’s weighing 1600 kg caused the collapse’, and as this statement is false according to Yablo, he owes us an explanation of why this error is so widespread. He also owes us an explanation of why initially it seems perfectly acceptable to say that the platform’s weighing 1600 kg caused the collapse (Statement1600kg) and we only tend to feel dissatisfied with it when we are offered an improved alternative (Statement>1000kg). The explanation in terms of the pragmatics of naming causal relata explains these features easily: we frequently make statements like Statement1600kg because this statement is true and it is a convenient way of making the same claim as Statement>1000kg. Yet Statement>1000kg seems like an improvement because it is more explicit. Let us now evaluate the claims that underpin this explanation: the claims that causal relata are fine-grained, and that there is a lot of flexibility and contextdependence involved in naming them. Recall Davidson’s coarse-grained account of events. He claims that events are individuated by the regions of space-time they occupy and this permits him to say that Flora’s drying of herself and Flora’s drying of herself with a coarse towel are the very same event, as they occupy the same region of space-time. So according to Davidson, events are widely redescribable. Many philosophers, for example Lewis and Kim, think that a coarse-grained account of causal relata does not provide enough events to capture all of our intuitive causal judgements, and so they are led to a fine-grained theory of causal relata. On Lewis’s view, there are at least two events involved in Flora’s drying of herself, which differ in their causes and their effects. One of these events (call it drying1) caused the rash and the other (call it drying2) didn’t. Furthermore, one of these events (drying1) was caused by the event of Flora’s sister’s hiding of the soft towel, and one (drying2) wasn’t. This is a fine-grained theory of events—there can be more than one event filling the very same spatio-temporal region. Yablo too accepts the need for a fine-grained theory of causal relata. Flora’s drying of herself and Flora’s drying of herself with a coarse towel are different events occupying the same region of space-time, related as determinable to determinate. Yablo seems to assume a one-to-one correspondence between properties and



PROPORTIONALITY CONSTRAINT ON CAUSATION

predicates, although this does not automatically follow from a fine-grained theory of causal relata. I agree with Yablo that causal relata are fine-grained but I do not think we can simply take names of causes at face-value.12 Instead, following Lewis, it seems that fine-grained causal relata are widely redescribable. So the phrase ‘Flora’s drying of herself ’ may be used to pick out either drying1 or drying2, as may the phrase ‘Flora’s drying of herself with a coarse towel’.13 The reason we sometimes include details in naming a cause that are irrelevant to its actual causal efficacy is because they are relevant to identifying the cause. Suppose I say ‘Flora’s drying of herself on Sunday’ caused her rash on Monday. Then the qualifier ‘on Sunday’ serves only to pick out the particular event of Flora’s drying of herself, rather than implying that its being on Sunday was causally relevant. The reason we sometimes fail to include details in naming a cause is that they aren’t necessary for identifying it. We may successfully refer to the event drying1 with the phrase ‘Flora’s drying of herself ’, as it is clear from other features in the context that these details are relevant. So it does seem plausible that we can pick out ‘Flora’s drying herself with a coarse towel’ as a cause of her rash by merely saying ‘Flora’s drying herself ’, when it is obvious from the context that the missing detail—the coarseness of the towel—is relevant. Although it seems correct, this view of flexible naming of causal relata unfortunately poses more questions than it answers. Lewis does not give us any guidance as to how to locate the appropriate event that is named by any event predicate. This is problematic for our explanation of the proportionality examples in terms of the pragmatics of naming causal relata. In fact, so far I have suggested that all of the causal event predicates within a proportionality example refer to the same event, but I haven’t yet stated which event is named by all these different predicates! One idea for answering this question is that any true causal claim is true by virtue of the fact that event predicates always refer to events that are proportionate causes and effects. For example, it is true to say that the platform’s weighing 1600 kg caused the collapse, in virtue of the fact that this expresses the proposition that the platform’s weighing more than 1000 kg caused the collapse. Note that although this explanation does not involve accepting Yablo’s proportionality constraint, there is still a

12 There are some different fine-grained theories on offer, but I want to put aside the question of which theory is most suitable, or whether the causal relata should really be called events, aspects, property instantiations, or whatever, because this is not the point at issue in this chapter. In what follows I talk about causal relata interchangeably as events or properties, as is convenient in discussing the views of Yablo and others. I hope this will not confuse the reader. 13 ‘We have two descriptions: “John’s saying ‘Hello’ ” and “John’s saying ‘Hello’ loudly.” But it does not follow from this alone that we have two events to describe. The second description as well as the first might denote the first event, since the second description might describe the first event in part accidentally. Alternatively, the first description as well as the second might denote the second event, since the first description might describe the second event by less than the whole of its essence...The real reason why we need both events, regardless of which description denotes which, is that they differ causally’ (Lewis 1986: 255).

CEI MASLEN



fundamental sense in which it respects the proportionality constraint. Apparently disproportionate causal claims may be true, but only by virtue of picking out proportionate causal links. A different promising idea is to postulate implicit existential quantifiers for each of the causal relata. For example, to say that the platform’s weighing 1600 kg caused the collapse is to say that there is a fine-grained event that fits the description of the platform’s weighing 1600 kg that caused a fine-grained event that fits the description of being a collapse.14 As I said above, although I find it plausible that causal relata are fine-grained events and that there is some flexibility and context-dependence involved in naming them, I do not think this yields a plausible explanation of the proportionality examples. The reason we sometimes include details in naming a cause that are irrelevant to its actual causal efficacy is because they are relevant to identifying the cause, and the reason we sometimes fail to include details in naming a cause is that they aren’t necessary for identifying it. However, the proportionality examples are subtly different. The missing details may not be obvious from the context of the proportionality examples. Imagine that the people who are making the claims do not know the specifics of the weight limit of the platform or the training of the pigeon. In such contexts of reduced knowledge it does not seem plausible to me that ‘the platform’s weighing 1600 kg’ picks out the same fine-grained event as ‘the platform’s weighing at least 1000 kg’ or that ‘the triangle’s being coloured’ picks out the same fine-grained event as ‘the triangle’s being red’. However, our reactions to the examples are no different in these reduced knowledge contexts. Hence, the explanation does not succeed.

5 The Contrastivist Explanation Let me finally present a third kind of pragmatic explanation of our intuitions about the proportionality examples arising from a contrastivist theory of causation. I think this has some interesting consequences for the ontology of causal relata, and comes from an approach to causation that is promising for many other reasons. The contrastivist approach to causation may be unfamiliar to the reader but is gaining in popularity.15 This kind of approach can be spelled out in many different ways and seems to fit particularly well with interventionist/causal modelling accounts of causation and other counterfactual accounts. The idea of a contrastivist account of causation is that contrast cases for the cause and effect are determined by the context. 14

Yet another idea for answering this question is that it often isn’t determinate exactly which causal relata are named by particular claims, in cases where it doesn’t matter to the causal claim. I will not develop this view further but I have in mind something like the supervaluationist treatment of vague objects. 15 For defences of Causal Contextualism see for example Hitchcock (1996), Maslen, Horgan, and Daly (2009), Menzies (2004), Price (2007), Schaffer (2005).



PROPORTIONALITY CONSTRAINT ON CAUSATION

Menzies and Woodward each apply a contrastivist approach to the proportionality examples and come up with slightly different conclusions (Menzies 2008; Woodward 2008). According to Menzies, applying the contrastivist account to the proportionality examples does generate our intuitive judgements: the triangle’s being red caused the pigeon to peck, and the triangle’s being scarlet did not. This is because the appropriate contrast with the triangle’s being red is with the triangle’s being nonred, while the appropriate contrast with the triangle’s being scarlet is the triangle’s being non-scarlet. So according to Menzies, the first counterfactual below (Red’) is true, while the second counterfactual below (Scarlet’) is false. (Red’) If the triangle had been non-red rather than red, then Sophie would not have pecked. (Scarlet’) If the triangle had been non-scarlet rather than scarlet, then Sophie would not have pecked. (Red’) and (Scarlet’) are somewhat confusing at first sight actually. Menzies explains that to contrast the triangle’s being red with the triangle’s being non-red is to contrast it with being a different colour altogether, like yellow or green. If the triangle had been yellow, say, Sophie would not have pecked, so (Red’) is true. However, if the triangle had been non-scarlet, say crimson, then Sophie would still have pecked, so (Scarlet’) is false. (Menzies also argues that correct judgements about the proportionality examples will follow from a correct account of causation and do not need to be stated separately as Yablo does.16) I think the clearest way to understand this is to realize that being non-red is a range property. It covers a range of different colours that are each ways of being non-red: yellow, green, blue... 17 Being non-scarlet is also a range property that covers even more colours and shades: not just yellow, green, blue, etc. but also non-scarlet shades of red. In order for (Red’) to be true, a lot of different counterfactuals have to be true: If the triangle were yellow, Sophie would not have pecked, if the triangle were green, Sophie would not have pecked, if the triangle were blue, Sophie would not have pecked...And all of these counterfactuals are true. For (Scarlet’) to be true, however, even more counterfactuals need to be true, and not all of them are. For example, it is false that if the triangle were crimson then Sophie would not have pecked. Overall, we can say that if the triangle had been non-scarlet, Sophie might still have pecked. I agree with most of what Menzies says. However, this leaves unexplained some of our reactions to the examples, namely why we so often make disproportionate causal

16 Menzies also argues that Yablo’s proportionality constraint is unclear and unhelpful because the counterfactuals that define screening off are so vague. So when we ask whether if the redness of the triangle had occurred without the scarletness, the pigeon would still have pecked, this counterfactual is very unclear. Certainly one strength of a contrastivist account is that it relies on counterfactuals with more specific antecedents. 17 Being non-red is a determinable of these different determinates.

CEI MASLEN



statements (like Statement1600kg) and why we only feel dissatisfied with disproportionate causal statements when we are offered an improved alternative (Statement>1000kg). I think that the contrastivist account is more flexible than Menzies suggests here. Woodward applies a contrastivist account to the platform example, in a slightly different way. He considers the two statements: ‘The weight on the platform’s being more than 1000 kg caused it to collapse’ (Statement>1000kg) and ‘The weight on the platform’s being 1600 kg caused it to collapse’ (Statement1600kg). He concludes that both claims are true, but that the second is misleading. There is a contrast that makes the second true, but the second naturally suggests a different contrast (or perhaps fails to suggest a contrast at all), and thus the causal claim is defective. This begins to give us an explanation of why Statement1600kg seems acceptable initially, and also why Statement>1000kg seems to be an improvement. Applying this to the pigeon example, it seems to me that the relevant contrasts with the triangle’s being scarlet can be with the triangle’s being yellow, green, blue... With these contrasts the claim that the triangle’s being scarlet caused Sophie to peck is true. According to Menzies, the natural contrasts with the triangle’s being scarlet described by Menzies are crimson, vermilion...yellow, green, blue. With this set of contrasts, the statement that the triangle’s being scarlet caused Sophie to peck is false. However, this set of natural contrasts can be narrowed down to give a charitable interpretation of the causal claim—one allowing it to be true. The relevant contrasts to the cause need not be determined entirely by the stated description of the putative cause, but also by other factors in the context and conversational principles. And a very important conversational principle is charity of interpretation. It may be helpful to group events and contrast events into rough levels, according to how specific they are. The triangle’s being red is on the same level as the triangle’s being yellow, but the triangle’s being scarlet is on a lower level, as it is a determinate of redness. We have a partial ordering of properties if we place determinates at a lower level than their determinables, and the determinates of those determinates on a lower level again. Then the natural contrasts to the cause normally include events on the same level as the cause.18 These will all be incompatible with the cause, as different determinates of the same determinable on the same level tend to be incompatible with each other. For example, natural contrasts with the triangle’s being scarlet include the triangle’s being vermilion and the triangle’s being crimson. However, cross-level contrasts are also possible, and will be relevant if required to make the causal claim true, provided that no other contextual features rule them out. So, the statement that the triangle’s being scarlet is a cause of Sophie’s pecking is true

18

Note that I am saying that being yellow, being green, being blue are all natural contrasts with being red, while Menzies is saying that being non-red is a natural contrast with being red. Being non-red is a determinable of the determinates being yellow, being green, etc. so in terms of these rough levels it counts as being at one higher level. I think it is slightly easier to talk of individual contrasts as being on the same level, instead of the range of contrasts coming from one higher level.



PROPORTIONALITY CONSTRAINT ON CAUSATION

in some contexts. Now, returning to Woodward’s platform example, Woodward does acknowledge a sense in which the weight on the platform’s being 1600 kg is a cause of the collapse, because there is a contrast that makes the second claim true. So the weight’s being 1600 kg, in contrast to being less than 1000 kg, is a cause of the collapse. However, Woodward does say that the claim that the weight’s being 1600 kg is a cause of the collapse is misleading, because it naturally suggests a different contrast (or perhaps fails to suggest a contrast at all), and thus the causal claim is defective. So Woodward seems to prefer the claim that the weight’s being more than 1000 kg is a cause of the collapse as it makes the contrasts clearer and avoids ambiguity. In general, what I have claimed is that, given the principle of charity, if there are some not-too-far-fetched cross-level contrasts that will make a causal claim true, then those contrasts will tend to be relevant in the context. And this does fit our intuitions about the proportionality examples. We do after all have some tendency to say that the triangle’s being scarlet is a cause of Sophie’s pecking, as well as that the triangle’s being red is a cause of Sophie’s pecking. Similarly, we do have some tendency to say that the platform’s being 1600 kg is a cause of the collapse, as well as that the platform’s being more than 1000 kg is a cause of the collapse. In conclusion, I think that the contrastivist account yields a plausible and full pragmatic explanation of our intuitions concerning the proportionality examples. Moreover, the contrastivist explanation has the advantage of springing from a new and promising approach to causation that can be developed in various ways into a full account of causation.

6 Cross-level Contrasts and the Metaphysics of Causation Allowing for cross-level contrasts leads to a very interesting consequence of a contrastivist approach to causation, at least on one way of spelling out the contrastivist view. Adopting a counterfactual contrastivist account, it turns out that the truth conditions for causal statements on different levels can be nearly exactly the same: (a) The triangle’s being scarlet, in contrast to its being yellow (/orange/...) is a cause of Sophie’s pecking is true iff (the triangle is scarlet and Sophie did peck) and had the triangle been yellow (/orange/...) then Sophie would not have pecked. (b) The triangle’s being red, in contrast to its being yellow (/orange/...) is a cause of Sophie’s pecking is true iff (the triangle is red and Sophie did peck) and had the triangle been yellow (/orange/...) then Sophie would not have pecked. What we have here are causal statements on different levels with the very same truth conditions, except for the clause that requires causes and effects to actually occur.19 19

Thanks to Phil Dowe for reminding me to include this first clause.

CEI MASLEN



Roughly speaking, we might say that contrastivism about causation allows for the same causal claim to have different meanings in different contexts and different causal claims to have the same meanings in the same context. However, we should be more cautious in stating this. Note that because the different causal claims relate different causal relata, and because of the clause requiring that causes and effects actually occur, these causal claims have different ontological presuppositions. So, the claim that the triangle’s being red is a cause of Sophie’s pecking presupposes the existence of the event of the triangle’s being red, while the claim that the triangle’s being scarlet is a cause of Sophie’s pecking presupposes the existence of an event of the triangle’s being scarlet. This is worth reiterating. My view is that causal relata only play a minimal role in the truth conditions for causal claims. The causal claim is really about the contrasts, the descriptions of the causal relata mainly serve to help pick out the contrasts, and only the contrasts appear in the main clause of the truth conditions: ‘had contrast1 occurred then contrast2 would have occurred’. According to the contrastivist, causation is the opposite of fussy (whatever the opposite of fussy is—robust, indiscriminate, laid-back, or obliging). Whenever a causal claim holds between determinables, there is a possible context in which a logically equivalent claim holds between determinates. So in many contexts, causal statements on different levels are logically equivalent—they express the same proposition—without the causal relata needing to be equivalent. Of course, if this is correct, it has interesting implications for philosophy of mind. It may be that even without the reduction of the mental to the physical that claims of mental causation are logically equivalent to claims of physical causation. What does this all mean for the ontology of causation? If contrastivism about causation is right, then we may need only the thinnest of ontological structures for causal claims to be true. (Think of a completely empty world with plenty of counterfactual truths.) The structure that supports causal claims is counterfactual connection between contrast events. And contrast events are not really events at all—they never actually occur. They are merely possible events that feature in counterfactuals.20

References Bontly, T. 2005. ‘Proportionality, Causation, and Exclusion’, Philosophia, 32: 331–48. Funkhouser, E. 2006. ‘The Determinable–Determinate Relation’, Noûs, 40: 548–69. Hitchcock, C. 1996. ‘Farewell to Binary Causation’, Canadian Journal of Philosophy, 26: 267–82. Ladyman, J., and Ross, D. 2007. Every Thing Must Go: Metaphysics Naturalized. Oxford: Oxford University Press. Lewis, D. 1986. ‘Events’, in his Philosophical Papers, Vol. II. Oxford: Clarendon Press, 241–69. 20

In fact, you can see that it is only a step away from here to a kind of structuralist or relation-only view of causation. See for example Ladyman and Ross 2007.



PROPORTIONALITY CONSTRAINT ON CAUSATION

Maslen, C., Horgan, T., and Daly, H. 2009. ‘Mental Causation’, in The Oxford Handbook of Causation, ed. H. Beebee, C. Hitchcock, and P. Menzies. Oxford: Oxford University Press, 523–53. Menzies, P. 2004. ‘Difference-making in Context’, in Causation and Counterfactuals, ed. J. Collins, N. Hall, and L. A. Paul. Cambridge, MA: MIT Press, 139–80. Menzies, P. 2008. ‘The Exclusion Problem’, in Being Reduced, ed. J. Hohwy and J. Kallestrup. Oxford: Oxford University Press, 196–217. Price, H. 2007. ‘Causal Perspectivalism’, in Causation, Physics and the Constitution of Reality: Russell’s Republic Revisited, ed. H. Price and R. Corry. Oxford: Oxford University Press, 250–92. Schaffer, J. 2005. ‘Contrastive Causation’, The Philosophical Review, 115: 297–328. Shoemaker, S. 2001. ‘Realization and Mental Causation’, in Physicalism and its Discontents, ed. C. Gillett and B. Loewer. Cambridge: Cambridge University Press, 74–98. Shoemaker, S. 2007. Physical Realization. Oxford: Oxford University Press. Williamson, T. 2000. Knowledge and its Limits. New York: Oxford University Press. Woodward, J. 2008. ‘Mental Causation and Neural Mechanisms’, in Being Reduced, ed. J. Hohwy and J. Kallestrup. Oxford: Oxford University Press, 218–62. Yablo, S. 1997. ‘Wide Causation’, Philosophical Perspectives, 11: 251–81. Yablo, S. 2003. ‘Causal Relevance’, Philosophical Issues, 13: Philosophy of Mind: 316–28.

5 Causation, Intervention, and Agency Woodward on Menzies and Price Huw Price

1 Introduction In ‘Causation as a Secondary Quality’ (Menzies and Price 1993; hereafter ‘CSQ’) Peter Menzies and I defended the view that, as we put it, ‘the ordinary notions of cause and effect have a direct and essential connection with our ability to intervene in the world as agents’ (CSQ: 187). We called this the agency theory of causation, and attributed it to Collingwood (1940), Gasking (1955), and von Wright (1975) before us (and tentatively also to Ramsey 1929). We argued that four common objections to this view are parallel to, and no more forceful than, four objections that could be raised to standard treatments of colour as a secondary quality (to all of which there are familiar responses). Hence our title: we were proposing that the agency view should be regarded as taking causation, too, to lie on the ‘secondary’ side of the primary/secondary divide; and that once this point is in the open, the usual objections to the agency view lose their force, because the familiar responses to the corresponding objections in the case of colour are easily transformed into the replies the agency theory needs in the case of causation. As it turned out—a matter much more of correlation than causation, unhappily for us!—the decade following the publication of our paper was extremely fruitful for the investigation of links between causation and manipulation, thanks to the work of Judea Pearl, Peter Spirtes and his collaborators, and Jim Woodward, amongst others. In Woodward’s case, the decade culminated in the publication of his widely acclaimed book, Making Things Happen (2003). There, and in some more recent papers, Woodward devotes some space to distinguishing his view from earlier manipulability approaches, including particularly that of CSQ, and to criticizing the latter view, on several points. In the present chapter, with the benefit of a further decade’s hindsight, I want to discuss Woodward’s criticisms. My response is mixed. On the one hand, I want to



CAUSATION , INTERVENTION , AND AGENCY

argue that the CSQ view is not as different from Woodward’s own as he believes, and that insofar as it is different, it has some advantages whose importance Woodward misses. On the other hand, I think that the CSQ view also lacks some elements whose importance Woodward rightly stresses, and I shall discuss the question as to whether it can be improved, to add those features. I shall thus be offering an updated, ‘Pricean’ version of the Menzies and Price view. Some of the updates are recent, reflecting what I feel I have learnt from Woodward’s work. Others are older, bringing in considerations from my own work on these topics in the years since CSQ was published. And some go right back to the period in which that paper was written, reflecting some respects in which my own take on the issues under discussion was not precisely aligned with the stance of the joint paper. My discussions with Peter Menzies in the 1980s were immensely illuminating, from my point of view, and a huge influence on the direction of my own work. But much of their value stemmed from the fact that our philosophical dispositions were always a little way apart: Peter tended to be more of a realist, and more of a metaphysician, than I was (or am). The formulation of the view in CSQ was to some extent a compromise, to bridge this gap, and I want to take the opportunity below to offer a revised formulation, in my own voice, in a couple of places. As I shall explain, I think this is relevant to our disagreement, or at least my disagreement, with Woodward, at some points. (In order to distinguish my voice from that of CSQ, I shall refer to its authors in the third person from now on, and usually simply as ‘MP’, for brevity.)

2 Causation as a Secondary Quality In their own words, the four arguments against the agency view of causation that MP consider are as follows: 1. Agency accounts confuse the epistemology of causation with its metaphysics. It is widely conceded that experimentation is an invaluable source of evidence for causal claims; the objection is that it is a confusion to suppose that the notion of agency should thereby enter into the analysis of causal claims. 2. Agency accounts are vitiated by circularity. It is argued that the bringing about is itself a causal notion, and that this introduces a vicious circularity into an agency account. 3. An agency account cannot make sense of causal relations between events which are outside the control of any agent. For example, it is argued that such an account cannot make sense of the claim that the earth’s revolution around the sun causes us to experience the seasons. 4. Agency accounts make causation an unacceptably anthropocentric phenomenon. Agency accounts are said to imply what is obviously false, namely that there

HUW PRICE



would be no causal relations if there were no human agents (or different causal relations if there were different human agents) (CSQ: 188). In the remainder of this section I shall summarize the replies that MP offer to these four objections, adding some comments about how I feel that these replies can be strengthened, in a couple of cases, if the project is given a more Pricean spin. I shall also take the opportunity to respond to some of Woodward’s criticisms, where these relate closely to what I want to say about the MP replies to the original objections. In the case of the third and fourth objections, however, I shall defer most of my response to Woodward until later in the chapter, to allow a more lengthy discussion.

2.1 Epistemology Confused with Metaphysics MP ask their readers to consider the familiar ‘dispositional theory of colour, according to which an object is red, say, just in case it would look red to a normal observer under standard conditions’ (CSQ: 192). They note that ‘[t]his theory makes colour a secondary quality in the sense that the concept of colour is taken to be an extrinsic or relational one, where the constitutive relation is to a certain kind of human response: in the case of the colour red, the “looks red” response’; and go on to say that although it is of course true that this theory has epistemological implications, it doesn’t confuse epistemology for metaphysics. The metaphysics of colour properly involves reference to human responses, on this view, but there is no confusion: that’s what it is to be a secondary quality, at least on this kind of elucidation of the primary–secondary distinction. And they suggest that the same is true of the agency view: ‘[T]he central point is that the concept of causation is to be explained by relation to our experience as agents in the same way that the concept of colour as a secondary quality is to be explained by relation to our experience as observers’ (CSQ: 193). As I shall note below, MP’s use of the phrase ‘experience as agents’ at this point turned out to be misleading, in that it obscured for some readers (including Woodward) a point MP had earlier stressed, concerning the extent to which their view differed from standard empiricism. As they had put it earlier: ‘Empiricists need to keep in mind that human subjects have access to the world in two ways: as observers, certainly, but also as agents, capable of intervening in the processes of the world at will’ (CSQ: 191). Putting that aside for a moment, I want to note that there is another way in which the response to this objection might go, more in keeping with my own predilections (then as well as now, so far as I can recall). It is explicitly to disavow that the project of the agency theory should be seen as metaphysics in the first place. Rather, it should be seen as what I have sometimes called philosophical anthropology: the task of explaining why creatures in our situation come to speak and think in certain ways—in this case, in ways that involve causal concepts. I think that this is one of a range of philosophically interesting cases in which the useful questions turn out to be questions about human thought and language, not questions about other aspects



CAUSATION , INTERVENTION , AND AGENCY

of the world (such as the nature of causation). I think the same about the standard secondary qualities, of course—this shift in no way undermines the analogy that Menzies and I drew in our paper, in my view. I cannot defend this general philosophical orientation here, and have done so at length elsewhere (see, e.g., the papers collected in Price 2011, and Price et al. 2013). My point is simply that if one has signed up for the view that the project of the agency theory is not metaphysics in the first place, there is no room for the objection that it confuses epistemology for metaphysics.

2.2 Vicious Circularity? The distinction between metaphysics and philosophical anthropology is also relevant to what I would now wish to say about MP’s response to the second of the four objections they consider. Here, the concern turns on the fact that the agentive notion of ‘bringing about’ is itself a causal notion. Doesn’t this introduce a vicious circularity into the proposed account of causation? MP replied that dispositional analyses of colour avoid this difficulty because their appeal to notions such as ‘looking red’ can be cashed out in ostensive terms. To put it very crudely, we can say something like this: ‘To be red is to be such as to illicit this response in normally sighted humans in normal conditions’ (while showing our normally sighted audience some red objects in normal conditions). MP thus construed the core of the circularity objection to be a point about concept acquisition, comprising two claims: (i) that according to the proposed analysis, grasp of the concept of causation requires prior grasp of the notion of agency, for the latter is ‘conceptually prior’ to the former; (ii) that such prior grasp is impossible, however, because agency is itself a causal notion. MP’s response is to accept (i) but reject (ii), arguing by analogy with the case of ‘red’ that the required concept of agency can be acquired by ostension definition: [F]rom an early age, we all have direct experience of acting as agents. That is, we have direct experience not merely of the Humean succession of events in the external world, but of...doing one thing and thence achieving another... .[T]hese cases provide direct non-linguistic acquaintance with the concept of bringing about an event; acquaintance which does not depend on prior acquisition of any causal notion. An agency theory thus escapes the threat of circularity. (CSQ: 194–5)

While I think this reply to the circularity objection stands up in its own terms—I shall respond below to some challenges Woodward raises to it—I would like to qualify it in two respects. The first is to note that there is at least one way to understand the project of a metaphysical analysis of causation to which it would not be an answer. Suppose we take ourselves to be puzzled by the nature of causality, expressing our puzzlement in questions like these: How does a world have to be to contain causation? Are the materials available in a bare ‘Hume world’ enough, for example, or do we need something else? And if so, then what, precisely? If a proponent of the agency

HUW PRICE



theory responds by saying something like this—‘If you’ve got agency in your world, you’ve got the basic raw materials for causation. Causation can be constructed from, or reduced to, the kind of materials that agency provides.’—then it does seem reasonable to object that the agency theorist has, in effect, helped herself to a special case of what we were looking for in the first place, in virtue of the fact that agency is a causal notion. (It would be as if bricks had to be made from a special kind of brick.) I conjecture that Woodward interprets MP as being in the business of answering this sort of question. If he were right, then I think he would also be right that MP do not adequately respond to the circularity objection (unless perhaps by making agency a metaphysical primitive, which would be equally bad). But as far as I can see there is little if anything in CSQ to support this interpretation of their project, and there are several passages that count against it. For example, MP say: [T]hese cases [of practical experience of agency] provide direct non-linguistic acquaintance with the concept of bringing about an event; acquaintance which does not depend on prior acquisition of any causal notion. An agency theory thus escapes the threat of circularity. (CSQ: 195, emphasis added)

And earlier (CSQ: 194), they mention but decline a possible response to the circularity objection that involves conceding that ‘the theories [of causation and colour] in question are not meant to be reductive analyses which reduce the concepts of causation and colour to their atomic constituents’. The implication, presumably, is that they take it that the theories are ‘meant to be reductive analyses which reduce the concepts of causation and colour to their atomic constituents’. Insofar as MP’s project is a reductive one, in other words, it seems much closer to a kind of conceptual analysis than to the kind of metaphysical enquiry that would be vulnerable to the circularity objection. (In this respect, then, it is closer to Woodward’s own project than he realizes, for he explicitly disavows the kind of reductive ambitions that would fall victim to the charge of circularity.) The second qualification I want to make about MP’s response to the circularity objection also turns on the issue of what we take the task of the agency theory to be. As I have explained, I think it is fair to say that MP take the task to be to answer questions such as ‘What is it for X to be a cause of Y?’, where the sought-for answer amounts to something like a conceptual analysis (this is how they differ from the more ‘material’ investigation just mentioned). Even in this conceptual form, the circularity objection has apparent bite. The agency theory is committed to giving an answer that mentions agency, after all, but how can we ‘get into the causal circle’, as it were, if the concept of causation reduces in this way to a concept that itself needs to be understood in causal terms? The appeal to ostension provides an answer at this point, but in my view it is an answer that we only (seem to) need because we have asked the wrong question in the first place. If we make it clear at the beginning that we are not concerned with the project of providing a reductive analysis of the concept of causation, but rather with



CAUSATION , INTERVENTION , AND AGENCY

the anthropological project of explaining its genealogy and use, then it is hard to see that there is even a prima facie concern about circularity. Our task as anthropologists is to explain a feature of what humans say—in this case, their use of causal concepts—in terms of what they do. It is no problem at all if we theorists characterize these doings in causal terms, so long as our subjects themselves don’t need to do so, in order to get the linguistic behaviour in question off the ground. This amounts to responding to the circularity objection by rejecting (i), rather than (ii), in the terminology I introduced above (in the second paragraph of this subsection). Once again, the colour case provides an example of the kind of thing that’s needed, at least as a first step, so long as we move away from the dispositional analysis in that case, too. We simply imagine proto-humans habituating to grunting ‘red’ when they experience what we sophisticated anthropologists would describe as ‘the seeing-red response’. Something akin to ostensive definition may well play a role here, too—proto-human Alice points at a tomato and grunts ‘red’ in the direction of proto-human Bob—but there is a crucial difference: this is an ostensive definition of ‘red’ itself, not of ‘seeing red’. As I said, the latter notion can be confined entirely to the anthropologist’s theoretical vocabulary, once the task is seen as anthropological explanation, rather than reductive analysis. The crudeness of this model doesn’t blunt its message: provided we are focusing on use, on what speakers need implicitly to know how to do, it is no problem at all if our theoretical characterization of the practical capacities concerned itself employs some sophisticated descendant of the very concepts whose origins are in question. This point is relevant to MP’s options for responding to Woodward. To explain why, I turn to what seems to me a confusion in Woodward’s reading of CSQ, albeit a confusion for which Menzies and Price deserve some of the blame.

2.2.1

WOODWARD ON MENZIES AND PRICE ’ S ‘ EMPIRICISM ’

One of the remarks that Woodward makes ‘by way of distinguishing [the Menzies and Price] position from [his] own’ is as follows: Menzies and Price’s view of the origin of our concept of causality is a thoroughly empiricist one: we derive or learn the concept entirely from a characteristic kind of experience. As they see it, what is wrong with Hume’s account is simply that he fixes on the wrong candidate for the relevant experience: it is our experience of acting as agents rather than the experience of regular succession that is crucial. But...the idea that our concept of causation is derived purely from experience (whether of agency or anything else) is simply mistaken. As with other concepts, the acquisition of the concept of causality involves a complicated interaction between prespecified neural mechanisms and ‘learning’. Moreover, only some forms of learning are based on experience in the sense of that notion that Menzies and Price have in mind. (2003: 126)

Woodward then adds the following note: A great deal of the learning that underlies the acquisition of causal concepts involves the acquisition of practical skills and habits that are not in any obvious sense ‘based on’ or derived from conscious experiences. There is now considerable evidence supporting the independence

HUW PRICE



of the systems involved in the acquisition of such ‘procedural’ memories from the ‘episodic’ memories of particular experiences on which classical empiricism is based...For this reason, among others, what is learned should not be equated with what is derived from conscious experience. (2003: 386)

He concludes: There is no reason why a theory that takes the connection between causation and agency seriously should also be committed to the empiricist picture of concept acquisition advocated by Menzies and Price. This point is of considerable importance because it is this feature of concept acquisition that helps to ground the reductive features of their project. (2003: 126)

Two comments about this passage. First, as I have already said, I think that MP’s account can be improved by explicitly rejecting its reductive aspects—by accepting that the relation between agency and our causal concepts is best exhibited in a different philosophical vocabulary. As I’ll explain in a moment, I think that this makes it very easy indeed for MP to respond to Woodward. Second, I think that Woodward’s charge is in any case based on a misreading of what MP have in mind. The distinction Woodward himself refers to here—that of ‘the acquisition of...“procedural” memories from the “episodic” memories of particular experiences on which classical empiricism is based’ (2003: 386)—is the same distinction that MP have in mind in the following passage, for example: In our view the best way to characterize these parallels between causation and colour is to say that both can be viewed as secondary qualities under a generalized understanding of this notion. The usual characterization of a secondary quality, as a quality which tends to elicit a characteristic sensory experience in human subjects under specified conditions, is too restrictive...[I]t applies only to those properties which have a sensory import. As such, it perpetuates a constant philosophical pre-occupation with passive observation to the neglect of active intervention in the world: it should be kept in mind that we interact with the world not only as observers but also as agents. We advocate the adoption of a more general notion of a secondary property, which expressly disavows [this restriction]. (CSQ: 201–2)

This point is obscured, unfortunately, because MP also characterize their view using such phrases as ‘direct experience of acting as agents’ (CSQ: 194). The term ‘experience’ seems to associate them with the very empiricist paradigm—that of passive observation—from which they here strive to distance themselves. But the use of the term ‘experience’ they have in mind is a perfectly ordinary one. It is the one we use when we advertise for job applicants with ‘teaching experience’. What we want, obviously, is candidates who have taught, not candidates who have simply observed teaching. Similarly, what MP have in mind when they speak of acquisition of causal concepts by subjects who have ‘direct experience of acting as agents’ is this practical, work-experience notion, not the conscious, episodic, perceptual notion. Elsewhere, for example, they characterize their proposal as ‘admitting action on a par with perception as a means of access to the world’ (CSQ: 191–2). In this respect, then, MP were always



CAUSATION , INTERVENTION , AND AGENCY

on Woodward’s page—always concerned to point out that what classical empiricism misses is that we do, as well as observe, in our interactions with the world.1 Once this is clear,Woodward’s charge of excessive empiricism can be set aside, I think. The resources that MP imagine to be available to our ancestors, as the basis for acquisition of causal concepts, are essentially the same as those that Woodward himself imagines to be available. From this point, there are two ways for MP to proceed. One, sticking closely to their original model, would employ this modified empiricist picture as the basis of an ostensive account of the acquisition of the notion of agency, which would then be available, without threat of circularity, in the services of their reductive analysis of the notion of causation.2 The other, abandoning the reductive aspect of the view, would simply aim to provide a direct account of the acquisition of causal concepts, turning on the idea that these are concepts we acquire in virtue of our practical activity as agents, in just the way that Woodward himself proposes. In the latter case, the response to the circularity objection is particularly direct. The suggestion was that if MP’s agency view were correct, our ancestors could never have found their way into the circle of using causal concepts, because they would have needed the concept of agency first, and that itself is a causal concept. As we have seen, MP try to meet this challenge by appeal to the possibility of ostensive definition of the concept of agency. Free from the constraints of the reductive model, however, there is no need to insist that our ancestors have the concept of agency, in any form, ostensively acquired or otherwise. They need to be agents, but they don’t need to think of themselves as agents. And at this point Woodward’s alternative story about the acquisition of causal concepts—which nowhere mentions reductive definition, but does, as we shall see, accord a central place to human agency—seems to be exactly what MP need, for this modified version of their project.

2.3 Unmanipulable Causes This objection turns on cases in which, as MP put it, ‘it is physically impossible, given the capacities of a normal agent, to manipulate the cause and effect at will’ (CSQ: 195). In response, MP first consider a counterfactual proposal: [I]t might be argued that it is in fact true that if, per impossibile,...an agent were able to manipulate continental plates, he would thereby be able to bring about earthquakes. Perhaps, one might try to make these counterfactuals plausible by invoking a conception of an ideal observer or agent, a conception which abstracts away from the usual limitations of human perception and manipulation. (CSQ: 196) 1 This needn’t mean that there is no role for experience in the passive sense, and indeed Woodward himself elsewhere (2007: 29) seems to allow that there might be: ‘I suggest that...human subjects do have a characteristic phenomenology which is associated with voluntary action; they typically have a sense of agency or ownership of their behaviour that is not present when they act involuntarily.’ (For more of this passage see §5.1 below.) 2 The difference from standard empiricist ostension is that the subjects under instruction will be required to do things, as well as to observe things.

HUW PRICE



They reject this idea for reasons to do with the possibility of finkish and masking dispositions, and instead propose this alternative: [W]hen an agent can bring about one event as a means to bringing about another, this is true in virtue of certain basic intrinsic features of the situation involved, these features being essentially non-causal though not necessarily physical in character. Accordingly, when we are presented with another situation involving a pair of events which resembles the given situation with respect to its intrinsic features, we infer that the pair of events are causally related even though they may not be manipulable. (CSQ: 197)

They note that ‘this inference relies on [a] principle of analogical reasoning’ that also seems operable in the case of colours. MP’s response to this objection is a particular focus of Woodward’s comments, and I shall return to this topic below, to discuss Woodward’s criticisms, possible responses to them, and alternative arguments that MP might give in response to the original objection. (My reason for deferring discussion of this point is to have some of Woodward’s remarks about his proposed alternative on the table first.)

2.4 Anthropocentricity Here the objection is that agency accounts are said to imply what seems obviously false, that is, that there would be no causal relations if there were no human agents, or different causal relations if there were different human agents. MP’s response, once again, is to point out that there are familiar answers to the analogous charge against standard treatments of colour as a secondary quality. Such accounts do not imply that sunsets were colourless before sighted creatures like us came along, or would have been a different colour if our colour vision had been different. We simply apply our actual standards, in considering the circumstances in question. There is anthropocentricity, certainly, but where it ought to be, in our colour concepts, not in the objects and their properties. Similarly for causation, MP claim. Woodward claims that his view is less anthropocentric than that of MP, and that this is an advantage. I now turn to those comments—once again, my strategy will be to argue that the two views are closer than Woodward appreciates, and that to the extent that they differ, that leads to problems for Woodward’s view.

3 Woodward’s ‘Manipulationist’ Theory Under the subheading ‘Nonanthropomorphism’, in a list of what he takes to be characteristics of his own view, Woodward says the following about the relation of his approach to the agency theory of Menzies and Price: Notions such as “human action”...do not occur as primitives [in my account]...In this respect [my view] is quite different from traditional agency theories (such as those of von Wright and Menzies and Price...). In these theories, the characterization of a manipulation (or intervention) makes essential reference to human agency or free choice, and the hope is



CAUSATION , INTERVENTION , AND AGENCY

that this can be somehow grasped or understood independently of the notion of causality. By contrast [in my theory] there is nothing logically special about human action or agency: human interventions are regarded as events in the natural world like any other and they qualify or fail to qualify as interventions because of their causal characteristics and not in virtue of being (or failing to be) activities carried out by human beings. (2003: 103–4)

But Woodward does allow that human agency plays a role in the development of our notions of causality and intervention, as he notes in a later passage in which he reintroduces the spectre of an excessively anthropocentric alternative: [O]n the view I am advocating, our notion of causality developed in response to the fact that there are situations in which we could manipulate X, and by so doing manipulate Y. This fact led us (3.3.1) to form the notion of a relationship between X and Y that would support such manipulations and to contrast this with the notion of a mere correlation that would not support such manipulations. However, it is built into the notion of a relationship that will support manipulations in this way that (3.3.2) such a relationship would continue to hold even if we do not or cannot manipulate X, or if our beliefs and attitudes were different, or even if we did not exist at all. If it is asked why (3.3.2) is built into our notion of causation, my response is that any other view of the matter would involve a bizarre and magical way of thinking, according to which our ability to manipulate X or our practical interest in manipulating X or our beliefs about the results of manipulating X somehow make it the case that a means–end connection comes into existence between X and Y where this connection would not exist if we did not have the ability or interest or beliefs in question. Taken literally, such a view, if intelligible at all, would require human beings to have god-like powers that they plainly do not possess. (2003: 120, emphasis in bold added)

3.1 Dismissing the Spectre of Anthropomorphism Woodward does not actually say at this point that he takes a commitment to his (3.3.2)—the view that causal relationships ‘would continue to hold even if we do not or cannot manipulate [the events in question], or if our beliefs and attitudes were different, or even if we did not exist at all’—to distinguish his theory from that of MP, but the formulation is strongly suggestive of the familiar anthropocentricity objection to the agency view. As noted above, however, and as MP themselves point out, the corresponding objection gets little or no grip in the case of familiar secondary qualities. We simply apply our actual standards to say that sunsets would have been red even if humans had developed different colour vision, or had never evolved at all. And this is entirely compatible with recognizing that had we evolved differently, we might have employed an entirely different set of colour concepts. Once again, MP argue that the same is true of causation, though they argue that there is a difference of degree: it is harder to imagine the required variation in the case of causation than colour. Indeed, MP suggest that there might be no variation possible in this case, except variation that would result in having no concept of causation: In the previous section we saw that by appealing to a principle of analogical reasoning an agency approach may extend its scope well beyond the domain of those things in a particular

HUW PRICE



world that the agents of that world can actually influence. (This was the gist of our reply to the non-manipulability objection.) In consequence, it is far from clear that any modification of mere degree in our powers as agents will issue in any modification in the causal relations we are thus inclined to ascribe. On the contrary, it seems that agents with different capacities will nevertheless envisage the same range of possible causal relations, provided that they employ the principle of analogical reasoning we noted earlier as licensing the extrapolations of their manipulative capacities. This suggests that in the case of agency, the only relevant possible world for the purposes of the anthropocentricity objection is the limiting case: the world in which, like Dummett’s intelligent trees, cognitive beings have no powers as agents. (CSQ: 200–1)

In more recent work (e.g. Price 1996, 2007), I have defended a different view. I have argued that there is at least one very significant variation that we can imagine, involving agents whose perceived direction of time is the opposite of ours. (They are imagined to live in a region of the universe in which the thermodynamic ‘arrow’ points in the other temporal direction.) I maintain that just as such agents would disagree with us about the direction of time, they would also disagree about the direction of causation. In Price 2007 I compare this to familiar perspectival categories, such as near and far, left and right, and foreigner and local. The people on the other side of the border mean the same by ‘foreigner’ as we do, in one obvious sense. (We assume for the sake of the example that they speak English too.) But whereas we apply it to them, they apply it to us—annoying of them, perhaps, but it is hard to maintain that they are actually wrong! I point out that this does not involve denying the reality of foreigners. Foreigners are ‘not figments of our collective imagination, or social constructions, or useful fictions’; on the contrary, they ‘are as real as we are’ (Price 2007: 250). Nevertheless, we learnt something when, minds broadened by travel, we realized that foreigners themselves use the very same concept, but apply it to us!...[T]he reality of foreigners notwithstanding, there’s a sense in which foreignness is a less objective matter than we used to think. (2007: 250–1)

Let me now relate this comparison—of causation to foreignness—to Woodward’s characterization of his own view. As I noted above, Woodward says the following: [O]n the view I am advocating, our notion of causality developed in response to the fact that there are situations in which we could manipulate X, and by so doing manipulate Y. This fact led us (3.3.1) to form the notion of a relationship between X and Y that would support such manipulations and to contrast this with the notion of a mere correlation that would not support such manipulations. (2003: 120)

Similarly, we might say, our notion of foreignness developed in response to our realization that there are people who are not of our tribe. This led us to form a notion of a characteristic—‘foreignness’, as we came to call it—possessed by all and only the people of whom this was true.



CAUSATION , INTERVENTION , AND AGENCY

In this case, we come to see that there is a contingency involved in the application of the term: had we been different in identifiable ways—had we been foreigners, in fact!—the same term would have applied to different objects. I claim that the same is true of causation, construed as Woodward here described. Had we been otherwise, the same procedure would have led us to pick out different relations between X and Y—or the same relation in the opposite direction, at least.

3.1.1

TWO LESSONS WE LEARN FROM ‘ FOREIGNERS ’

It is worth distinguishing two lessons that emerge from the case of the notion foreignness, both of which I take to be applicable to causation, too. The first is what we might call the context-sensitivity or perspectivity of the concept, the fact that for speakers in different circumstances (in the case of foreignness, belonging to different tribes), the concept picks out something different. Our use of the concept picks out them, and vice versa, but there’s an obvious sense in which it is the same concept in both cases. The second is more subtle—we might call it the interest-relativity of the concept. In the case of foreignness, it turns on the contingent fact that we are tribal in the first place. Creatures who were not tribal would not be in a position to employ the notion of foreignness at all (because, as we might put it, the rule for using the concept requires that one be the member of a tribe). This distinction corresponds to a distinction between two ways in which speakers may differ. The first kind of difference—call it an intramodal difference—is that between speakers who both have the kind of context or perspective required for the use of a perspectival concept, but occupy different contexts of that kind. This is the difference between us and them with respect to foreignness, in a tribal society. The second kind of difference—extramodal difference—is that between speakers who occupy a context of the relevant kind and those who occupy no such context. This is the difference between us and our distant non-tribal descendants, for whom the notion of foreignness is an unusable relic of another age. In my view, we can make sense of both kinds of difference with respect to causation, too. We differ intramodally compared to creatures who are also agents, but have the opposite temporal perspective to our own. We differ extramodally with respect to creatures who are not agents at all, and therefore lack ‘what it takes’ to employ the concept of causation in the first place. To appreciate the sense in which causation is an anthropocentric notion, we need to recognize the possibility (in principle!) of both kinds of variation, with respect to our own situation, and its implication for the use of the concept, in each case.3

3 It is worth emphasizing that this kind of anthropocentricity is something visible from the anthropological viewpoint (focusing on concepts), not from the metaphysical viewpoint (focusing on the causal relations themselves). When we adopt the latter standpoint, we typically rigidify on the basis of our actual perspective, as in the colour case.

HUW PRICE



The upshot, I think, is to undermine or at least significantly qualify the view that interventions are simply a mind-independent category, to which our manipulative practices give us access (by instantiating interventions themselves, at least to some extent). The possibility of intramodal variation reveals that nature offers (at least) two alternative ways of carving out such a category, and that which one we latch onto depends on contingencies about us. The possibility of extramodal variation reveals that in a deeper sense, too, the kind in question reflects a way of modelling the world that depends on the fact that we are agents.4

3.1.2

HOW MANY ALTERNATIVE CAUSAL VIEWPOINTS ?

Agents with the opposite temporal orientation to our own would provide a stark illustration of intramodal variation with respect to causation, but do we need to go so far afield? The question is of pragmatic as well as theoretical interest, from my point of view, for my experience is that the ‘sci-fi’ nature of the time-reversal case tends to limit its impact—at least among recipients not already au fait with ‘the view from nowhen’ (Price 1996)! But I think we can bring the point down to earth, and indeed connect it with some issues raised by Woodward himself, if we think about the general features of an agent’s perspective that the time-reversal case exploits. I discussed these features in Price 2007, and proposed this general characterization of the nature of deliberation: In any deliberative process, presumably, there must be a range of things that the deliberator in question takes to be matters for deliberation: in other words, the alternatives among which she takes herself to be deliberating. For formal convenience, let’s regard these alternatives as a class of propositions, denoted by OPTIONS. These are the propositions the agent takes herself to have the option of ‘deciding to make true’, in other words. It will be helpful to subdivide this class into DIRECT OPTIONS, comprising those matters over which an agent takes herself to have immediate control, and INDIRECT OPTIONS, comprising those ends she takes herself to be able to accomplish indirectly, by an appropriate choice from her DIRECT OPTIONS. And let the FIXTURES denote everything else—all matters of fact that are not held to be a matter of choice in the deliberation in question. FIXTURES will contain a subset, KNOWNS, comprising those facts the deliberator takes herself to know at the time of deliberation, and also a larger subset, KNOWABLES, comprising matters she regards as either known or knowable, at least in principle, before she makes her choice. Why must KNOWNS and KNOWABLES be subsets of FIXTURES? Because it seems incoherent to treat something both as an input available to the deliberative process, at least in principle, and as something that can be decided by that process. Control trumps a claim to knowledge: I can’t take myself to know that P, in circumstances in which I take myself to be able to decide whether P, in advance of that very decision. (2007: 275)

4 Again, terms such as ‘near’ and ‘far’ provide an excellent analogy. There, too, we have both intramural variation, in virtue of the fact that speakers may occupy different locations, and at least a possibility of extramodal variation, in virtue of the fact that a speaker might in principle occupy no particular location.



CAUSATION , INTERVENTION , AND AGENCY

As I go on to say, this gives us a very simple template, characterising a deliberator’s view of the world. In terms of this template, acting, or intervening, is a matter of fixing something not already fixed—of moving something from OPTIONS to FIXTURES, as it were. (2007: 276)

For present purposes, the importance of this characterization of the abstract structure of an agent is that it brings into view the real sources of the contingency of our causal perspective. Everything turns on what we can know before5 we act, and what we take to be under our control (under idealization, no doubt, in both cases). The possibility of time-reversed agents provides a dramatic and (at least in some sense) physically well-motivated way to vary these factors, and so produce alternative causal viewpoints, but it isn’t the only way, and the abstract characterization provides a recipe for constructing more. And at this point, in fact, a consideration noted by Woodward himself as a source of some ‘subjectivity’ (2003: 89) in ordinary causal judgements seems to fit neatly into this abstract model. Woodward (2003: 86–91) discusses the dependence of the acceptability of ordinary causal claims on what speakers take to be ‘serious possibilities’ in the circumstances under consideration. When a patient dies for lack of antibiotics, for example, we don’t hold a stranger in a distant city causally responsible for the death, even though it may be true that had the stranger visited the patient, bearing antibiotics, he would have survived. Such an occurrence is not regarded as a ‘serious possibility’, and is hence discounted as a causal factor. Woodward acknowledges that the decision as to what to treat as a serious possibility depends in various ways on our own interests and beliefs, and concludes that this does introduce at least a small element of ‘subjectivity’ into his interventionist account—though, as he argues, it is an element that other approaches to causation will be hard-pressed to avoid. As he puts it later, the fact seems to be that there is ‘a limited respect in which... which causal claims we accepted as true...are influenced by what we take to be a “serious possibility” ’ (2003: 118). In terms of my model, the way to describe this kind of case is to say that by default, we treat the behaviour of distant strangers as part of the FIXTURES, rather than the OPTIONS, direct or indirect. But these choices are contextual, in the way that Woodward notes, and this shows up in our causal judgements. Differences between speakers—in Woodward’s terms, cases in which one speaker treats something as a serious possibility and another does not—can thus represent familiar, homely examples of intramodal variation, in my notation. In the homely as in the sci-fi cases, I take the lesson to be that when Woodward says that ‘our notion of causality developed in response to the fact that there are situations in which we could manipulate’ (2003: 120, emphasis added), the indexical term ‘we’ is ineliminable. Agents with different epistemic ‘situations’ to our own will 5

As I note, this ‘before’ should be understood in terms of the personal time of the deliberator.

HUW PRICE



make different judgements about what could be manipulated by manipulating what, and there’s no objective sense in which we are right and they are wrong—to think otherwise is to accord our own viewpoint a god-like priority that, as Woodward says, it plainly does not possess. (Here, as in many other cases in the history of science and philosophy, it is the modest, ‘subjectivist’, Copernican view that does the better job of recognizing the contingencies and limitations of the human standpoint, and the objectivist view that confuses us with gods.)

3.2 Wasteful and Gratuitous? Similar comparisons also provide a response to a further objection that Woodward raises to the MP view, immediately following the passage quoted above: This conclusion [i.e. if I interpret Woodward correctly, the conclusion that the MP view ‘would involve a bizarre and magical way of thinking’—HP] is reinforced by [a] naturalistic, evolutionary perspective...According to subjectivist accounts, causal relationships have their source in facts about us—facts about our expectations, attitudes, and so on—which we ‘project’ on to the world...[W]hat is the evolutionary story about the benefits we derive from this projective activity? After all, our projectivist tendencies systematically lead to beliefs that, by the subjectivist’s own account, are mistaken or ungrounded—mistaken in the sense that they ascribe a false objectivity to causal claims or involve thinking of the distinction between causal and correlational claims as having an objective basis in nature rather than in facts about us. Why should we and other animals go to the trouble of distinguishing between causal and correlational relationships if all that is ‘really out there’ in the world are correlations? All that projecting seems wasteful and gratuitous. (2003: 120–1)

Once again, we need only think about the case of the secondary qualities, or of ‘perspectival’ asymmetries such as there–here, past–present, you–me, or foreigner– local. None of these properties or asymmetries are simply ‘there’ in the world, visible from an Archimedean point of view. They all reflect our viewpoint, or ‘location’, in one way or another. But there’s no mystery about why we have evolved so as to draw such distinctions. Take the case of the familiar indexicals, for example. To paraphrase Woodward, why should we go to the trouble of distinguishing between here and there, now and then, self and other, if all that is ‘really out there’ in the world are the bare nonindexical facts? All that projecting seems wasteful and gratuitous! But Perry (1979) and others have shown us why it isn’t wasteful and gratuitous, in the indexical case. On the contrary, as Perry puts it, the indexical is essential, for creatures in our circumstances: creatures who need to coordinate their own actions and observations with third-person maps of their environment. The general lesson is something like this. Many of our concepts are useful to us in virtue of contingent features of our own circumstances—for example, in the indexical case, the fact that we are ‘located’ in space, time, and communities of individuals. It is not surprising at all, from a naturalistic perspective, if some of our concepts reflect



CAUSATION , INTERVENTION , AND AGENCY

these ‘located’ features in essential ways—that is, roughly, in such a way that we cannot understand the concept in question except with reference to the feature in question. (At least one way in which this might happen is for the ‘location’, in this generalized sense, to play a role in the use-rules governing the concept.) There is no affront to naturalism in this idea: on the contrary, it would surely be extraordinary if our conceptual structures did not reflect these contingencies. We are not gods, so why should we think in the kind of conceptual repertoire that gods might use? I take the insight of the agency view to be that causation is one of these ‘located’ concepts. Its particular link is to the fact that we are agents, capable of intervening in our environment at will. This might seem to leave the view open to the charge that, as Woodward puts it, it ‘flies in the face of any plausible version of naturalism: it makes agency out to be a fundamental, irreducible feature of the world and not just one variety of causal transaction among others’ (2003: 123). But, as I noted above, this is a mistake (perhaps encouraged by MP’s tendency to characterize the project of an agency theory in a metaphysical key rather than an anthropological key). The agency view requires that we have a practical acquaintance with agency ‘from the inside’, as it were, so that we are able to acquire implicit use-rules that, if made explicit, would need to refer to it. But this is in no way incompatible with regarding agency as an element in the causal web, ‘one variety of causal transaction among others’, once we have the concepts and start to reflect on such matters. All of this seems to be entirely in keeping with the way in which Woodward frames the motivation for his own project, at one point: As a preliminary motivation, let me begin with a question that is not often asked in philosophical treatments of causation: What is the point of our having a notion of causation (as opposed, say, to a notion of correlation) at all? What role or function does this concept play in our lives? An important part of the appeal of a manipulability account of causation is that it provides a more straightforward and plausible answer to this question than its competitors. (2003: 28)

The difference, if there is one, is that I have on the table the possibility that the answer to this question will need to appeal to contingencies of our own nature, in such a way that any theory of concepts that sees their role in crudely representationalist terms will simply be blind to the need for some interesting theoretical work somewhere else (i.e. in the story about how the use of the concepts depends on the contingencies in question, in the sense manifest in possibility of intramodal and extramodal variation).

4 The Problem of Unmanipulable Causes Let us now return to objection three. Woodward says that MP ‘face the obvious problem about the extension of causal concepts to circumstances in which manipulation by human beings is not possible’ (2003: 123). He argues that MP’s response (as above) in terms of resemblances in intrinsic properties is unsatisfactory because,

HUW PRICE



as he puts it, he sees ‘no reason to believe...that this notion of resemblance can be characterized in noncausal terms’ (2003: 125). The problem with this suggestion becomes apparent when we consider, for example, the nature of the ‘intrinsic’ but (allegedly) ‘noncausal’ features in virtue of which the movement of the continental plates ‘resemble’ the artificial models the seismologists are able to manipulate. It is well-known that small-scale models and simulations of naturally occurring phenomena that superficially resemble or mimic those phenomena may nonetheless fail to capture their causally relevant features because, for example, the models fail to ‘scale up’—because causal processes that are not represented in the model become quite important of the length scales that characterize the naturally occurring phenomena. Thus, when we ask what is [it] for a model or simulation that contains manipulable causes to ‘resemble’ phenomena involving unmanipulable causes, the relevant notion of resemblance seems to require that the same causal processes are operative in both. I see no reason to believe (and Menzies and Price provide no argument) that this notion of resemblance can be characterized in noncausal terms. But if the extension of their account to unmanipulable causes requires a notion of resemblance that is already causal in character and that, ex hypothesi, cannot be explained in terms of our experience of agency, then their reduction fails. (2003: 125)

However, I think that if there were a problem here for MP, it would equally be a problem for Woodward’s own view. As Woodward will agree, we extend our causal notions into many regions in which we can be sure that we will never intervene: the inside of the sun, distant galaxies, and the distant past, for example. We take it for granted both that there is causation in these regions, and that it is broadly similar to causation in more familiar regions—it doesn’t work backwards, for example. On what basis do we take these distant regions to be so similar to our own, in causal respects? There are two possibilities at this point. One is that we rely on similarities in noncausal respects to ground the inference. But this would be to grant what Woodward here wants to deny to MP, namely, that there are relevant similarities, characterizable in noncausal terms. The second option is that there are inference principles of some kind—perhaps grounded in physical symmetries, and/or whatever else might be held to underpin the normal inductive procedures of science—that are taken to license the inference directly. What are these inferences? Just the ones needed to support counterfactuals. As Woodward puts it elsewhere: It seems uncontroversial that the claim that C causes E can be true even if C is not actually manipulated—any account that suggests otherwise is a non-starter. This observation suggests that manipulationist accounts should be formulated as counterfactual claims connecting causal claims to claims about what would happen if certain manipulations were performed. (2009: 236)

In this passage Woodward is using the term ‘manipulation’ in a way I take to be neutral between his own preferred version of the manipulationist account—the ‘interventionist’ approach, as he calls it—and MP’s agency view. But it is hard to



CAUSATION , INTERVENTION , AND AGENCY

see what basis there could be for the claim that the required counterfactuals are harder to justify in one case than the other. Indeed, if MP had opted for their first suggestion, and responded to the problem on unmanipulable causes by appealing explicitly to counterfactuals, then it would be even more difficult to see how there could be space for them to be in trouble at this point, while Woodward is not.

4.1 Extension to Remote Cases Moreover, I think that Woodward’s view that his approach is more ‘realist’ than that of MP is likely to prove more of a hindrance than a help at this stage, in that it makes him more prone to sceptical worries about whether there is really causation inside the sun, or whether causation really runs past-to-future in neighbouring galaxies. To introduce this point, let me appeal once more to the analogy with indexicals. Wearing our old Newtonian hats, we have no trouble in making sense of the question as to whether it is now light or dark at some specified point on the surface of a distant planet, where no sentient creature could possibly exist. Does this commit us to the view of the so-called A-theorists, that the distinction between past, present, and future is an intrinsic feature of reality? Pretty obviously not. A B-theorist will say that our extension of the indexical notion now to remote places requires only the nonindexical notion of simultaneity: an event is happening now on a remote planet if and only if it is simultaneous with what is happening now, here. Simultaneity thus provides a tenseless notion of similarity, that grounds our extension of the tensed notion from one context (our own neighbourhood) to another (the remote planet). The A-theorist might object at this point that the notion of simultaneity is not tenseless: on the contrary (she claims), two events are simultaneous iff it is, was, or will be the case that they are co-present (or something of that kind), so that the notion of simultaneity depends on that of presentness. Whatever might be said in favour of this view, however, it had better not stand in the way of whatever ordinary processes we take to determine whether it is now night or day on the distant planet—the A-theorist needs those inferences as much as anybody. (And, prima facie, her additional realism about tensed properties makes things more difficult, in that it introduces new sceptical possibilities. How do we know that the A-theorist’s notion of simultaneity tracks the physicist’s notion of simultaneity, after all?) Notice that relativity cuts equally on both sides of this debate. It undermines the idea that there is an objective notion of simultaneity to ground the extension of an indexical now to remote locations, thus requiring the B-theorist to acknowledge that what she took to make sense—the question whether it is now night or day at the remote location—actually does not make sense (unless relativized to a suitable reference frame). But it surely requires the same concession of the A-theorist, too, unless she is to be left in the position of arguing that there is a fact of the matter, but that it is inaccessible to us. Can we imagine the same state of affairs in the case of causation, read in manipulationist terms? I think that we can. Imagine that some distant region in spacetime turns out to be linked to our own region only via two wormholes; and that

HUW PRICE



these wormholes turn out to have opposite temporal parity, in the sense that if one of a matched pair of clocks is sent through each, the clocks are running in opposite temporal senses when they reach the other side. (We do not assume that there is a fact of the matter about which is ‘right’.) In these circumstances, I think it is difficult to maintain that we have a clear sense of what we could do to manipulate what, in the region on the far side of the wormholes. It would all depend on which wormhole we used! By my lights, this is an example of how the extension of our anthropocentric notion of causation to regions in which we cannot actually manipulate things is in principle always provisional, and subject to correction in the light of learning more about the relevant physics. (I want to say the same about Woodward’s example involving scaling—of course we can get things wrong!) And once again, I think Woodward faces a dilemma: either he relies on the same principles of extension, and is hence subject to the same exigencies; or he is left defending an implausible objectivity, vulnerable to scepticism in cases such as these.

4.2 Summary—the Objectivist’s Dilemma The problem was to explain how an agency account of causation could explain the extension of the concept of causation from cases in which we can make manipulations to cases in which we cannot. Let us call this the problem of extending causal models from local cases to remote cases. (‘Local’ and ‘remote’ are thus terms of art, for present purposes.) The MP proposal was that the extension works by dropping down to a subcausal level of description, and extending our models exploiting similarities at that level (plus, presumably, some sort of supervenience principle). The new proposal we have on the table is that the extension from local to remote cases takes place at the higher level, exploiting such things as physical symmetries (‘spatial translation doesn’t make a difference’, for example). My argument has been that Woodward’s own view requires some such extension principles at this point, and whatever he uses, MP can use too. A possible response on Woodward’s behalf is that he has in mind extension principles that would take us to regions where human agency cannot sensibly be considered to go (inside the sun, or into distant galaxies, for example). My reply is to point out that unless the extension does avail itself of constraints grounded in our (actual) agents’ perspective, it cannot resolve ambiguities that stem from the contingencies of that perspective. (It cannot provide any justification for taking causation to have the same temporal orientation in the distant galaxy, for example.) So there is a dilemma for anyone more objectivist than MP about these cases.6 Without the constraint imposed by being able to extend our standards into 6 Strictly speaking this argument isn’t available to MP in the causal case, because they claim that there are no other possible causal perspectives (except the ‘no causation’ option associated with intelligent trees). But as I have said, I think that MP were wrong at this point.



CAUSATION , INTERVENTION , AND AGENCY

counterfactual cases, we are left unable to resolve the ambiguity that stems from the contingency of the original notion—its relativity to our situation and interests! Once again, objectivism leads to scepticism, and any principle the objectivist invokes to deal with the problem will serve equally well for the more subjective view. Moreover, I stress that there is nothing unique about causation here. The same is true of any of the vast range of concepts that have some in-built relativity to our own situation and interests. In all cases, an unambiguous extension to remote cases depends on our being able to map the relevant aspect of our situation and interests into those remote circumstances—to the extent that we can’t do that, we have no basis to resolve the ambiguities in one way rather than another, in the remote circumstances. (Where the extension of our particular perspective really doesn’t make sense, in other words, objectivism is in trouble.)

5 Objectivity Again So far, I have been arguing that Woodward’s criticisms of the MP view are largely unsuccessful, especially if the latter view is tweaked and clarified in various respects. I have suggested that the MP view is actually closer to Woodward’s own position than he realizes, and moreover that if Woodward tries to establish a difference by moving in the direction of ‘greater objectivity’, then danger lurks—danger that MP’s more modest view avoids. But I now turn to one aspect of Woodward’s discussion of the objectivity of causality that seems to me a clear advance on the MP view, and that I want to endorse (almost) without qualification. Once again, I think that the MP view can take it into account, in ways that turn out to be fully in the spirit of the original comparison between causation and the familiar secondary qualities. In that sense, then, it doesn’t in the end represent a damaging objection, but it is certainly an important addition. The point turns on a distinction between three varieties of agent that Woodward draws in the following terms: 1. An agent whose instrumental behaviour and learning is purely egocentric. That is, the agent grasps (or behaves as if it grasps) that there are regular, stable relationships between its manipulations and various downstream effects but stops at this point, not recognizing (or behaving as though it recognizes) that the same relationship can be present even when it does not act, but other agents act similarly or when a similar relationship occurs in nature without the involvement of any agents at all. 2. An agent with an agent causal viewpoint: the agent grasps that the very same relationship that it exploits in intervening also can be present when other agents act. 3. An agent with a fully causal viewpoint: The agent grasps that the same relationship that the agent exploits in intervening also can be present both

HUW PRICE



when other agents intervene and in nature even when no other agents are involved. This involves thinking of causation as a tertiary relationship (Woodward 2007: 32). One of the interesting things about this three-way distinction, from my point of view, is that it, too, has obvious echoes in the case of the familiar secondary qualities. There, too, there seems to exist a similar range of options: one might think of what one’s senses deliver as a private, purely egocentric experience; as an experience that other observers will share; or as a revelation of a property of the object, present in nature in the absence of observers. Much concern about the nature of the secondary qualities turns, in effect, on whether they reach the third level. (If a tree falls in an uninhabited forest, does it make a sound? Or, as Galileo puts it, do the sensory properties ‘have their residence solely in the sensitive body’?) But there is also fascinating work—here I am thinking particularly of Sellars’s classic discussion in ‘Empiricism and the Philosophy of Mind’ (Sellars 1956)—of the step from stage one, on the one hand, to stages two and (perhaps also) three, on the other. Here, at least at first pass, the question is something like this: What is involved in coming to regard our colour experience as a means of access (and therefore fallible access) to something objective?7 I mention this mainly to call attention to the importance and interest of the comparison between the ways these issues play out in the two cases—causation, on the one hand, and colour and the other secondary qualities, on the other. It now seems to me (this is what I take from Woodward) that a full defence of the thesis of CSQ would require a study of these analogies. It might be felt—perhaps Woodward himself would feel this way—that the analogy will fail, because the end point (what we get to at stage three) is clearly more objective in the causal case than in the colour case. In the colour case, stage three is always a little half-hearted, in the sense that we recognize that the contingencies of our visual systems are never entirely eliminated: once we’ve noticed those contingencies, then there’s no getting away from the fact that had we been different, we would have reached a ‘different’ stage three. Whereas for causation (it might be felt), there’s only one possibility: one set of relations on which any creature capable of making the journey will inevitably converge. But I’ve argued that this is a mistake. There are ineliminable contingencies in the causal case, too—most strikingly those of temporal perspective, though these are merely the most stark manifestation of something deeper, and elsewhere much more familiar. 7 One concern about this formulation of the question might be that it doesn’t adequately distinguish the situation of the individual from that of the community as a whole. It is not all clear that an individual language learner needs to ‘come to’ the objective view, rather than simply taking it to be the default. (In the latter case, we could read Sellars’s story of John and the tie shop as telling us how we learn about subjectivity, having started from a presumption of objectivity.) So less contentiously, then, we could say that the general concern is simply to understand the relationship between ‘objective’ and ‘subjective’ viewpoints, in the cases in question.



CAUSATION , INTERVENTION , AND AGENCY

5.1 ‘Not All Actions are Interventions’ These issues are also relevant to another objection that Woodward raises against the MP view. He points out that there are cases that an overly naive agency theory will be liable to get wrong: As an illustration, consider a case in which an experimenter’s administration of a drug to a treatment group (by inducing patients to ingest it) has a placebo effect that enhances recovery, even though the drug itself has no effect on recovery. There is a correlation between ingestion of the drug and recovery that persists under the experimenter’s free act of administering the drug even though ingestion of the drug does not cause recovery. (Woodward 2013: §4)

Woodward then goes on to say that to deal with this problem we need the notion of what has come to be called an intervention—the problem, in effect, is that not all ‘free actions’ actually count as interventions, and it is the latter notion that matters, if we are to ‘get the causal facts right’. Examples like those just described show that if we wish to follow Menzies and Price in defending the claim that if an association between A and B persists when A is given the right sort of ‘independent causal history’ or is ‘manipulated’ in the right way, then A causes B, we need to be much more precise by what we mean by the quoted phases. There have been a number of attempts to do this in the recent literature on causation. The basic idea that all of these discussions attempt to capture is that of a ‘surgical’ change in A which is of such a character that if any change occurs in B, it occurs only as a result of its causal connection, if any, to A and not in any other way. In other words, the change in B, if any, that is produced by the manipulation of A should be produced only via a causal route that goes through A. Manipulations or changes in the value of a variable that have the right sort of surgical features have come to be called interventions in the recent literature...The characterization of the notion of an intervention is rightly seen by many writers as central to the development of a plausible version of a manipulability theory. (2013: §5)

I think that Woodward is entirely right here, but that the point in no way requires that we abandon the basic thought of CSQ, that causation is analogous to a secondary quality, with agency substituted for sensory perception. For again, as Sellars (1956) teaches us, a similar dialectic exists in the case of colour, too. There, too, as Sellars’s example of John and the tie shop illustrates so vividly, naive colour judgements come to be treated as provisional, and subject to revision. What John learns, in that example, is something important about how to revise his colour ascriptions (e.g. to take into account unusual lighting conditions). The upshot is that while our initial colour judgements are taken as prima facie reliable, they come to be embedded within a socially mediated practice that allows them to be revised—indeed, that’s what it is for them to come to be genuine judgements, in Sellars’s view. This Sellarsian picture of revisable positive-presumptive judgement, based on our usually reliable abilities to track colours, seems to me to be strikingly analogous to the

HUW PRICE



picture that Woodward himself proposes with respect to agency and intervention. Woodward bases his proposal on ‘the following hypothesis’: Human beings (and perhaps some animals) have (a) a default tendency to behave or reason as though they take their own voluntary actions to have the characteristics of interventions and (b) associated with this a strong tendency to take changes that temporally follow those interventions (presumably with a relatively short delay) as caused by them. (2007: 29)

He goes on to say that this hypothesis suggests a way in which ‘it is...possible for such subjects to use their interventions...to reach fairly reliable causal conclusions’ (2007: 29), provided two conditions are met: First, subjects must have some way of determining (some signal that tells them) when they have performed a voluntary action and this signal must be somewhat reliable, at least in ordinary circumstances. Second, voluntary actions (again in ordinary, ecologically realistic circumstances) must—not always, but often enough—have the characteristics of an intervention. (2007: 29)

Woodward suggests that ‘both claims are true’. Concerning the second, he notes that ‘the correlation between voluntariness and satisfaction of the conditions for an intervention is imperfect’ (2007: 29). In a badly designed clinical trial, an experimenter might be subconsciously influenced, in his decisions to give a drug to some patients and withhold it from others, by the health of the patients; his decisions are voluntary and yet correlated with an independent cause of recovery in a way that means that the conditions for an intervention are not satisfied. (2007: 29–30)

‘Nonetheless,’ Woodward says, ‘[i]t seems plausible that many voluntary actions do, as a matter of empirical fact, satisfy the conditions for an intervention’ (2007: 30). If I come upon a wall switch in an unfamiliar house and find that there is a regular association between my flipping the position of the switch and whether a certain overhead light is on or off, then often enough my flippings will satisfy the conditions for an intervention on the position of the switch with respect to the state of the light...The existence of causal illusions in which we experience or ‘perceive’ salient changes that follow our voluntary actions as caused by them similarly suggests that such a heuristic is at work. (2007: 30)

Thus Woodward, like Sellars, offers us a story in which we reach our mature concept by learning to correct the deliverances of our naive judgements—judgements which ‘get things right’ not all the time, but often enough. If there is a difference between a Sellarsian version of the view of CSQ and Woodward’s view, I think it will lie in the conception of the order of explanation between the notion of intervention and that of agency—in the thought on Woodward’s part that his notion of intervention is somehow ‘more objective’ than anything that could be achieved by Sellarsian objectification, beginning with our (practical, not perceptual) experience of agency. However, I have argued that if there is such a difference, it counts against Woodward’s view: interventions are not a sufficiently natural category, and scepticism looms, if we



CAUSATION , INTERVENTION , AND AGENCY

try to imagine that they are. So the more plausible approach will be the modified MP view, to the extent that there is a difference of this kind.8

6 Summary I close by summarizing what I take to be right about MP’s responses to the four objections they consider, and how I think these responses can be improved: 1. Agency accounts confuse the epistemology of causation with its metaphysics. The MP response stands, in my view, but the point can be strengthened by a version of the agency view that takes itself to be in the business of philosophical anthropology, not metaphysics. 2. Agency accounts are vitiated by circularity. Again, the MP response stands up in its own terms, in my view, and Woodward’s accusation that it depends on excessive empiricism rests on a misreading. But again the response is greatly strengthened by an anthropological rather than a metaphysical conception of the project, for in this case there is no need to say that acquisition of the concept of causation depends in any sense on prior acquisition of a concept of agency, ostensively defined or not. On the contrary, such a version of the view can help itself to Woodward’s own account of the acquisition of causal concepts. 3. An agency account cannot make sense of causal relations between events which are outside the control of any agent. Here, too, MP seem able to allow Woodward to do the required work on their behalf. If Woodward seeks to establish a difference, based on the idea that his view is ‘more objectivist’, or extends causation into regions that an agency view can’t reach, then he faces a major difficulty: scepticism looms. Hence my conclusion: either MP and Woodward are on the same side at this point, or his side is at a disadvantage, due to the threat of scepticism. 4. Agency accounts make causation an unacceptably anthropocentric phenomenon. Again, the original MP reply survives unscathed, in my view, in the sense that the analogy with colour does show that the anthropocentricity can be ‘contained’—we are not committed to the view that ancient sunsets were colourless, or absurdities of that kind. Again, the anthropological stance makes this easier to say, because it focuses from the beginning on the concepts, which is where the anthropocentricity resides. However, I have argued that the concept of causation is more anthropocentric than either Woodward or MP themselves realize—there are more contingencies, more opportunities for variation, at least 8

Both sides agree that within the practice, a speaker must take there to be a fact of the matter—that is, to take her naive judgements to be subject to correction, subject to a norm that makes it possible for them to be right or wrong. The issue is whether we conceive of this practice on the model of Sellarsian objectification built on shared contingencies, or as something more metaphysically robust. I’ve argued that the latter view runs into trouble.

HUW PRICE



in principle. This may be surprising, but that’s a feature, not a fault: the firstorder anthropological investigation of our concept of causation reveals to us a contingency that isn’t obvious ‘from the inside’. Objecting that this makes causation unacceptably anthropocentric is like objecting that Copernicus makes our ordinary description of the heavens unacceptably anthropocentric. Finally, I hope that these comments give some impression of the extent to which I feel that Woodward’s work can be read as a magisterial vindication of the philosophical viewpoint whose colours Peter Menzies and I nailed to the mast in CSQ.9 I think that the arguments of that paper, updated as above, do have something to offer to Woodward, by way of a commentary on the task of locating his project on a bigger philosophical map. Even if accepted, however, this contribution does little to repay the debt that Menzies and I, and the agency tradition in general, owe to Woodward (and to Pearl, Spirtes, and others), for showing us how much can be done with the insight that causation is intimately linked to manipulation.10

References Collingwood, G. 1940. An Essay in Metaphysics. Oxford: Oxford University Press. Gasking, D. 1955. ‘Causation and Recipes’, Mind, 64: 479–87. Menzies, P., and Price, H. 1993. ‘Causation as a Secondary Quality’, British Journal for the Philosophy of Science, 44: 187–203. Perry, J. 1979. ‘The Problem of the Essential Indexical’, Noûs, 13: 3–21. Price, H. 1996. Time’s Arrow and Archimedes’ Point. New York: Oxford University Press. Price, H. 2007. ‘Causal Perspectivalism’, in H. Price and R. Corry (eds), Causation, Physics, and the Constitution of Reality: Russell’s Republic Revisited. Oxford: Oxford University Press, 250–92. Price, H. 2011. Naturalism Without Mirrors. New York: Oxford University Press. Price, H., with Blackburn, S., Brandom, R., Horwich, P., and Williams, M. 2013. Expressivism, Pragmatism and Representationalism. Cambridge: Cambridge University Press. Ramsey, F. P. 1929 (1978). ‘General Propositions and Causality’, in D. H. Mellor (ed.), Foundations: Essays in Philosophy, Logic, Mathematics and Economics. London: Routledge and Kegan Paul, 133–51. Sellars, W. 1956. ‘Empiricism and the Philosophy of Mind’, in H. Feigl and M. Scriven (eds), Minnesota Studies in the Philosophy of Science, vol. I. Minneapolis: University of Minnesota Press, 253–329. Published separately in R. Brandom (ed.), Empiricism and the Philosophy of Mind: With an Introduction by Richard Rorty and a Study Guide by Robert Brandom. Cambridge, MA: Harvard University Press, 1997. von Wright, G. 1975. Causality and Determinism. New York: Columbia University Press.

9 It was nailing to the mast from my point of view, at any rate, though Peter may have felt that we were merely testing the waters! 10 Thanks to Helen Beebee, John Maier, Alejandro Pérez Carballo, and Jim Woodward for helpful comments and discussion.



CAUSATION , INTERVENTION , AND AGENCY

Woodward, J. 2003. Making Things Happen: A Theory of Causal Explanation. Oxford: Oxford University Press. Woodward, J. 2007. ‘Interventionist Theories of Causation in Psychological Perspective’, in A. Gopnik and L. Schulz (eds), Causal Learning: Psychology, Philosophy, and Computation. New York: Oxford University Press, 19–36. Woodward, J. 2009. ‘Agency and Interventionist Theories’, in H. Beebee, C. Hitchcock, and P. Menzies (eds), The Oxford Handbook of Causation. Oxford: Oxford University Pres, 234–63. Woodward, J. 2013. ‘Causation and Manipulability’, in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Summer 2013 edition), https://plato.stanford.edu/archives/ sum2013/entries/causation-mani/.

6 The Glue of the Universe David Braddon-Mitchell

1 Introduction Which parts of the complex web of the physical universe count as causes, for various purposes, of the events we are interested in?1 I take that to be key question that interventionist models of causation are in the business of providing machinery to settle, and to which Peter Menzies has provided a range of important and interesting contributions. Pearl (2000), Hitchcock (2001, 2012a), Woodward (2003), Menzies (2007), and others have together developed a powerful framework for understanding and predicting causal judgements, and not just predicting and explaining them, but making them as well. Woodward, of course, explicitly calls the enterprise he’s engaged with a theory of causal explanation which, most recently, he described as primarily of methodological interest in contrast to concerns about the ontology or metaphysics of causation.2 And for a long time I was tempted to say that these kinds of considerations amount to an admission that it shouldn’t be called a theory of causation. Indeed this was the tenor of many an argument between me and Peter Menzies over the years. I now have some reservations about the view I defended, but sadly too late to tell Peter. In any case, here was the thought: causation is the underlying thing in the actual world which makes it true that the patterns hold which allow us to engage in causal explanation. The right theory of causal explanation will be what tells you what causally explains what: it is the set of pragmatics which select from the overabundance of causal facts offered by nature those relevant to the explanatory task at hand, given the alternatives to the actual event that we are considering and the interventions that we are considering. On this way of seeing things causation in sensu stricto is extremely undiscriminating. There are causal connexions between an event and all of its past and future

1 Thanks to Helen Beebee and Huw Price and for many useful comments on an earlier draft of this chapter, and to Andrew Latham for much useful discussion of these issues. 2 Most explicitly in Woodward (forthcoming: 1).



THE GLUE OF THE UNIVERSE

light cones. From this nexus of causal connexions we do some selection: the pragmatics offered by van Fraassen3 and others (offered at the time as a theory of explanation) were perhaps the first move in that direction, and the interventionist account we now have is its state of the art. So causation is the underlying thing, and a theory of explanation over the top of that gives you an account of causal explanation. But this is of course a terminological regimentation of the issues. And it’s one which has some serious problems. For one thing the theory of selection of relevant parts of causal history is what is at issue in most debates about what the cause of something is. Of course it is easy to say that this just means it is causal explanation that we care about for most practical purposes (it doesn’t matter for an epidemiologist what the underlying nature of the causal web is, just which bits of it matter for their purposes). But that is to give little weight to the point of causal talk.4 A second serious issue is that the interventionist account can be seen as a descendant of Lewis’s counterfactual theory of causation—which was intended as a theory of causation, not as something that provides an overlay on the causal facts. Once you provide a set of mechanisms to account for the bulk (but only the bulk) of counterexamples to that theory, you have something which looks like a draft of the formalisms of the interventionist account. So if we see interventionism as a fully fledged version of that theory, taken by the geekiest of metaphysicians as an account of the nature of causation, it’s surely churlish by everybody’s lights to argue about who gets to use the word ‘causation’. But to see this model as an account of causation is not, of necessity, to see it as something which is in competition with others. For perhaps there are a number of different things which might pretty much equally deserve to be called causation. For this to be the case what we would need is a set of desiderata for being causation not all of which can be met by one thing, but a reasonable number of which can be met by at least two things. Just such a thought has been urged, of late, by Ned Hall (2004) amongst others. For Hall there are at least two things you might call causality: one given by the counterfactual theory, the other by some notion like production. Part of what I will be suggesting in this chapter is that there is a third notion which may, or may not, be in competition with production. This is the notion of structural causal connectedness—the way the world fits together across time in the micro scale. Think of it like as the parts of a jigsaw puzzle connecting. Or think of it as like glue— it’s the way the universe is glued together over time. Such a notion is symmetrical (there’s no direction in the glueing relation, if A is glued to B, then B is glued to A). Such a notion need not even support counterfactuals (if extreme actualism is true, and all non-trivial counterfactuals are false5 then there will be no true counterfactuals, but there will still be causal connexions in this sense). One can think of this 3

4 Van Fraassen 1977. See the attempt at unification in Strevens 2013. To get this result you need to need the analysis of counterfactuals to be something like ‘P □➞Q’ is true just if there is at least one P world, and the nearest of those is a Q world’. 5

DAVID BRADDON - MITCHELL



notion as lying in between the idea of production on the one hand, and mere succession on the other. With mere succession the slices are not glued—there are no structural connexions—they merely abut each other. Whether there is a feature of the world which supports the idea of glueing is of course open. But something like the trope persistence account of Dough Douglas Ehring,6 or versions of the integration of slices delivered by preserved quantity account of causation,7 according to which there is a close line up of preserved quantities at the micro level as you move across time, might count as accounts of something that could ground the idea. The notion of production is one according to which the existence of the produced is dependent on that which produces it. Mere succession on the other hand simply has time slices of the universe abutting each other. They have no connexion beyond the order in which they occur. The notion of structural connectedness, on the other hand, is the idea that these slices are integrated together. There are features of the structure that allow you to predict future slices (and retrodict earlier ones), but not because the existence of the later or earlier ones in any way depends on the slice being used to predict or retrodict. They could, as it were, all have been created together: but constraints on how the whole is created fix the possible patterns of connexion in ways that make the prediction or retrodiction possible. The other part of what I’ll be exploring is a methodological concern which discussing this idea usefully exemplifies. It explores the idea of what the minimal content of a concept is. The minimal content of a concept is the weakest condition which, if satisfied—and no stronger condition is satisfied—will be enough to give us a reasonable alternative to eliminativism with respect to that concept. Any readers familiar with the conditional analysis of qualia8 might recognize this notion as a component there: there is a strong condition which, if met, is deemed to be necessary (and perhaps sufficient) for qualia, but if it isn’t met then meeting a set of weaker criteria is sufficient (and perhaps necessary). There the idea was that there is a kind of conceptual priority to dualist ideas about experience, such that if there were to turn out that there were indeed non-physical properties that played a special role in consciousness, then these would be the best candidates for being qualia. But if not, then functionalist accounts would be sufficient. The idea was, then, that explicating the concept of qualia should be done as a conditional. So in this conditional story, the functionalist account of qualia is the minimal content of the concept of . I’ll say a little more about this idea later in the chapter: for now it’s worth noting that it is no part of the idea that it is a simple conditional, and that there are only two conceptions in the hierarchy. In the present case of causation there may be many. So I’ll be arguing that in the case of causation we should embrace a kind of pluralism. The kind of pluralism I will advocate is complicated and according to it we should be pluralists in at least two ways. The first way is pluralism about, on the 6 8

7 Ehring 1997. Dowe 2000. Braddon-Mitchell (2003) Hawthorne (2002).



THE GLUE OF THE UNIVERSE

one hand, counterfactual/interventionist accounts, and on the other accounts where causation is intrinsic to causal processes. In this first sense of pluralism there is no competition between the conceptions: they are doing different work. The second way is a kind of prima facie pluralism about accounts which make causation intrinsic to causal processes.9 But the focus of this chapter will be on the second kind of pluralism: pluralism within the intrinsic accounts. In this second way the pluralism is weaker—the different intrinsic accounts are in competition, but just not competition that can be settled entirely a priori. All that can be settled a priori is the weakest account which would be acceptable on discovering that the ontological postulates of the stronger account are not offered up by the world. Which is the right account, then, depends on what is actual, and my interest here is on what the weakest discovery about the actual world could be that would vindicate causality in the intrinsic sense. The interest in the weakest notion is not idle curiosity about how little would do. It’s also motivated by the suspicion that the world may offer us only candidates at the very weak end of the spectrum. This investigation itself, though, sets the stage for a final concern—which is yet another methodological one. What exactly is the role of philosophy in all of this? If there really is a complicated set of conditionals about what counts as causation, what kind of fact is this and whose job is it to determine its nature? Is it a psychological fact, and if so does it vary from person to person? Should we be trying to average out what this looks like equilibrated over the species? How would we do that? Ought we to care?

2 Pluralism of the First Kind The idea that there needs to be some kind of pluralism about causation ought now to be reasonably uncontroversial. From having once thought that there should be a causal explanation/causation distinction according to which causal explanations are not causes, it now seems to me that that was an unnecessary terminological debate. Much fruitless debate can be avoided by accepting that the phenomena captured by ‘causal explanation’ and ‘causation’ are both kinds of causation. This is because there is a range of commonplaces about causation, not all of which can be satisfied by any relations that we are likely to find in the world. These include commonplaces about countless individual causal claims, the idea that the most ordinary instances of causal explanation are citing causes rather than simply citing states which supervene on unknown processes that are real causes, and the idea that in agency we perform actions which are themselves causes. All these ideas push in the direction of letting the macroscopic entities that feature in our causal explanations count as causes. 9

Dowe 2011.

DAVID BRADDON - MITCHELL



But equally there are considerations that push the other way. In the industry of generating neuron diagrams of causation we keep finding cases that count as causal, but no one theory that will account for them all. Ned Hall,10 for instance, cites cases of ‘double prevention’ where counterfactual analyses (and in some versions interventionist successors) seem to fail to deliver the right verdict as to what causes what. At a more global scale, any theory of causation in the interventionist model will find it very hard to make sense of massive causal claims which don’t seem to admit of alternatives within the model, such as the claim that the initial conditions of the Big Bang are the cause of everything. When there seems to be no notion that gets all the cases right you might be tempted to simply use the strategy David Lewis was wont to call ‘spoils to the victor’: let the more successful theory on other grounds settle all the controversial cases. But in this case something like an explanation of the failure of any theory to get the cases right makes that a little less tempting. The explanation is that as well as the commonplaces mentioned above, there are others in tension with them. Hall, for instance, correctly diagnoses the idea that causation is intrinsic, local, and productive as what underlies the problems associated with double prevention cases. Here is the idea. A double prevention case is where something prevents what otherwise would have prevented something from happening. Suppose I cause you to survive by shooting someone who otherwise would have shot you. If this is so then my causing you to survive is no part of the continuous chain of causal process that make up your world line. Causation (if double prevention is causation) can be extrinsic, and something that can take place by omission (i.e. the absence of the act of shooting you is also a cause). But if we take it that causation is an intrinsic process that continuously and locally connects events, we will have to rule these cases out. The intrinsicality and locality intuition in turn may explain why some take there to be no causation by omission.11 Intrinsicality is the idea that the causal nature of a connexion is intrinsic to that connexion; locality is essentially what is meant in physics: causal connexions are continuous (if spacetime is continuous, otherwise an unbroken chain at the finest quantized grain). Omissions is the idea that lots of examples which feature causation by omission are genuine instances of causation. So the general idea is that there are two sets of intuitions around causation that are in tension with each other. The first is the set, just mentioned, which favours macro causation, together with the idea that there are cases of causation by omission. The second is a cluster around intrinsicality, locality, and production which will predispose you to take certain cases as more important. Of course the idea that there are cases of causation by omission or double prevention is favoured by the fact that there are counterfactual connexions between omissions or double preventers and events.

10

Hall 2004, Hall and Paul 2013.

11

Beebee 2004.



THE GLUE OF THE UNIVERSE

With this diagnosis in hand the spoils to the victor strategy starts to look as though it is pushing important distinctions under the rug. Suppose we were to say that the undoubted importance of Menzies’ work on the interventionist model, and its use in causal modelling and assessing the strength of causal contributions, meant that whatever the interventionist story suggests to settle all the problem cases. Then it would seem we would be forgetting these other features which look like they are an important theory of something which might exist, and which could be a very important part of the way the world works. Spoils to the victor would mean the victor, as so often, rewriting history and seeing these other intuitions as mistaken intuitions about causation as the interventionist sees it, rather than intuitions about something else. Mutatis mutandis should the other conception of causation become sociologically dominant, and be the only way the term is used. Thus is vindicated the first kind of pluralism: pluralism between broadly interventionist or counterfactual accounts of causation on the one hand, and intrinsic or process-oriented ones on the other.

3 Pluralism of the Second Kind But what is the right account insofar as we are concerned with the second idea, the idea that causation is intrinsic to causal processes, or perhaps that causation is, in some way which may be hard to spell out, productive? There is no shortage of candidates here. And the second kind of pluralism is a pluralism within this group—a pluralism within the second idea. Hall has a candidate, involving the use of very local counterfactuals in a way very different from ordinary counterfactual theories. Tim Maudlin12 proposes that causation is more or less primitive, and tied to the idea of metaphysical becoming, because true production involves the bringing of something into being. Others tie this notion to an A-theory of time, using the frisson of production to mark out the objective now.13 I don’t propose to survey all such accounts. I just want to note that many are metaphysically rich. Most require that there is a fundamental anisotropy in the world, so that the causal relation can be directed and asymmetric. Some require in addition that the A-theory be true. Let’s call a theory a production theory if it is one of these. But what if the world offers none of that? Would there be anything of the second kind that is worth calling causation if there were no production in this general sense? Pluralism of the second kind is the suggestion that while these rich accounts are fine insofar as, if the properties they posit exist, then they are good accounts of causation, there are other alternatives that come into play should those properties not exist. The thought, though, that the metaphysically rich stories that posit fundamental anisotropies and relations of production are richer than the world supports is not that controversial a story about space and time. Many philosophers of time 12

Maudlin 2007.

13

Forrest 2004.

DAVID BRADDON - MITCHELL



are B-theorists who believe in a block universe, and in addition one with no fundamental anisotropies (and only local apparent directions explained by extrinsic facts like the local direction of entropy). The lack of the ontology of an A-theory (a theory which has objective becoming in it, or irreducible ontological bases for tense) means you can’t have a becoming which requires that feature, and the lack of intrinsic anisotropy means you can’t even say that there are asymmetric intrinsic causal relations. The point of this chapter is to say something about what you might still identify as causation of the intrinsic kind, even if all this deflationary ontology were true, and how this might be better even if you were inclined to think that truly productive relations, if actual, would be necessary conditions for intrinsic causation obtaining.

4 Less Acceptable Deservers So if production is thought to be something unlikely to be realized in an eternalist universe, and if we take some kind of limited actualism to be true, and are not realists about counterfactuals14 at the micro level,15 does that mean that there’s nowhere to go for the second concept of causation? The thought would be that unless we think there’s a metaphysical primitive of production (more likely if some kind of A-theory is true), or that there are meaty metaphysical truthmakers for the counterfactuals that underlie something like Hall’s analysis, then there’s no real scope for a second concept of causation. The idea that there’s something important to the intrinsic connexions fails. The successors of the counterfactual idea in the interventionist tradition would inherit the only decent notion of causation, and it turns out to be an anthropocentric notion insofar as it will depend on facts about what humans take to be explanatory, and on their psychology of agenthood. Perhaps not: we should look instead for what might seem less acceptable deservers for causation in the second sense. We can set a benchmark by looking for the least good deserver which is still good enough. The idea here is to think of what would keep us from error theories as progressively we become disillusioned about what the world contains as candidates to match our concepts. Consider the account of qualia that I offered in 2003.16 The idea was that there is a kind of conceptual priority to dualist ideas about experience, such that if it were to turn out that there were indeed non-physical properties that played a special role in consciousness, then these would be the best candidates for being qualia. But if not,

14 I am taking something like these hypotheses to be consistent with at least a fairly deflationary version of interventionism, in which we have a non-realist gloss on counterfactual talk. 15 One way of honouring intrinsicality intuitions is through an account of causation in which a necessary condition of causal chains is that they be composed of chains of fundamental-level or at least micro-level counterfactuals, consistent with there being macro-counterfactual connexions that aren’t causal. 16 Braddon-Mitchell 2003, Hawthorne 2002.



THE GLUE OF THE UNIVERSE

then functionalist accounts would be sufficient. To slightly simplify, the story might look like this: If there are states (call them SS for ‘spooky states’), whose essential and intrinsic nature is revealed in and only in experience, then SS are qualia and necessarily so. Otherwise qualia are the states that play such-and-such a set of functional roles (perhaps representational roles).

The point of this is to explain how eliminativism can seem plausible to someone who thinks that there are states like the SS. If you think there are such states, then you think that they are necessary for qualia. If you think that there are likely such states, then you think that it is likely that they are necessary for qualia. So you will judge that in the absence of such states, that there are (or are likely) not qualia. When you are in the habit of judging that absent SS there are no qualia, you will be likely to form the view that if you came to think that actually there are no SS, there would be no qualia. But this doesn’t mean that’s what you would do if you in fact came to that view.17 What a conditional analysis predicts, is if our concepts have the structure of the indented simplified analysis above, then if our beliefs are formed rationally in line with our concepts, then on forming the view that there are no SS you would instead decide that qualia are functional states (or perhaps some other surrogate that exists actually). It predicts additionally, that having formed that last view, if you were to switch back to believing that SS actually exist, you would—or would soon—revert to thinking that SS are necessary for qualia. Much the same might be true in the case of causation. The productivity intuition is a powerful one, and if you are very convinced that in the actual world there are intrinsic states whose nature ‘produces’ the next state, or has ‘biff ’ as people sometimes say in the literature, then you might be inclined to make the judgement that where there is no productivity there is no causality of the second kind. Thus looking out from what you take to be a world with productive intrinsic states, you see the Humean worlds (for example) as ones in which there is no causation—and you see the regions of your world which lack productive relations as regions which lack causation. But perhaps something like the model I sketched in the philosophy of mind might be right here too. If you come to think that actually the world contains no productive relations (either on empirical grounds or even on a priori grounds if you come to think that the idea of production is incoherent or otherwise able to be ruled out a priori) then perhaps your view about what it takes for there to be causation might change. Of course that requires that there be something to change to.

17 Preliminary results of some experimental philosophy by David Braddon-Mitchell and Andrew Latham suggest that in fact when you properly conditionalize on beliefs about what is actual, judgements will follow the conditional pattern (Braddon-Mitchell and Latham 2015b).

DAVID BRADDON - MITCHELL



5 Causation as Structural Glue What I’m looking for, then, is something which can survive the possibility that time is deeply isotropic: there’s no intrinsic anisotropy in time to serve as a direction of causation. But I’m looking also for something that may not be merely predictive or retrodictive, as the laws of nature might be on something like a best systems account. I think the best way to proceed is to start with an analogy.

5.1 The Structure of Crystals Consider the structure of a crystal, say a copper sulphate crystal. Given certain constraints, a two-dimensional slice of that crystal allows us to predict the shape of the whole crystal, rather like how a three-dimensional slice of the universe together with the laws allows us to predict the whole of the universe (at least if many worlds is true or some other deterministic reading of quantum mechanics). Are there mere informational generalizations that allow us to do this? Probably not. When you look into that two-dimensional slice you see arrangements of particles that fit into particles in constrained ways. Given the covalent bonds, ionic bonds, possible mathematical arrangements of lattice sites, van der Wahls forces, etc., that are some of the ways crystals are held together, it’s possible to calculate what can fit into the slices on each side (which we could call the ‘next’ and ‘previous’ side conventionally).18 It’s a real, local intrinsic matter of fact that these slices fit together the way that they do, in much the way that parts of a jigsaw fit together. The slices are as it were glued together, and they are glued together by their geometric and other physical properties. Now I’m going to ask the reader, for the sake of a thought experiment, to imagine three-dimensional beings (on the assumption that we are four-dimensional ones) that occupy regions of crystals. These beings—let’s call them in the spirit of puppet-based science fiction of the 1960s the Crystalons—experience a spatial axis through the crystal in a time-like way. They wonder whether each slice of the crystal produces the next slice. There is some relation that they call ‘causation’ which some of them think requires such production, which is asymmetric: one slice produces the next but not vice versa. Others wonder whether ‘causation’ could be mere regularities; many think not. Then they decide that ‘production’ is either incoherent or not in the crystal. Will mere regularity do? No it won’t, they decide. But on discovery that there are these interlocking structural regularities, they see that the slices are connected in a physical way, and the structure of those joints explains why we can ‘predict’ (and ‘retrodict’) regions of the crystal, that is, determine what other parts are like given how a slice is. 18

In some cases there are multiple candidates where the factors that determine one rather than another are not, as it were, remembered by the crystal: this is a nice analogy with indeterminism.



THE GLUE OF THE UNIVERSE

Presumably everyone has guessed that this is meant to be an analogy with our experience if we are four-dimensional beings in a block universe with no special relations of becoming, production, intrinsic temporal asymmetries, and so on. What our apparently dynamical physics is telling us is structural: it’s about what fits to what. But what fits to what is a perfectly symmetrical relationship. If A fits to B, then B fits to A. But this fit is an intrinsic fact about regions of the world, and it’s a feature which tells us why, if things are thus and so at a certain location, they are another way at a different point. These structural features can be no less structural for being mathematical. Geometrical relations of fit can be described mathematically: perhaps the evolution of the Schrödinger equation could be seen as a mathematicization of relations of fit of this kind. Perhaps now it’s easier to see why I’ve called this account ‘causation as glue’. The idea is that causation is the glue of the universe. It’s what holds it together (in some suitably non-temporal understanding of that phrase) and explains how the parts hang together. And, with glue, if A is glued to B, then B is glued to A. There’s no anisotropy there.

5.2 A Disanalogy: The Real, Dynamical Past As I type I almost hear the chorus of readers telling me that the crystal has a history. The structure of the crystal is the result of a real, dynamical process of crystal growth of which this three-dimensional slice is just a frozen representation. So there is a powerful disanalogy here that should make us wary of taking the analogy too seriously. It’s not clear to me how important this is, though. Remember that the analogy is supposed to be the (nomically impossible) fiction that there are threedimensional beings who experience the third dimension as time-like. Given their concepts all they could have access to is the idea that each two-dimensional slice is different from another along an axis in the third dimension, and that they fit together in a structural way, with that structure providing an explanation of why ‘prediction’ is possible and successful. Nothing about that is false just because there is a further explanation about how the whole three-dimensional structure came into being. We, as four-dimensional beings, can see that there is a dynamics of crystal growth which accounts for that, and which maps better onto our four-dimensional understanding of causation. But for three-dimensional beings any talk of further explanation of the whole three-dimensional structure is armchair metaphysical speculation. At best it would be interesting speculation (as it happens correct speculation). But this further explanation of why the whole three-dimensional world is the way that it is doesn’t seem to correspond to a better understanding of their concept of causation, for that was a concept that always was concerned with the relations between the twodimensional slices. This further explanation involves something like a hypothesis that there is an ensemble of three-dimensional worlds, and the fact that the threedimensional world they live in has certain features is because it is a member of an ensemble for which there is a grand explanation of why its members have certain features. Maybe there’s even a kind of productive relation between the members of

DAVID BRADDON - MITCHELL



this ensemble, explained by laws of 4-space. But even then that would not necessarily say that this meta-explanation of their laws is true causation. Absent the better deserver for causation—productive relations between the planar slices—one might think the merely structural relations between the slices is to be preferred to some productive relation of a cosmological kind that does not even link planar slices. Consider again our own case. Suppose that there are only these structural relations between three-dimensional slices, and that this is the best way to understand what were thought of as dynamical laws—laws that tell us what glues on to what. Someone might hypothesize that there is an ensemble of universes that in some strange way connect to each other in a productive way, and the reason that our universe is the way that it is in virtue of the fact that there is such an ensemble, and that ours was born from another. There is of course next to no evidence for such an hypothesis, but even if were to take it seriously we wouldn’t be forced to the idea that there is no intrauniverse causation: forced to the idea that there is a causal story about the whole universe, but not about how one thing in the universe causes another. For causation, if there is any, is the relation between things in the universe, and strange productive explanations of the nature of the whole universe get to be causal, if they are, by sharing relevant features with the paradigms.19 Of course this story about causation as glue will be one which leaves out much of what is plausibly enough part of our core intuitions about causation. It’s symmetrical for one thing. It’s likely exclusively micro-causal for another. So if it does turn out to be the only understanding of causation which respects the intrinsically intuitions, then there will be even more reason than ever to accept that something in the causal explanation family of views plays a very important role—for that will (with luck) respect asymmetry, link macro-states, and be involved in everyday discourse about causality. If something stronger, like productive relations in the microstructure, turned out to be instantiated then there would perhaps be less such reason. So the connexion might be that the causal-explanatory relations would supervene on the glue-causal relations. The issue of which to call ‘causation’ would still remain. Someone for whom the intrinsicality intuition is an important one about something, but not something they call ‘causation’, might be inclined to say that the interventionist theory is a theory of causation, but that causation depends on structural connectedness relations. What kind of an issue that is, and how it should be addressed, is the job of the last section. This would be to reject pluralism of the first kind, whilst allowing that the intuitions which underly it give reason to think the things that these pluralists are inclined to call ‘causation’ are nevertheless important.

There is a version of this hypothesis that might fly as genuinely causal. Suppose you believe a version of the growing block according to which there is a series of block universes that are progressively larger in an A-series. In each block universe there is a B-series of time slices. Then in some sense each block universe is a productive cause of the next (though oddly there would be no true causal relations between the time slices of each block in the series). 19



THE GLUE OF THE UNIVERSE

One thing to make clear here is that this glue analogy is supposed, primarily, to show that there could be something conceptual which is in the ballpark of causation which survives anisotropy. There’s a concept we possess, perhaps even a primitive one, of connectedness or attachedness, which doesn’t have anything anisotropic built into it. It’s easy enough to see, on broadly evolutionary grounds, why we might have such a concept, and its application across time rather than space might be part of what constitutes our ideas of causation, at least if there is nothing more full blooded on offer. But the concept itself is silent on its realization: on what, if anything, answers to gluedness in the world. There are candidates from the most full blooded, to the most deflationary. There could be something in the world which is rather like the notion of production, minus the anisotropy: a kind of primitive, symmetrical relation of ontological dependence in re. There could be merely geometrical relations of fit revealed by future physics, which cast light on how one time slice connects to the next (perhaps the dynamical laws, stripped of their dynamical aspect, are a draft of this). The glue relations might be important only because they are the shadows of the real relations that some future quantum gravity might reveal between the underlying reality and the emergent time slices. I take it, though, that it is far from guaranteed that the glue relation be instantiated. Not only because the world might not offer up enough raw material, but also because we don’t know which of the above realizers are good enough. Consider my remarks about quantum gravity above. According to certain reconciliations of quantum mechanics with general relativity, time slices exist but are unconnected to each other, possessing no order with respect to each other: at very best they possess a common explanation in supervening on some underlying unitary reality.20 Would relations of similarity between slices that supervene on that reality be enough to vindicate a glue conception? I don’t know, and I doubt even if there is a fact of the matter. But if I’m right that the glue conception is the weakest one that doesn’t lead to an error theory, then there is still a reasonable (epistemic) chance that we will need to be error theorists about the intrinsic notion.

6 How to Rank the Conditionals, and How to Find Out What’s There So far, then, I’ve sketched a story where there are at least two kinds of pluralism that you might want in your account of causation. This first pluralism is about the broadly counterfactual or interventionist accounts of causation, and the range of stories that honour locality and intrinsicality intuitions.

20

Deutsch (1997) gives a sketch of how things might be that have this feature.

DAVID BRADDON - MITCHELL



The broadly counterfactual stories make causation at best only sometimes intrinsic, often macroscopic, and frequently interest or contrast dependent. The argument for retaining something in this family is that this family describes what we are doing when we look for the causes of things, at least in the macroscopic world, and plan our behaviour in terms of what it will cause. These are very central human and scientific projects that are not going to go away. The alternative within this first kind of pluralism is a family of stories, according to which causal relations are intrinsic to causal processes. They are microstructural, and—I’ve argued—perhaps they are asymmetrical and productive. But crucially if no such processes exist we can live without those features. The argument for retaining the alternative story is that it captures key intuitions that the first does not, and it might provide an explanation about what it is in virtue of which those larger patterns obtain. But the second pluralism is about members of this second family of stories. Aspects of this pluralism can be shown to have a hidden structure which makes it less pluralistic at the most abstract level: it can be described as a chain of conditionals, or so I’ve asserted. If there’s something in the microstructure that plays the relevant roles, which is asymmetrical and productive and intrinsic, so much the better. If we delete asymmetry, though, what’s left still counts as causation (even though we would take asymmetry to be essential if it were actually instantiated). If both asymmetry and production go, then relations of structural interconnectedness—symmetrical glueing relations—remain. One question you might ask concerns the status of the above claim that what is left ‘counts as causation’. Is this a theoretical conclusion about what causation is, or a practical choice about how to use the word ‘causation’? This depends a lot on what counts as a theoretical conclusion. What does such a theoretical conclusion amount to? Suppose that there are two ways to form such a conclusion. One is to engage in a kind of analysis, and discover what features it takes to be a paradigm instance of something that falls under the concept. The other is to discover, empirically, important new features of these instances. A purely practical choice might be what you are left with if these methods deliver no answer—say it turns out that there is nothing that falls under the concept as possessed by almost everyone, but there are practical reasons for wanting that not to be the case, so conceptual or linguistic revision is on the table, and for reasons that are contingent on current circumstances, some kind of choice has to be made. My suggestion here is that the change is under the governance of the original concept, and so it is not a purely practical choice. The disposition to change reference depending on what is actual was already there in the concept, not something which emerges to meet the new needs. Of course this is not an a priori claim—and a little later I’ll discuss some preliminary results in experimental philosophy which support this claim. What I’ve said has been light on argument for why these conditionals are structured as I claim they are. There’s a reason for this. It’s that these conditionals are



THE GLUE OF THE UNIVERSE

analytic a priori. The source of the truth about claims about how they work is a priori only in relation to the nature of a set of concepts—concepts which may or may not be widely shared. So a lot of further argument from me would just be revealing something about the nature of my concepts. Of course it’s possible that my concepts are the same as everyone’s because there is some kind of deeply hardwired set of cognitive roles played by concepts in the causation family. But whether that’s true or not is, of course, not an a priori matter of any kind. It’s something that we would have to do by a level of detailed cognitive science of a kind that is not really being done.21 So how would an argument that the conditionals are as I describe them proceed? It seems like an empirical matter, and a very complex one at that. We need to establish whether something like this chain of conditionals reflects the concepts in use by many individuals, and we need to devise a way to equilibrate over the individuals if it turns out that there is a lot of variance over individuals. It won’t suffice to reach for the usual tools of experimental philosophy, which has to a large degree been concerned with trying to find out what untutored intuitions on a range of cases are (and is so attempting, finding out nothing that we don’t already know according to Dunaway, Edmonds, and Manley).22 Only individuals fairly carefully primed will be able even to understand the diagnostic questions. If I’m right and the conditional structure is there, then once you have taught someone all the various possibilities for the kinds of relations that there might be in the world, and you have had them engage in the kinds of discourses and explanatory projects for which talk and thought about causation is important, you’ll then be able to ask diagnostic questions. First you’ll ask if the richest option is instantiated, whether it is sufficient for the intrinsic conception of causation. Then you’ll ask whether, if they were to discover that actually it wasn’t instantiated, it would still count as necessary (and hence that there is no causation), or whether the next conception would suffice (and be necessary) and so on. My prediction was that on imagining that they discover that one relation is not instantiated,23 they’ll revise to the weaker version as necessary, until reaching the glue conception, at which point they’ll revert to the error theory if it turns out that even that conception fails to be instantiated. I do have some preliminary data in a study just completed with Andrew Latham which bears on this prediction.24 The study was conducted using the Mechanical Turk web survey for small payment. One hundred and three respondents answered

21

Medin and Atran (1999) propose that there is just such a basic set of concepts in the case of biology to which human psychology defaults. 22 Dunaway, Edmonds, and Manley 2013. 23 In the study that we discuss in the following we used imagining that you changed your view as a proxy for actually changing your view. But it is the latter that I take to be theoretically important, and we have some work in progress which attempts to directly test it via questions over a year of studying metaphysics to see what happens to the views of those who change some of their central commitments. 24 Braddon-Mitchell and Latham 2015b.

DAVID BRADDON - MITCHELL



our questions on causation. The answers were systematic enough, and the test questions answered well enough, that we are (surprisingly!) confident that the respondents understood the conceptions well. We explained the glue conception and the production, and asked them whether (a) they thought the actual world was a glue world or a production world, and (b) regardless of what they took in fact to be actual, whether if these worlds are actual there is causation in them. We then asked for each of the worlds taken to be actual, whether there would be causation in a world taken as counterfactual with the other property. So, for example, we asked them whether, if the actual world is a world that contains production, a world containing glue would contain causation (in virtue of that glue). The results were as follows. Around a quarter of the MT participants take the actual world to lack production and be a glue world; the rest take it that the actual world is a production world. Almost all the participants think that if the actual world is a production world, then there is causation, suggesting that those who take the actual world to be a glue world also think that production is sufficient for causation. A substantial majority think that if the actual world is a glue world, then the actual world contains causation in virtue of that, suggesting that many of those who think that causation is actually productive, think that glue would be sufficient if actual. The lower proportion, though, suggests—as expected—that glue is a less good deserver. Almost all the respondents think that if the actual world contains only glue, then a counterfactual world with production would contain causation. This suggests that production is thought of as sufficient for causation regardless of what is actual. On the other hand, if the actual world is fixed as a production world, only a narrow majority think that a counterfactual glue world would contain causation. This is a significantly smaller majority than those who think that if the actual world is thought of as containing only glue then it therefore contains causation, which suggests a moderately strong conditional effect. Glue is more likely to be thought of as sufficient for causation if it is all the actual world offers. The asymmetry is that the sufficiency of production is unconditional—regardless of how the actual world is, almost all participants take production to be sufficient for causation. One thing to note is that almost all those who as a matter of fact think that the world does only contain glue, think that glue is sufficient for causation. One thing which the study does not test is whether there is a difference between the attitudes of those who think the actual world in fact contains causation and are then asked to suppose it contained only glue as a candidate for causation, and the attitudes of those people if they really came to believe that the actual world contained only glue. We hypothesize that we would find an even bigger proportion prepared then to accept that glue was sufficient for causation. So that’s the first set of questions about pluralism of the second kind—questions about the structure of these conditionals. Answer: it’s an empirical matter, and one on which we hope experimental philosophy can cast some light.



THE GLUE OF THE UNIVERSE

The next set of questions is about which of these candidates for causation is actually instantiated, or better, which is the richest actually instantiated candidate (for if my prediction about the conditionals is correct, then that’s what is both necessary and sufficient for intrinsic causation). Here again the answer is: it’s an empirical matter. Well perhaps that is too fast: one might think that the idea of production is incoherent or some such, in which case some elimination might be able to be done a priori. But on the whole, it’s also an empirical matter. So it’s starting to look as if there’s not a lot of work for philosophy. What are the conceptual truths? Put on the white coats. Which are the candidates that are actually here? More white coats. So what is the added value? I suppose what philosophy can do is ask the questions and set some directions for what needs to be discovered. That is pretty deflationary; but there’s something else that it can do too. It can discover what the candidates are. So in this chapter, amongst all the methodological chatter, there is a suggestion for a candidate—the glue conception of causation. It’s hard to see how the creation of candidates can be left to purely empirical means. It’s something of an imaginative process. So in fields like the metaphysics of causation, perhaps the philosophy lies in the context of discovery—not so much in the context of justification. It’s just that what we are discovering is candidates for being causation. McDowell is often said to have claimed in conversation that philosophy is not about arguments, it’s about making ideas so lucid that they seem compelling. I’ve never been attracted to the thought that that is all we can do. But perhaps now it is starting to look like there is something right about it. But rather than lucidity and compellingness of ideas being thought of as ends in themselves, rather they should mark the beginning of an investigation into two things: first, who is so compelled and under what conditions, and second, whether the world has anything in it that corresponds to those ideas, and if so, what the consequences are of using our talk to pick those things out. The next phase, then, is to see if anything does glue the slices of the world together.

References Beebee, H. 2004. ‘Causing and Nothingness’, in Causation and Counterfactuals, ed. J. Collins, E. J. Hall, and L. A. Paul. Cambridge, MA: MIT Press, 291–308. Braddon-Mitchell, D. 2003. ‘Qualia and Analytical Conditionals’, The Journal of Philosophy, 100: 111–35. Braddon-Mitchell, D., and Latham, A. 2015a. ‘Experimental Philosophy, Qualia and Conditional Concepts’. MS. Braddon-Mitchell, D., and Latham, A. 2015b. ‘Causality, Production, Glue and the Folk’. MS. Deutsch, D. 1997. The Fabric of Reality. London: Allen Lane. Dowe, P. 2000. ‘The Conserved Quantity Theory Defended’, Theoria, 15: 11–31.

DAVID BRADDON - MITCHELL



Dowe, P. 2011. ‘The Causal-Process-Model Theory of Mechanisms’, in Causality in the Sciences, ed. P. McKay Illari, F. Russo, and J. Williamson. Oxford: Oxford University Press, 865–79. Dunaway, B., Edmonds, A., and Manley, D. 2013. ‘The Folk Probably Do Think What You Think They Think’, The Australasian Journal of Philosophy, 91: 421–41. Ehring, D. 1997. Causation and Persistence: A Theory of Causation. Oxford: Oxford University Press. Forrest, P. 2004. ‘The Real but Dead Past: A Reply to Braddon-Mitchell’, Analysis, 64: 358–62. Hall, E. J. 2004. ‘Two Concepts of Causation’, in Causation and Counterfactuals, ed. J. Collins, E. J. Hall, and L. A. Paul. Cambridge, MA: MIT Press, 225–76. Hall, E. J., and Paul, L. A. 2013. ‘Metaphysically Reductive Causation’, Erkenntnis, 78: 9–41. Hawthorne, J. 2002. ‘Advice for Physicalists’, Philosophical Studies, 109: 17–52. Hitchcock, C. 2001. ‘Causal Generalizations and Good Advice’, The Monist, 84: 218–41. Hitchcock, C. 2012a. ‘Contrastive Explanation’, in Contrastivism in Philosophy: New Perspectives, ed. M. Blaauw. London: Routledge. Hitchcock, C. 2012b. ‘Theories of Causation and the Causal Exclusion Argument’, Journal of Consciousness Studies, 19: 5–6. Maudlin, T. 2007. The Metaphysics Within Physics. Oxford: Oxford University Press. Medin, D., and Atran, S. 1999. Folkbiology. Cambridge, MA: MIT Press. Menzies, P. 2007. ‘Causation in Context’, in Causation, Physics, and the Constitution of Reality: Russell’s Republic Revisited, ed. H. Price and R. Corry. Oxford: Oxford University Press, 191–223. Pearl, J. 2000. Causality: Models, Reasoning, and Inference. Cambridge: Cambridge University Press. Strevens, M. 2013. ‘Causality Reunified’, Erkenntnis, 78: 299–320. Van Fraassen, B. C. 1977. ‘The Pragmatics of Explanation’, American Philosophical Quarterly, 14: 143–50. Woodward, J. 2003. Making Things Happen: A Theory of Causal Explanation. Oxford: Oxford University Press. Woodward, J. Forthcoming. ‘Methodology, Ontology, and Interventionism’, Synthese.

7 Actual Causation What’s the Use? Christopher Hitchcock

1 Introduction This chapter connects two themes in the work of Peter Menzies. The first is the agency theory of causation (Menzies and Price 1993); the second is the analysis of actual causation in terms of counterfactuals represented in structural equation models, together with considerations of normality (Menzies 2004, 2007, this volume Chapter 9). According to agency theories of causation, causes are ‘handles’ that we can use to intervene in the world in order to achieve our desired ends. According to the type of analysis of actual causation favoured by Menzies, actual causation involves certain kinds of path-specific effects, as well as considerations of normality or the default behaviour of systems. In this chapter, I ask about the practical advantage of knowledge of actual causation. If causes are handles on the world, then actual causes are handles of a specific kind. What kind of handle are they?

2 Actual Causation By ‘actual causation’, I mean the kind of causal relationship described in sentences like: 1.

A meteor strike in the Yucatan caused the extinction of the dinosaurs;

2. Sparks cast by a locomotive caused the fire that destroyed Jacob Anderson’s house;1 3. The emission of X-rays from a charged vacuum tube in Roentgen’s lab caused an image to appear on a screen.

1

Based on the facts of the legal case of Anderson v. Minneapolis, St. Paul & Sault St. Marie Railroad Company.

CHRISTOPHER HITCHCOCK



Actual causation has been of considerable interest to philosophers and legal theorists, in part because it is involved in the concepts of moral and legal responsibility, as well as in the explanation of particular events. Actual causation has frequently been the target of philosophical analysis. Often, it is just called ‘causation’.2 It is also sometimes called ‘singular causation’3 or ‘token causation’.4 The latter terminology indicates that actual causation involves causal relations between particular events,5 which occur at particular times and places, and involve particular people or objects. For example, claim (1) concerns a particular meteor, which had a diameter of roughly 10 km, and which struck the earth roughly 66 million years ago at a site near present-day Chicxulub in the Yucatan peninsula of Mexico. Claims of actual causation are often contrasted with causal generalizations, such as: 4. 5. 6.

Meteor impacts cause species to become extinct; Sparks cause fires; X-rays cause images to appear on photosensitive screens.

While this distinction between singular and general causation is familiar to philosophers, I do not think that singularity by itself distinguishes actual causation from other kinds of causal relation. In particular, I think that there is an important sense in which relations of actual causation are backward-looking. Sentences (1)–(3) are all expressed in the past tense, but this is mainly because they are historical examples. I don’t mean to deny that claims of actual causation can be stated in the present or future tense. For example, I might pessimistically predict: 7. The epidemic of devil facial tumour disease (DTFD) will cause the extinction of the Tasmanian devil. In so doing, I would predict that a certain relation of actual causation will obtain. Nor do I deny that we are often interested in relations of actual causation because they are informative about potential future outcomes. For instance, claim (2) refers to a 1920 lawsuit.6 One reason for allowing homeowners to sue railroad companies for fires sparked by locomotives is to provide an incentive for the railroad companies to contain those sparks in the future. Nonetheless, considerations of actual causation most naturally arise when some event has already occurred, and we want to assign responsibility for that event, or explain why it occurred. That is, an inquiry into actual causation is typically triggered by the occurrence of an effect, and involves a search for the cause; it involves a kind of

2

This is the terminology used by Lewis 1973, 2000, for example. 4 See Cartwright 1989, chapter 3, for example. See Eells 1991, chapter 6, for example. 5 Other types of relata have been proposed; see Ehring 2009 for a survey. These other types of relata can also be singular in the sense described. 6 See note 1 above. 3



ACTUAL CAUSATION : WHAT ’ S THE USE ?

effect-backward reasoning, rather than cause-forward reasoning. Assignments of moral praise and blame, and of legal responsibility, typically have this form. So do explanations of particular events. One of my goals in the present chapter is to clarify the sense in which actual causation is backward-looking.

3 Counterfactuals Following Lewis (1973), there have been many attempts to analyse actual causation in terms of counterfactuals. Let c and e be distinct particular events that both occur.7 We say that e counterfactually depends upon c just in case: if c hadn’t occurred, e wouldn’t have occurred. Lewis (1973) took counterfactual dependence to be sufficient, but not necessary for causation. The problem, as Lewis already recognized, is that counterfactual dependence can fail in cases of causal pre-emption and overdetermination. Here is a standard example of pre-emption: Billy and Suzy are facing a window with rocks in their hands, ready to throw. Suzy throws her rock at the window, which shatters. Billy does not throw his rock, but he would have thrown it if Suzy had not thrown first. Had Billy thrown his rock, it would have shattered the window.

Suzy’s throw causes the window to shatter, but the latter event does not counterfactually depend upon the former: if Suzy hadn’t thrown, Billy would have thrown, and the window would have shattered anyway. The history of counterfactual theories of causation since 1973 has, to a large extent, been the history of attempts to overcome the problem posed by pre-emption and overdetermination.

4 Structural Equation Models Following the influential work of Pearl (2009), it has become common to represent the patterns of counterfactual dependence in this sort of case using structural equation models (SEMs). I will not attempt a general introduction to SEMs here— see Chapters 8, 9, and 10 in this volume respectively by Cartwright, Menzies, and Blanchard and Schaffer for three excellent expositions. Instead, I will illustrate their use by providing a SEM for the pre-emption example just given. We represent the occurrence and non-occurrence of events in the story by variables. Let SR be a variable representing Suzy’s readiness: SR = 1 if Suzy is ready to throw, SR = 0 if she is not. Similarly, BR = 1 if Billy is ready to throw, and BR = 0 if not. Analogously, ST = 1 if Suzy throws her rock, ST = 0 if not; BT = 1 if Billy throws, BT = 0 if not. Finally, WS = 1 if the window shatters, WS = 0 if not. Next, we specify the values of 7

See Lewis 1986a for detailed discussion of what makes events ‘distinct’ in the relevant sense.

CHRISTOPHER HITCHCOCK

SR



ST WS

BR

BT

Figure 7.1 Billy and Suzy throw rocks at a window

the two exogenous variables, SR and BR, and use equations to represent the counterfactual dependence of the other variables on their immediate predecessors: SR = 1 BR = 1 ST = SR BT = BR  (1 – ST) WS = max(ST, BT) The fourth equation, for example, tells us that Billy would throw just in case he is ready, and Suzy doesn’t throw. The fifth equation tells us that the window will shatter just in case either Suzy or Billy throws. If we solve for the equations, we get the result that Suzy throws, Billy doesn’t throw, and the Window shatters. We can represent the qualitative structure of this SEM (but not the specific functions that figure in the equations, nor the values of the variables) using a directed acyclic graph. This is shown in Figure 7.1. We represent a counterfactual by replacing one or more equations with new equations stipulating the values of the variables given in the antecedent of the counterfactual. For instance, suppose we wish to consider the hypothetical case in which Suzy does not throw. Then we replace the third equation with a new equation that specifies that ST = 0. The idea is that we are to imagine that Suzy’s throw no longer depends upon her readiness in the way specified by the equation ST = SR. Instead, an exogenous intervention (Woodward 2003) or a miracle (Lewis 1979) prevents Suzy from throwing, regardless of the value of SR. When we make this substitution, we get the result that Suzy is still ready, she doesn’t throw (as specified in the antecedent of the counterfactual), Billy throws, and the window shatters. Thus, for example, the counterfactual ‘if Suzy hadn’t thrown, the window still would have shattered’ comes out true. Note that counterfactuals do not backtrack in the sense of Lewis (1979). For instance, the counterfactual ‘If Suzy hadn't thrown, she wouldn’t have been ready’ comes out false. Note that the values of the variables in this SEM represent particular events. For example, ST = 1 represents Suzy’s throwing a particular rock at a particular time and place. With this interpretation, the equations represent patterns of counterfactual dependence among particular events. The equations do not express generalizations, such as ‘throwing rocks causes windows to break’ (although one could in principle represent such a generalization with a similar-looking equation). The structure that is represented is also causal: it shows how the value of each variable depends upon its



ACTUAL CAUSATION : WHAT ’ S THE USE ?

immediate causes. But even though the SEM, interpreted in this way, represents a structure that is both causal and singular, one cannot simply read off information about actual causation from the SEM. This is one of the reasons why I claim that singularity, by itself, is not the distinguishing feature of actual causation.

5 Path-specific Effects Most recent accounts of actual causation can be interpreted as identifying actual causation with certain kinds of path-specific effects. Indeed, this idea is already present in nascent form in Lewis 1973, when he identifies causation with chains of counterfactual dependence, and in Lewis 1986b when he formulates a new account in terms of ‘quasi-dependence’.8 The idea is more explicit in Hitchcock 2001, Woodward 2003, and Halpern and Pearl 2005, among others. Pearl (2001) provides a detailed account of path-specific effects. I will again illustrate the idea with our running example of Suzy and Billy. In Figure 7.1, we can see that that there are two directed paths connecting the variable ST to WS: one direct, and one mediated by BT. This indicates that Suzy influences the shattering of the window in two distinct ways. She influences it directly, by sending a rock in the direction of the window. But she also influences it indirectly, by influencing Billy’s action. These two causal pathways cancel one another out, so that Suzy’s throw makes no difference for whether the window shatters. As we hypothetically change whether Suzy throws, we can imagine ourselves ‘wiggling’ the variable ST. We can then imagine this wiggle creating waves (like snapping one end of a rope that is attached to a wall) that are transmitted along the two pathways. When these waves arrive at WS, they have opposite phases, and cancel one another out. However, we can isolate the influence of Suzy’s throw along just one of these pathways. We can ‘clamp’ the indirect path at BT, and prevent the wave travelling any further along that path. This corresponds to assessing the counterfactual ‘if Suzy had not thrown her rock...’ while also holding fixed that Billy does not throw. That is, instead of imagining just one intervention or miracle, we imagine two: one to prevent Suzy from throwing her rock, and a second to prevent Billy from throwing his rock. To evaluate this new counterfactual, we replace the equations ST = SR and BT = BR  (1 – ST) with ST = 0 and BT = 0. The result is that in this new counterfactual scenario, the window doesn’t shatter. Hence, the window’s shattering does depend upon Suzy’s throw when we hold fixed that Billy doesn’t throw. In the terminology of Hitchcock (2001), the direct path from ST to WS is active; there is a path-specific effect of changing ST from 1 to 0. (In some accounts, such as Menzies (2004, 2007) and Hall (2007), the ‘clamping’ is done indirectly. Instead of setting 8 Although see Hitchcock 2001, section VIII, for discussion of how Lewis’s chain of counterfactual dependence differs from path-specific dependence. Maslen (2004) proposes a modification to Lewis’s chain definition that would yield a definition very close to that of Pearl (2001).

CHRISTOPHER HITCHCOCK



BT to 0, we set the exogenous variable BR to 0, which then has the effect of fixing BT at 0. While I think there are subtle and important differences here, I will ignore them in this chapter.) This is just a start, but it is enough to begin to flesh out in a bit more detail the sense in which actual causation is backward-looking. Suppose one were to witness the events in the story play out. As it happens, Billy does not in fact throw his rock. We tend to think of events in the past as fixed, so it is not unnatural to fix the fact that Billy does not throw while engaging in counterfactual reasoning. That is, we see Suzy throw, her rock fly towards the window, and the window break. We focus on this series of events, and ask how these events might have unfolded if Suzy hadn’t thrown. Those events that are not explicitly considered are implicitly assumed to be fixed. Thus we reason: ‘If Suzy hadn’t thrown, her rock would not have sailed towards the window, and it would not have shattered,’ Billy’s failure to throw taken as fixed.9 By contrast it would be very unnatural to fix Billy’s action when thinking about the various possibilities before they unfold. I will say a bit more about the unnaturalness of this reasoning shortly. Although this may seem unnatural, this kind of after-the-fact path-specific counterfactual reasoning is actually easier than ordinary counterfactual reasoning. Suppose again that one witnesses the events in the story unfold. In hindsight, Billy’s rock did not come near the window, nor did any other large objects. Holding these facts fixed, it is straightforward to infer that the window would not have broken without Suzy’s throw.10 To determine that Suzy’s throw was the actual cause of the shattering, and that her throw had a path-specific effect on the shattering, we do not need to know whether Billy would have thrown if Suzy hadn’t, whether his throw would have been on target, whether he would have thrown hard enough to shatter the window, and so on. By contrast, to assess the simple counterfactual ‘if Suzy hadn’t thrown, the window wouldn’t have shattered’, we would need to know all of these things.11 Much more needs to be said, however, before we have a fully fleshed-out theory of actual causation. We need to know specifically what kinds of path-specific effects correspond to relations of actual causation. In particular, we need to know which ways of fixing the values of ‘off-path’ variables are to be allowed. This has proven to be extremely difficult. One recent trend, started by Menzies (2004) and developed in different ways by Hall (2007), Hitchcock (2007), Menzies (2007, this volume Chapter 9), Halpern (2008), Hitchcock and Knobe (2009), and Halpern and Hitchcock (2015), is to appeal to considerations of normality or of the default behaviour of systems to restrict the ways in which the off-path variables can be fixed.12 9

See also the discussion in section 8 of Hitchcock 2013. Maudlin (2004) makes a similar point, although he develops the idea in a very different sort of theoretical framework. 11 Thanks to Michael Strevens for helpful discussion of the issues raised in this paragraph. 12 For criticism of this strategy, see the contribution to the present volume by Blanchard and Schaffer (Chapter 10). 10



ACTUAL CAUSATION : WHAT ’ S THE USE ?

I will not attempt to answer this question directly here, but rather I will approach it somewhat obliquely. Instead I wish to ask: What could be the practical value of having the kind of information about path-specific effects that is provided by claims of actual causation? Once we have a clearer picture of the role of actual causation in our conceptual economy, we may be better placed to develop a normative theory of actual causation.

6 The Agency Theory According to agency, manipulationist, or interventionist accounts of causation, causes are like handles that are used to manipulate the world. An early version of this approach was suggested by Ramsey (1978). Menzies and Price (1993) is one influential development of the approach. More recently, Woodward (2003) has provided a detailed and systematic version of this view. In Woodward’s formulation, causal relations are distinctive in being invariant under interventions. Interventions exert a specific kind of exogenous, independent causal influence on the value of a variable. Interventions are not defined in terms of human agency, but free human actions often are interventions in the relevant sense. Woodward argues that the interventionist approach is implicit in many areas of science, especially in the social sciences, and in fields with a policy orientation such as epidemiology. An interventionist perspective also underlies recent approaches to causal inference and causal discovery, such as Spirtes et al. (2000) and Pearl (2009). I am not here concerned with whether the interventionist approach to causation can provide an analysis of causation. But I do think that this approach is successful in articulating what is distinctive about causal relationships, and in telling us why causal knowledge is to be valued. For example, it is a platitude that ‘correlation is not causation’. There may be a correlation between having yellow teeth and having heart disease, but we do not think that yellow teeth cause heart disease; rather, the correlation exists because smokers tend to have both conditions. But why do we have and care about a concept that differs from correlation in this way? If we are only concerned with prediction, we could make do with just correlations. Observing that someone has yellow teeth, we could predict that he is more likely to suffer from heart disease. However, if we wish to intervene in the world to reduce heart disease, knowledge of correlations will not suffice. Suppose, for example, that we implement a large-scale campaign to whiten people’s teeth; such a campaign would not be successful in reducing heart disease. The reason is that in implementing such a campaign, we would be overriding the existing causal structure that gave rise to the correlation in the first place. Once our campaign is sufficiently widespread, smokers will no longer be more likely to have yellow teeth, and the correlation between yellow teeth and heart disease will disappear. In attempting to exploit the correlation, we would destroy it. However, the correlation between smoking and heart disease would not be disrupted by an intervention to reduce smoking (assuming that it has the

CHRISTOPHER HITCHCOCK



genuine properties of an intervention, in the technical sense elaborated by Woodward (2003)). As Cartwright (1979) aptly puts it, reducing smoking is an effective strategy for reducing heart disease. This is not to say that it is always possible to intervene on causes to produce desired effects. The needed interventions may be impossible for practical, technological, or even physical reasons. The idea is rather that causation is the type of dependency relationship in the world that is capable of supporting effective strategies, and this is the primary reason why we value causal knowledge. Once we have identified this kind of relationship, we may find it, or close analogues of it, even in situations where intervention is not possible.13 Where does actual causation fit in this picture? If causes are handles in the world, then actual causes are presumably handles of a specific kind. What kind of handles are they? What is the value of the distinctive kind of causal information that is conveyed by claims of actual causation such as 1–3 above?

7 Causal Decision Theory In order to flesh out this question, I will detour through causal decision theory (CDT). CDT seems to be built on the central idea behind interventionist theories of causation: causes are means to achieve desired ends. CDT advises us to deliberate about which actions to choose by considering what our actions might cause. I will not provide a formal exposition of CDT here.14 I will only point out that CDT is often formulated in terms of counterfactuals or subjunctive conditionals (see e.g. Gibbard and Harper (1978), Joyce (1999)). Thus if Suzy is deliberating about whether to throw her rock, she must entertain the hypotheticals: ‘If I were to throw the rock...’ and ‘If I were to refrain from throwing...’. She must evaluate the probability of various outcomes under each hypothetical, and calculate the expected payoff from each hypothetical action. Suppose, for example, that Suzy fully understands the causal structure of her situation, including that Billy will throw if she doesn’t, that his rock would shatter the window if he throws, and so on. Suppose, moreover, that all she cares about is whether the window is broken: she wants the window to be broken, but doesn’t care intrinsically about whether she throws or Billy throws. Then CDT would counsel her to reason as follows: ‘If I were to throw, the window would shatter. If I were to refrain, Billy would throw and the window would shatter. Both outcomes are equally good, so I should be indifferent between throwing and refraining.’ This reasoning seems entirely cogent in the situation described. 13

Readers may notice similarities to the proposal of Menzies (1996) to understand causation in the manner of the ‘Canberra plan’. According to that approach, we first articulate a set of platitudes about a concept such as causation, and then identify the natural property or relation in the world that typically (but perhaps not always) satisfies those platitudes. 14 See Hitchcock 2013 for a more formal development of the ideas in this paragraph and the next.



ACTUAL CAUSATION : WHAT ’ S THE USE ?

Note that in her reasoning, Suzy need only consider how various outcomes counterfactually depend upon her action. In cases of pre-emption, actual causation and counterfactual dependence can come apart. Considerations of actual causation, as distinct from counterfactual dependence, do not enter into Suzy’s reasoning. If she were to throw, her throw would be an actual cause of the window’s shattering (despite the lack of counterfactual dependence), but this piece of causal information does not figure in her deliberations. Nor does Suzy need to entertain the counterfactual that is involved in the path-specific effect of her throw: ‘If I were to refrain from throwing, and Billy were also to refrain...’ It makes little sense for her to hold fixed that Billy does not throw while reasoning about her own actions. Billy’s throw is just the kind of thing that depends on her action. CDT is forward-looking. It involves consideration of one’s possible actions, and then reasoning about the downstream effects of those actions. Actual causation, I have suggested, is backward-looking. So what use is it in guiding our interventions in the world?

8 Goal-directed Reasoning My suggestion is that claims of actual causation describe the sorts of path-specific effects that play a role in a different kind of reasoning problem. Suppose that one has a specific goal in mind, and must plan a sequence of interventions in order to reach that goal. For instance, suppose that I want to achieve goal G0 at time t0. I might reason backward from this goal, and conclude that at time t–1 I must perform an action that realizes A–1. Reasoning backward further still, I think about what I must do at time t–2. In doing so, I have to think about how my action at t–2 will work in combination with the action I intend to perform later at t–1. For instance, I must ask: ‘Given that I am going to realize A–1 at t–1, what would happen if I were to realize A–2 now?’ In reasoning this way, I am reasoning about the path-specific effect of my action A–2 on my goal G0. This reasoning differs from the reasoning process I would use if my only choice were whether to perform action A–2. It may be that performing A–2 would prevent A–1, an event that is conducive to G0. In this case, performing action A–2 might frustrate me in my attempt to realize G0. However, if I can also intervene to realize A–1, it may turn out that A–2 will be conducive towards G0. For example, suppose that I want the window to remain intact. If my only option is to intervene on Suzy, my goal will be thwarted. If I prevent Suzy from throwing, Billy will throw and the window will shatter. However, if I can intervene on both Billy and Suzy, I can succeed. In order to arrive at the right combination of interventions, I need to know how Suzy’s action will work in combination with Billy’s action. That is, I need to know that preventing Suzy from throwing will prevent the window from shattering, if I also intervene to prevent Billy from throwing.

CHRISTOPHER HITCHCOCK



9 Illustration: Bicycle Helmet Laws Here is another illustration—oversimplified,15 but still giving a flavour of real-world complexity. Suppose that members of a city council want to make their city more bicycle-friendly. Their goal is to encourage cycling, but also to make cycling as safe as possible. They are considering a number of steps, including adding bicycle lanes, educating the public about bicycle safety, advertising the benefits of cycling instead of driving, and so on. One of the actions they are considering is passing a law that would make it mandatory to wear a helmet while cycling. Their goal in passing such a law would be to reduce the incidence of head trauma suffered in traffic accidents involving bicycles. But of course they wish to do this without decreasing the overall number of cyclists, and without increasing the number of accidents. Figure 7.2 represents the causal structure facing a typical cyclist (or potential cyclist). If the helmet law is passed, the individual may simply choose not to ride a bicycle at all, rather than ride with a helmet.16 Alternately, she may ignore the law and ride without a helmet. Both decisions will be potentially influenced by the

Cost

Wear Helmet

Convenience

Fashion

Helmet Law

Head Trauma Ride

Accident

Bicycle Lanes

Education

Figure 7.2 The effect of a bicycle helmet law

15 In particular, my discussion will ignore inter-unit causation and feedback. As an example of inter-unit causation, the safety of a given cyclist may depend, in part, upon how many other cyclists are on the road. A group of cyclists may be more visible to a motorist than a single cyclist, or perhaps the prevalence of cyclists will influence how attentive drivers are to the possibility of cyclists riding near them. See, e.g., Robinson (2005) for a discussion of the ‘safety in numbers’ phenomenon. (I first learned about this phenomenon from Livengood (2011).) As an example of feedback, an increase or decrease in the number of cycling accidents may influence people’s later decisions about whether to ride a bicycle. (Thanks to Alan Dorin for pointing this out.) Both factors substantially complicate the causal story. 16 Carpenter and Stehr (2011) found substantial declines in ridership among people aged 16–30 in US states that adopted mandatory helmet laws.



ACTUAL CAUSATION : WHAT ’ S THE USE ?

passage of the law, but they will also be influenced by a variety of other factors. For example, these decisions may be affected by the cost of bicycle helmets, by their convenience (e.g. whether there is a convenient place to store the helmet at work), and by considerations of fashion (e.g. whether helmets are perceived as unattractive). The choice to ride a bicycle will affect the likelihood of being in an accident (or at least an accident of a particular kind). Wearing a bicycle helmet may also influence the likelihood of being in an accident, perhaps by interfering with vision or hearing, by encouraging riskier cycling behaviour,17 or by encouraging drivers to leave less space when passing.18,19 Whether one suffers head trauma will depend both on whether one is in an accident, and on whether one wears a helmet. The causal structure depicted in Figure 7.2 is schematic in a variety of ways. Most of the variables will not be simple binary (yes/no) variables. For example, there are many forms a helmet law could take, different levels of punishment for noncompliance, and so on. Similarly, it is not sufficient to buy a bicycle helmet and put it on one’s head. A helmet may do little to protect the head if it is the wrong size, or if it is not properly strapped in place. Accidents vary considerably in type and severity, and some kinds of accident will make head injuries more likely than others. So the individual variables cover a wide range of possibilities. The causal influences represented by the arrows in the diagram may not be present in every individual. For example, ‘safe Sally’ is a very safety-conscious rider: she would wear a bicycle helmet with or without the law. Or perhaps it is more accurate to say that the causal influence would only be present under very specific conditions. For example, there may be a narrow price range—between $900 and $1000—such that if helmets were that expensive, she would wear a helmet only if it is required by law. Some of the relationships between variables may be probabilistic rather than deterministic. All of the relationships will depend upon the values of variables that are not represented in Figure 7.2. And so on. Nonetheless, Figure 7.2 includes a substantial amount of causal information that may help guide the members of the city council in their decision-making. In particular, it shows that the proposed helmet law has the potential to influence the occurrence of head trauma in multiple ways. Specifically, Figure 7.2 shows five distinct causal paths from the helmet law to head trauma (marked by thick arrows): hHelmet Law, Wear Helmet, Head Traumai, hHelmet Law, Wear Helmet, Accident, Head Traumai, hHelmet Law, Ride, Wear Helmet, Head Traumai, hHelmet Law, Ride, Wear Helmet, Accident, Head Traumai, and hHelmet Law, Ride, Accident, Head Traumai. The path-specific effect of passing the helmet law on head trauma along the first path will be a tendency to prevent head trauma. The path-specific effect

17

See, e.g. Phillips, Fyhri, and Sagberg 2011. As found by Walker (2007). By contrast, wearing a long blond wig encouraged drivers to keep a safer distance. Thanks to Thomas Richardson for pointing me to Walker’s study. 19 Another mechanism is the ‘safety in numbers’ phenomenon mentioned in note 15 above. 18

CHRISTOPHER HITCHCOCK



along the last path will also be a tendency to prevent head trauma, but in an undesirable way: by discouraging bicycle riding (and similarly for the fourth path). The path-specific effect along the second path will be a tendency to cause head trauma (and similarly for the third path).20 If the members of the city council were to pass the helmet law, and do nothing else, it is hard to predict what effect this might have on the incidence of head trauma. It will depend upon the strength of the causal influence along each of these five paths, and upon how the different paths interact with one another. However, the members of the city council do not have to just pass the helmet law and let the chips fall where they may. Instead, they may plan further interventions to prevent the undesired consequences of the helmet law. Specifically, they can intervene separately to boost ridership, and to decrease accidents. For example, they can offer rebates on the purchase of helmets; or perhaps they could offer free advertising on city buses and park benches to bicycle shops that offer discounts on helmet prices. The city council could try to improve the fashion image of bicycle helmets by running an advertising campaign featuring local celebrities looking chic in their helmets. By installing bicycle lanes, they can make cycling safer and more attractive. They can educate drivers about the importance of leaving adequate space between their cars and bicycles when they pass. And so on. In the ideal case, the city council will be able to adopt policies that will ‘clamp’ Ride and Accident at desired levels. This will have the effect of isolating the influence of the helmet law on head trauma to a single path: hHelmet Law, Wear Helmet, Head Traumai. This path-specific effect, unlike the others, is crucial to realizing their goals. If this path-specific effect is not present—either because the helmet law will not persuade people to wear helmets when they ride (despite rebates, advertising campaigns, and so on), or because helmets provide no protection against head trauma in accidents—then passing the helmet law would be pointless. This path-specific effect, unlike the others, is crucial for the realization of their goal. So here is a practical reasoning problem where knowledge about a particular pathspecific effect is essential. The problem has two important features: First, there is a goal. In this case, the goal is complex; it is not merely to reduce head trauma, but also to reduce accidents and to increase ridership. Second, there are opportunities for multiple interventions. The members of the city council can pass a law mandating the use of helmets, but they can also take other steps to mitigate the undesired consequences of this law. Let us call a sequence of such steps a strategy.

20 Observant readers will notice that it is not possible to isolate all of these paths by fixing the values of variables shown in Figure 7.2. For example, you can’t isolate the path-specific effect along the path hHelmet Law, Ride, Wear Helmet, Accident, Head Traumai by holding fixed variables that are off this path. Doing so yields the net effect of Helmet Law on Head Trauma along all of the paths together. To isolate the pathspecific effect along this path (and some of the others), we must either interpolate further variables, or adopt the alternate definition of path-specific effects presented in Pearl 2001.



ACTUAL CAUSATION : WHAT ’ S THE USE ?

What more can be said about the kinds of path-specific effects that underwrite goal-directed strategies? They must be path-specific effects that operate in combination with further interventions that might reasonably be made. This means those further interventions must be feasible, expected, and desirable. They might be intrinsically desirable, desirable because they are conducive to the same goal, or because they are conducive to some other goal. In our example involving bicycle helmets, the further interventions are to increase ridership, and to decrease the frequency of accidents. It is desirable to increase bicycle ridership, since riding a bicycle is a good form of exercise; riding a bicycle instead of driving a car can prevent obesity, heart disease, and otherwise promote health. Decreasing the number of cars on the road will also reduce air pollution, which also promotes the health of the city’s residents. Decreasing the number of accidents contributes to decreasing the number of head injuries (the goal of the helmet law), and also to decreasing the number of injuries in general. Thus all of the interventions in this example are aimed at the same general goal: promoting the physical health of the city’s residents. These criteria for further interventions—that they be feasible, expected, and desirable—are to a certain extent vague and subjective. They are relative to the aims and interests of agents. They may also pull in different directions; for example, it may be that the optimal intervention is less feasible than another sub-optimal intervention. In our example involving bicycle helmets, it would obviously be optimal to intervene to prevent all accidents. But this is not realistic. So long as the number of accidents involving cyclists is small compared to the public health benefits—reduced rates of obesity, reductions in heart disease, etc.—the outcome is desirable.

10 Actual Causation (Again) My conjecture is that claims of actual causation identify the kinds of path-specific effects that can be exploited in this kind of goal-directed strategy. For example, suppose that prior to the helmet law, Suzy did not wear a bicycle helmet. After the law was passed, Suzy wore a helmet while riding. One day while riding, she was clipped by a car, fell off her bicycle, and hit her head. Fortunately, she did not suffer any serious harm. Then, I think we would be inclined to say that the helmet law was an actual cause of her suffering only minor injuries. In section 6 I presented a weak version of the agency theory of causation. The proposal there was that causal relations are the kinds of relations that can support effective interventions. A relation of this kind can be present in particular cases when intervention is not possible. This is not intended as an analysis of causation, but as an explanation of our interest in causation. Similarly, my proposal here is that relations of actual causation involve the kinds of path-specific effects that can support goaldirected strategies. This kind of path-specific effect can be present in particular cases where it would not be feasible or desirable or even possible to implement the strategy in question. This is not intended as an analysis of actual causation, but as an explanation of our interest in actual causation.

CHRISTOPHER HITCHCOCK



This account makes sense of a number of features of actual causation. First, it explains why actual causation involves path-specific effects. Second, it makes sense of why relations of actual causation depend in part on considerations of normality. As developed by Hitchcock and Knobe (2009) and Halpern and Hitchcock (2015), this notion of normality is deliberately ambiguous. It involves statistical normality, frequency and expectancy; compliance with moral norms, laws, rules, and policies; and compliance with norms of proper functioning. This makes sense if a central function of identifying actual causes is to identify interventions that will work in combination with other interventions that are feasible, expected, and desirable. These interventions are the kinds that serve to make a system more normal, in the relevant senses. Third, this account explains why the relation of actual causation is central to considerations of legal and moral responsibility. Assignments of moral and legal responsibility are directed, in part, towards the goal of regulating behaviour. In particular, they aim to encourage behaviours that will allow people to work together in a functioning society. It makes sense to encourage individual behaviours that will be conducive towards this goal when they are combined with other behaviours that we hope to encourage. For instance, suppose Suzy drives through an intersection while the light is green, and collides with Billy, who is running a red light. While the accident could have been avoided by either one of them stopping before the intersection, it is Billy’s behaviour that we hope to discourage, for it is his behaviour that will be disruptive when other drivers are obeying the rules of the road.

11 A Warning This account of the role of actual causation also underscores a familiar warning. We noted in section 5 that with hindsight, it is often easier to identify actual causes than it is to evaluate counterfactuals. For example, after seeing Suzy throw her rock through the window, we can judge that her throw was an actual cause of the window shattering. We don’t need to know whether Billy would have thrown if Suzy hadn’t, whether his throw would have hit the window, how hard he would have thrown, etc. Similarly, when Suzy’s bicycle is clipped by a car and she hits her head, we can judge that her wearing a helmet was an actual cause of her only suffering minor injuries. We don’t need to know whether the car would have given her a wider berth if she weren’t wearing a helmet, whether she would have been riding at a slower speed, whether either of these conditions would have prevented the accident, etc. But the ease with which we can identify actual causes is a double-edged sword. Knowledge of such path-specific effects can be useful, because path-specific effects can form part of an effective goal-directed strategy. But one part of an effective strategy may not be an effective strategy without the other parts; indeed, it may achieve the opposite of the desired effect. If we mandate wearing bicycle helmets and make no



ACTUAL CAUSATION : WHAT ’ S THE USE ?

other interventions, we may find that we increase the frequency of head injuries. Our actions can have unintended consequences.21

References Anderson v. Minneapolis, St. Paul & Sault St. Marie Railroad Company, 179 MW 45 (Minnesota 1920). Carpenter, C., and M. Stehr. 2011. ‘Intended and Unintended Consequences of Youth Bicycle Helmet Laws’, Journal of Law and Economics, 54: 305–24. Cartwright, N. 1979. ‘Causal Laws and Effective Strategies’, Noûs, 13: 419–37. Cartwright, N. 1989. Nature’s Capacities and Their Measurement. Oxford: Oxford University Press. Collins, J., Hall, N., and Paul, L. A. (eds). 2004. Causation and Counterfactuals. Cambridge, MA: MIT Press. Eells, E. 1991. Probabilistic Causality. Cambridge: Cambridge University Press. Ehring, D. 2009. ‘Causal Relata’, in The Oxford Handbook of Causation, ed. H. Beebee, C. Hitchcock, and P. Menzies. Oxford: Oxford University Press, 387–413. Gibbard, A., and Harper, W. 1978. ‘Counterfactuals and Two Kinds of Expected Utility’, in Foundations and Applications of Decision Theory, ed. C. Hooker, J. Leach, and E. McClennen. Dordrecht: Reidel, 125–62. Hall, N. 2007. ‘Structural Equations and Causation’, Philosophical Studies, 132: 109–36. Halpern, J. 2008. ‘Defaults and Normality in Causal Structures’, in Principles of Knowledge Representation and Reasoning: Proceedings Eleventh International Conference, ed. G. Brewka and J. Lang. Menlo Park, CA: AAAI Press, 198–208. Halpern, J., and Hitchcock, C. 2015. ‘Graded Causation and Defaults’, British Journal for the Philosophy of Science, 66: 413–57. Halpern, J., and Pearl, J. 2005. ‘Causes and Explanations: A Structural-model Approach— Part I: Causes’, British Journal for the Philosophy of Science, 56: 843–87. Hitchcock, C. 2001. ‘The Intransitivity of Causation Revealed in Equations and Graphs’, Journal of Philosophy, 98: 273–99. Hitchcock, C. 2007. ‘Prevention, Preemption, and the Principle of Sufficient Reason’, The Philosophical Review, 116: 495–532. Hitchcock, C. 2013. ‘What is the “Cause” in Causal Decision Theory?’ Erkenntnis, 78 (Issue 1 Supplement): 129–46. Hitchcock, C., and Knobe, J. 2009. ‘Cause and Norm’, Journal of Philosophy, 106: 587–612. Joyce, J. 1999. The Foundations of Causal Decision Theory. Cambridge: Cambridge University Press. Lewis, D. 1973. ‘Causation’, Journal of Philosophy, 70: 556–67. Reprinted in Lewis 1986c: 159–72.

21 For comments and suggestions, thanks go to Frederick Eberhardt, Antti Hyttinen, Huw Price, Hendrik Rommeswinkel; and also to audience members at Monash University; the workshop ‘Causality: Perspectives from Different Disciplines’ in Vals, Switzerland; and the conference ‘New Directions in Causation’ at the Collège de France.

CHRISTOPHER HITCHCOCK



Lewis, D. 1979. ‘Counterfactual Dependence and Time's Arrow’, Noûs, 13: 455–76. Reprinted in Lewis 1986c: 32–52. Lewis, D. 1986a. ‘Events’, in Lewis 1986c: 241–70. Lewis, D. 1986b. ‘Postscripts to “Causation” ’, in Lewis 1986c: 172–213. Lewis, D. 1986c. Philosophical Papers, Volume II. Oxford: Oxford University Press. Lewis, D. 2000. ‘Causation as Influence’, Journal of Philosophy, 97: 182–97. Livengood, J. 2011. ‘Natural and Non-natural Causation’, Unshielded Colliders (blog), http:// www.unshieldedcolliders.net/2011/12/natural-and-non-natural-causation.html. Maslen, C. 2004. ‘Causes, Contrasts, and the Non-transitivity of Causation’, in Collins, Hall, and Paul 2004: 341–58. Maudlin, T. 2004. ‘Causation, Counterfactuals, and the Third Factor’, in Collins, Hall, and Paul 2004: 419–43. Menzies, P. 1996. ‘Probabilistic Causation and the Pre-emption Problem’, Mind, 105: 85–117. Menzies, P. 2004. ‘Causal Models, Token Causation, and Processes’, Philosophy of Science, 71: 820–32. Menzies, P. 2007. ‘Causation in Context’, in Causation, Physics, and the Constitution of Reality, ed. H. Price and R. Corry. Oxford: Oxford University Press, 191–223. Menzies, P., and Price, H. 1993. ‘Causation as a Secondary Quality’, British Journal for the Philosophy of Science, 44: 187–205. Pearl, J. 2001. ‘Direct and Indirect Effects’, in Proceedings of the Seventh Conference on Uncertainty in Artificial Intelligence. San Francisco: Morgan Kauffman, 411–20. Pearl, J. 2009. Causality: Models, Reasoning, and Inference, Second Edition. Cambridge: Cambridge University Press. Phillips, R. O., Fyhri, A., and Sagberg, F. 2011. ‘Risk Compensation and Bicycle Helmets’, Risk Analysis, 31: 1187–95. Ramsey, F. P. 1978. ‘General Propositions and Causality’, in Foundations: Essays in Philosophy, Logic, Mathematics and Economics, ed. D. H. Mellor. London: Routledge, 133–51. Robinson, D. L. 2005. ‘Safety in Numbers in Australia: More Walkers and Bicyclists, Safer Walking and Bicycling’, Health Promotion Journal of Australia, 16: 47–51. Spirtes, P., Glymour, C., and Scheines, R. 2000. Causation, Prediction, and Search, Second Edition. Cambridge, MA: MIT Press. Walker, I. 2007. ‘Drivers Overtaking Bicyclists: Objective Data on the Effects of Riding Position, Helmet Use, Vehicle Type and Apparent Gender’, Accident Analysis and Prevention, 39: 417–25. Woodward, J. 2003. Making Things Happen: A Theory of Causal Explanation. Oxford: Oxford University Press.

8 Can Structural Equations Explain How Mechanisms Explain? Nancy Cartwright

1 What’s in this Chapter Peter Menzies has made a great number of important contributions to studies of causation over his career.1 Not only his specific ideas but his imagination, his approach, his excitement about the work, and his engagement with others and the way they think have had a huge influence in our field and especially on my own work ever since we first thought together about causality when Peter was a graduate student at Stanford. Here I shall discuss one of these contributions, a new one that Peter developed very recently. In ‘The Causal Structure of Mechanisms’ (Menzies 2012), Menzies deploys an interventionist account of causation to tackle the question of what a mechanism is, with special attention to Carl Craver’s theory of mechanisms. Menzies has done so in his usual generous way, not by fitting Craver’s mechanisms into a Menzies version of an intervention or manipulation account, but by following up Craver’s own suggestion to use James Woodward’s invariance-under-intervention account. In his own words, Menzies aims ‘to show how the interventionist approach to causation, especially within a structural equations framework, provides a simple and elegant account of the causal structure of mechanisms’ (2012: 796). In particular Menzies wants to show how mechanisms explain the causal regularities they are supposed to explain. I have for a very long time been an advocate of just the kind of mechanism that Craver advocates,2 along with his sometimes co-authors Peter Machamer and

1 I would like to thank Alex Marcellesi and Gil Hersch for research assistance as well as the Templeton project ‘God’s Order, Man’s Order and the Order of Nature’ and the AHRC project ‘Choices of Evidence: Tacit Philosophical Assumptions in Debates on Evidence-based Practice in Children’s Welfare Services’ for support for research for this chapter. 2 Cf. ‘Where Do Laws of Nature Come From’ (Cartwright 1997), reprinted in Cartwright 1999. Except I have emphasized not the activities of the components, as Machamer, Craver, and Darden do, but rather their causal capacities.

NANCY CARTWRIGHT



Lindley Darden, as well as my colleague Bill Bechtel, and that Menzies is concerned with: ‘a set of entities and activities that are spatially, temporally and causally organized in such a way that they exhibit the phenomenon to be explained’,3 where ‘the aim of mechanistic explanation is...to reveal the mechanism underlying [the phenomenon]’ (Menzies 2012: 796). But I make almost the exact opposite claim to that of Menzies. I distinguish between the underlying structure, the mechanism— which I have called a ‘nomological machine’, and the ‘surface’ phenomena that result when the machine operates. The interventionist approach to causation, especially within a structural equations framework, is not, I shall argue, at all well suited to represent the mechanism; but it can be very well suited to represent the causal regularities that the repeated operation of the machine gives rise to. Menzies concentrates on Carl Craver’s 2007 book Explaining the Brain, since there Craver provides such a fully developed account of the causal structure of mechanisms, and it is the details of the causal structure that Menzies is concerned with. Yet, Menzies thinks, Craver’s account suffers from important omissions. It leaves the central notion of activity unelucidated and does not adequately show how the component entities and their activities are ‘organized so as to exhibit the explanandum phenomenon’. Structural equations that satisfy interventionist criteria can do both jobs in one fell swoop, Menzies argues. I will sketch how he proposes to use interventionist structural equations to do so. Then I will explain why I have had a different view from the one Menzies defends. I shall argue that there is something absolutely essential that is still left out—the very facts about the components and their organization that are responsible for the machine’s capacity to produce the causal regularities we are trying to explain, which can often be well represented in interventionist structural equations. In the end, though, I will admit that there is no fact of the matter. We can refuse my two-tiered account, with its distinction between, on the one hand, an underlying mechanism and its organization, and on the other hand, the surface phenomena, described in structural equations, that the mechanism gives rise to. We can, as Menzies advocates, use structural equations to represent the missing organization, and this can have some advantages, both for inference about the causal relations generated by the mechanism, and for purposes of systematic representation. But this representation is not transparent. If we do use it, the equations themselves do little of 3 Language here can be confusing since there are a handful of expressions in use in the causation literature that get assigned very different meanings by different researchers. I have used the word ‘capacity’ to mark out something like J. S. Mill’s tendencies: a feature has a stable capacity when it makes the ‘same contribution’ to a specific kind of effect across a wide range of arrangements, regardless of what the actual ‘overall’ effect is in those arrangements. I take this to be a central notion in any science that works by the analytic method, which assumes for many kinds of factors that what happens when factors operate in conjunction can be (at least in part) analysed into the separate contributions that each make, which are just what each would produce were it to operate just ‘on its own’. As we see in section 2, Menzies too uses the word ‘capacity’ but his expression picks out what I have always called (local) ‘causal laws’ or ‘causal principles’.



CAN STRUCTURAL EQUATIONS EXPLAIN HOW MECHANISMS EXPLAIN ?

the work of representing the structure of the underlying mechanism; rather the important information gets buried in the description of the quantities that the variables in the equations are supposed to stand for. This strategy can also be dangerous in practice. To estimate these equations, or to confirm them, we have to measure the quantities represented by the variables. It becomes all too easy then to focus on the measurement procedures and to act as if these procedures identify the quantities. But they don’t at all. Those same procedures will measure very different variables when applied in systems with different underlying mechanisms. We don’t have to conceive of the situation in terms of mechanisms and their organization; we can stick with variables and equations. But without knowledge of the facts about organization and what it does that I take to be central to characterizing a mechanism, we don’t know what variables we are talking about. I shall also in the course of discussion endorse G. E. M. Anscombe’s view that ‘cause’ is a highly general notion, what I call a ‘Ballung’ concept. I shall point out that these kinds of notions need to be made more precise if they are to play a proper role in scientific investigation and discourse and I shall defend Menzies’ assumption that the intervention account provides sufficient conditions for picking out causal relations when what counts as a causal relation is precisely specified via a structural equations framework. This will, however, lead me to a minor disagreement with Menzies over the admission of transitivity as one of the characterizing features of a structural equations framework.

2 What is an Activity? As in his previous work with Peter Machamer and Lindley Darden (2000), in Explaining the Brain Craver takes activities to be central to characterizing mechanisms, where, as Menzies quotes, Craver uses ‘the term “activity” as a filler-term for productive behaviours (such as opening), causal interactions (such as attracting), omissions (such as occur in cases of inhibition), preventions (such as blocking), and so on’ (Menzies 2012: 798). Menzies points out that in the 2007 book Craver adopts James Woodward’s interventionist account of causation as an aid to explaining causal relevance, whereas Machamer, Darden, and Craver (2000) ‘endorse Anscombe’s remark that the word “cause” is highly general and only becomes meaningful when filled out by other more specific causal verbs, e.g., scrape, push, carry, eat, burn’ (Menzies 2012: 798). Menzies praises Craver for going beyond these ‘platitudinous remarks’ by adopting an interventionist account. Menzies’ focus will be on causal relations expressed through functionally correct equations, where the effect is to be represented on the left, and only causes of that effect appear on the right. At one stage Menzies uses these equations to discuss a case of singular causation but for the most part the discussion concerns causal regularities, following Machamer, Darden, and Craver’s claim (which he quotes) that the activities of a mechanism are ‘productive of regular changes’ (Menzies 2012: 798,

NANCY CARTWRIGHT



emphasis added). I call equations like this ‘causal principles’ or (local) ‘causal laws’. Menzies (2012: 800) calls them ‘causal capacities’ because, he explains, the kinds of equations in question imply ‘a battery of interventionist counterfactuals’, that is, counterfactuals about what would happen if interventions were to occur on righthand-side variables,4 where, according to Menzies, ‘Roughly speaking, an intervention on a variable X with respect to Y is a hypothetical experimental manipulation of X that is ideal for determining its causal influence on Y’ (2012: 798). The interventionist account then that Menzies subscribes to in this chapter is like that of Judea Pearl and Woodward in demanding invariance under interventions on all righthand-side variables: ‘in order for these equations to capture causal relations correctly they must hold invariantly under interventions, or, in other words, the equations must continue to hold not only when variables on the right-hand side take on values in the normal course of events,5 but also when these variables have their values set by a range of possible interventions’ (2012: 800). An intervention is akin to the miracles that David Lewis uses to determine the truth values of causal counterfactuals—the value of X is changed and only the value of X and the effects this change produces, leaving unchanged the remainder of other causes of Y (except for the downstream effects of changing X) as well as the causal principles at work (excluding the principles that govern the production of X). The main difference from Lewis is that for Woodward6 somehow the change in X must be producible at least in principle by some at least possible happening. Woodward calls his account indifferently both an intervention account and a manipulation account. It is presumably this insistence that there be at a least some possible happening that can change a cause in the right way that earns it the ‘manipulation’ title.7, 8 If there is no possible way to change a factor on its own, then that factor can never be labelled a cause on Woodward’s account, even should it pass other usual tests for causality (for instance, process tracing tests). Perhaps this aspect of Woodward’s view makes it especially attractive for Menzies, who has long stressed the importance of manipulation

4

Interventions, being happenings in the world, affect quantities, not the variables that represent the quantities. But this longer expression is often cumbersome so I will, where little confusion could result, often just speak of variables for short rather than the quantities represented by variables. 5 This mirrors my remark above that the equations are meant always to be functionally correct. 6 Unlike for Pearl or Spirtes, Glymour, and Scheines, who can do with a purely conceptual notion of intervening: in an intervention a new system of causal equations replaces the old, but there is no need for it to be possible to create a system satisfying these equations. They can be seen as a mere calculational device to fix the truth value of counterfactuals and new probability claims. 7 It is unclear whether Woodward means ‘there is something that is a possible happening that changes X in the right way’ or ‘possibly there is some happening that changes X in the right way’; nor is it clear that he would adopt the Barcan formula to move from the latter to the former. For more on the troubles with Woodward’s notion of a possible intervention, see Marcellesi (n.d.). 8 It is also this insistence that makes for the chief difference between Woodward’s and the already long available accounts by Spirtes, Glymour, and Scheines (2001) or by Pearl (2000) (if he is prepared to accept the causal Markov condition, as it seems he wishes to do) or by me (Cartwright 1999, 2007) (that does not suppose the causal Markov condition).



CAN STRUCTURAL EQUATIONS EXPLAIN HOW MECHANISMS EXPLAIN ?

to the concept of causation, though Woodward very much stresses, oppositely to Menzies, that manipulations in the required sense need have nothing to do with anything we conceive of doing. Like Machamer, Darden, and Craver I too have long followed Anscombe’s view that the ordinary concept of ‘cause’ is highly general. It is what, following Otto Neurath, I call a ‘Ballung’ concept. A Ballung concept is a concept with rough, shifting, porous boundaries, a congestion of different ideas and implications that can in various combinations be brought into focus for different purposes and in different contexts. Many of our ordinary concepts of everyday life are just like this. Ballung concepts also can, and often do, play a central role in science and especially in social science. But they cannot do so in their original form. To function properly in a scientific context they need to be made more precise. This will be done in different ways in different scientific sub-disciplines, serving different ends and to fit with the different concepts, methods, assumptions, and standards operating in these disciplines. The more precise scientific concepts that result will in general then be very different from each other and different yet again from the original Ballung concept. I sometimes use the ugly word ‘precisification’ to describe the process by which a Ballung concept is transformed into one fit for science. Sophia Efstathiou (2009) calls this process ‘found science’ on the analogy of found art. Damien Hirst’s shark in formaldehyde is still a shark but it is not the same shark as when it was swimming in the sea. It has been made suitable for an artistic context, to serve specific artistic purposes. In Efstathiou’s words, the found shark has been ‘founded’—given a form appropriate to serve its new purposes—in the artistic context. But the shark now ‘founded’ as art has lost many of its original functionings, including its ability to be founded in other contexts, such as shark soup. So long as causation remains a Ballung concept, it is ill suited to serve scientific purposes. But it can be founded in various ways to make it more suitable—causal pluralism in the flesh. As with the shark—and as Efstathiou argues for other scientific concepts (‘race’ being one leading example), once causation is founded in one of these ways it can no longer carry out all of its original functionings. Importantly, the functions it can perform given one founding will not generally be available given other ways of founding it. That’s where causal pluralism bites. The different foundings are not different ways of measuring or characterizing what remains the same concept. So what can be shown true of causation under one founding cannot be presumed true under another, and empirical methods that work for telling where one obtains do not normally secure a causal relation that has been founded in any other way. In particular they do not license inferences that follow given other foundings. Consider for example the set of relations that provide me with my morning toast,9 relations that, as I argue in Cartwright 2007, have familiar thick descriptions of the

9

Cf. Macaulay (1988: 159).

NANCY CARTWRIGHT



kind that Anscombe refers to: pressing the lever on my toaster lowers the springloaded rack where my bread sits, lowering the rack closes the circuit, closing the circuit switches on the heating element, the temperature rise expands a metal strip,...the movement of the catch trips a lever, the lever releases the toast rack, the rack springs back, loaded with the bread that has been browned by the same heating element that expanded the metal strip. These are all good examples that fairly clearly fall under the everyday Ballung concept of causality. But that is not a sufficiently precise concept for use in science, especially not for precise prediction. For that we must found the concept more precisely and more explicitly. Perhaps, as I describe in Cartwright 2007, we can classify the set of relations involved as causal in the sense prescribed by the axioms for causal Bayes nets, or in the causal structural equations sense that I shall describe, or what in Cartwright 2007 is called ‘Hoover causality’ after the economist and philosopher Kevin Hoover. But we must be careful not to pun. Generally a set of relations that is causal under one characterization will not be causal under another. In Cartwright 2007 I provide one simple illustration where ‘mechanical causation’ and ‘Hoover causation’ give opposite verdicts about one and the same pair of event-types in one and the same machine. One has it that A causes B, the other that B causes A. Of course this problem is not restricted to concepts of causality but is endemic throughout the sciences. Nor am I alone in my concerns. William Wimsatt, for example, makes a similar warning as mine against punning in science: ‘Application of a heuristic to a problem yields a transformation of the problem into a non-equivalent but intuitively related problem. Answers to the transformed problem may not be answers to the original problem’ (2007: 346, emphasis original). To return to mechanisms. Menzies takes the structural equations framework, which I shall explain in section 3, to be the appropriate one for making precise what the causal principles (or in his terminology, the ‘causal capacities’) are that mechanisms give rise to.10 He does so in part because it provides an answer to the question Anscombe, Machamer, Darden, Craver, and I all leave unanswered: ‘what [do] all these activities [like scrape, push, carry, eat, burn] have in common that makes them causal’? (Menzies 2012: 798). My own view is that there is nothing, and that that is not a problem. That’s just what many of our everyday concepts are like: they involve a loosely connected set of ideas, different ones of which can be highlighted on different occasions to play different roles, from assigning moral or legal responsibility to describing reasons for actions to providing advice about how to repair a system or how to avoid a catastrophe. Often they work like J. L. Austin’s ‘trouser words’: they get their sense in a context from what they are meant to rule out

10 Menzies calls these ‘causal capacities’, using the term differently from the usage I have made of that term in discussing mechanisms (see note 2). These are at any rate whatever it is that the causal equations represent.



CAN STRUCTURAL EQUATIONS EXPLAIN HOW MECHANISMS EXPLAIN ?

in that context.11 So I think the attempt by philosophers to find something in common across all these activities is a mistake. In making this attempt we philosophers are ‘bringing more rigour to a subject than it can bear’12 (as we too often do). In particular, the intervention account is stronger and more restrictive than other claims about the centrality of manipulation to the concept of causation that Menzies has developed and defended. Consider for instance his joint paper with Huw Price arguing that causation is a secondary quality like colour (Menzies and Price 1993). What makes a scraping a scraping or a pushing a pushing depends just on how the world is. What makes us label them both causings depends on our engagements with the world, though not, as with colour, via a particular sensory modality, but rather, in the case of causation, via our role as agents and as rational deliberators about how to achieve our goals. We strategize about the world, engaging in means-ends reasoning; the relations we label ‘causal’ are ones we imagine could be used as strategies, or relations that we consider analogous to them with respect to the intrinsic properties that allow them to serve as means to the specified ends. Objects can sometimes be moved by pushing; surfaces cleaned by scraping. Other pushings get called causings by analogy. As Menzies and Price explain, on analogy with why we can claim that various objects that never could be viewed are nevertheless coloured, ‘a pair of events are causally related just in case the situation involving them possesses intrinsic features that either support a means-ends relation between the events as is, or are identical with (or closely similar to) those of another situation involving an analogous pair of means-end related events’ (1993: 197, emphasis original). So Menzies and Price do not require that there be a possible manipulation in every case. In addition it should be noted that the demand that a causal relation that a mechanism affords between X and Y should ‘support a mean-ends relation’ does not require that X appear in causal equations for Y deemed correct under the invariance-under-intervention account. Causal regularities can fail where there are genuine means-ends relations for a variety of reasons. Consider: X might be a means to increase Y but Y doesn’t change because X is also a means to decrease Y in some other way and the two cancel each other. Then X will not appear (non-trivially) in many equations for Y deemed causally correct under the invariance-under-intervention account that Menzies and Craver adopt. Still we do in this case have two means-ends relations between X and Y—and very often we need to know that. For instance, if Y is undesirable and there is a danger that the strength of the ‘decreasing Y’ wing will diminish, knowing that X is a means to increase Y can help us plan to avert the bad effect of X on Y, or at least to prepare for it. Another reason is that requisite supporting factors may be regularly missing so that a means-ends relation that the mechanism affords may never be realized, so no related causal regularity of the kind mechanisms are meant to explain actually

11

Cf. Austin 1962.

12

As my late husband Stuart Hampshire put it.

NANCY CARTWRIGHT



obtains. For instance, I have bought a special flashlight for camping that will produce light by cranking a handle if, but only if, the battery is low. But also, I always check the batteries before setting out, so the handle never gets cranked. Still the fact that cranking is a means to produce light when low battery is added is a critical causal fact to know about this flashlight.13 So when we are talking about criteria for the causal relations that a mechanism affords, very much depends on what kinds of causal facts we have in view. The invariance-under-intervention account is also stronger than another view that Menzies is famous for: that ‘causes’ is a theoretical term that, when correctly used of a pair of events in a situation, picks out a relation in the world intrinsic to those events in that situation but not one definable in non-theoretical terms.14 The relation is rather picked out by a handful of platitudes that are often but not always true of it. One could even then take something like invariance under intervention to express one of these platitudes in cases where the relation could appropriately be represented in an equation of the type to which the invariance-under-intervention account applies. As an aside to my main point here, I should like to note that this view of Menzies has been part of the inspiration for my own claims that ‘causes’ is a Ballung concept; that when used in rigorous contexts, it needs to be specified precisely in a way that inevitably loses some of the features in the ordinary bundle of platitudes associated with it; and that when correctly applied, it refers to real causal relations in the world. I have not however tried to saddle Menzies with this inspiration since we have one big difference here. Menzies usually talks as if there is one intrinsic relation that is picked out whenever the term is applied correctly, whereas I (following Anscombe) think that there are countless different relations that we pick out in this way, which we also refer to with other more concrete, ‘thicker’ descriptions like scrape, burn, push, and eat. Returning to the central point: the invariance-under-intervention account is stronger than either of these two accounts that Menzies himself has defended. In taking it up in his discussion of mechanisms, however, Menzies is following Craver’s lead, since Craver himself suggests that the productive activities of mechanisms may be characterized using this intervention account. Perhaps then Menzies is not favouring intervention over his own previous views but exploring and developing Craver’s idea, by adding on the structural equations framework to show how successful it can be in representing the causal structure of mechanisms. I shall proceed in the same manner. Structural equations may not be appropriate to represent all the different kinds of causal relations afforded by mechanisms, and they may not be appropriate to all mechanisms, but they certainly are appropriate 13 In my terminology, the flashlight has the stable capacity to produce light by cranking even if repeated operation of it never gives rise to a causal regularity exhibiting this capacity. 14 Cf. Menzies 1996.



CAN STRUCTURAL EQUATIONS EXPLAIN HOW MECHANISMS EXPLAIN ?

in a great many cases to represent the causal principles that describe causal regularities that could result from the repeated unimpeded operation of mechanisms of the right sort and that the mechanisms are supposed to explain.15 In that case I also agree with what Menzies takes for granted, that an invariance-under-intervention criterion is appropriate to a causal structural equations framework, at least under some probably widely assumed assumptions about such a framework. That is what I shall explain next.

3 What is a Structural Equations Framework? First, we shall deal with linear equations only. I am fairly certain that the result I shall mention holds for non-linear equations, but I have not seen nor produced a proof. Linearity is not however such a strong constraint since products can be given a linear form by taking logs and also variables can be introduced that represent clusters of non-linear terms, though of course with great loss of information. I shall also deal only with deterministic equations since the understanding of what exactly the invarianceunder-intervention account says about probabilistic equations is unclear.16 Menzies does not describe what a causal structural equations system is but it is clear both from his work and from the account of Woodward that he endorses that it is meant to look like this: x1 c ¼ u x2 c ¼ a21 x1 x3 c ¼ a31 x1 þ a32 x2 ::: P xn c ¼ ani xi : The idea is that the equations in the system are supposed to represent true causal principles that hold for a given kind of situation, with effects on the left-hand side and causes, and only causes, on the right-hand side. The symbol ‘c=’ expresses this asymmetry. There are a number of necessary conditions commonly assumed for equations of this form (linear, deterministic) to represent generic causal truths. The relations between right-hand-side variables (meant to represent causes) and lefthand-side variables (meant to represent their effects) are irreflexive and asymmetric. Third, any equation that is causally correct in a given kind of situation must be functionally true in that situation type. Fourth, the causally correct equations for a 15

What sort is that? The answer is: what I call nomological machines. And what is a nomological machine? I answer to that in what I take to be a reasonable but unenlightening way: a nomological machine is an arrangement of features that have the capacity when operating repeatedly together unimpeded in that arrangement to generate the kind of causal regularity we record in a (local) causal principle, where I put ‘local’ only in parentheses because I hazard that all, or almost all, causal principles are local in this way to the operation of an underlying mechanism with the capacity to generate the regularity referred to in that principle. 16 For one account of what reasonably might be intended see Cartwright 2007, chapter 10.

NANCY CARTWRIGHT



situation are the foundation for all other functionally correct equations that hold in that situation, in the sense that equations that are functionally true but not causally correct are obtainable by linear transformations and substitutions from those that are. This latter is the kind of assumption invoked when we suppose that spurious correlations, as between the fall of the barometer and the storm, must be explained by a common cause, like low pressure (or in some other way by reference to genuine causal principles). So, let x1 = low pressure, x2 = barometer drop, and x3 = storm, and suppose the following causal structural equations system: LP 1Þx2 c ¼ a21 x1 2Þx3 c ¼ a31 x1 Then it follows that, 3Þx3 ¼ ða31 =a21 Þx2 —a ‘spurious’ relation between joint effects of the common cause, low pressure, that is readily derivable from the two properly causal equations. These four are standard everywhere. They are either explicitly stated or implicit in the use to which these systems are put. Though not providing a reductive account of ‘correct causal principle’ together they constrain the notion, just as the intervention account of generic causal claims does. I add in addition an assumption that is widespread in use though is subject to controversy among philosophers, a requirement that I have called ‘transitivity’ of causal principles: an equation that results from substituting the right-hand-side causes of a variable in a causally correct equation for the variable when it appears as a cause in a causally correct equation is itself causally correct. I will discuss this further in section 5. I have fleshed out the account of what a causal structural equations system is a bit more than Menzies but nothing I have said is incompatible with anything he says or uses in his discussion, with the exception of transitivity. Menzies also, following Woodward, adds what they both call a ‘modularity’ assumption as a world-involving requirement on a correct causal equations set. Menzies explains modularity this way: ‘a set of equations is modular if and only if it is possible to intervene on a variable on the left-hand side of an equation without disturbing the other equations in the set, i.e. without rendering the other equations false’ (2012: 800). For a fair test of a causal principle by intervention on its putative causes, it is clear that when those causes change value, other causal principles in the system should not be allowed to vary; otherwise we could be severing causal connections that a cause depended on to produce its change, or putting in connections that weren’t there before that then bring about changes, or altering the functional form of the causal dependence. The modularity assumption does that job. But it is stronger than needed for just that job since it not only requires that what gets



CAN STRUCTURAL EQUATIONS EXPLAIN HOW MECHANISMS EXPLAIN ?

called an intervention leaves the other equations in the system intact. It also requires that such interventions are always possible on any quantity that can get labelled a cause. This is just the requirement I have already made note of in section 2. I myself argue that it is far too strong.17 But that is not relevant to the issues about whether the causal structure of mechanisms should get represented as two-tiered, as I have been urging, or on one plane, as Menzies depicts, so I won’t discuss it further. In what follows I shall not take modularity as a necessary condition on a correct causal equation system. Suppose we adopt, as is common, the four necessary conditions I have laid out for a generic causal claim expressed in a linear deterministic equation to be correct, with or without my fifth sufficient condition of transitivity. This provides an informative characterization that constrains the undefined concept of a correct generic causal claim of this form. We also, though, have the invariance-underintervention account that constrains the concept of a correct generic causal claim. As Menzies reports, ‘Pearl and Woodward espouse the view that in order for these equations to capture causal relations correctly they must hold invariantly under interventions’ (2012: 800).18 But exactly what is the connection between these two different characterizations? For instance, is invariance under intervention an additional requirement? If so, can it always be added consistently to the causal structural equations constraints? Woodward defends application of his invariance-under-intervention account of causation to structural equations by example. For instance, if an intervention of the right sort occurs to x2, which appears on the right-hand side of equation LP 3), equation LP 3) will no longer hold: breaking the barometer will not bring on the storm, whereas an intervention on x1 will leave both equations LP 1) and LP 2) invariant. Menzies provides similar examples to illustrate the invariance-underintervention requirement. But it is not obvious that the two different criteria will always yield the same result for equations of the right form. Examples can illustrate how this works, but not show it. We can do better. It is possible to prove that if all a set of equations satisfy the four necessary conditions for being causally correct (and ‘transitivity’ holds for causal correctness), they also satisfy the invariance-underintervention requirement.19 This shows that the way in which Menzies marries the

17

Cf. Cartwright 2007, chapter 7. Though, as Alex Marcellesi points out (in correspondence, 16 April 2013), it is not clear that Pearl insists that invariance implies causal correctness since he takes the idea of causally correct equations to be given, as the starting point for his analysis, whereas Woodward takes invariance under intervention to be the central informative characterizing feature of causal correctness. But Pearl certainly claims that correctness implies invariance and where invariance seems to be missing, the system must be misspecified. 19 Cf. Cartwright 2007, chapter 10. The reverse is also true if intervention is defined as I think it must be. My proof of these results assumes transitivity because, as I argue in section 5, I suppose that is the right thing to do. Those who do not wish to assume this yet wish to marry a structural equation framework satisfying the four necessary conditions in general use to some other constraints on generic causal relations will need to produce their own proof that the two at least are consistent. 18

NANCY CARTWRIGHT



two in his discussion of mechanisms is entirely justified. Not only are the two sets of constraints consistent—the usual constraints for causally correct structural equations secure the principle of invariance under intervention.

4 How Menzies Uses Structural Equations to Describe Mechanisms What then does Menzies do with this apparatus? He uses it to explain what a causal mechanism is and what are and are not its constituents, and in such a way that the notion of activities is made sense of—via the invariance-under-intervention requirement that ensures that the equations represent causal relations, not mere associations. Menzies supposes that the aim is to use a mechanism to explain what I would call a generic input–output causal relation,20 a relation describing a causal regularity generated by the repeated operation of the mechanism, of form O c= f(I1,..., In). Menzies calls each structural equation a ‘capacity’. As he explains, ‘This terminology is motivated by the fact that a structural equation that is invariant under interventions implies a battery of interventionist counterfactuals’ (2012: 800). Then, ‘any variable that lies on a pathway between the input variable and output variable of the capacity [generic causal relation] to be explained counts as part of the mechanism underlying the capacity [generic causal relation to be explained]’ (2012: 801). So what Menzies calls the causal structure of the mechanism that explains the input–output capacity (generic input–output causal relation) to be explained is a set of modular equations that, first, constitute a causal structural equations system (so, each passes the invariance-under-intervention test) and, second, compose to yield the input–output generic causal relation/capacity to be explained, where composition consists in substitution of the initial causes of later effects everywhere a later effect appears.21 (Note: this is what I have called ‘transitivity’.) So, ‘the causal structure of a mechanism is given by a set of modular subcapacities [generic causal relations] whose sequential exercise has the input–output profile of the capacity [generic causal relation] to be explained’ (2012: 800–1, emphasis original). This last is what solves the problem that Menzies worries about, of how the mechanism is supposed to explain the targeted input–output relation. Craver says that it is not covering law explanation. If not that, then what? Menzies’ answer is that the mechanism is a sequence of causal regularities that are instanced one after another, resulting in the regular causal connection between input and output. That, I take it, is the intended material mode version. In the formal mode, the equations representing this sequence By calling it this I mean to imply that relations of this sort satisfy the five conditions for causally correct generic causal relations described in section 3. I take it from all he says that Menzies’ ‘capacities’ do so as well. 21 So the principle to be explained is what econometricians often call the ‘reduced form’ of the system. Note too that what Menzies calls composition here is just what I call ‘transitivity’ in section 5. 20



CAN STRUCTURAL EQUATIONS EXPLAIN HOW MECHANISMS EXPLAIN ?

of regularities compose via a sequence of substitutions to yield the equation that represents the causal regularity between inputs and outputs. I want to suggest that this system of causal equations that describe activities or capacities that will be exercised sequentially between input and output does not represent mechanisms of the kind Craver and others and I have been concerned with (unless excessive work is done by the characterization of the variables in the equations). It does though represent a mechanism in the sense of the term often used in the medical literature: the step-by-step causal pathway that leads from the input to the output. That is the topic of section 6. But first a diversion on transitivity.

5 Transitivity? I suppose that causal correctness is transitive in the sense that taking the causes of a factor from a causally correct generic equation and substituting them for that factor where it appears in another causally correct equation yields an equation that is also causally correct. Woodward has used this fact to fault the proof that grounds the invariance-under-intervention account in an account that supposes the five conditions for causally correct generic equations that I have described here. He does so on the grounds that causation is not transitive. I want to discuss this briefly for two reasons. First, in defining mechanisms, Menzies also explicitly rejects transitivity. He says, ‘A sequence of causal capacities [generic causal relations] described by structural equations do not by themselves constitute a mechanism’ (2012: 801). Second, the rejection of transitivity would undercut my defence of the way Menzies marries the invariance-under-intervention account with the causal structural equations framework (though perhaps another proof can be provided that does not suppose transitivity). In reply I should like to point out, first, that I don’t see how an advocate of invariance under intervention as a characterizing feature of causation can deny this particular kind of transitivity since it is easy to prove that if the input principles pass the invariance test, so will an output principle that is derived by substitutions of the kind admitted by transitivity. I won’t prove that here but will at least illustrate below with Menzies’ own example. Second, the usual counterexamples—and in particular those cited by both Woodward and Menzies—involve singular causation, whereas the issue here concerns causal regularities. Whatever the case is with the former, exactly what is assumed in characterizing the latter is a matter of what more precise concepts find good uses in those settings where precise concepts matter. Let me illustrate, using Menzies’ example, the familiar case of ‘boulder’: enemy pushes boulder, walker ducks, walker survives. The pushing causes the ducking and ducking causes survival but pushing the boulder does not cause survival, or so intuitions seem to go. This is a case of singular causation, where each step is fixed. Yet Menzies, along with many others, writes it in terms of equations involving variables. His equations look like this:

NANCY CARTWRIGHT



BW 1Þ 2Þ 3Þ 4Þ

P¼1 D¼P S¼ P v D So S ¼ P v  P:

Menzies maintains: ‘But the enemies pushing the boulder does not cause the walker to survive. For whether or not the enemy were to push the boulder, the walker would survive. This is brought out by the fact that when we compose the structural equations, we obtain the result S = P v P, which implies that S gets the value 1 whatever the value of P’ (2012: 801). Menzies’ version of the equations is a mix of Boolean notation and that of mathematical equations stating relations between variables. If we write the same information in pure equation form, we get: BW0 1Þ 2Þ 3Þ 4Þ 5Þ

Dc¼P S c ¼ ðPxDÞ þ ð1  PÞ  ðPxDx½1  PÞ So S c ¼ 1  P þ P3 : P ¼ 0 □➞ S ¼ 1 P ¼ 1 □➞ S ¼ 1:

Notice I have not put in P = 1 because that is not an equation describing regimes of change among variables but rather the setting of a variable to a particular value— presumably the value that variable actually takes on some occasion under consideration. Equations BW0 4) and 5) make clear Menzies’ point though: S = 1 no matter whether P occurs or not. So equation BW0 3 shows that the different values of what is pictured in it as a cause of survival do not make a difference to the value of survival. What’s to notice though is that equation BW0 3) is invariant under interventions on right-hand-side variables. So if invariance under intervention is the mark of a correct causal principle, we had better let it in. Of course we can stiffen the demands on our concept of ‘causally correct generic relation’; we can add a requirement of change. I suppose it would be: If Q is a causally correct equation for effect Y, then for each right-hand-side variable, X, in Q, there are at least two values X and X0 for X and some arrangement of values for the other right-hand-side variables in Q such that Y takes different values when X = X than when X = X0 . Should one add such a requirement? Why? There is no right or wrong about the matter. These constitute two different foundings of the undefined concept ‘causally correct generic relation’ (or for Menzies, ‘capacity’), one more restrictive than the other. There certainly is a use for the weaker way of founding the concept that does not demand that the effect value change with the cause value. Consider: if there are likely to be boulder pushers around, it is very important to know that the



CAN STRUCTURAL EQUATIONS EXPLAIN HOW MECHANISMS EXPLAIN ?

machine we have is designed to ensure the output survival regardless of whether a boulder is pushed or not. It is worth introducing the more restrictive notion if there are different sets of relations to which the stronger applies and sets to which only the weaker applies and we can do something with the information about which is which. What we must not do, however, is to ignore my warning in section 2. We must not test for ‘causes’ in one sense, then draw inferences allowed only by a different sense without solid empirical evidence that the two co-occur in the kinds of cases where we draw the inferences. We must not do science by pun. For purposes of thinking about Menzies’ views on mechanisms, I think we can now set this issue aside. If a demand for change is not added, then invariance under intervention is a sure test that we have equations that satisfy the conditions stated for being causally correct, where transitivity is one of those conditions. If you don’t like transitivity of generic causal relations, you will have to modify both the assumptions I propose about them and add the requirement for change to the invariance-underintervention account, and in a way that ensures the two line up as Menzies desires.

6 Is There More to Mechanisms than Structural Equations Reveal? My answer to this question is ‘Yes’. I have proposed some more serious scientific examples elsewhere, in particular of socio-economic machines to make clear that the machines that generate the kinds of regularities we record in our scientific principles need not be made of material parts. But here I shall illustrate with a more lighthearted example that makes the point very apparent, an example I take from Cartwright and Hardie (2012: 77). You can look there for a picture. When I want to sharpen pencils I don’t crank a handle nor close a circuit on a battery-operated sharpener. I fly a kite. I can do it that way because I have a very special pencil sharpener, designed by Rube Goldberg. We can represent the generic input–output causal relation from my Rube Goldberg machine in the form Menzies suggests: S = K, where S and K are two-valued variables with S = 1 for pencils being sharp and 0 for not sharp, K = 1 for kite flies and K = 0 for not flying. (I shall use twovalued variables throughout for simplicity.) Let me tell you about the causal structure of this mechanism in Menzies’ sense: ‘a set of modular subcapacities [generic causal relations] whose sequential exercise has the input–output profile of the capacity [generic causal relation] to be explained’ (2012: 801). The flying kite pulls open a door (D = 1; closed door, D = 0). The open door allows hungry moths to escape from a cage (M = 1; moths contained in cage, M = 0). The moths eat a flannel shirt (F = 1; shirt does not disappear, F = 0). Reducing the weight of the shirt causes a shoe to step on a switch (SH = 1; shoe not on switch, SH = 0)... and many more steps till eventually a cage with a woodpecker under it lifts (C = 1; cage unlifted, C = 0) and a woodpecker pecks the pencil (W = 1; woodpecker

NANCY CARTWRIGHT



doesn’t peck the pencil, W = 0) resulting in a sharpened pencil. Each of these is a causal regularity that is instanced each time the kite flies and that can get represented in the form of a causal structural equations system of just the kind Menzies recommends. Here then are the set of modular subcapacities (generic causal relations) that exercise sequentially to generate the capacity (generic causal relation) to be explained: RB 1Þ D c ¼ K 2Þ M c ¼ D 3Þ F c ¼ M 4Þ SH c ¼ F ... 11Þ W ¼ C 12Þ S c ¼ W So S c= K, as required. Now we know the step-by-step sequential causal process that results in kite flyings sharpening pencils. But we do not know the structure of the underlying machine that gives rise to this sequence. Suppose you want to build a machine that affords the causal regularity recorded in S = K. There are an indefinite number of designs you could produce. Suppose you had a more ambitious aim: to build a machine that not only generates the input–output regularity S = K but the entire causal structural equations system recorded in RB. There are still an indefinite number of designs you could use. The machine that Rube Goldberg in fact designed is like this: the kite string goes under a lower pulley then up over a higher pulley and is tied onto a door that slides up and down easily, on a fine net cage full of hungry moths; the entire environment is safe for moths; the flannel shirt is attached to a string that runs over a third pulley with a shoe tied on the other end of the string that just balances the flannel shirt before the moths get to it; the shoe hangs immediately above a switch...eventually...a cage is raised from over a hungry woodpecker allowing the woodpecker to reach over to the pencil and peck it sharp. This is the information that is still missing, even once we have recorded the sequence of causal regularities that produce the overall input–output relation. It is the reason that I urge that we conceive of two tiers: the underlying arrangement of parts with their associated features and capacities—‘capacities’ in my sense; and the surface causal principles that are afforded by the underlying structure. Both are causal, in some sense, and both kinds of information are important to know. Both are necessary for a full understanding of how the pencils get sharpened. And both are useful for prediction and for means-ends reasoning.



CAN STRUCTURAL EQUATIONS EXPLAIN HOW MECHANISMS EXPLAIN ?

First consider the surface equations. The other day Lucy was playing games with me and put her finger on the door to keep it closed every time I went out to fly the kite. She knew I would get no sharp pencils then. She knew that because she could read it off from setting M = 0 in RB 2) and following through the downstream effects. One day later in the month the moths were gone from the cage because Lucy had taken them out the night before to see if they really were attracted to candle flames. We knew no sharp pencils that day either, from RB 3). Or on another day I couldn’t get the kite to fly because there was no wind. And anyway I was in a hurry. So, guided by RB 11) and 12) I went straight to the cage over the woodpecker and lifted it. The point is that these all reflect proper capacities in Menzies’ sense (generic causal relations in my terminology), passing the invariance-under-intervention test and thus supporting ‘a battery of interventionist counterfactuals’ (2012: 800) as Menzies wishes. Now consider the underlying structure. One day I flew the kite but the door didn’t open. I had been really cautious against Lucy’s tricks and all other such hazards and had locked the machine up well the night before. So I was sure no external intervention had set any of the variables in RB to 0. I knew the machine must be broken and I would have to look inside to fix it. Indeed, the top pulley had split in half. I knew to check on the pulley because I understood the parts of the machine and how they worked together to afford the generic causal relations I usually could rely on to get sharp pencils. Or, more recently I decided I was bored by this machine and would like another, but one that sharpens faster and more evenly. So I have been busy reviewing how gears work and trying to figure out how to hook a knife blade to a windmill. The point here is that with knowledge of the parts that compose a machine and how they operate, we know what it takes to repair it. And with ingenuity and knowledge of the capacities (in my sense) of lots of different kinds of parts, we can build entirely new machines, hopefully better than the old.

7 Putting It All in One Flat Plane You don’t have to conceive of machines in terms of two-tiers, as I recommend. There are a couple of fixes if you do want to represent them on one flat plane. First you can complicate the causal equations, like those in RB, by adding a new variable that takes value 1 when the machine parts and activities are all in place and working properly and 0 otherwise. Call this variable RB-NM (RB for Rube Goldberg, NM for my term—‘nomological machine’). Then you multiply by RB-NM each cause in each principle in the original surface system of equations. Some machines allow a more detailed breakdown: those that are modular, but in a different sense of ‘modular’ than that of Woodward and Menzies described in section 3. A machine is modular in this alternative sense when input from separate causes depends on separate parts. Then each cause gets multiplied by a yes-no variable representing the proper functioning of the associated part. This is not an efficient

NANCY CARTWRIGHT



design for a machine though since it means there are a lot of parts and the machine may then grow big and unwieldy. But it can have advantages. For instance, it will have advantages when we want to design the machine so that it will be easy to trouble-shoot. Perhaps the parts of the machine are difficult to access, so we want to make it easy to discover which piece is broken based on the surface behaviour of the machine; or when parts are likely to wear out and we do not want too many principles compromised at once, or when we think we may be able to secure one or another broken link with some different part. Apparently this was one of the demands of the MIT World War II radar project because it was expected the radars would have to function in isolated environments and it was important to make repair as likely as possible.22 This fix does not of course do away with the need for exactly the same information required for the two-tiered picture. It just allows us to use a single representational scheme. This is fine so long as we do not suppose that all the variables in the equations have the same status and so can be treated in the same way. For instance, often because of the kinds of underlying machines that generate the surface equations, the surface variables satisfy the conditions for random variables, in particular, there is a probability measure over their values. But generally there isn’t any probability for whether a machine of a specific design will be built or not, in which case RB-NM is not a random variable. So, too, often with the ‘variables’ that would appear in equations from machines with more modular structures. A second fix is to add the information about the parts and activities of the machine into the variables themselves. So, for instance, in the system RB, K would no longer represent the feature ‘Kite flies’ but rather ‘Kite attached to a string that goes under a low pulley and over a high pulley before attaching to the top of a little door flies’. And so forth. This too has problems, especially in practice. For one, as with the first fix, in this case too we can no longer assume that the variables in our new equations will be random variables, even if those in the original surface equations were. Another problem has to do with how we connect our measurement procedures with the variables we measure. Whether a kite is flying is easy to measure. What about measuring whether or not a kite affixed to my Rube Goldberg pencil sharpener is flying? That is a different matter and requires hugely more information, information that we seldom have. Nor do we need it in order to confirm or estimate the surface equations—and recall, we do want to know these surface equations because they show us effective means for achieving our ends. All we need to be sure enough of is that the data we gather is all generated by the same mechanism (in the sense of a nomological machine); and there are a lot of things that can provide good assurance of this far short of having a complete description of the mechanism and checking through each of the details. That’s a danger in one direction: that we may lose power

22

Cf. Galison 1997.



CAN STRUCTURAL EQUATIONS EXPLAIN HOW MECHANISMS EXPLAIN ?

to discover useful principles because we do not know what our procedures measure when these very complex variables are in play. There is also a danger in another direction. Since we can perform the simple operations it takes to tell if a kite is flying and to tell if pencils are being sharpened no matter what mechanisms (nomological machines) are involved, we can lose sight of the importance of the mechanism. This I think happens regularly in evidence-based policy nowadays. There are now a great many agencies, like the US Department of Education’s What Works Clearinghouse, that publicize ‘What works’, from educational to health to criminal justice to international development. How do they decide what works? They look at scientific studies, where they are all keen to ensure that the studies are of the right kind and right standard to establish a genuine generic causal relation (‘capacity’ in Menzies’ terminology). So their basis is composed of studies, like controlled trials, well designed to test claims about generic causal relations/capacities—describing regularities of the surface variety— in one or two or a handful of sites. If a causal relation is established between two surface variables, like kite flying and pencil sharpening, or, more seriously say between hot spot policing and burglary reduction,23 the cause gets recorded under the heading ‘What works’. Then policy makers are advised to consult the relevant clearinghouse and to use only policies listed there under ‘What works’. This seems to suggest that a cause known to have produced a desired outcome in a handful of settings will work in new places unless something special goes wrong, or that the assumption that it will work in a new place is the default assumption. But when, as is typical, the generic causal relations under consideration are surface relations, whether a proposed cause will work in a new place depends on whether the new location has the right underlying structure to support the same causal relations. But no one says that finding a policy in a ‘What works’ list gives you negligible reason to use it if you have no information about the underlying mechanisms (nomological machines) needed to produce the causal relations you’d be relying on. The two-tier picture keeps this firmly in view.

8 The Job Done and the Job to be Done One of Peter Menzies’ aims in offering the structural equations system characterization of a mechanism was to show how the mechanism explains the input–output relations it is supposed to. When a mechanism is conceived, as Menzies urges, as the sequence of causal regularities instanced in between cause and effect, the goal has been achieved: the in-between regularities are expressed in structural equations and they explain the input/output regularity by implying it, via composition.

23

Cf. http://www.hmic.gov.uk/pcc/what-works-in-policing-to-reduce-crime/ (accessed 25 April 2013).

NANCY CARTWRIGHT



But there is still another layer of explanation, I have urged, and another sense of mechanism that does the explaining: mechanisms in the sense of the underlying arrangements that give rise to the entire set of regularities recorded in the causal structural equations system. We still need an account of how the underlying arrangement explains these principles. Nor is this problem an artefact of the two-tier picture; it simply appears in another guise if you look at everything on one flat plane, say by using variables that refer to the machine structure. In that case the causal relations we are considering will be very unfamiliar when written out fully; and there will be innumerably many of them, considering all the mechanisms that might occur in nature and society. Where did these all come from? They certainly won’t look like the kinds of things we are used to thinking that God wrote in the Book of Nature. I do not think we have a good answer. That’s why the question that Menzies has tackled is so pressing. I have offered an answer for some special kinds of cases but my answer is not all that good. I start from my view that many of our basic so-called ‘laws of nature’ are best seen as ascriptions of capacities (in my powers-like sense) to features independently identifiable: like assigning to the feature of having mass M the capacity of strength GMm/r2 to attract other masses. The capacity itself is identified not by what effect results when it activates but by the contribution it makes to the effects that actually occur, where it is supposed that the capacity makes the same contribution across a wide range of circumstances. In some nice cases a mechanism (nomological machine) will consist of parts with features that carry capacities for which there is a rule of composition about what happens when the capacities all contribute together. The well-known example is vector addition, which is how the contributions from various sources of attraction and repulsion combine. I have also described a number of other rules of composition we find in other disciplines for the capacities they study.24 In these cases the how question has an easy answer. A mechanism (nomological machine) explains the resulting causal regularities in that those regularities can be derived from the facts about capacities (in my sense) associated with the features of the mechanism plus a rule of composition. In paradigm cases the capacity claims employed as well as the rule of composition do look like what we have pictured God to write in the Book of Nature, since these will be more familiar ‘laws of nature’, like the law of gravitational attraction, Coulomb’s law of electromagnetic attraction and repulsion, and vector addition; or the laws of simple machines and how they combine. The trouble is that not many of the underlying mechanisms (nomological machines) we find on offer in the natural and social sciences to explain generic causal relations local to those mechanisms can be cast into this simple form. Even if my answer were good enough for these special cases, it just doesn’t go very far. And

24

See Cartwright 1999, chapter 3.



CAN STRUCTURAL EQUATIONS EXPLAIN HOW MECHANISMS EXPLAIN ?

Menzies is right to have underlined the question. I have not seen an answer yet that works. In offering the structural equations framework, Menzies has succeeded in answering the important how question for one sense of mechanistic explanation. But what are we to say about how familiar mechanisms from toasters to socio-economic structures explain generic causal relations, like pressing on the lever will brown the bread or installing CCTV camera will reduce car crime?

References Austin, J. L. 1962. Sense and Sensibilia. Oxford: Oxford University Press. Cartwright, N. 1997. ‘Where Do Laws of Nature Come From?’ Dialectica, 51: 65–78. Cartwright, N. 1999. The Dappled World. Cambridge: Cambridge University Press. Cartwright, N. 2007. Hunting Causes and Using Them. Cambridge: Cambridge University Press. Cartwright, N., and Hardie, J. 2012. Evidence-Based Policy: A Practical Guide to Doing it Better. New York: Oxford University Press. Craver, C. 2007. Explaining the Brain. New York: Oxford University Press. Efstathiou, S. 2009. ‘The Use of “Race” as a Variable in Biomedical Research’, PhD thesis, University of California, San Diego. Galison, P. 1997. Image and Logic. Chicago: University of Chicago Press. Macaulay, D. 1988. The Way Things Work. Boston: Houghton Mifflin. Machamer, P., Darden, L., and Craver, C. 2000. ‘Thinking about Mechanisms’, Philosophy of Science, 67: 1–25. Marcellesi, A. n.d. ‘Interventions, Counterfactuals, and Causation: Some Unfinished Business’, unpublished manuscript. Menzies, P. 1996. ‘Probabilistic Causation and the Pre-emption Problem’, Mind, 105: 85–117. Menzies, P. 2012. ‘The Causal Structure of Mechanisms’, Studies in History and Philosophy of Biological and Biomedical Sciences, 43: 796–805. Menzies, P., and Price, H. 1993. ‘Causation as a Secondary Quality’, British Journal for the Philosophy of Science, 44: 187–203. Pearl, J. 2000. Causality: Models, Reasoning, and Inference. Cambridge: Cambridge University Press. Spirtes, R., Glymour, C., and Scheines, R. 2001. Causation, Prediction, and Search. Cambridge, MA: MIT Press. Wimsatt, W. 2007. Re-Engineering Philosophy for Limited Beings: Piecewise Approximations to Reality. Cambridge, MA: Harvard University Press.

9 The Problem of Counterfactual Isomorphs Peter Menzies

1 Introduction Over the last forty years philosophers have devoted much effort to tracing out the conceptual connections between actual or token causation and counterfactuals.1 The first wave of philosophical interest in this project started with David Lewis’s classic paper (1973), setting out a counterfactual analysis of causation. As the difficulties facing this analysis emerged, Lewis twice amended the analysis in his 1986 and 2000 works, but in ways that preserved the basic counterfactual character of the analysis. His former Princeton students have carried on this work (see Collins, Hall, and Paul 2004; Paul and Hall 2013). The second wave of philosophical interest in counterfactual accounts of causation occurred as philosophers became familiar with the causal modelling tradition, exemplified by the work of Judea Pearl (2000, 2009) and his collaborators (Halpern and Pearl 2005) and made familiar to philosophers by Christopher Hitchcock (2001a, 2001b, 2007a) and James Woodward (2003). This work has done much to instruct philosophers about the insights to be gained about causation from employing the causal modelling apparatus of variables, structural equations, and causal graphs. Both these approaches—Lewis’s approach and the causal modelling approach— make central use of counterfactuals to explicate causation. (The counterfactual content of causal models is conveyed by their structural equations.) There are, however, subtle differences between the kinds of counterfactuals the two approaches employ and, more generally, between their technical apparatuses. Proponents of the causal modelling approach have argued that the representational resources of their framework are richer than those of Lewis’s possible worlds framework (see Glymour et al. 1 I am grateful to informative conversations about the topic of this chapter with Sam Baron, Mark Colyvan, Chris Hitchcock, and Christian List. I am also grateful to Huw Price for his comments on an earlier, very different version of the chapter and to Christopher Hitchcock again for his very helpful comments on an earlier version.



THE PROBLEM OF COUNTERFACTUAL ISOMORPHS

2010; Hitchcock 2007b). Without entering this debate, I simply remark that it will be more convenient for my purposes to frame the discussion of this chapter in terms of the causal modelling framework. I leave it as an open question how much of the argument of the chapter could be preserved using Lewis’s technical apparatus. Progress has been made on the project of developing a counterfactual approach to causation, at least to the extent that a range of different kinds of examples have been developed for testing counterfactual theories—examples of early and late pre-emption, symmetric overdetermination, trumping, short circuits and switches, prevention, double prevention, pre-emptive pre-emption, and many others. There is, however, still no consensus about the best way to frame a counterfactual account of causation to deal with all these test cases. As troubling as this situation is, it has been made worse by the discovery of a class of counterexamples that appear to constitute an especially potent objection to counterfactual theories (see Bjornsson 2007; Hall 2004; Halpern and Hitchcock 2010; Hiddleston 2005; Hitchcock 2007a). Roughly speaking, the counterexamples consist of pairs of cases with identical counterfactual structures but different causal structures. To put this more precisely in terms of the causal modelling framework, their distinctive feature is that they have different causal structures while possessing identical structural equations; and this is problematic because the structural equations for the examples encode the patterns of counterfactual dependences that hold true of them. The examples seem to show that our causal judgements are sensitive to considerations that go beyond considerations about the counterfactual dependences encoded in the structural equations. In this chapter I propose a solution to the problem posed by these pairs of counterfactually isomorphic examples—call it the problem of counterfactual isomorphs. Essentially, the solution appeals to a counterfactual theory of actual causation, couched, as usual, in terms of counterfactual dependence. But the concept of counterfactual dependence employed by the theory requires that the dependence between cause and effect hold under ideal conditions. Accordingly, I shall call such a dependence an ideal-conditions counterfactual dependence. The stipulation of which conditions are to count as ideal is guided by the idea that causation is an intrinsic matter depending on the sequence of events occurring between cause and effect. I argue that this counterfactual theory obviates the problem of counterfactual isomorphs because the ideal-conditions counterfactual dependence that is appropriate for a causal judgement about one example may differ from that appropriate for an isomorphic example, even when they are governed by the same structural equations. I conclude that the examples indeed show that our causal judgements are sensitive to considerations that go beyond structural equations—namely, considerations about the ideal conditions— but these do not invalidate a counterfactual approach to causation. I plan to proceed as follows. In section 2, I sketch the basic elements of the causal modelling or structural equations framework. In section 3, I outline two pairs of examples that illustrate the problem of counterfactual isomorphs. In section 4, I outline an account of actual causation in terms of ideal-conditions counterfactual

PETER MENZIES



dependence. Section 5 returns to the pairs of examples from section 3, applying the proposed account of causation to explain our divergent causal judgements about them. Section 6 states some brief conclusions. But before we embark on this discussion, it is worth remarking that I aim to offer a conceptual explication rather than an analysis of actual causation. I take the difference to be that an analysis tries to reduce the concept of causation to more basic concepts, whereas an explication tries to provide non-reductive but nevertheless informative truth conditions for causal judgements. So understood, an explication of actual causation may make appeal to causal concepts—so long as they do not trivialize the statement of truth conditions. This will be the case with the explication to be provided, as it will make essential use of the concept of an intervention in many places. Without doubt, this is a causal concept, but, as Woodward (2003) has argued, the invocation of this concept does not automatically trivialize the truth conditions for actual or type causation.

2 Models, Structural Equations, and Interventionist Counterfactuals In this section, I shall describe the basic apparatus of the causal modelling or structural equations framework. A distinctive feature of this framework is that it assigns truth conditions to causal judgements relative to a model. This feature represents the idea that our causal judgements do not project onto reality directly, but are mediated by map-like representations one of whose functions is to abstract away from the complexity of real-world processes.2 Models are the formal expressions of these map-like representational structures. It is best to introduce the elements of a model by way of an example. Consider the following example, Backup, due to Hitchcock (2001a). Example 1: Backup Under the guidance of Supervisor, Trainee Assassin shoots Victim, who dies. If Trainee had not shot, Supervisor, who is a very accurate marksman, would have done so. The first step in constructing a model for this system is to choose a set of variables and values to represent the basic states of the system. In this case it is natural to choose the following variables and values: T = 1 if Trainee 1 shoots, 0 otherwise; S = 1 if Supervisor shoots, 0 otherwise; V = 1 if Victim dies, 0 otherwise.

2

See Giere 2010 for an illuminating discussion of this issue.



THE PROBLEM OF COUNTERFACTUAL ISOMORPHS

In principle, the variables may have many values, but in all of the examples to be discussed the variables are binary. In the examples I shall assume that one value a variable takes represents the occurrence of a state or an event, and the other value represents the non-occurrence of a state or an event. Variables are divided into two classes: exogenous variables whose values are determined by causal factors outside the model, and endogenous variables whose values are determined by factors inside the model. In this example, the variable T is exogenous, while S and V are endogenous. The second step in constructing a model is to formulate a set of structural equations to model the way in which some variables have causal influence over others. The set must include an equation for each variable, which is written on the left-hand side of the equation. The equation for an exogenous variable states its actual value, with the general form of such an equation being Xi = a. The equation for an endogenous variable states it as a function of other variables, with the general form of such an equation being Y = f(X1,..., Xn). To simplify things, I shall assume that the structural equations are deterministic. The structural equations for Backup can be formulated in this way: T ¼ 1: S ¼  T; V ¼ T ∨ S:3 The first equation states the actual value of the exogenous variable T. The second equation states that the value of S is 1 minus the value of T: in other words, S is 1 if T is 0 and 0 if T is 1. The third equation states that the value of V is a maximum of the values of T and S: in other words, V is 1 if either T or S is 1; and 0 if both of T and S are 0. The structural equations are not symmetric like ordinary mathematical equations. They encapsulate a direction of determination: the values of the variables on the lefthand side are determined by the values of the variables on the right-hand side, and not vice versa. For example, if Victim dies, the equations do not imply that the value of T or S must be 1. This asymmetry corresponds to the asymmetry in Lewis’s nonbacktracking counterfactuals. For example, supposing that the actual situation is one in which neither Trainee nor Supervisor shoots and Victim does not die, the nonbacktracking counterfactual, ‘If Trainee or Supervisor had shot, Victim would have died’ would be true, but the counterfactual, ‘If Victim had died, Trainee or Supervisor would have shot’ would be false. Some use a different symbol from ‘=’ to mark the asymmetry. But it is useful to retain this symbol, and, provided we keep in mind that it comes with a direction of determination, we should not become confused.

3 It will be convenient to use symbols of propositional logic to represent mathematical functions. So I shall use the following ~X to represent 1 – X, X ∨ Y to represent max{X, Y}, and X & Y to represent min {X, Y}. When the variables are binary, as they will be in all cases, these functions work the way the corresponding connectives in propositional logic do.

PETER MENZIES



How are we to interpret the structural equations? Pearl (2009) regards the structural equations as the conceptual primitives of his system, describing them as representing ‘the basic mechanisms’ of the system under investigation. Hitchcock (2001a) and Woodward (2003), on the other hand, think of the structural equations as expressing certain privileged counterfactuals. For them, a structural equation of the form Y = f(X1,..., Xn) encodes a battery of primitive counterfactuals of the form ‘If the variables were set by interventions at X1 =x1,..., Xn =xn, then it would be the case that y = f(x1,..., xn)’. I think that both ways of interpreting the structural equations have merit. But it is more convenient for my expository purposes to follow Pearl and to read an equation like Y = f(X1,..., Xn) as stating a basic functional dependence of the value of the endogenous variable Y on the values of the variables X1,..., Xn. Such an equation must satisfy certain constraints. First, it must satisfy a certain minimality condition: the variables stated on the right-hand side of the equation must include all and only the variables on which the variable on the left-hand side depends.4 Secondly, the equation Y = f(X1,..., Xn) must hold not only for the actual values of X1,..., Xn, but for all possible values (within an intended range of application) of these variables, since the equation must cover counterfactual as well as actual instances of the system being modelled. If some informal gloss of a structural equation is needed, one might say that when the variable Y functionally depends on variables X1,..., Xn, then the latter are causally relevant factors for the former.5 This notion of causal relevance must be understood as covering both positive and negative relevance so that even when a variable plays an inhibitory role with respect to another variable it still counts as causally relevant to it. Furthermore, this informal gloss is useful only if it is understood in such a way that causal relevance does not imply the existence of actual causal relations. As we shall see, the fact that the value of Y functionally depends on the values of X1,..., Xn does not show that the values of any of the latter variables counts as an actual cause of any value of Y. Formally, a causal model M is a pair (V, E), where V is a set of variables divided into exogenous and endogenous variables, and E is a set of structural equations. When a variable X appears on the right-hand side of an equation for Y, X is said to be a parent of Y. (Exogenous variables have no parents.) It is useful to represent the information contained in a model in the form of a causal graph. The nodes of the graph correspond to the variables in V. Arrows connect nodes according to the rule that an arrow goes

4

As we shall see, a variable Xi appears non-redundantly on the right-hand side of an equation for variable Y if and only if there is some combination of values for the other variables appearing on the righthand side such that when these variables are held fixed by interventions, an intervention on Xi that changes its value will also change the value of Y. 5 This informal gloss should not to be understood as saying that each of the variables X1,..., Xn is a type cause of Y. For one thing, the variables that appear in the structural equations are not suitable type causes as they often concern whether or not particular events or states occur. The structural equations are best thought of as describing what Hitchcock (2007a) calls token causal structure. See his (2007a) for further discussion.



THE PROBLEM OF COUNTERFACTUAL ISOMORPHS

S

T

V

Figure 9.1 Causal graph for Backup

from X to Y just in case X is a parent of Y. A directed path from variable X to variable Y is a sequence of arrows connecting X and Y, all pointing in the same direction from X to Y. A model is acyclic if no directed path in the corresponding graph runs in a loop from a node back into itself. All the systems to be considered here will be acyclic, the virtue of this being that an acyclic system of equations yields a unique solution. The model for the example Backup can be given graphical representation in terms of Figure 9.1. This graph does not contain as much information as the model, since it does not specify the values of the exogenous variables, nor the exact form of the functional dependences of the endogenous variables on other variables. Nonetheless, it is useful in providing a rough guide to the general form of a model. The crucial feature of the structural equations is that they encapsulate a great deal of counterfactual structure. In particular, the equations of a model enable us to derive counterfactuals about what would happen if variables were set at certain values by interventions—call these interventionist counterfactuals. Setting the value of some variable X to x by means of an intervention in a model M results in a new model, MX=x , where MX=x is the same as M except that the equation for X is replaced by X = x. (In graphical terms, this is equivalent to removing all the arrows directed into X.) So a counterfactual of the form ‘If interventions were to set X1 = x1 &...& Xn = xn, then it would be the case that Y = y’ is true just in case Y = y is true in the new model MX1 = x1 ...Xn = xn. I shall symbolize this interventionist counterfactual as (X1 = x1 &... & Xn = xn) ⊡➞ Y = y, where ‘⊡➞’ denotes a special interventionist counterfactual operator. Note that talk of interventions should not be interpreted as talk about human manipulations. Rather the notion of an intervention is a technical notion that idealizes the procedures used for testing counterfactuals and causal claims. Roughly, an intervention on a variable is an exogenous process that fixes the value of the variable by overriding the usual causal influences on it. If it is useful, they can be thought of as akin to ‘the small miracles’, which Lewis says realize the antecedents of non-backtracking counterfactuals. Woodward (2003) provides a detailed account of interventions, which allows human manipulations to count as interventions provided they satisfy certain stringent conditions.6 When I use the term ‘counterfactual’ in this chapter, I almost invariably mean interventionist counterfactual. It is tempting to think that these counterfactuals might be understood as variants of possible-world counterfactuals. But important work by Rachael Briggs (2012) shows that interventionist counterfactuals cannot be given a possible-worlds semantics. For this reason, I use a special symbol for the interventionist counterfactual operator to mark it off from the standard possible-worlds operator. 6

PETER MENZIES



These truth conditions enable us to derive all the counterfactuals true of the example Backup. For example, we can derive the counterfactual ‘If Trainee had not shot, Supervisor would have shot and Victim would have died’ by substituting T = 0 for the existing equation for T, and deriving S = 1 and V = 1. We can also derive the truth of counterfactuals with more complex antecedents such as ‘If neither Trainee nor Supervisor had shot, Victim would have survived’ by replacing the existing equations for T and S with T = 0 and S = 0, respectively, and deriving V = 0. The truth conditions also enable us to define a notion of counterfactual dependence: Definition 1: Y = y counterfactually depends on X = x in a model M if and only if (i) it is actually the case that X = x and Y = y; and (ii) it is true that (a) X ¼ x ⊡➞Y ¼ y; and (b) X 6¼ x ⊡➞Y 6¼ y: This says that if an intervention were to set X = x, then it would be the case that Y = y; and if an intervention were to set X 6¼ x, then it would be the case Y 6¼ y. Theorists within the causal modelling tradition have used this notion of counterfactual dependence, or some more sophisticated version, to frame a definition of causation.7 But, as we shall see in the next section, our concept of causation includes elements that are not captured solely in terms of counterfactual dependence.

3 Isomorphic Counterfactual Structures In this section I describe pairs of examples that are isomorphic in their counterfactual structure but have divergent structures of actual causation.8 To say that two examples have isomorphic counterfactual structure is to say that their patterns of counterfactual independence and dependence are identical, modulo the use of different variables. The identity of the patterns can be revealed by the substitution of suitable variable letters. The examples I cite are well known in the literature; and have been put forward to make the very point that counterfactual structure does not uniquely determine the structure of actual causal relations. The first pair of examples consists of the example Backup, which I will relabel Example (1a), and another example, Careful Poisoning, due to Hitchcock (2007a).9

7

See, for example, Hitchcock 2001a; Halpern and Pearl 2005; Pearl 2000; Weslake 2014; and Woodward 2003. 8 The examples are taken from Hitchcock 2007a and Halpern and Hitchcock 2015, who use them to make the very point that counterfactual structure does not uniquely determine the structure of actual causal relations. I am much indebted to Hitchcock 2007a, Halpern and Hitchcock 2015, and Weslake 2014 for setting out the different categories of counterexamples to counterfactual theories, and for highlighting the problem of counterfactual isomorphs. 9 Hitchcock says that Michael McDermott and Bjornsson (2007) also identified this kind of example.



THE PROBLEM OF COUNTERFACTUAL ISOMORPHS

Example (1b): Careful Poisoning Bodyguard puts a harmless antidote in Victim’s coffee (B = 1). Confederate then laces the coffee with a normally lethal poison (C = 0),10 which is neutralized by the antidote. Confederate would not have put the poison in the coffee if Bodyguard had not first administered the antidote. Victim drinks the coffee and lives (L = 1). The example can be modelled using the following structural equations. B ¼ 1: C ¼  B; L ¼ B ∨ C: We can see that the causal graph and the structural equations for this example are the same as those for Backup if we make the following substitutions of variable letters throughout the equations above: substitute T for B; substitute S for C; and substitute V for L. We then obtain the following structural equations, which are those of Backup: T ¼ 1: S ¼  T; V ¼ T ∨ S: It follows that the causal graph for Careful Poisoning is identical with that of Backup and that the same counterfactual independences and dependences hold of the two examples. For example, the following counterfactuals are true of Backup, which shows there is no straight counterfactual dependence between Trainee’s shooting and Victim’s death: ðaÞ T ¼ 1 ⊡➞V ¼ 1; and T ¼ 0 ⊡➞V ¼ 1: However, a more complex counterfactual dependence, which holds fixed the fact that Supervisor did not shoot, obtains in Backup: ðaÞ ðT ¼ 1 & S ¼ 0Þ ⊡➞V ¼ 1; and ðbÞ ðT ¼ 0 & S ¼ 0Þ ⊡➞V ¼ 0: As is predictable on the basis of the identity of the structural equations of the two examples, we find exactly the same pattern of counterfactual independence and dependence in Careful Poisoning. Thus, there is no counterfactual dependence between Bodyguard’s putting the antidote in the coffee and Victim’s living: ðaÞ B ¼ 1 ⊡➞L ¼ 1; and ðbÞ B ¼ 0 ⊡➞L ¼ 1: But there is a counterfactual dependence when the fact that Confederate put poison in the coffee is held fixed: ðaÞ ðB ¼ 1 & C ¼ 0Þ ⊡➞L ¼ 1; and ðbÞðB ¼ 0 & C ¼ 0Þ ⊡➞L ¼ 0:

10

Note the unusual assignment of value 0 to C to signify that Confederate puts poison in the coffee. This assignment more readily reveals the isomorphism with Backup.

PETER MENZIES



Notwithstanding the fact that the same counterfactual truths hold of the two examples, we make different causal judgements about the two examples. We judge that Trainee’s shooting was a cause of Victim’s death in Backup, but we do not judge that Bodyguard’s putting antidote into the coffee was a cause of Victim’s living in Careful Poisoning. It seems inappropriate to credit Bodyguard’s putting the antidote in the coffee with causal status, given that it initiates the very action—Confederate’s poisoning the coffee—that threatens Victim’s life.11 Another pair of counterfactually isomorphic examples that have been discussed in the literature consists of the following examples, the first due to Hall (2004) and the second due to Hiddleston (2005): Example (2a): Window Suzy (S = 1) and Billy (B = 1) throw rocks at a window, each with sufficient force to shatter it. The rocks strike the window at exactly the same time. The window shatters (W = 1). We can model this using the following structural equations and causal graph, as shown in Figure 9.2: S ¼ 1; B ¼ 1: W ¼ S ∨ B: The other example that is counterfactually isomorphic is Careful Antidote. Example (2b): Careful Antidote Assassin is about to put a lethal poison into the coffee of Victim, but has a lastminute change of heart and refrains from doing so (A = 1).12 Independently, S

W

B

Figure 9.2 Causal graph for Window 11 I am not in complete agreement with the verdict that Bodyguard’s action is not a cause of Victim’s living. For, as well as initiating Confederate’s action that threatens Victim’s life, Bodyguard’s action also prevents Victim from dying and so, in a sense, is a cause of his living. Still, several philosophers have expressed the conviction that the initial verdict is correct. See Hall 2007; Hitchcock 2007a; and Weslake 2014. I think that a theory of causation should be able to explain this verdict and so have chosen to focus on how it might be explained. On the other hand, a theory of causation should, I believe, also be able to explain the contrary view that Bodyguard’s putting the antidote in the coffee prevents Victim’s death and so is a cause of his living. The theory to be proposed in the next section is able to do this if it is supplemented with an appropriate rule of adjustment and a definition of the concept ‘prevents’. It is an interesting question why different people find one intuition more dominant than the other. 12 Again this unusual assignment of values to the variable A helps to reveal the isomorphism between Careful Antidote and Window.



THE PROBLEM OF COUNTERFACTUAL ISOMORPHS

Bodyguard puts an antidote in the coffee (G = 1), which would have neutralized the poison. Victim drinks the coffee and lives (L = 1). The structural equations for the example are: A ¼ 1; G ¼ 1: L ¼ A ∨ G: Substituting S for A, B for G, and W for L in these structural equations, we obtain those for the example Window. Accordingly, the causal graphs for the examples are the same, modulo the use of different variable letters. Once more the identity of the structural equations in the two examples generates an identical pattern of counterfactual independences and dependences. First, there is failure of counterfactual dependence between Billy’s throw and the window: ðaÞ B ¼ 1 ⊡➞W ¼ 1; and ðbÞB ¼ 0 ⊡➞W ¼ 1: Correspondingly, there is a failure of counterfactual dependence between Bodyguard’s putting the antidote in Victim’s coffee and Victim’s living: ðaÞ G ¼ 1 ⊡➞L ¼ 1; and ðbÞ G ¼ 0 ⊡➞L ¼ 1: Secondly, a counterfactual dependence emerges when more complex counterfactuals are considered. Holding fixed Suzy’s not throwing her rock, a counterfactual dependence holds between Billy’s throw and the window shattering: ðaÞ ðB ¼ 1 & S ¼ 0Þ ⊡➞W ¼ 1; and ðbÞ ðB ¼ 0 & S ¼ 0Þ ⊡➞W ¼ 0: Similarly, holding fixed Assassin’s putting poison in the coffee, there is a counterfactual dependence between Bodyguard’s putting the antidote in the coffee and Victim’s living: ðaÞ ðG ¼ 1 & A ¼ 0Þ ⊡➞L ¼ 1; and ðbÞ ðG ¼ 0 & A ¼ 0Þ ⊡➞L ¼ 0: However, notwithstanding the fact that the same pattern of counterfactual independences and dependences holds in the two examples, they differ in their actual causal relations. We judge that Billy’s throw was a cause of the window shattering, but we do not judge that the Bodyguard’s administering the antidote was a cause of Victim’s living. It seems inappropriate to describe Bodyguard’s administering the antidote as a cause of Victim’s living as there is no threat for it to counter—since Assassin did not poison the coffee after his last-minute change of mind. So we have the problem of counterfactual isomorphs before us. The pairs of examples just described seem to indicate that our causal judgements are sensitive to considerations that go beyond the counterfactual independences and dependences encoded in structural equations. Exactly what kind of considerations are these?

PETER MENZIES



4 Definitions of Causation In this section I try to answer this question by arguing that causal judgements involve certain idealizations, which determine the form of the counterfactual dependence used to test the existence of causal relations. In order to describe these idealizations it is necessary to introduce some preliminary causal concepts. In the causal modelling literature these concepts are characterized at the level of type-causation (Pearl 2009; Woodward 2003; Hitchcock 2001b), but I shall characterize them at the level of actual causation. To introduce the first concept let us consider an example of early pre-emption and its model. Example 3: Bottle Suzy throws a rock at a bottle (ST = 1), as does Billy (BT = 1). Suzy’s rock hits the bottle first (SH = 1) and the bottle shatters (BS = 1). Billy’s rock does not hit the bottle (BH = 0). But his throw is accurate and it would have shattered the bottle if Suzy’s had not. The structural equations for this example are below and the causal graph is shown in Figure 9.3. ST ¼ 1; BT ¼ 1: SH ¼ ST; BH ¼ BT &  SH; BS ¼ SH ∨ BH: An initially attractive thought is that we can define the concept of causation straightforwardly in terms of counterfactual dependence. But the example Bottle shows that this is not correct. Here a causal relation between Suzy’s throw and the bottle shattering is not reflected in a counterfactual dependence. For if Suzy had not thrown her rock, the bottle would still have shattered, due to Billy’s throw. A common diagnosis of the difficulty presented by such examples is that the counterfactual dependence that should exist between Suzy’s throw and the bottle shattering is masked by the existence of an alternative possible cause. If we consider a more complex kind of counterfactual that holds fixed the absence of this alternative possible cause, we will find there is a counterfactual dependence that reflects the existence of this causal relation. This diagnosis suggests a more complex counterfactual definition of causation. Let us say that variables V1,..., Vn feed into a path from X to Y if and only if they are parents of any variable (except X) that itself lies on the path; and let {V1,..., Vn} be the (possibly empty) set of variables that feed into the path from X to Y. Then the following is an appealing first stab at defining actual causation: ST

SH BS

BT

BH

Figure 9.3 Causal graph for Bottle



THE PROBLEM OF COUNTERFACTUAL ISOMORPHS

Definition 2: X = x is a contributing cause of Y = y in model M iff (i) it is actually the case that X = x and Y = y; and (ii) there is a path from X to Y such that the variables that feed into this path have actual values—call them v1,..., vn—that make the following counterfactuals true: (a) ðX ¼ x&V1 ¼ v1 &:::&Vn ¼ vn Þ ⊡➞Y ¼ y; and (b) ðX ¼ 6 x&V1 ¼ v1 &:::&Vn ¼ vn Þ ⊡➞Y ¼ 6 y: This definition issues the right verdicts about the example Bottle. It implies that Suzy’s throw (ST = 1) is a contributing cause of the bottle’s shattering (BS = 1). Consider the path from ST to BS. There is only one variable that feeds into this path and that is the variable BH. When this variable is held fixed at its actual value (BH = 0), the bottle’s shattering counterfactually depends on Suzy’s throw: i.e. (a) ðST ¼ 1 & BH ¼ 0Þ ⊡➞BS ¼ 1; and (b) ðST ¼ 1 & BH ¼ 0Þ ⊡➞BS ¼ 0: On the other hand, the definition implies that Billy’s throw is not a contributing cause of the bottle’s shattering. Consider the path from BT to BS. Only one variable feeds into this path (SH) and when it is held fixed at its actual value (SH = 1), there is no counterfactual dependence between Billy’s throw and the bottle shattering: i.e. (a) ðBT ¼ 1 & SH ¼ 1Þ ⊡➞BS ¼ 1; and (b) ðBT ¼ 0 & SH ¼ 1Þ ⊡➞BS ¼ 1: So far so good. Unfortunately, however, Definition 2 is not ultimately satisfactory. For it is too restrictive in that it rules out plausible cases of causation, as can be seen in the example Window. In this example of overdetermination, Suzy’s throw and Billy’s throw are each causes of the window shattering. But Definition 2 does not deliver this result. In this example, only one variable, B, feeds into the path from the variable representing Suzy’s throw, S, to the variable representing the window breaking, W, and when this variable is held fixed at its actual value (B = 1), there is no counterfactual dependence between Suzy’s throw and the window breaking: i.e. (a) ðS ¼ 1 & B ¼ 1Þ ⊡➞W ¼ 1; and (b) ðS ¼ 0 & B ¼ 1Þ ⊡➞W ¼ 1: Similarly, only one variable feeds into the path from B to W, and when this variable is held fixed at its actual value (S = 1), there is a failure of counterfactual dependence between Billy’s throw and the window breaking. Yet the judgement that Suzy’s throw and Billy’s throw are both causes is secure enough that a definition of causation ought to agree with it. One obvious way to repair Definition 2 is to make it less restrictive by permitting the variables that feed into the path from putative cause to effect to be held fixed at non-actual values. This would certainly overcome the difficulty in the case of Window. For in evaluating whether Suzy’s throw is a cause of the window shattering, we could then hold fixed the variable B that feeds into the path from S to W at its non-actual value (B = 0), and when we do this we would find there is a counterfactual dependence between Suzy’s throw and the window shattering: i.e. (a) ðS ¼ 1 & B ¼ 0Þ ⊡➞W ¼ 1; and (b) ðS ¼ 0 & B ¼ 0Þ ⊡➞W ¼ 0: This would permit Suzy’s throw to count as a cause of the window shattering. A similar line of reasoning would also allow Billy’s throw to count as a cause. Despite its initial appeal, this strategy for repairing Definition 2 does not take us as far as it has to. If restricting the values of the variables that feed into the path

PETER MENZIES



from putative cause to effect to actual values is too restrictive, the strategy of allowing these variables to take non-actual values is too permissive. To see this, reconsider the example Careful Antidote in which, after a change of mind, Assassin refrains from putting poison in Victim’s coffee (A = 1) while Bodyguard independently puts an antidote in the coffee (G = 1), which would have neutralized the poison. Bodyguard’s putting the antidote in the coffee is not a cause of Victim’s survival (L = 1) since Assassin’s action posed no actual threat to his life. Yet the strategy under consideration would predict a causal relation. For with the variable representing Assassin’s action A, which feeds into the path from G to L, held fixed at the non-actual value (A = 0), representing Assassin’s putting poison in the coffee, there is a counterfactual dependence between the bodyguard’s action and Victim’s survival: i.e. (a) ðG ¼ 1&A ¼ 0Þ ⊡➞L ¼ 1; and (b) ðG ¼ 0&A ¼ 0Þ ⊡➞L ¼ 0: This is clearly the wrong result. We arrive here at a crucial choice point in developing a counterfactual account of causation. On the one hand, Definition 2 is too restrictive in that it excludes genuine causes. On the other hand, the suggested amendment that would permit variables to be held fixed at non-actual values is too lax in that it would permit noncauses to count as causes. What is needed is a version of the suggested amendment to Definition 2 that allows variables to be held fixed at non-actual values, but does this in a principled way in accordance with some well-motivated rule. A common objection to causal modelling theories that define actual causation in terms of counterfactual dependences that hold fixed contingent conditions is that they are ad hoc and unmotivated. Even if they are extensionally adequate, it is claimed, they do not provide principled reasons for the restrictions they impose on the contingent conditions to be held fixed. In order to counter this objection, it is imperative that any such account should be based on compelling arguments that justify the restrictions beyond showing that they are extensionally adequate. In the remainder of this section, I propose an amendment to Definition 2, which delivers the right verdicts about the examples we have discussed and does so in a principled way. The central idea is that we assess the existence of a causal relation in terms of a simple two-step test. In the first step, we assess whether a counterfactual dependence exists between putative cause and effect under certain ideal conditions, in particular under conditions in which the variables that feed into the path between putative cause and effect take on certain ideal values. I call this an ideal-conditions counterfactual dependence. In the second step of the test, we compare the values that variables on this path would have if an intervention realized the putative cause under these ideal conditions with the values that these variables actually have when the putative cause occurs. In order to explain this two-step test in more detail, it is useful to introduce some terminology. Again let {V1,..., Vn} be the (possibly empty) set of variables that feed into a path from X to Y. Let these variables have the actual values V1 = v1,..., Vn = vn. Let Vj be any variable in this set. Finally, let us abbreviate the assignment of actual



THE PROBLEM OF COUNTERFACTUAL ISOMORPHS

values to the remaining variables in the set (after Vj is taken out) V* = v*. With these stipulations in hand, we can introduce the concept of an enabling condition, which will be extremely helpful. Definition 3: A condition Vj = vj is an enabling condition for a possible causal connection between the actual conditions X = x and Y = y in model M iff (i) Vj feeds into the path from X to Y and it is actually the case that Vj = vj; and (ii) the assignment of actual values to other variables that feed into the path, V* = v*, makes the following counterfactuals true: (a) ðX ¼ x & Vj ¼ vj & V* ¼ v*Þ ⊡➞Y ¼ y; and (b) ðX ¼ x & Vj 6¼ vj & V* ¼ v*Þ ⊡➞Y 6¼ y:

The intuitive idea is that an enabling condition for a possible causal connection between X = x and Y = y is a condition but for which X = x would not have the power in the actual circumstances to bring about Y = y. In other words, when the enabling condition is present along with other actual conditions X = x brings about Y = y, but when it is absent X = x does not bring about Y = y. Let us now consider how we might test whether a causal relation between two conditions, X = x and Y = y, exists in a generic model M. I suggest the process can be broken down into two steps. The first step consists in evaluating whether an idealconditions counterfactual dependence exists between these conditions. The relevant ideal conditions are ones in which the enabling conditions for the connection between X = x and Y = y are preserved, but all other conditions are given values that represent the absence of the corresponding states or events. (Recall that we are operating with the simplifying assumption that all variables are binary variables with one value representing the presence of a state or an event and the other value their absence.) The underlying rationale for this suggestion is that, provided the enabling conditions for the connection are preserved, the existence of a causal relation between X = x and Y = y depends on the intrinsic character of what happens on the path from X = x to Y = y. If a causal relation between X = x and Y = y does indeed depend on what happens on the path from X to Y, then we should expect that, provided that the enabling conditions for the connection are preserved, the relation will continue to hold even if all other states and events that are not essential for what happens along the path are rendered absent by interventions.13

13 To be sure, it is controversial whether actual causation is an intrinsic matter of what happens along the path from cause to effect. The whole question deserves much more discussion than I can give it here. I restrict myself to the following brief remarks. The most decisive counterexamples to the intrinsicality of causation are cases of so-called double prevention, in which a cause prevents some event, which would have prevented the effect from occurring. (For discussion see Hall 2002; Lewis 2004; Menzies 2003.) These examples involve the causal concepts of ‘preventing an event’ and ‘enabling or allowing an event to occur’, concepts that involve different kinds of idealizations, and so different definitions from the concept of ‘being a cause’. I would argue that when these definitions are framed satisfactorily, they do not undermine, but actually support, the view that causation is an intrinsic matter of what happens on the path from cause to effect. Due to space limitations, I have restricted the present discussion to the explication of the concept of ‘being a cause’, omitting as far as possible any examples involving prevention or double prevention.

PETER MENZIES



So, in short, I am suggesting that the first step in assessing whether X = x is a cause of Y = y consists of applying the following adjustment rule and counterfactual test: Adjustment Rule 1: Adjust the values of variables that feed into the path from X to Y to their ideal values according to this rule: if the variable has an actual value which makes it an enabling condition for the connection between X = x and Y = y, then leave the variable at its current value; if the variable has a value which does not make it an enabling condition for this connection, adjust the value of the variable, if necessary, so that it is the value that represents the absence of the underlying state or event. Counterfactual Test: Assess whether a counterfactual dependence exists between X = x and Y = y when all the variables that feed into the path from X to Y are held fixed at their ideal values by interventions.14 While this rule may seem complex, it is easy enough to apply in practice. Let us consider its application to the Bottle example. Consider first how the rule applies to the connection between Suzy’s throw (ST = 1) and the bottle shattering (BS = 1). Only one variable feeds into the path from ST and BS, namely BH, which has the actual value 0. The condition BH = 0 is not an enabling condition for this connection, and so the adjustment rule says that we should apply the counterfactual test by holding fixed this variable at the value that represents the situation in which Billy’s rock does not hit the bottle—namely BH = 0. As we have seen already, a counterfactual dependence holds when BH = 0 is held fixed. However, when we apply the adjustment rule and test whether Billy’s throw (BT = 1) is a cause of the bottle shattering (BS = 1), we get an unwanted result: there is a counterfactual dependence between Billy’s throw and the bottle shattering when SH is held fixed at its ideal value of 0, even though Billy’s throw is not a cause of the bottle shattering. (SH = 1 is not an enabling condition of the connection between BT = 1 and BS = 1, and so the ideal value of SH is 0, representing the situation in which Suzy’s rock does not hit the bottle.) This example shows that the process of evaluating a putative causal relation must involve more than the first step described above. As we have just seen, the first step in the process of assessing a putative causal relation is motivated by the idea that if a causal relation exists between two conditions, it should be revealed by the counterfactual dependence test applied in ideal 14 The distinction between ideal and non-ideal values of variables is similar to a distinction between default and deviant values of variables that several philosophers have drawn on to do important work in the account of causation. (See Hall 2007; Halpern 2008; Hitchcock 2007a; and Menzies 2004a, 2004b, 2007, 2009.) Indeed, some counterfactual theorists (Halpern and Hitchcock 2015) have appealed to this distinction to solve the problem of counterfactual isomorphs. However, Halpern and Hitchcock’s employment of the default/deviant distinction is quite different from my employment of the ideal/non-ideal distinction. They do not employ anything like ideal-conditions counterfactual dependences to define causation as I do, but rather appeal to the distinction between default and deviant values to determine which counterfactuals are psychologically available and so which linked causal claims are thereby also psychologically available.



THE PROBLEM OF COUNTERFACTUAL ISOMORPHS

circumstances. But why should a counterfactual dependence holding in ideal conditions bear at all on the actual situation, which may be very far from ideal? In answer, I suggest that the second step of the test procedure consists in determining whether what happens in the ideal circumstances matches what happens in the actual circumstances in one important respect. In particular, I suggest that what happens on the path from X to Y when we intervene to set X = x in ideal circumstances should match what happens on this path when X = x is realized in the actual circumstances. Another way of putting this is that the intrinsic sequence of events that occur on the path from X = x to Y = y in the ideal circumstances when X = x is realized by intervention should match the actual sequence of events along this path. Again this second step in the evaluation process is motivated by the intuition that causation is an intrinsic matter that depends on what happens on the path between cause and effect: if X = x is an actual cause of Y = y, the sequence of events that occurs in the ideal circumstances in which a counterfactual dependence holds between them should exactly match the actual sequence of events by which X = x leads to Y = y. This second step provides us with a way of distinguishing Suzy’s throw from Billy’s throw in the example Bottle. For in the case of Suzy’s throw, what happens when an intervention ensures that Suzy throws in the ideal circumstances in which BH = 0 is held fixed exactly matches what happens in the actual circumstances when Suzy throws: what happens in both scenarios is that Suzy throws, her rock hits the bottle and the bottle shatters. In contrast, there is no such match in the case of Billy’s throw. What happens when an intervention ensures that Billy throws in the ideal circumstances in which SH = 0 is held fixed is that Billy throws, his rock hits the bottle, and the bottle shatters. In actuality, Billy’s rock does not hit the bottle, indicating that the process that would connect Billy’s throw with the bottle shattering does not go through to completion. This two-step procedure for evaluating causal claims translates into a counterfactual definition of actual causation as follows:15 Definition 4: X = x is a cause of Y = y in model M iff there is path from X to Y such that (i) there is a counterfactual dependence between X = x and Y = y when the variables that feed into this path are set to their ideal values by interventions; and (ii) the actual values of variables on this path agree with the values they would have if an intervention were to set X = x when the variables that feed into this path are held fixed at their ideal values.16

15 My exploration of this kind of definition goes back to Menzies 1996, 1999, 2003, and 2004b. Of all the definitions of causation to be found in the literature, the proposed definition is most similar to Hall’s ‘reduction of situations’ definition in his 2007 and to the ‘blueprint strategy’ discussed in Paul and Hall 2013. 16 Christopher Hitchcock has pointed out to me that the second clause of this definition runs into trouble with the ‘Voting Machine’ example discussed by Halpern and Pearl (2005: 881). Discussion of this example will have to await another occasion.

PETER MENZIES



It is important to note that this definition applies to just one causal concept—the concept of ‘being a cause’. Other causal concepts involve, in my opinion, a similar difference-making counterfactual test, but differ in their rules of adjustment, reflecting the fact that each concept has its proprietary kind of idealization.

5 Examples Revisited In this section I apply Adjustment Rule 1 and Definition 4 to explain the divergent causal intuitions we have about the pairs of counterfactually isomorphic examples described in section 3. Let us start with the pair of examples (1a) Backup and (1b) Careful Poisoning. Applying Adjustment Rule 1 and Definition 4 to Backup, we can see that it makes predictions in accord with our actual judgements. The definition predicts that Trainee’s shooting (T = 1) is the cause of Victim’s death (V = 1). Only one variable feeds into the direct path from T to V; and when it takes its actual value (S = 0), it is not an enabling condition for the connection between T = 1 and V = 1. So the adjustment rule says its ideal value is its actual value because it represents the absence of Supervisor’s shooting. With this variable held fixed at its ideal value, there is an ideal-conditions counterfactual dependence between Trainee’s shooting and Victim’s death: i.e. (a) ðT ¼ 1 & S ¼ 0Þ ⊡➞V ¼ 1; and (b) ðT ¼ 0 & S ¼ 0Þ ⊡➞V ¼ 0: Furthermore what happens on the path from T to V when an intervention brings about Trainee’s shooting in the ideal circumstances matches what actually happens. So Trainee’s shooting counts as a cause of Victim’s death. (A straightforward application of Definition 4 shows that Supervisor’s not shooting is not a cause of Victim’s death.) Turning to the example Careful Poisoning, we can see that Adjustment Rule 1 and Definition 4 predict that Bodyguard’s putting the antidote in Victim’s coffee (B = 1) is not a cause of Victim’s living (L = 1). We need to consider both the direct path from B to L and the indirect path from B to L that goes through C. Taking the direct path first, we can see that one variable feeds into this path; and when it takes its actual value (C = 0 representing that Confederate puts poison in the coffee), it is not an enabling condition for the connection between B = 1 and L = 1. So the adjustment rule says its ideal value is C = 1 signifying that Confederate does not put poison in the coffee. With this variable held fixed at its ideal value, there is no counterfactual dependence between Bodyguard’s administering the antidote and Victim’s living: i.e. ðB ¼ 1 & C ¼ 1Þ ⊡➞L ¼ 1; and (b) ðB ¼ 0 & C ¼ 1Þ ⊡➞L ¼ 1: Now taking the indirect path from B to L that goes through C, we can see that there is no variable that feeds into this path and so the definition requires simply that there should be a straightforward counterfactual dependence between B = 1 and L = 1. But there is no such counterfactual dependence as (a) B ¼ 1 ⊡➞L ¼ 1; and (b) B ¼ 0 ⊡➞L ¼ 1: So it follows that Bodyguard’s administering the antidote is not a cause of Victim’s



THE PROBLEM OF COUNTERFACTUAL ISOMORPHS

living. (A straightforward application of Definition 4 shows that Confederate’s putting poison in the coffee does not count as a cause either.) The initial puzzle we faced with this pair of examples arose from the fact that the examples have identical structural equations and yet the examples invite different causal judgements. But Adjustment Rule 1 and Definition 4 show how this puzzle can be resolved. For they imply that the ideal-conditions counterfactual dependence used to test the causal judgement about Backup (‘Trainee’s shooting was a cause of Victim’s death’) does not match that used to test the judgement about Careful Poisoning (‘Bodyguard’s putting the antidote in the coffee was a cause of Victim’s living’). Recall that to reveal the isomorphism between the examples, we used the following correspondences between the variables of Backup and the variables of Careful Poisoning: T corresponds to B, S corresponds to C, and V corresponds to L. If we had used these correspondences to construct a counterfactual test for Careful Poisoning to match the test for Backup, we would have considered whether there is a counterfactual dependence between Bodyguard’s putting the antidote in the coffee and Victim’s living, holding fixed Confederate’s putting poison in the coffee: i.e. (B = 1 & C = 0) ⊡➞L =1; and (b) (B = 0 & C = 0) ⊡➞L = 0. This counterfactual dependence does indeed hold, matching the dependence between Trainee’s shooting and Victim’s death when Supervisor’s not shooting is held fixed: i.e. (T = 1 & S = 0) ⊡➞V = 1; and (b) (T = 0 & S = 0) ⊡➞V =0. However, Adjustment Rule 1 implies that in Careful Poisoning, the variable C is to be held fixed at its ideal value (C = 1 signifying that Confederate does not put poison in the coffee) rather than its actual value; and, as we have seen, when this variable is held fixed at its ideal value, there is no ideal-conditions counterfactual dependence between Bodyguard’s administering the antidote and Victim’s living. In essence, then, Adjustment Rule 1 and Definition 4 explain the divergence of causal judgements in terms of the fact that the idealconditions counterfactual dependences used to test the causal judgements about these examples are different and are not the counterparts implied by the correspondences between variables. Let us turn now to the pair of examples (2a) Window and (2b) Careful Antidote. Again Adjustment Rule 1 and Definition 2 make predictions that agree with our intuitive causal judgements about these examples. For example, applying the rule and the definition to the example Window, we can see that they imply that Billy’s throwing a rock (B = 1) is a cause of the window breaking (W = 1). The only variable that feeds into the path from B to T is S; and when it takes its actual value (S = 1), it is not an enabling condition for the connection between B = 1 and W = 1. So Adjustment Rule 1 dictates that we should adjust its value to the ideal value 0 to represent Suzy’s not throwing her rock. Then Definition 4 implies that Billy’s throwing his rock is a cause of the window breaking. First, there is a counterfactual dependence between these conditions when we hold fixed Suzy’s throw at its ideal value (S = 0): i.e. (B = 1 & S = 0) ⊡➞W =1; and (b) (B = 0 & S = 0) ⊡➞W = 0. Secondly, what happens on the path between B and W when B = 1 is realized by an

PETER MENZIES



intervention in the ideal circumstances in which S = 0 is held fixed matches what actually happens. (An exactly parallel line of reasoning shows that Suzy’s throw also counts as a cause of the window breaking.) Turning now to the example Careful Antidote and reasoning in accordance with Adjustment Rule 1 and Definition 4, we can conclude that Bodyguard’s putting the antidote in the coffee (G = 1) is not a cause of Victim’s survival (L = 1). There is only one variable that feeds into the path from G and L; and when it takes its actual value (A = 1), it is not an enabling condition for the connection between G = 1 and L = 1. So Adjustment Rule 1 dictates that its ideal value is its actual value since A = 1 signifies that Assassin does not poison the coffee. Hence Definition 4 implies that we should consider whether there is a counterfactual dependence between Bodyguard’s administering the antidote and Victim’s survival when it is held fixed that Assassin does not poison the coffee. This counterfactual dependence fails to hold: i.e. in fact (a) (G = 1 & A = 1) ⊡➞L = 1; and (b) (G = 0 & A = 1) ⊡➞L = 1. Accordingly, Bodyguard’s action is not a cause of Victim’s survival. (Parallel reasoning shows that Assassin’s not poisoning the coffee also fails to be a cause of Victim’s survival.) Again the initial conundrum that this pair of examples posed was that a causal relation holds between Billy’s throw and the window breaking, but not between Bodyguard’s administering the antidote and Victim’s survival even though these are counterpart causal judgements given the correspondences that were set up between the variables in Window and the variables in Careful Antidote: S corresponds to A, B corresponds to G, and W corresponds to L. Given the identity of the structural equations of the two examples holding in virtue of these correspondences, we might initially expect that the counterfactual dependence used to test the causal relation between Billy’s throw and the window breaking would match the counterfactual dependence used to test Bodyguard’s administering the antidote and Victim’s survival. But the conjunction of Adjustment Rule 1 and Definition 4 imply that this is not the case. Adjustment Rule 1 dictates that we test the causal relation between Bodyguard’s administering the antidote and Victim’s survival in terms of an idealconditions counterfactual dependence that holds fixed the fact that Assassin does not put poison in the coffee, whereas the counterfactual dependence that would match the dependence used to test the causal relation between Billy’s throw and the window breaking would hold fixed Assassin’s putting poison in the coffee: i.e. A = 0 to match S = 0, Suzy’s not throwing her rock. So, once more, Adjustment Rule 1 and Definition 4 explain the fact that different causal relations hold in this pair of examples despite their counterfactual isomorphism. They explain this fact because they imply that the ideal-conditions counterfactual dependences used to test the causal relations in these examples are different from those that would be used if we simply followed the correspondences between variables in the isomorphic counterfactual structures. In conclusion, then, we now have an explanation of how a counterfactual theory of actual causation might explain the existence of counterfactually isomorphic examples that differ in the structure of their actual causal relations. The explanation consists in the



THE PROBLEM OF COUNTERFACTUAL ISOMORPHS

fact that a counterfactual theory conforming to Adjustment Rule 1 and Definition 4 need not employ the same ideal-conditions counterfactual dependences to test causal judgements about examples even when the examples have identical structural equations.

6 Conclusion The aim of this chapter has been to solve the problem of counterfactual isomorphs. The problem consists in the fact that we make divergent causal judgements about examples with identical structural equations and isomorphic counterfactual structures. This poses a challenge for counterfactual theories of causation that seek to elucidate causal judgements in terms of counterfactual dependences, whether simple or complex in form. For if a causal judgement about one example is true in virtue of some counterfactual dependence, then it seems reasonable that a corresponding causal judgement about an isomorphic example should hold in virtue of a counterpart counterfactual dependence. I have attempted to resolve this puzzle by arguing that causal judgements involve idealizations that dictate the kind of the counterfactual dependence used to test causal judgements. The particular form of the idealization involved in the concept of ‘a cause’ implies that a causal judgement about one example might be tested by one kind of ideal-conditions counterfactual dependence while the counterpart causal judgement about an isomorphic example might be tested by a quite different kind of ideal-conditions counterfactual dependence. This resolution enables us to retain the key insight of counterfactual theories—that a central component of every causal concept involves a difference-making counterfactual dependence—while showing how divergent causal judgements can be made about counterfactually isomorphic examples. Of course, this resolution depends on a particular contestable theory of actual causation. The full merits of this theory can only be assessed by seeing how it fares with the full panoply of test cases that have been constructed by theorists about causation—test cases involving early and late pre-emption, symmetric overdetermination, trumping, prevention, double prevention, short circuits, switches, and many others. This assessment is work for the future.

References Bjornsson, G. 2007. ‘How Effects Depend on Their Causes, Why Transitivity Fails, and Why We Care about Causation’, Philosophical Studies, 133: 349–90. Briggs, R. 2012. ‘Interventionist Counterfactuals’, Philosophical Studies, 160: 139–66. Collins, J., Hall, N., and Paul, L. A. 2004 (eds). Causation and Counterfactuals. Cambridge, MA: MIT Press. Giere, R. 2010. Scientific Perspectivism. Chicago: University of Chicago Press. Glymour, C., Danks, D., Glymour, B., Eberhardt, F., Ramsey, J., Scheines, R., Spirites, P., Teng, C. M., and Zhang, Z. 2010. ‘Actual Causation: A Stone Soup Essay’, Synthese, 175: 169–92.

PETER MENZIES



Hall, N. 2002. ‘Non-locality on the Cheap? A New Problem for Counterfactual Analyses of Causation’, Noûs, 36: 276–94. Hall, N. 2004. ‘Two Concepts of Causation’, in Causation and Counterfactuals, ed. J. Collins, N. Hall, and L. A. Paul. Cambridge, MA: MIT Press. Hall, N. 2007. ‘Structural Equations and Causation’, Philosophical Studies, 132: 109–36. Halpern, J. 2008. ‘Defaults and Normality in Causal Structures’, in Proceedings of the Eleventh International Conference on Principles of Knowledge Representation and Reasoning (KR 2008), 198–208. Halpern, J., and Hitchcock, C. 2010. ‘Actual Causation and the Art of Modeling’, in Heuristics, Probability, and Causality: A Tribute to Judea Pearl, ed. R. Dechter, H. Geffner, and J. Halpern. London: College Publications, 383–406. Halpern, J., and Hitchcock, C. 2015. ‘Graded Causation and Defaults’, British Journal for the Philosophy of Science, 66: 413–57. Halpern, J., and Pearl, J. 2005. ‘Causes and Explanations: A Structural-Model Approach. Part I: Causes’, British Journal for the Philosophy of Science, 56: 843–87. Hiddleston, E. 2005. ‘Causal Powers’, British Journal for the Philosophy of Science, 56: 27–59. Hitchcock, C. 2001a. ‘The Intransitivity of Causation Revealed in Equations and Graphs’, Journal of Philosophy, 158: 273–99. Hitchcock, C. 2001b. ‘A Tale of Two Effects’, Philosophical Review, 110: 361–96. Hitchcock, C. 2007a. ‘Prevention, Preemption, and the Principle of Sufficient Reason’, Philosophical Review, 116: 495–532. Hitchcock, C. 2007b. ‘What’s Wrong with Neuron Diagrams?’ in Causation and Explanation, ed. J. K. Campbell, M. O’Rouke, and H. Silverman. Cambridge, MA: MIT Press, 69–92. Lewis, D. 1973. ‘Causation’, Journal of Philosophy, 70: 113–26. Lewis, D. 1986. Philosophical Papers, Volume II. New York: Oxford University Press. Lewis, D. 2000. ‘Causation as Influence’, Journal of Philosophy, 157: 182–97. Lewis, D. 2004. ‘Void and Object’, in Causation and Counterfactuals, ed. J. Collins, N. Hall, and L. A. Paul. Cambridge, MA: MIT, 277–90. Menzies, P. 1996. ‘Probabilistic Causation and the Pre-emption Problem’, Mind, 105: 85–117. Menzies, P. 1999. ‘Intrinsic versus Extrinsic Conceptions of Causation’, in Causation and Laws of Nature: Australian Studies in History and Philosophy of Science, ed. H. Sankey. Dordrecht: Kluwer, 313–29. Menzies, P. 2003. ‘Is Causation a Genuine Relation?’ in Real Metaphysics: Festschrift for D. H. Mellor, ed. G. Rodriguez-Pereya and H. Lillehammer. London: Routledge, 120–36. Menzies, P. 2004a. ‘Difference Making in Context’, in Causation and Counterfactuals, ed. J. Collins, N. Hall, and L. A. Paul. Cambridge, MA: MIT Press, 139–80. Menzies, P. 2004b. ‘Causal Models, Token Causation, and Processes’, Philosophy of Science, 71: 820–32. Menzies, P. 2007. ‘Causation in Context’, in Causation, Physics, and the Constitution of Reality, ed. H. Price and R. Corry. Oxford: Oxford University Press, 191–223. Menzies, P. 2009. ‘Platitudes and Counterexamples’, in The Oxford Handbook of Causation, ed. H. Beebee, C. Hitchcock, and P. Menzies. Oxford: Oxford University Press, 191–223. Paul, L. A., and Hall, N. 2013. Causation: A User’s Guide. Oxford: Oxford University Press. Pearl, J. 2000. Causality: Models, Reasoning, and Inference. Cambridge: Cambridge University Press.



THE PROBLEM OF COUNTERFACTUAL ISOMORPHS

Pearl, J. 2009. Causality: Models, Reasoning, and Inference, Second Edition. Cambridge: Cambridge University Press. Weslake, B. 2014. ‘A Partial Theory of Actual Causation’. Forthcoming in the British Journal for the Philosophy of Science. Woodward, J. 2003. Making Things Happen: A Theory of Causal Explanation. New York: Oxford University Press.

10 Cause without Default Thomas Blanchard and Jonathan Schaffer

[A] cause is an intervention, analogous to a human action, that brings about changes in the normal course of events. (Menzies 2011: 356)

Must causal models distinguish default from deviant events? Much recent work on actual causation is conducted within the structural equations framework (Spirtes et al. 1993; Pearl 2000), via the notion of a causal model. In standard causal models one sets up a system of variables, allots values to these variables, and connects these variables via structural equations. Menzies (2004, 2007), Hitchcock (2007), Hall (2007), and Halpern (2008) have all argued, however, that standard causal models must be supplemented with a distinction between default (or normal, or expected) and deviant (or abnormal, or surprising) events. We aim to critically evaluate this proposal. We grant that the notions of ‘default’ and ‘deviant’ influence causal judgement, but we claim that this influence is best understood as arising through a general cognitive bias concerning the availability of alternatives. (Alternatives to deviant events are more likely to leap to mind.) So we think that care must be taken to distinguish between those intuitions arising from our competence with the specific concept of actual causation, and those intuitions arising merely from general background biases of cognitive performance. It is a mistake to try to capture intuitions of the latter sort within an account of causation itself (just as it would be a mistake, on noting availability effects on probability judgements, to try to incorporate the notions of default and deviant into the probability calculus itself). We also claim that some key arguments for default-relativity rely on non-apt models. So we think that a second thing to be learned from these arguments is that more attention is needed concerning what counts as an apt causal model in the first place. Overview: In }1 we introduce the structural equations framework and the notion of a causal model, discuss its connection to actual causation, and ask what makes a given model apt. In }2 we review the main case for incorporating default-relativity into causal models. Default-relativity is said to provide a conservative and psychologically plausible extension of standard causal modelling, in ways that solve multiple



CAUSE WITHOUT DEFAULT

problems. Finally in }3 we argue for excluding default-relativity from causal models. We think that default-relativity brings in complicating and under-constrained unclarities, while failing to be psychologically plausible and failing to solve the very problems it is said to solve. Overall we conclude that default-relativity belongs to the background biases of general cognitive performance, not to the specific facts of actual causation.

1 Background: Apt Causal Models for Actual Causation We live in exciting times. By ‘we’ I mean philosophers studying the nature of causation. The past decade or so has witnessed a flurry of philosophical activity aimed at cracking this nut, and, surprisingly, real progress has been made. (Hitchcock 2001: 273)

1.1 Causal Models Much recent work on actual causation is conducted within the structural equations framework (Spirtes et al. 1993; Pearl 2000), via the notion of a causal model. In standard causal models one sets up a system of variables, allots values to these variables, and links these variables via structural equations. It may be helpful to begin with a brief summary of this standard technology. (For simplicity we focus only on the deterministic case, though the technology can be fairly smoothly extended to the indeterministic case.) Following Halpern (2000), it is helpful to distinguish three layers of structure involved in causal models. First, one introduces the signature, which roughly speaking describes the situation under study. More formally, the signature is a triple S=, where U is a finite set of exogenous variables modelling the initial conditions of the system, V is a finite set of endogenous variables modelling the subsequent conditions of the system, and R is a function mapping every variable V2U [V to an at-least-two-membered set of allotted values modelling the contrast space for the conditions of the system. Graphically these are the nodes of our system, divided into root and non-root nodes (but not yet linked by any edges), each decorated with a name and a set of multiple ‘possible’ values. For instance, to model a rock being thrown through a window, one might opt to work with the very simple signature S1=, where R1 maps Throw to {0, 1} (contrasting the rock’s being left unthrown with its being thrown) and maps Shatter to {0, 1} (contrasting the window’s remaining intact with its being shattered). On top of the signature one then introduces the linkage, which roughly speaking adds in the dynamics of the system. The linkage is a pair L= where S is a signature as just characterized, and E is a set of modifiable structural equations characterizing, for every endogenous variable V2V, a function outputting a value v to V on the basis of values allotted to certain other variables, which thereby count as

THOMAS BLANCHARD AND JONATHAN SCHAFFER



the parents of V.1 Each equation in E corresponds to a series of counterfactuals of the form: ‘if the parents of V had taken these values, V would have taken that value’. E is also subject to the global constraint that the parenthood relations it induces never form loops. Graphically, the equations provide the directed edges between the nodes provided by the signature, under a global acyclicity constraint. In the case of the rock being thrown through the window with the signature S1 just described, a natural dynamics is L1=, where E1 is {Shatter←Throw} (outputting a 0 for Shatter given a 0 for Throw, and a 1 for Shatter given a 1 for Throw).2 Finally, on top of the dynamics one then adds the assignment, which effectively says what actually happened. Given our focus on the deterministic case the assignment is a pair M= where L is the linkage as just characterized, and A is a function assigning values to every exogenous variable V2U. In the deterministic case one only needs to set the initial conditions. Graphically, the assignment function adds a further decoration to the root nodes, highlighting a unique ‘actual’ value. So in the case of the rock being thrown through the window one just adds M1=, where A1 is the (smallest) function mapping Throw to 1. So far we have built up a very simple causal model: One Rock S1 = , where R1 maps both Throw and Shatter to {0, 1} L1 = M1 = Associated with every causal model is a directed acylic graph which partly conveys the causal information.3 Suppressing all decoration save for the names on the nodes, here is the graph associated with One Rock: Throw

Shatter

We pause to build out one further illustrative example, which recurs in the discussion below. This is a representative case of (symmetric) overdetermination, involving two rocks being thrown through a window at the same time, each of which is individually sufficient to shatter the window:

1 There is an assumption of discreteness here, enforced by the earlier requirement that U and V be finite. If one had a dense causal series, no variable in the series would have a direct parent at all. 2 Notational convention: We are using ‘Φ←Ψs’ to notate the idea of the value of one variable (schematically:‘Φ’) being determined by the values of some plurality of parent variables (schematically:‘Ψs’). One sometimes sees ‘=’ used instead, followed by a caveat that the determination in question is not really the symmetric relation of identity. 3 Graphs associate many-one with models. Each model uniquely induces a graph. But many distinct models uniquely induce the same graph. All models with the same cardinality of variables and structure of parenthood relations induce the same graph. These graphs are thus useful but impoverished representations.



CAUSE WITHOUT DEFAULT

Two Rocks

S2 = , where R2 maps all variables to {0, 1} L2 = (Shatter gets set to 1 iff either Throw1 or Throw2 is at 1) M2 = The associated graph is: Throw1 Shatter Throw2

1.2 Actual Causation So far we have offered a brief summary of the notion of a causal model within the structural equations framework. We haven’t yet said anything about what causes what. More precisely, we haven’t yet said anything about any of the many notions of causation, including the relation of actual (or token, or singular) causation, which is supposed to relate one token event c to another token event e just in case c was in fact causally responsible for bringing about e. Rather we have sketched a (fruitful and elegant) framework in which various accounts of various notions of causation may be phrased.4 From the perspective of actual causation, the main advantage of causal models is that they permit a precise evaluation of counterfactuals whose antecedents and consequents specify situations corresponding to values of the model’s variables. To evaluate such counterfactuals in a given model M, one considers a modified counterpart M* that stipulates the new values of the variables as per the antecedent. More precisely, one may consider a counterfactual of the following schematic form, assessed in a given assigned causal model M: If Φ1 ¼ ϕ1 and Φ2 ¼ ϕ2 and Φ3 ¼ ϕ3 ::: then Ψ 1 ¼ ψ1 and Ψ 2 ¼ ψ2 and Ψ 3 ¼ ψ3 ::: To assess whether this counterfactual is true in M, first modify M into M* via the following recipe (while doing nothing further): 1. Cut any incoming links: For all variables Φj in the antecedent such that Φj2V, (i) delete Φj from V to obtain V*, (ii) insert Φj into U to obtain U*, and (iii) delete the equation in E with Φj on the left to obtain E*. 4 Perhaps the main selling point of this framework is the development of ‘discovery algorithms’ that allow for causal structure to be inferred from correlational data (something which statisticians had once widely decried as impossible). The power and precision of this framework is, in our opinion, unrivalled. Not for nothing is virtually all recent work on actual causation couched in its terms. An account couched in other terms—without a development of the rival framework to comparable levels of sophistication— becomes hard to take seriously.

THOMAS BLANCHARD AND JONATHAN SCHAFFER



2. Reassign the stipulated values: For all variables Φj in the antecedent (all of which are now in U*), modify the assignment A into A* by assigning Φj to the value ϕj specified in the antecedent. The counterfactual is true in M if and only if the consequent (Ψ1=ψ1 and Ψ2=ψ2 and Ψ3=ψ3...) holds in M*. Effectively one has modified the model in order to surgically ‘intervene’ on the variables in the antecedent, by first converting them into initial conditions and then hand-setting their values. By permitting such precise evaluation of counterfactuals, causal models permit the precise implementation of counterfactual theories of actual causation as developed previously by Lewis (1986a; cf. Menzies 1989, inter alia), including theories that offer precise solutions to many (and some say all) long-standing problems with overdetermination and pre-emption cases. This is an active and ongoing research programme. There is as of yet no consensus on how best to understand actual causation within the causal models framework. Indeed this is part of why there is space to argue that standard causal models should be supplemented with a default function, in order to allow for an understanding of actual causation tied into the default/deviant distinction.5 But for the sake of illustration, it may be useful to consider an account presented in Hitchcock (2001: 290), as it is elegant and handles many of the cases under discussion naturally. To begin with, say that there is a directed path from variables V1 to Vn in model M if and only if there is a sequence of variables such that every variable Vj (for 1j C to (A>C). (B>C). I take (6) to be valid within an interventionist framework; I believe that List and Menzies’ treatment follows Lewis in judging it to be invalid. Supposing that N11 and N12 are followed by A1 and N13 is not and that N11, N12, N13 are the only possible realizations of the N-variable, the antecedent of (2b) is equivalent to ‘If N12, or N13 had occurred’. By (6), it follows from (2b) that ‘If N12 had occurred, A1 would not have occurred’, which is false; hence that (2b) is false. For an ‘interventionist’ account of counterfactuals in which (6) is valid and which I find congenial in other respects, see Briggs 2012. 9 Consider a variant on Glymour’s (1986) example of S, who smokes 4 packs of cigarettes a day and develops lung cancer. Assume that if S had smoked any amount in excess of 2 packs, S should have developed lung cancer. Is it true that (7) S’s smoking 4 packs a day caused his lung cancer? Applying (P) and evaluating counterfactuals in the way List and Menzies suggest, (7) comes out false, since S will develop lung cancer in close-by worlds, such as those in which he smokes 3.9 packs. I find it more natural to follow (M) in regarding claims like (7) as true, albeit less informative than one might like. In general, it seems that our usual practice is not to follow (P) in requiring that for C causes E to be true, the counterfactual (8) ‘if C had not occurred, then E would not have occurred’ must be true, when this counterfactual is evaluated in the way that List and Menzies suggest. It is worth noting in this connection that Lewis (1986) tells us that in evaluating the counterfactual ‘if C had not occurred, then E would not have occurred’ in connection with the claim ‘C causes E’ we would consider worlds in which C is ‘wholly excised’, rather than worlds which, so to speak, involve very small departures from C. Presumably this means that the relevant counterfactual for evaluating (7) is one whose antecedent has S not smoking at all (or smoking very little) rather than smoking 3.9 packs, which in turn leads to (7) being regarded as true in Lewis’s framework. I am grateful to Chris Hitchcock for helpful discussion of this issue.



INTERVENING IN THE EXCLUSION ARGUMENT

Baumgartner, M. 2010. ‘Interventionism and Epiphenomenalism’, Canadian Journal of Philosophy, 40: 359–83. Briggs, R. 2012. ‘Interventionist Counterfactuals’, Philosophical Studies, 160: 139–66. Eberhardt, F., and Scheines, R. 2007. ‘Interventions and Causal Inference’, Philosophy of Science, 74: 981–95. Glymour, C. 1986. ‘Comment: Statistics and Metaphysics’, Journal of the American Statistical Association, 81: 964–6. Lewis, D. 1986. Postscripts to ‘Causation’, in his Philosophical Papers II. Oxford: Oxford University Press. List, C., and Menzies, P. 2009. ‘Nonreductive Physicalism and the Limits of the Exclusion Principle’, Journal of Philosophy, 106: 475–502. Marcellesi, A. Forthcoming. ‘Manipulation and Interlevel Causation’. MS. Salmon, W. 1970. ‘Statistical Explanation’, in Statistical Explanation and Statistical Relevance, ed. W. Salmon. Pittsburgh: University of Pittsburgh Press, 29–87. Spirtes, P., and Scheines, R. 2005. ‘Causal Inference of Ambiguous Manipulations’, Philosophy of Science, 71: 833–45. Woodward, J. 2003. Making Things Happen: A Theory of Causal Explanation. New York: Oxford University Press. Woodward, J. 2008. ‘Mental Causation and Neural Mechanisms’, in Being Reduced: New Essays on Reduction, Explanation, and Causation, ed. J. Hohwy and J. Kallestrup. Oxford: Oxford University Press, 218–62. Woodward, J. 2015. ‘Interventionism and Causal Exclusion’, Philosophy and Phenomenological Research, 91: 303–47.

14 My Brain Made Me Do It The Exclusion Argument Against Free Will, and What’s Wrong with It Christian List and Peter Menzies

Did I consciously choose coffee over tea? No. The choice was made for me by events in my brain that I, as the conscious witness of my thoughts and actions, could not inspect or influence . . . The intention to do one thing and not another does not originate in consciousness—rather, it appears in consciousness, as does any thought or impulse that might oppose it. (Harris 2012: 7–8)

1 Introduction There are at least two challenges that a scientifically oriented world view may seem to pose for the idea that human beings have free will.1 The first is the familiar challenge from determinism. Suppose we accept The alternative-possibilities thesis: could have acted otherwise; and

Someone’s action is free only if he or she

The purported implication of determinism: to act otherwise.

Determinism rules out the ability

1 We are very grateful for detailed written comments from Helen Beebee. We also thank Eddy Nahmias for helpful suggestions. Christian List’s work was supported by a Leverhulme Major Research Fellowship. The slogan ‘My brain made me do it’ has been used as a title before. See, for example, Bloom 2006, Sternberg 2010, Mackintosh 2011, and Szalavitz 2012. This illustrates the attention that exclusion arguments against free will have received, albeit typically formulated in neuroscientific rather than philosophical terms. The slogan further appears in the title of a recent study of people’s intuitions about free will, published after we finished this chapter (Nahmias et al. 2014). A personal note from Christian List: I am immensely grateful to have had the privilege to work with Peter Menzies. I have learnt a huge amount from him over the years and will always remember him with great admiration.



MY BRAIN MADE ME DO IT

Then we must accept The classical incompatibilist conclusion: deterministic world.

There can be no free actions in a

From a scientific perspective, determinism is still a live option, since a future theory of physics might represent the world as deterministic, even if current quantum physics seems to go against this.2 This challenge has been extensively discussed and has generated a vast philosophical literature.3 However, there is a second challenge for free will, which is less discussed in philosophy, though, as we shall see, it resonates with recent discussions of neuroscience. This is what we may call the challenge from physicalism. It targets a slightly different thesis about free will:4 The causal-source thesis: Someone’s action is free only if it is caused by the agent, particularly by the agent’s mental states, as distinct from the physical states of the agent’s brain and body. Suppose we conjoin this with The purported implication of physicalism: Physicalism rules out any agential or mental causation, as distinct from causation by physical states of the agent’s brain and body. Then we must accept The source-incompatibilist conclusion: world.

There can be no free actions in a physicalist

Why might one think that physicalism rules out agential or mental causation—the purported implication of physicalism? The argument is a version of Jaegwon Kim’s (1998) famous exclusion argument. The present version goes roughly as follows. Consider any action that is supposedly caused by an agent’s mental states. Physicalism implies that those mental states supervene on (are determined by) physical states, most plausibly the agent’s brain states. But then it is arguable that the real cause of the agent’s action lies, not in the supervenient mental states, but in the underlying physical states.5 The supervenient mental states are at most an epiphenomenon of the real, physical cause. If so, the action is not caused by the agent’s mental states, contrary to our supposition, and thus, according to the causal-source thesis, does not qualify as free.6 2

At least, this is so on standard interpretations. For a recent contribution and further references, see List 2014. 4 Frankfurt-style examples are often taken to de-emphasize the alternative-possibilities thesis about free will and to strengthen our intuition that a key criterion for a free action is a causal source in the agent. 5 This follows, in particular, from two widely accepted principles: the causal closure of the physical world and the exclusion principle, as explained in more detail below. 6 To be precise, the action is not caused by the mental states unless these are identical to the underlying physical states. But any such mind-brain identity would go against the spirit of the causal-source thesis about free will and is something that all but the most reductively minded physicalists deny. 3

CHRISTIAN LIST AND PETER MENZIES



In this chapter, we critically assess this exclusion argument against free will. While the exclusion argument has received much attention in the literature on mental causation, it is seldom discussed in relation to free will, or it is mentioned only in passing.7 However, the argument expresses an idea that underlies the popular view that neuroscience, with its mechanistic picture of how the brain generates thought and behaviour, raises a serious challenge for free will. If our brains, rather than our conscious minds, cause our actions, how can those actions be free? This sceptical view is conveyed by the slogan ‘my brain made me do it’, suggesting that ‘I’ am not responsible. It is illustrated by our opening quote from the neuroscientist Sam Harris, who says that his choice of coffee over tea was ‘made for [him] by events in [his] brain’; he was only a ‘witness’. An analysis of the exclusion argument can help us assess this neuroscientific scepticism.8 We proceed as follows. In section 2, we introduce two distinct versions of the exclusion argument against free will. In section 3, we discuss several responses to it and suggest that most of them are not compelling. In section 4, we explain our preferred response, which involves showing that a key premise—the exclusion principle—is false under what we take to be the most natural account of causation in the context of agency, namely the difference-making account. It says, roughly, that to be the cause of an effect is to be the difference-maker of that effect. We argue that, if we understand agential or mental causation in this way, we can uphold both the causalsource thesis and physicalism, while avoiding the source-incompatibilist conclusion. In developing this response, we draw on our earlier work on mental causation in List and Menzies (2009).9 In section 5, finally, we return to the topic of neuroscientific scepticism about free will. 7 Philosophers who have discussed the coherence of compatibilism with a physicalist world view include Cover and O’Leary-Hawthorne (1996), O’Connor (2000), Merricks (2001), Roskies (2012), and Nahmias (2014). The three earlier works in this list focus on incompatibility arguments different from the one we formulate. One of these incompatibility arguments runs as follows: every action an agent performs supervenes on what the atoms composing his body do; no agent has a choice about what the atoms in his body do; therefore no agent has a choice about what actions he or she performs, in which case there is no free will. One problem with arguments of this kind is that they employ van Inwagen’s notorious Beta Rule: if p entails q and no one has a choice about p, then no one has a choice about q. The arguments we formulate do not employ this rule. The more recent works we have cited are closer to ours. Roskies (2012) offers a naturalistic defence of free will against ‘source-incompatibilist’ challenges and discusses some debates about mental causation in relation to free will, arriving at a picture that seems broadly compatible with the one we defend (see also List and Menzies 2009 and List 2014). Nahmias (2014) offers a survey of several scientific challenges to free will and also arrives at compatibilist conclusions consistent with ours. Finally, in an unpublished manuscript, Wilson and Bernstein (2012) discuss some structural parallels between non-reductive physicalism as a response to the problem of mental causation and compatibilism as a response to the problem of free will. Their focus, however, is not so much on formulating and assessing an exclusion argument against free will or on exploring the non-reductive physicalist stance on free will, but rather on identifying parallels between the debate on mental causation and the debate on free will. 8 Neuroscientific scepticism has increasingly been debated in the popular press. For discussion of these debates, see Roskies 2006 and, again, Nahmias 2014. 9 For another, independent discussion of how to respond to Kim’s original exclusion argument on the basis of a difference-making account of causation, see Raatikainen 2010.



MY BRAIN MADE ME DO IT

2 The Argument We present two versions of the exclusion argument against free will. The first and simpler version explicitly invokes a physical causal-closure principle as a premise, while the second, more involved version replaces this with the premise that causation implies causal sufficiency. It is needless to say that we do not endorse all of the argument’s premises. Indeed, our goal will be to explore which of them to give up.

2.1 The First Version Both versions of the argument have four premises. Here we begin with the first version: Premise 1: An agent’s action is free only if it is caused (in a relevant sense of causation simpliciter) by the agent’s mental states.10 Premise 2: Any effect that has a cause has a sufficient physical cause (i.e. a causally sufficient physical condition) occurring at the same time.11 Premise 3: The agent’s mental states are not identical to any physical states, but supervene on underlying physical states. Premise 4: If an effect has a sufficient physical cause C, it does not have any cause C* (simpliciter) distinct from C occurring at the same time (except in cases of overdetermination).12 Premise 1 is a version of the causal-source thesis about free will, introduced above. Premise 2 is a very weak physical causal-closure principle, namely a conditional one: it asserts only that if an effect has a cause at a particular time, then it has a sufficient physical cause at that time. Note that the antecedent of this conditional refers to a cause simpliciter, while the consequent refers to a causally sufficient condition; these two notions need not coincide. Later we discuss the notions of cause and sufficient 10

We discuss different notions of causation in section 4 below. We use the term ‘sufficient cause’ as a shorthand for ‘causally sufficient condition’. For the purposes of the present argument, we do not make any assumptions about whether a sufficient cause (i.e. a causally sufficient condition) automatically qualifies as a cause simpliciter. For example, we might say that, if the world is deterministic, the event of the big bang was causally sufficient for all subsequent events, and yet not prejudge the question of whether it should also count as a cause simpliciter of all subsequent events. Indeed, on the account of causation that we ultimately defend (the difference-making account), causally sufficient conditions are conceptually distinct from causes. As discussed further below, Premise 2 does not by itself imply or presuppose determinism. Consistently with Premise 2, there could be events without any causes in an indeterministic world. We also discuss a version of our argument that invokes a probabilistic notion of causation. 12 To avoid certain trivial counterexamples, one might fine-tune this premise by referring to a minimal sufficient physical cause in its antecedent. There can easily be distinct sufficient physical causes for the same effect, occurring at the same time, and so it can happen that C is a minimal sufficient physical cause for E and C* is a non-minimal one which entails C. Even if we stipulated that only C but not C* qualifies as a cause simpliciter for E, Premise 4 would be violated in its original form, since it would imply that C*’s being a sufficient physical cause for E excludes C, which is distinct from C*, from being a cause simpliciter. With the minimality restriction in the antecedent, Premise 4 would be satisfied. For simplicity, however, we use the original, unrestricted formulation in the main text. Later we discuss non-trivial counterexamples to Premise 4. 11

CHRISTIAN LIST AND PETER MENZIES



cause in more detail. Premise 3 is the central claim of non-reductive physicalism, according to which the relationship between mind and body, or the physical world more generally, is one of supervenience without identity: mental states supervene on underlying physical states, but are not reducible to them. Premise 4, finally, is a version of Jaegwon Kim’s exclusion principle. It rules out the existence of two or more competing causes for the same event, but does not apply to cases of genuine causal overdetermination. Genuine overdetermination involves distinct causes that are unconnected or at most contingently connected, such as two assassins simultaneously shooting at the same target. The cases to which the exclusion principle applies are those in which the supposed rival causes are necessarily connected, especially via a supervenience relation. Examples are a brain state and a mental state that supervenes on it, which might both be candidate causes of the same effect, such as an agent’s action. Note that, in its present formulation, the exclusion principle refers to a sufficient cause in its antecedent clause, and to a cause simpliciter in its consequent clause.13 Premises 1 to 4 entail The conclusion:

There are no free actions.

To see this, suppose a particular action is free. By Premise 1, it is caused by the agent’s mental states; call the relevant set of mental states C*. By Premise 2, since the action has a cause (namely C*), it has a sufficient physical cause occurring at the same time; call it C. By Premise 3, C* is not identical to C, but supervenient on C; we assume that C is specified sufficiently richly to include the supervenience base of C*. In light of the supervenience relationship between C and C*, we are not dealing with a case of causal overdetermination. Hence, by Premise 4, C’s being a sufficient cause for the action excludes C* from being a cause, a contradiction.

2.2 The Second Version The second version of the argument replaces Premise 2 with Premise 2*:

Causation implies causal sufficiency.14

Again, the resulting premises entail The conclusion:

There are no free actions.

To see this, we first require a preliminary result: Lemma: If C* is causally sufficient for some effect E, and C* supervenes on C, then C is causally sufficient for E. 13 Sufficient causes need not compete with one another. As we have already noted, it is entirely possible for C to be causally sufficient for E, and for C*, which is distinct from C but entails C, to be causally sufficient for E as well. 14 Whether Premise 2* is plausible depends on how causation and causal sufficiency are understood. For the premise to be plausible, both causation and causal sufficiency might have to be understood as referring to the relevant background circumstances. Below we briefly assess different interpretations of Premise 2*.



MY BRAIN MADE ME DO IT

The proof of this lemma is straightforward. Suppose C* is causally sufficient for E, and C* supervenes on C. Assume, for a contradiction, that C is not causally sufficient for E. Then C could occur without E. But the occurrence of C necessitates the occurrence of C*, which is sufficient for E, a contradiction. To show that Premises 1, 2*, 3, and 4 entail that there are no free actions, suppose a particular action is free. By Premise 1, it is caused by the agent’s mental states; call the relevant set of mental states C*. By Premise 2*, since C* is a cause of the action, it is a sufficient cause. By Premise 3, the agent’s mental states C* are not identical to any physical states, but supervenient on underlying physical states; call the relevant set of physical states C. By our lemma, since C* is causally sufficient for the agent’s action, and C* supervenes on C, C is itself causally sufficient for the agent’s action. In light of the supervenience relationship between C and C*, we are not dealing with a case of causal overdetermination. Hence, by Premise 4, C’s being a sufficient cause for the action excludes C* from being a cause, a contradiction.

3 Some Responses to the Argument We can avoid the conclusion that there are no free actions only by giving up at least one of the premises of each version of the argument. Let us briefly discuss the options, considering each premise on its own terms. Although we are ultimately interested in responses to the argument that are consistent with a scientifically oriented world view, we note that some of the premises do not, by themselves, imply or presuppose any version of physicalism. In this sense, the premises are quite ecumenical.

3.1 Giving up Premise 1 Recall that Premise 1 says that a necessary condition for an action to be free is that it is caused by the agent’s mental states. This is a version of the causal-source thesis and captures an important intuition about free will. It is even weaker than the causalsource thesis as formulated in the introduction. While that thesis included the requirement that the mental states causing the agent’s action be distinct from the physical states of the agent’s brain and body, Premise 1 does not include this requirement. Thus, Premise 1 is consistent with the possibility that the relevant mental states could be identical to underlying brain and bodily states. So, even proponents of reductive physicalism should have little grounds for rejecting Premise 1 by itself. Furthermore, just as Premise 1 does not rule out an identity between mind and brain, so it does not rule out a complete disconnect between the two. Without additional assumptions, it allows the mental states that cause the agent’s action to be non-supervenient on any physical states. Thus Premise 1 on its own is compatible even with interactionist dualism of the traditional Cartesian sort.

CHRISTIAN LIST AND PETER MENZIES



The only way to reject this premise while holding on to the idea that free actions have a causal source in the agent would be to insist on a form of agent causation under which actions are caused not by the agent’s mental states but by some other aspect of the agent. This idea, however, seems metaphysically mysterious, and we set it aside. In sum, we think Premise 1 is hard to give up.

3.2 Giving up Premise 2 or 2* We have considered two versions of the second premise, 2 and 2*. As already noted, Premise 2 is a very weak physical causal-closure principle. It only asserts the existence of sufficient physical causes for those events that have a cause. This is entirely consistent with the occurrence of non-physical events that have no cause and even with the occurrence of physical events that have no cause (for example, genuinely uncaused events in an indeterministic world). Physicalists, whether of a reductive or non-reductive kind, should have no problem with this premise. We would only have to relax Premise 2 if we accepted physical indeterminism and were nonetheless prepared to say that some physically undetermined events have causes. We turn to the issue of indeterministic causation in our discussion of Premise 2* below. Non-physicalists may find it harder to accept Premise 2. Interactionist dualists would presumably reject it, though their metaphysical picture does not fit with a scientific world view, so we set it aside. Naturalistically minded dualists might accept Premise 2 against the background of a nomological supervenience relation between the physical and the non-physical, and thus accept that, given the laws of our world, any event that has a cause has a sufficient physical cause, understood as a physical condition whose presence would nomologically necessitate the event in question. In sum, Premise 2 seems hard to give up unless we are prepared to depart significantly from a scientifically oriented world view. Premise 2*, unlike Premise 2, requires no form of physical causal closure and instead constrains the notion of causation. It says that any event C that is the cause of an effect E (in the sense of causation simpliciter) is also causally sufficient for E. Whether this principle is acceptable or not depends on how we understand the notions of causation and causal sufficiency. If causal sufficiency merely required that if C were to occur, then E would occur (a counterfactual conditional), then Premise 2* would be hard to deny under almost any notion of deterministic causation. By contrast, if causal sufficiency required nomological necessitation (something akin to the strict conditional: necessarily, if C then E) while causation required counterfactual difference-making, Premise 2* would be questionable. Difference-making causes make two counterfactual conditionals true: first, if C were to occur, then E would occur; and second, if C were not to occur, then E would not occur. But they do not generally make true the strict conditional: necessarily, if C then E. Finally, it is possible to formulate the second version of our exclusion argument in terms of a probabilistic notion of causation: any reference to causal sufficiency in the argument must then be replaced by a reference to high conditional probability.



MY BRAIN MADE ME DO IT

Suppose, in particular, we replace the premise that causation (simpliciter) implies causal sufficiency with the premise that causation (simpliciter) implies high conditional probability: i.e. C’s causation of E implies that Pr(E|C) is high. Then it is easy to demonstrate that high conditional probability is transmitted across supervenience when a plausible ‘Markov condition’ obtains: if (i) Pr(E|C*) is high, (ii) a subvenient event C entails C*, and (iii) C* screens off C from E (i.e. Pr(E|C*&C) = Pr(E|C*)), then Pr(E|C) = Pr(E|C*). Given this new premise and the new lemma, the causal source argument proceeds much as above. In sum, although Premise 2* can be denied under some assumptions about causation and causal sufficiency, it would seem unsatisfactory to let the vindication of free will hinge on those assumptions.

3.3 Giving up Premise 3 Giving up Premise 3 would be to deny non-reductive physicalism. Kim advocates this, espousing reductive physicalism, which involves the denial of non-identity. But we think that this would be an unsound response to the exclusion argument against free will, for at least two reasons. First, the multiple-realizability objection to reductive physicalism seems broadly correct. For all we know, mental states are more coarse-grained than their subvenient brain states and can be physically realized in multiple ways. Hence mental states cannot be identified with their physical realizers. Second, even if we set the issue of multiple realizability aside, most proponents of the causal-source thesis about free will are likely to accept a non-reductive view about the relationship between brain and mind. This is because they wish to emphasize that free actions are those caused by an agent’s mental states, qua rationalizing intentional states, not qua physical states of the brain. Free will, on this picture, is a higher-level, agential phenomenon, not a lower-level, physical one.15 It is plausible to think that free will presupposes rational capacities for controlling one’s actions. While one can rationally control one’s conscious intentional states, one cannot rationally control one’s brain states, in part because one is seldom aware of them. So, free action seems to require causal explanation at the intentional level rather than at the physical level. This, in turn, makes the non-identity part of Premise 3 hard to give up. Another way to relax Premise 3 would be to maintain that mental states need not supervene on physical states. Consistently with the other premises, we could then conclude that free actions are genuinely causally overdetermined: they have both an agential cause and a physical cause, which stand at most in a contingent relationship 15

On free will as a higher-level phenomenon, see also List 2014. The present picture is further supported by the discussion offered by Roskies (2012), who emphasizes the role of psychological, as opposed to physical, control variables for intentional action. By a control variable, Roskies means roughly a variable which, when changed by certain interventions, leads to systematic changes in other variables. For discussion of the notion, see Hitchcock and Woodward 2003.

CHRISTIAN LIST AND PETER MENZIES



to one another. (The lack of a necessary relationship is important, since in the presence of a necessary relationship we would not be able to apply the exemption clause in Premise 4, which permits cases of overdetermination.) Giving up supervenience of the mental on the physical, however, seems not very satisfactory. Not only would the present route involve a significant departure from a scientifically oriented world view, but the exclusion argument against free will would be reinstated if we strengthened Premise 4 by dropping its exemption clause (referring to causal overdetermination). In sum, we see little promise in dropping Premise 3.

3.4 Giving up Premise 4 As should be evident by now, if we wish to resist the exclusion argument against free will without sacrificing other central tenets of a scientifically oriented world view, we must give up Premise 4: the exclusion principle. Drawing on our previous work on mental causation (List and Menzies 2009), we now show that this principle is false if we accept the account of causation that is arguably most natural in the context of agency: the difference-making account.

4 Our Diagnosis of the Argument’s Flaw 4.1 Causation There are at least two fundamentally different ways in which the notion of causation can be understood: as ‘production’ or as ‘difference-making’.16 Each of these labels corresponds to a family of accounts of causation. On a production account, to be the cause of an effect is to be the producer of that effect, in some metaphysical sense of production. Causation here involves a causal ‘oomph’, i.e. the production of an outcome through some causal force or power, on the model of a billiard ball’s causing the motion of another by transmitting a force on impact. On a difference-making account, by contrast, causation is a form of counterfactual or probabilistic dependence: to be the cause of an effect is to be the difference-maker of that effect. For convenience, we here spell this out in counterfactual terms: C causes E if and only if two conditionals are satisfied, as already mentioned above: The positive conditional: If C were to occur, then E would occur. The negative conditional: If C were not to occur, then E would not occur. Arguably, a difference-making account is more in line with the practices of causal attribution and explanation in the sciences than a production account is. When scientists obtain evidence for counterfactual difference-making on the basis of careful See, for example, Armstrong 2004, Hall 2004, and Kim 2005. Hall speaks of ‘production’ and ‘dependence’. 16



MY BRAIN MADE ME DO IT

experimental or statistical controls, they usually interpret this as evidence for causation. On a production account, which involves the idea of a ‘causal oomph’, such an interpretation would involve a leap of faith: evidence for counterfactual differencemaking is not automatically evidence for a causal ‘oomph’. On a difference-making account, on the other hand, evidence for counterfactual difference-making is naturally evidence for causation, because causation is just counterfactual difference-making. A difference-making account also fits well with the connection that is frequently made between causation and intervention in a system.17 For C to be the cause of E, on this picture, it must be the case that interventions on C make a difference to E. Further, as we have argued in our earlier work (List and Menzies 2009), the most natural way to spell out the idea of mental causation is to say that an agent causes an action if and only if his or her mental state is the difference-maker of the action. Conceptually, producing causes and difference-making causes must be distinguished from one another. When a flask of boiling water breaks due to the pressure, the producing cause may well be the motion of a specific subset of the water molecules; yet, the difference-making cause is the boiling of the water. Only the latter but not the former satisfies the two (positive and negative) conditionals stated above.18 We return to this example below. Causally sufficient conditions—whether or not they qualify as producing causes— are not the same as difference-making causes. A man’s taking a contraceptive pill is causally sufficient—in some vacuous sense—for his not becoming pregnant, but there is no genuine causal relation here: neither of the producing kind, nor of the difference-making kind.19 In sum, we suggest that the best interpretation of causation in the context of agency is a difference-making one: to say that an action is caused by the agent’s mental states is to say that those mental states are the difference-making causes of the action.20 What does this imply for the exclusion argument against free will?

4.2 The Falsity of the Exclusion Principle Recall that the exclusion principle states that if an effect has a sufficient physical cause C, it does not have any cause C* distinct from C occurring at the same time, 17

See Pearl 2000 and Woodward 2003. In this particular example, we are broadly in agreement with Jackson and Pettit’s analysis (1990). See also Pettit 2013. 19 Note that, since a man (under standard assumptions) can never become pregnant, his taking a contraceptive pill cannot change that fact and hence will vacuously qualify as a sufficient cause for his not becoming pregnant, no matter whether we interpret causal sufficiency in nomological terms, counterfactual terms, or probabilistic terms. Further, note that the claim that causal sufficiency does not imply causation is consistent with the reverse claim that causation implies causal sufficiency, asserted by Premise 2*, though we need not commit ourselves to the latter claim either. 20 We set aside cases of pre-emption and overdetermination, for which the simple analysis of differencemaking causation in terms of the positive and negative conditionals does not work. A more sophisticated analysis is required for such cases. 18

CHRISTIAN LIST AND PETER MENZIES



except in cases of overdetermination. Kim defended this principle on the basis of a production account of causation. The idea is that, except in cases of genuine overdetermination, the causal responsibility for any effect must be uniquely attributable: the same effect cannot be due to two or more simultaneous but competing sources of causal power. Regardless of whether this principle is plausible under an account of causation as production, it is easy to see that it is false when causation is understood as difference-making. Again, consider the flask of boiling water. Its full molecular microstate at the time of the breaking may well be a sufficient cause for the breaking, and the boiling of the water supervenes on that microstate. Yet, it is the boiling that is the differencemaking cause of the breaking, not the underlying microstate. If the boiling had occurred, but had been realized by a slightly different microstate, the flask would still have broken, and if the boiling had not occurred, the flask would have remained intact. So, the positive and negative conditionals for difference-making are satisfied when C is the boiling of the water and E is the breaking of the flask. By contrast, although it is true that if the microstate of the flask had been exactly as it was, the flask would have broken, it is not true that if the microstate had been slightly different, the flask would have remained intact. The boiling could have been realized in many different ways, through different configurations of molecular motion, and would still have led the flask to break. So, while the positive conditional for differencemaking is satisfied when C is the microstate and E is the breaking of the flask, the negative conditional is not. This shows that the difference-making cause for the breaking of the flask is the boiling event, not the microstate on which it supervenes. Nonetheless, the microstate of the flask is causally sufficient for the breaking. Consequently, we have a counterexample to the exclusion principle. Similarly, it can be argued that when an agent intentionally moves his or her arm, the difference-making cause of the action is (plausibly) not the subvenient brain state, but the supervenient intention (List and Menzies 2009; for a similar argument, see also Raatikainen 2010). Only the intention, but not the brain state, satisfies the two conditionals for difference-making. If the intention were present, the action would be performed, and if the intention were absent, it would not. The brain state, by contrast, satisfies only the positive conditional, but arguably not the negative one. If the precise realizing brain state were absent, but the same intention were realized by another brain state, the action would presumably still be performed. Accordingly, the exclusion principle is violated here: the brain state is causally sufficient for the action, and the intention supervenes on it; yet, on the difference-making account, it is the intention, not the brain state, that is the cause of the action. These considerations show that the exclusion principle is false when causation is understood as difference-making. In sum, we reject Premise 4 and can therefore consistently accept Premises 1 to 3 while still holding the view that there can be free actions. This, we believe, is the most compelling response to the exclusion argument against free will.



MY BRAIN MADE ME DO IT

5 Neuroscientific Scepticism about Free Will Revisited Neuroscientific scepticism about free will is the view that advances in neuroscience, especially discoveries of the neural causes of thought and behaviour, raise serious challenges for free will. For any of our purportedly intentional actions, we seem increasingly warranted in saying: ‘My brain made me do it. Hence it was not my own free choice.’ Thus Harris concludes: Free will is an illusion. Our wills are simply not of our own making. Thoughts and intentions emerge from background causes of which we are unaware and over which we exert no conscious control. We do not have the freedom we think we have. (2012: 5)

Similar claims can be found in the popular writings of other neuroscientists, who, like Harris, attempt to startle their readers with the claim that free will is an illusion and that human action is a consequence of physical processes beyond our control. Gazzaniga (2011) is another prominent example of this genre. To assess such neurosceptical claims, we need to make the argument for them more precise.21

5.1 The Neurosceptical Argument The argument that proponents of neuroscepticism tend to invoke—albeit often implicitly—has two premises: The purported exclusion of free will by neural causes: If an agent’s choices and actions are wholly caused by neural states and processes that are inaccessible to his or her consciousness, then these choices and actions are not free. The thesis of neural causation: Human choices and actions are wholly caused by neural states and processes that are inaccessible to the agent’s consciousness. These premises then support The neurosceptical conclusion:

Human choices and actions are not free.

What should we say about this argument? The argument is certainly valid, and its premises seem at first sight plausible. Consider the first premise, the purported exclusion of free will by neural causes. To the extent that the causes of an agent’s choices and actions bypass the conscious mental states that are supposed to play a role in deliberation, it would appear that these choices and actions are indeed not free. As Nahmias (2006) has shown through survey evidence, this thesis is something that most ordinary people who are not trained in philosophy believe. Thus the first premise is a widely accepted assumption about free will. Similarly, the second premise, the thesis of neural causation, is plausible, as it appears to be supported by a growing body of experimental work. Libet’s classic 21

For a helpful review of scientific challenges to free will, see Nahmias 2010.

CHRISTIAN LIST AND PETER MENZIES



study of the neuronal readiness potentials that precede conscious intentions to perform actions is a widely cited piece of evidence. Libet (1983) showed that the neuronal activity leading to the performance of an action tends to begin several hundred milliseconds before a subject appears to be consciously aware of his or her intention to act. Although the precise interpretation of this finding remains controversial, Libet’s experiment has been replicated by others, in a number of variations. In a particularly dramatic study of the neural correlates of intention formation, Haynes and colleagues (2007) were able to use brain-scan data to predict subjects’ choices between two actions 7–10 seconds before the action took place.22 All these findings seem consistent with the claim that human choices and actions are ultimately the result of subconscious processes beyond an agent’s control. Despite their initial plausibility, however, the two premises do not withstand closer scrutiny. Let us discuss them in turn.

5.2 The Purported Exclusion of Free Will by Neural Causes The first premise—the purported exclusion of free will by neural causes—is most plausible when it is interpreted as relying on an exclusion argument of the kind we have investigated in previous sections. To show that the premise holds, one might argue as follows. Let us assume that an agent’s actions are wholly caused by neural states and processes; it then follows from the non-identity of mental states and neural states, together with an exclusion principle, that these actions are not caused by any mental states occurring at the same time; and so, by the causal-source thesis, the actions are not free. But our preceding discussion should alert us to the fact that this reasoning depends on the relevant exclusion principle. If this principle states that the existence of a physical sufficient cause for an action excludes any simultaneous mental state from being a difference-making cause of that action—as formulated in Premise 4—we have good reason to reject it. We showed in the last section that sufficient causes at the physical level can co-exist with distinct, higher-level difference-making causes of the same effects. For example, the fact that a specific molecular microstate of a gas is sufficient to break the walls of its container is consistent with the fact that the macrostate of the gas’s pressure on the walls is the difference-making cause of the breaking. In the case of human action, the same is true of sufficient causes at the neural level and difference-making causes at the mental level. As we have seen, the existence of a neural state that is causally sufficient for some action is consistent with the existence of a difference-making cause at the mental level, such as the agent’s intention. Thus the reasoning in support of the first premise of the neurosceptical argument does not go through. 22

For a detailed critical discussion to which we are indebted, see Nahmias 2014.



MY BRAIN MADE ME DO IT

Alternatively, suppose we try to support that premise by reinterpreting the exclusion principle as follows: Reinterpreted exclusion principle: If an effect has a difference-making cause C at the physical level, it does not have any other difference-making cause C* at the mental level, occurring at the same time. This is distinct from the exclusion principle on which we have focused so far, which refers to a sufficient cause, not a difference-making cause, in the antecedent. Therefore our rejection of the earlier principle—in the form of Premise 4—does not carry over to the present, reinterpreted version. The present principle only says that there cannot simultaneously exist more than one difference-making cause for the same effect, at different levels. This is consistent with the possibility that a lower-level sufficient cause might co-exist with a higher-level difference-making cause. Indeed, as we have shown in List and Menzies (2009), there are conditions under which the reinterpreted exclusion principle holds, despite the failure of the original principle. But now it is reasonable to ask: Does the reinterpreted principle vindicate the neurosceptical argument? We reply: Not automatically, because the sceptic still has to establish the second premise of the argument, the thesis of neural causation, interpreted in terms of difference-making causation. In other words, the sceptic has to show that there are difference-making neural causes for all actions. It is not enough to show this in a single instance. So, let us turn to the thesis of neural causation.

5.3 The Thesis of Neural Causation As already noted, when we understand causation as difference-making, we are likely to conclude that the cause of an agent’s action is not the agent’s brain state, but his or her mental state. Only the supervenient mental state, but not the subvenient brain state, may satisfy the two conditionals for difference-making. Recall, in particular, that the realizing brain state plausibly violates the negative conditional: if it were absent, the action might still be performed, provided the same mental state is realized by some other brain state. More generally, we can identify conditions under which a supervenient event alone, rather than its physical realizer, is the difference-making cause of an effect. The following result holds (List and Menzies 2009): Proposition: A supervenient event C* is the difference-making cause of an effect E, and its subvenient realizer C is not, if and only if C* and E satisfy the positive and negative conditionals for difference-making and this causal relationship is realization-insensitive. Realization-insensitivity means that the effect E continues to occur under some small perturbations in the physical realization of the cause C*; formally, E occurs in some closest not-C-worlds that are C* worlds. Figure 14.1 (adapted from List and Menzies 2009) provides an illustration. The figure shows a space of possible worlds. The small dot in the central circle corresponds to the actual world. The concentric circles around it correspond to increasingly distant

CHRISTIAN LIST AND PETER MENZIES

C*



E

W

C

Figure 14.1 Realization-insensitive causation

possible worlds. Any worlds within the same circle (i.e. either within the innermost circle, or within the second circle but outside the innermost circle, or within the third circle but outside the second, and so on) are deemed to be equidistant from the actual world. The large half-oval region on the left-hand side corresponds to the set of worlds in which the supervenient event C* occurs. The smaller half-oval with the diagonal lines corresponds to the set of worlds in which C* has the physical realizer C. The shaded region in the centre corresponds to the set of worlds in which the effect E occurs. It is easy to see that, under this configuration, C* but not C is a difference-making cause of E: relative to the actual world, E is present in all nearest possible worlds in which C* occurs, and absent in all nearest possible worlds in which C* does not occur. By contrast, while E is present in all nearest possible worlds in which C occurs, it is not absent in all nearest possible worlds in which C does not occur; indeed, E continues to occur in those worlds in the central circle in which C* has a different physical realizer. In sum, C*, but not C, is a difference-making cause of E, and the causal relationship is realization-insensitive. Here, contrary to the familiar idea of a lower-level cause excluding a higher-level one (‘upwards exclusion’), the supervenient event C* excludes the subvenient event C from being a difference-making cause of E: a ‘downwards exclusion’ result. The bottom line is that the sceptic cannot take the thesis of neural causation for granted; the existence of a mental difference-making cause of some action may well exclude the existence of any underlying physical difference-making cause of the same action. These conditions for ‘downwards exclusion’ are fully consistent with the reinterpreted exclusion principle we have discussed. Of course, it is an empirical question whether the difference-making cause of an agent’s action is some mental state or not. However, psychological experimentation should enable us to answer this question, by establishing whether it is true that if an agent were to possess a particular mental state, he or she would perform the action, and if the agent were not to possess that mental state, he or she would not perform it. When there is such a causal relationship and this relationship is realizationinsensitive, our ‘downwards exclusion’ result implies that no subvening neural



MY BRAIN MADE ME DO IT

cause can be a difference-making cause of the action. The control variables for an agent’s actions may well be the relevant mental states rather than their physical realizers.23

5.4 Concluding Remarks Although the reinterpreted exclusion principle goes some way towards vindicating the first premise of the neurosceptical argument, the possibility of ‘downwards exclusion’, which is consistent with the principle, goes an equal distance in limiting the credibility of the second premise. If mental states, rather than their physical realizers, are the difference-making causes of an agent’s actions, we must reject the thesis of neural causation, the second premise of the neurosceptical argument. In sum, the neurosceptical argument against free will is unsound. The argument depends crucially on the plausibility of an exclusion principle underlying its first premise. When this principle is formulated in terms of the compatibility of sufficient physical causes with difference-making mental causes, we have good reason to reject it. When the principle is formulated in terms of the compatibility of difference-making physical causes with difference-making mental causes, the principle has some credibility under suitable conditions. But the support it lends to the first premise of the argument is counterbalanced by the doubt that the possibility of ‘downwards exclusion’ casts on the second.24

References Armstrong, D. 2004. ‘Going through the Open Door: Counterfactual vs. Singularist Theories of Causation’, in Collins, Hall, and Paul 2004: 445–57. Bloom, P. 2006. ‘My Brain Made Me Do It’, Journal of Cognition and Culture, 6: 209–14. Collins, J., Hall, N., and Paul, L. A. (eds) 2004. Causation and Counterfactuals. Cambridge, MA: MIT Press. Cover, J., and O’Leary-Hawthorne, J. 1996. ‘Haecceitism and Anti-Haecceitism in Leibniz’s Philosophy’, Noûs, 30: 1–30. Gazzaniga, M. 2011. Who’s in Charge: Free Will and the Science of the Brain. New York: HarperCollins. Hall, N. 2004. ‘Two Concepts of Causation’, in Collins, Hall, and Paul 2004: 225–76. Harris, S. 2012. Free Will. New York: Simon & Schuster. Haynes, J.-D., Sakai, K., Rees, G., Gilbert, S., Frith, C., and Passingham, R. E. 2007. ‘Reading Hidden Intentions in the Human Brain’, Current Biology, 17: 323–8. Hitchcock, C., and Woodward, J. 2003. ‘Explanatory Generalizations, Part II: Plumbing Explanatory Depth’, Noûs, 37: 181–99. 23

On this point, see also Roskies 2012 and note 15 above. For a recent empirical study suggesting that most people are not persuaded by a certain common form of neuroscientific scepticism about free will (which claims that the possibility of perfect prediction of behaviour based on neural information undermines free will), see Nahmias et al. 2014. 24

CHRISTIAN LIST AND PETER MENZIES



Jackson, F., and Pettit, P. 1990. ‘Program Explanation: A General Perspective’, Analysis, 50: 107–17. Kim, J. 1998. Mind in a Physical World. Cambridge, MA: MIT Press. Kim, J. 2005. Physicalism, Or Something Near Enough. Princeton: Princeton University Press. Libet, B. 1983. ‘Time of Conscious Intention to Act in Relation to Onset of Cerebral Activity (Readiness Potential): The Unconscious Initiation of a Freely Voluntary Act’, Brain, 106: 623–42. List, C. 2014. ‘Free Will, Determinism, and the Possibility of Doing Otherwise’, Noûs, 48: 156–78. List, C., and Menzies, P. 2009. ‘Non-Reductive Physicalism and the Limits of the Exclusion Principle’, Journal of Philosophy, 105: 475–502. Mackintosh, N. 2011. ‘My Brain Made Me Do It’, New Scientist, 212: 26–7. Merricks, T. 2001. Objects and Persons. New York: Oxford University Press. Nahmias, E. 2006. ‘Folk Fears about Freedom and Responsibility: Determinism vs. Reductionism’, Journal of Cognition and Culture, 6: 215–37. Nahmias, E. 2010. ‘Scientific Challenges to Free Will’, in A Companion to the Philosophy of Action, ed. T. O’Connor and C. Sandis. Oxford: Wiley-Blackwell, 345–56. Nahmias, E. 2014. ‘Is Free Will an Illusion? Confronting Challenges from the Modern Mind Sciences’, in Moral Psychology, Vol. 4: Free Will and Moral Responsibility, ed. W. SinnottArmstrong. Cambridge, MA: MIT Press, 1–26. Nahmias, E., Shepard, J., and Reuter, S. 2014. ‘It’s OK if “My Brain Made Me Do It”: People’s Intuitions about Free Will and Neuroscientific Prediction’, Cognition, 133: 502–16. O’Connor, T. 2000. Persons and Causes: The Metaphysics of Free Will. New York: Oxford University Press. Pearl, J. 2000. Causality: Models, Reasoning, and Inference. Cambridge: Cambridge University Press. Pettit, P. 2013. ‘The Program Model, Difference-makers, and the Exclusion Problem’. Unpublished paper. Raatikainen, P. 2010. ‘Causation, Exclusion, and the Special Sciences’, Erkenntnis, 73: 349–63. Roskies, A. 2006. ‘Neuroscientific Challenges to Free Will and Responsibility’, Trends in Cognitive Science, 10(9): 419–23. Roskies, A. 2012. ‘Don’t Panic: Self-authorship without Obscure Metaphysics’, Philosophical Perspectives, 26: 323–42. Sternberg, E. J. 2010. My Brain Made Me Do It: The Rise of Neuroscience and the Threat to Moral Responsibility. Amherst, NY: Prometheus Books. Szalavitz, M. 2012. ‘My Brain Made Me Do It: Psychopaths and Free Will’, Time, August. Wilson, J., and Bernstein, S. 2012. ‘Free Will and Mental Causation’. Unpublished manuscript. Woodward, J. 2003. Making Things Happen: A Theory of Causal Explanation. Oxford: Oxford University Press.

15 Epiphenomenalism for Functionalists Helen Beebee

1 Introduction The debate about the alleged incompatibility between non-reductive physicalism and the causal efficacy of the mental—often referred to as the ‘exclusion problem’ or ‘the problem of mental causation’—continues to rage.1 In recent years, that debate has focused almost exclusively on the alleged problem posed by the non-reductive physicalist’s claim that mental properties are multiply realizable: in any given population or kind of being (humans, dogs, Martians, or whatever), or indeed perhaps in any given individual at different times, the property of, say, being in pain, call it M, might, for all we know, be realized by any of various neurological (or other physical) properties P1, P2, P3,... .The problem is then supposed to be that ‘all the causal work’ is being done by the realizer property. Given the causal closure of the physical, it would seem that whichever of P1, P2, etc. is instantiated is causally sufficient in the circumstances for the occurrence of a given effect e (saying ‘ouch’, say). Hence there is nothing left over for M to do: being in pain does not cause people to say ‘ouch’. And, since epiphenomenalism about mental properties is unacceptable, non-reductive physicalism must be abandoned. Non-reductive physicalists disagree with this conclusion, of course, and various robust defences of it have recently been offered.2 I’m pretty confident that some such defence of the claim that multiple realization does not preclude causal relevance succeeds. (If I had to put money on which, I’d plump for Woodward’s defence, which relies on conceiving causation as difference-making (Woodward 2008 and this volume); see §4 below.)

1

Many thanks to Huw Price, Frank Jackson, Matt Tugby, and Philip Pettit, as well as various seminar audiences, for many helpful comments. Special thanks are due—though they cannot now be delivered—to Peter Menzies, whose warm enthusiasm and support have been a constant throughout my philosophical career. 2 See, for example, List and Menzies 2009, Raatikainen 2010, Weslake forthcoming.

HELEN BEEBEE



The vast majority of the recent literature focuses exclusively on the alleged problem of multiple realization. In doing so, however, it ignores a second—and, I think, less tractable—problem of mental causation, which remains even once we accept one of the available solutions to the problem of multiple realization. I shall call it ‘the Causal Role Problem’—although it is a very close relative of what has become known as ‘the Problem of Metaphysically Necessitated Effects’. The non-reductive physicalist takes mental properties to be multiply realized because mental properties are assumed to be functional properties. To be in pain, for example, is to be in some physical state or other, such that being in that state typically has certain causes (e.g. bodily damage) and effects (avoidance behaviour, utterance of expletives, etc.). Functional properties are defined in terms of their causes and effects. And that’s where the problem lies: given a standard—and plausible—account of the individuation of events—one that can be reformulated as a plausible account of the kinds of properties that are apt for causal relevance—such properties are simply inapt for playing a causal role. Qua functional property, being in pain can no more be a cause of saying ‘ouch’ than (to use a well-worn example) having dormitive virtue can be a cause of sleep.3 Now, there are of course moves that can be made, which one might take to solve the Causal Role Problem. I argue in §5 that one such move (Antony 2008) fails, after explaining in a bit more detail what the Causal Role Problem is in §2, distinguishing it from the Problem of Metaphysically Necessitated Effects in §3, and arguing that existing promising solutions to the Exclusion Problem are not solutions to the Causal Role Problem in §4. That leaves the non-reductive physicalist facing the allegedly unwelcome prospect of embracing epiphenomenalism about mental properties. As I argue in §6, however, it is far from clear that what Gabriel Segal (2009) calls ‘epiphobia’ is warranted. Very many—perhaps even most—of our ordinary beliefs about the mental are entirely consistent with epiphenomenalism; in particular, epiphenomenalism is consistent with both the explanatory nonredundancy and the practical usefulness of mental properties, and with the causal efficacy of mental events.

2 The Causal Role Problem We need, first, to distinguish between events on the one hand and properties on the other. Much of the mental causation literature proceeds as though properties are, or can be, the relata of token causation: we are generally explicitly asked to consider whether or not some mental property M is a cause of some physical property P, 3 Authors who do discuss versions of this problem include Block (1990), Lyons (2006), Rupert (2006), and Segal (2009). What I say in this chapter overlaps to some extent with what they say—although, as we’ll see in §3, the focus is usually on the Problem of Metaphysically Necessary Effects rather than the Causal Role Problem.



EPIPHENOMENALISM FOR FUNCTIONALISTS

whereas in fact we are really being asked to consider a particular case, for example whether or not my being in pain, just now, was a cause of some subsequent bit of physical behaviour. Properties, just by themselves, make good candidates for the relata of a general causal relation (‘being in pain generally causes avoidance behaviour’, say), but not for the relata of a token one. At the token level, properties are most naturally seen not as the relata of causation but as candidates for causal relevance.4 Imagine, for example, that John says ‘hello’ to Jane as he walks into the office—as he often does—but on this occasion he says it in an unusually jaunty manner. Jane has two responses: she replies (‘hello, John’) in her customary fashion, but is simultaneously surprised at the jauntiness of John’s greeting. Intuitively, the jauntiness of John’s greeting is causally relevant to Jane’s surprise but not to her reply; after all, if John had greeted her in his usual, rather more dour, tone of voice, she would not have been surprised, but she would nonetheless have given the same reply as she actually gave. Counterfactual dependence, then, would seem to be a marker (at the very least) of the causal relevance of properties in cases of token causation. But what of the relata of token causation itself? For the purposes of this chapter, I shall assume the standard Lewisian story (Lewis 1986a). For Lewis, an event is a region of spacetime that has both essential and accidental properties, so that many events can (and normally do) occur in the very same spatio-temporal region, differing only in which properties are essential and which are accidental. Thus we can distinguish between two events, c1 and c2, where being a saying of ‘hello’ by John and being a jaunty saying of ‘hello’ by John are the essential properties of c1 and c2 respectively. These are different (though not fully distinct) events, even though they occur in the very same spatio-temporal region, because there are possible worlds where c1 occurs but c2 does not—these being worlds where John says ‘hello’, but not jauntily. Similarly, Jane’s reply (e1) and her feeling of surprise (e2) are distinct effects of John’s behaviour, but again they are distinguished not by their spatio-temporal location (since they occur in the same spatio-temporal region, viz., the region occupied by Jane at the time in question) but by their essential properties: e1 is essentially Jane’s utterance of ‘hello, John’, and e2 is essentially her being surprised. So—given a counterfactual analysis of causation—it turns out that c2 causes e2 but not e1 (had John not said ‘hello’ jauntily, Jane would still have replied but would not have been surprised). c1, by contrast (given some additional assumptions about the situation, at any rate), causes e1 but not e2. I shall assume that counterfactual dependence is sufficient for the causal relevance of properties in cases of token-level causation, and that the causal relevance of properties can itself be captured by appealing to the distinction between accidental and essential features of events. In effect, then, I am assuming that the instantiation of property F is (on a given occasion) causally relevant to the instantiation of property G if and only if there are events c and e, such that F is an essential property of c and G is I’m using ‘causal relevance’ in a pretheoretical way here. I briefly discuss Jackson and Pettit’s account of causal relevance (as opposed to what they call ‘causal efficacy’) in §6 below. 4

HELEN BEEBEE



an essential property of e, and c caused e. Thus the jauntiness (F) of John’s saying ‘hello’ is causally relevant to the Jane’s being surprised (G) because F is an essential property of c2, G is an essential property of e2, and c2 caused e2. Intuitively, F is causally relevant to G because it makes a difference to whether or not some G-event occurs, and its making a difference consists in the fact that an essentially-F event causes an essentially-G event. By contrast, F is not causally relevant to whether or not Jane says ‘hello, John’, and this lack of causal relevance consists in the fact that c2 is not a cause of e1. Various aspects of the above story are, of course, open to dispute. The connection between the causal relevance of a property and the causal relation between events (or between whatever one thinks the relata of causation are) will vary depending on the account of causation and its relata that one adopts. Broadly speaking, since a difference-making approach to causal relevance (here conceived in terms of counterfactual dependence) seems easily the best bet, difference-making accounts of causation itself are going to be pretty closely aligned with some story about the causal relevance of properties. Things are going to be less straightforward for nondifference-making accounts of causation; but since our topic here is the causal relevance of properties, such accounts can safely be ignored. The real underlying point of assuming a Lewis-style account of causation is that it serves as a hook on which to hang the Causal Role Problem. But the problem will remain, so far as I can tell, whatever account of causation we sign up to. The problem, then, is this: as Lewis notes (and given an abundant view of properties), not just any property is apt for featuring as an essential property of an event. If we are too permissive, we will find spurious counterfactual dependence, and hence spurious causation, between events; and functional properties—properties that are individuated according to causal roles—fall the wrong side of the line. To illustrate the general idea, let’s consider three kinds of property that fairly obviously (to me anyway) give rise to spurious counterfactual dependence: disjunctive properties, dispositional properties, and what I’ll call ‘causally loaded’ properties. Let’s start with disjunctive properties. Suppose Jagbir smiles at Jake, and this makes Jake smile back. Jagbir’s smiling is also a smiling-or-an-ascent-of-Everest. But if we allow that an event occurs that has that disjunctive property as its essential property, then we’ll get spurious counterfactual dependence: assuming that possible worlds where Jagbir climbs Everest are very distant from the actual world, the closest world where Jagbir fails to smile-or-climb-Everest is just the closest world where she fails to smile. So Jake’s smiling counterfactually depends on that event, as well as on the more mundane event whose essential property is Jagbir’s smiling. But that is surely spurious dependence: Jagbir’s smiling causes Jake to smile back, but her smiling-or-climbing-Everest does not.5 5 Lewis doesn’t ban disjunctive properties all together; just those that are ‘overly’ disjunctive; see his 1986a, §VIII. One might try to argue that mental properties evade the Causal Role Problem by virtue of being (a) disjunctions of physical properties, but (b) not ‘overly’ disjunctive. That’s a possibility I consider in §5.



EPIPHENOMENALISM FOR FUNCTIONALISTS

Dispositional properties similarly give rise to spurious dependence. The classic example is, of course, Molière’s virtus dormitiva. If we count ingesting a soporific (that is, something with the disposition to induce sleep), as well as ingesting something with the categorical basis of that disposition, as a cause of someone’s falling asleep on the grounds that their falling asleep counterfactually depends on their having ingested a soporific, we are clearly double-counting: the counterfactual dependence of falling asleep on having ingested a soporific is spurious. If that doesn’t sound obvious, consider the fact that pretty much any time we have a true causal claim of the form ‘c caused e’, the laws of nature together with some additional facts about the circumstances surrounding the occurrence of c will, along with the occurrence of c itself, entail (or perhaps merely make likely) the occurrence of e. This being so, dispositions are extremely cheap. Pillowcases, for example, have the disposition to move in such-andsuch a manner (the way mine are in fact currently moving) when hung on the line just so and exposed to exactly the strength and direction of wind that they’re currently being exposed to; pigeons relevantly similar to the one I’m now observing have the disposition to flap about in circumstances that are exactly similar to those that are currently causing the pigeon I’m observing to flap about; and so on. To count such dispositional properties as causally relevant to the movement of my pillowcases or the flapping of the pigeon would seem to be double-counting if anything is.6 Third, consider properties like being a cause of, being a potential cause of, and being a likely cause of—call these ‘causally loaded’ properties. The seminar currently going on in the next room, e, is caused by many and various other events, each of which instantiated one or more properties that were causally relevant to the seminar’s occurrence. Each of them, trivially, instantiated the properties being a cause of the seminar and being a potential cause of the seminar; and some (but perhaps not all) of them also instantiated the property being a likely cause of the seminar. Are those properties of the various causes of the seminar themselves causally relevant to the seminar? Surely not. Again, counting causally loaded properties as themselves bearers of causal relevance is surely double-counting if anything is. While there are differences between functional properties on the one hand and dispositional and causally loaded properties as just conceived on the other, there is enough commonality between them to make it clear that to count functional properties as genuine bearers of causal relevance would, as in these other cases, be double-counting. Consider being in pain again, where to be in pain is to be in some physical state or other, such that being in that state typically has certain causes and 6 Some philosophers—in particular, dispositional essentialists—claim that not all dispositions have categorical bases (e.g. Molnar 2003; Bird 2007), or, more strongly, that since there are no genuinely categorical properties, all dispositions lack categorical bases. Such views escape the argument just presented. Nonetheless, it’s not obvious that all dispositionalist views escape an argument in the same general ballpark. In particular, prima facie at least, non-fundamental dispositions, such as fragility or being a hallucinogen, would still seem to generate the double-counting worry—though a position like Shoemaker’s subset view (2001) might evade this worry.

HELEN BEEBEE



effects. In relevant respects at least, such a property is indistinguishable from many run-of-the-mill dispositional properties. Being a hallucinogen, for example, is multiply realized (there are many substances that typically cause hallucination), and is explicitly defined in terms of its (typical) effect. Being in pain is of course defined in terms of both its typical causes and its typical effects. But it’s hard to see how that’s going to help. Let’s hoke up a new case in order to drive the point home. Define what it is to be a letter-maker as to be in a state that typically causes a letter of the alphabet to appear on my computer screen, and is typically caused (at least in part) by my presence at the computer. I have been instantiating that property, off and on, for the last hour or so. So, currently, is Fang, who is wandering on my desk looking for some affection and, as it happens, standing on the ‘k’ key with his paw—something that typically (and indeed on this occasion), but not invariably, causes a ‘k’ to appear on the screen. Being a lettermaker is, at present, a property of Fang, and it generates counterfactual dependence between the event essentially specifiable as Fang’s currently being a letter-maker (c)— if there is such an event—and a ‘k’ appearing on my screen (e): in current circumstances, had c not occurred, nor would e. But being a letter-maker is clearly not a property that is genuinely causally relevant to the ‘k’ appearing on the screen. If we were to grant causal relevance to functional properties, then, we would have no reason not to grant causal relevance to a whole host of other properties—properties that (so I claim) manifestly lack causal relevance. The lack of causal relevance of dispositions, in particular, is (excepting views according to which dispositions can be fundamental) pretty widely accepted. (See for example Prior, Pargetter, and Jackson 1982; Lewis 1986a: 268; Pettit, this volume, 234) The fact that we can, in addition, hoke up disposition-like properties for any given instance of token causation (as in the pillowcase and pigeon examples) adds grist to that particular mill. The argument for the Causal Role Problem, then, is that we cannot countenance genuine causal relevance for functional properties (or, equivalently, we cannot countenance such properties as essential features of events) without allowing unacceptable double-counting.7 I conclude that, given some pretty standard and apparently plausible assumptions about causal relevance, the standard version of non-reductive physicalism—viz., functionalism—entails epiphenomenalism about mental properties.

3 The Causal Role Problem and the Problem of Metaphysically Necessitated Effects As I said earlier, the Causal Role Problem is not a new problem; in fact, it is a very close relative of what Richard Rupert (2006) calls ‘the Problem of Metaphysically 7

One might wonder at this point whether the Causal Role Problem is just the Exclusion Problem under another name. It isn’t; see §4 below.



EPIPHENOMENALISM FOR FUNCTIONALISTS

Necessitated Effects’. The problem articulated above is that functionally specified properties cannot do duty as essential properties of events (equivalently: cannot be bearers of causal relevance)—since, if they did, they would generate non-causal counterfactual dependence relations. The Problem of Metaphysically Necessitated Effects (hereafter PMNE) is that, since whether a physical property P counts as a realizer of pain depends upon its being a property that has certain effects (some event of kind G, say), the instantiation of G is metaphysically necessitated by the instantiation of pain. This violates the Humean claim that causal relations are contingent.8 As Rupert puts it: Functionalist mental properties are individuated partly by their relation to the very effects those properties’ instantiations are thought to cause. Consequently, functionalist causal generalizations would seem to have the following problematical structure: The state of being, among other things, a cause of e (under such-and-such conditions) causes e (under those conditions). The connection asserted lacks the contingency one would expect of a causal generalization. (2006: 256)

PMNE and the Causal Role Problem clearly have the same general shape. They are not, however, quite the same problem—and I think the latter is a harder problem than the former. Note that PMNE gains its force from the idea that a functional property is (as Rupert puts it) ‘the state of being...a cause of e’—and hence the having of that property cannot itself cause (be causally relevant to) e. Other authors who have raised the general problem posed by the lack of distinctness between functional properties and their alleged effects have, in effect, also been raising a version of PMNE: the problem, they claim, is the entailment relation that holds between the two (see Ludwig 1994 and Lyons 2006).9 But entailment is a stronger relation than what is needed to generate spurious counterfactual dependence, which is what the Causal Role Problem is concerned with. Recall an example from §2: Jake’s smiling counterfactually depends on Jagbir’s smiling-or-ascending-Everest—but the former does not entail the latter. Instead, what generates the dependence is (a) the entirely contingent counterfactual dependence of Jake’s smiling on Jagbir’s smiling, and (b) the fact— again, an entirely contingent fact—that worlds where Jagbir climbs Everest are much further away from actuality than are ones where she fails to smile, and so the closest possible world where Jagbir does neither is simply the closest possible world where she fails to smile. Moreover, the standard functionalist specification of mental properties, like the property of being a hallucinogen, is considerably looser than that assumed by

8 The Humean claim of course can be, and has been, denied. See Rupert 2006: 258–60, for arguments that denying it is not a promising way to go in the context of the problem under discussion. 9 A notable exception is Lewis 1986a, as we’ll see in §4.

HELEN BEEBEE



proponents of PMNE. Take the case of pain again. First, whether we take the definition of the ‘pain role’ to be a matter for conceptual analysis (analytic functionalism) or for fleshing out by appeal to our best scientific, psychological theory (psycho-functionalism), or whatever, no remotely plausible specification of pain’s definitive causes and effects is going to be precise enough to establish a metaphysically necessary connection between being in pain and exhibiting any maximally specific kind of behaviour. The precise kind of behaviour elicited by being in pain will vary enormously between species, between individuals, and even between different occasions for the same individual. Come at me with a needle while we’re in the pub and I’ll rapidly remove myself from your vicinity; my behaviour when having a blood test is quite different. Having pain inflicted on one might elicit a string of expletives, or a simple ‘ouch, that hurts!’, or merely moaning or yelping (or indeed, in the doctor’s surgery, no more than a slight wince). The most that any plausible specification of the definitive effects of pain will necessitate is that one exhibit some form of behaviour of a very general kind; it will not necessitate any maximally specific form of behaviour that a given person (or animal) manifests on a given occasion. Second—and more problematically for PMNE—any plausible definitive specification of the effects of pain is going to be hedged: there’s going to be a ‘typically’ in there, or perhaps a ‘ceteris paribus’. On a good day I can manage a blood test without even so much as a mild wince. (It still hurts, though. I’m just pretending that it doesn’t.) As we saw with the case of being a hallucinogen, it’s entirely conceptually and metaphysically possible that a particular person, on a particular occasion, is in pain and nonetheless fails to exhibit the typical behaviour that partially defines what it is to be in pain. It is therefore unclear whether PMNE itself really is a problem for functionalism. First, even if we assume that some form of, say, avoidance behaviour is necessitated by being in pain, the fact that the specific behaviour exhibited is not metaphysically necessitated may be enough to avoid the problem. Second, and more seriously, once we note the presence of the ‘typically’ in our functional specification, again we lose metaphysical necessitation: if avoidance behaviour is only typically caused by being in pain, then such behaviour is not metaphysically necessitated by my being in pain. The Causal Role Problem remains, however, since nothing in the argument of §2 depended on any necessitation between the instantiation of the property in question and the occurrence of the effect. Recall Fang, who, while wandering on my desk, acquired the property of being a letter-maker. His instantiating this property did not metaphysically necessitate the appearance of a ‘k’ on my screen (e): in the circumstances, e might not have occurred, consistent with Fang’s being a letter-maker in the right circumstances. For he might have trodden on a different key, or he might have trodden on the ‘k’ key but failed thereby to produce a ‘k’ on the screen.



EPIPHENOMENALISM FOR FUNCTIONALISTS

4 Who is the Causal Role Problem a Problem For? 4.1 Role functionalism vs realizer functionalism A distinction is often made between ‘role’ functionalism on the one hand and ‘filler’ or ‘realizer’ functionalism on the other. According to role functionalism, a mental term such as ‘pain’ rigidly designates a second-order property—the property of having such-and-such causal role—whereas according to realizer functionalism, a mental term non-rigidly denotes the first-order, physical property that realizes that causal role (see e.g. McLaughlin 2007: 151–2; Bennett 2007: 323). Realizer functionalism is incompatible with multiple realization: if more than one physical property actually plays the pain role, then pain cannot be the physical property that plays the pain role. However, following Lewis (1980), we might relativize the concept of pain to different species in order to account for the possibility of, say, a Martian, for whom (thanks to a very different physical make-up to us) some entirely different state occupies the pain-role. Thus Lewis endorses the claim that ‘X is in pain simpliciter if and only if X is in the state that occupies the pain role for the appropriate population’ (1980: 219), where the appropriate population would be, say, normal human beings in my case, and normal Martians in the case of our Martian. It is often said that, since realizer functionalism is, in effect, a version of the typetype identity theory (since on this view pain-for-humans, say, just is the firing of C-fibres, or whatever), it is immune to the Exclusion Problem (Kim 1989; Bennett 2007; McLaughlin 2007). Once we grant that it is pain-for-humans (or perhaps something even more relativized than this—see Kim 1989: 38)—call this pain*— that is our candidate for causal relevance, there is no problem of a competition for causal relevance between mental and physical properties, since a property cannot be in competition with itself. If this is a convincing response to the Exclusion Problem, then of course it looks as though the same will be true of the Causal Role Problem. If, in saying that my being in pain* caused me to wince, I am merely referring to whatever property P realizes pain*, then—assuming that P was causally relevant to my wincing—my being in pain* really did cause it. If this constitutes a solution to both problems, then so be it. Since the kind of functionalism that allegedly solves the problem is a version of the type-type identity theory, it is (as Kim (1989: 39) notes) a reductionist position—and hence it is no help to genuinely non-reductive physicalism, which is the position I’m interested in here. For what it’s worth, however, I’m not so sure realizer functionalism does solve the Causal Role Problem. If mental terms only non-rigidly refer to the physical roleplayers then while, in the actual world, mental terms are not multiple realized, they are nonetheless multiply realizable. After all, human beings could have evolved differently, and some other physical property could have ended up playing the pain*-role—and then that property, and not P, would have been pain*. So the ‘identity’ between pain* and P is mere contingent identity. This being so, it seems

HELEN BEEBEE



coherent to ask whether being in pain* gets to be causally relevant (to my wincing, say) by virtue of being the physical property it is or by virtue of playing the causal role that it does. And it’s hard to see, given the argument of §2, how the answer could be ‘both’. Lewis himself concurs: Whenever some term nonrigidly designates the occupant of a role, and that role could be occupied in a variety of ways, the term becomes unsuitable for essential specification of events. If being fragile means having some or another basis for a disposition to break when struck, and if many different properties could serve as such bases (under this or otherworldly laws), then no genuine event is essentially classifiable as the window’s being fragile. There is a genuine event which is accidentally classifiable in terms of fragility; essentially, however, it is a possession of such-and-such molecular structure, that being the actual basis of the window's fragility...And if I am right to think that mental states are definable as occupants of causal roles, then no genuine event is essentially classifiable as my being in pain. There are pain events, no doubt of it; but they are pain events only accidentally, just as pain itself is a property that only contingently occupies its role and deserves its name. Essentially, the events are firings of neurons, perhaps—unless ‘firing’ and ‘neuron’ also are terms for occupants of roles, in which case we must get more physical before we finally reach an essential classification. (Lewis 1986a: 268)

4.2 Counterfactual-based Solutions to the Exclusion Problem Here is a line of thought that has motivated many recent attempts to solve the Exclusion Problem (see e.g. List and Menzies 2009: 489). The idea that the causal sufficiency of the physical precludes the mental from having any causal status is grounded in a ‘production’ conception of causation, of which paradigmatic cases would be things like shooting people and the collision of billiard balls: cases where there is a localized process or transfer of some entity or quantity (a bullet, energymomentum, etc.). On such a conception of causation, it looks as though P (a physical property that is causally sufficient in the circumstances for some effect e) and M (a supervening mental property) could only both cause e if each, separately, was involved in some sort of productive process culminating in the effect, as with two assassins independently shooting the victim at the same time, or my reaching for the aspirin because I have simultaneously stubbed my toe and banged my head. But since widespread overdetermination is unpalatable (and, in any case, overdetermination of the kind just described is manifestly nothing like what happens in putative cases of mental causation), the causal inefficacy of the mental follows. But we can reject this way of thinking. A way of thinking about causation that is considerably more conducive to accommodating the mental is as a matter of difference-making, which we can define in terms of—or at least legitimately take to be very closely related to—counterfactual dependence. Once we make this basic move, the Exclusion Problem starts looking a lot more tractable. After all, it’s pretty uncontroversial that plenty of things counterfactually depend on the instantiation of mental properties: if I hadn’t been in pain I wouldn’t have taken the aspirin, if



EPIPHENOMENALISM FOR FUNCTIONALISTS

I hadn’t wanted a beer I wouldn’t have ordered one, if I hadn’t believed that today was Wednesday I wouldn’t have put the rubbish out, and so on. I myself am inclined to think that responses to the Exclusion Problem along the lines that Woodward, List and Menzies, and others have pursued are pretty promising—or rather, and here’s the rub, they would be if it weren’t for the fact that mental properties are conceived by these and similar solutions as functional properties. As I said right at the beginning, the feature of non-reductive physicalism for which the Exclusion Problem is (at least prima facie) a problem is multiple realization: it is the problem that multiply realizable properties (such as functional properties) would seem to have no additional causal ‘work’ left for them to do, since quite enough work is being done by the realizer properties on their own. The Causal Role Problem is a more basic problem, in that the reason why non-reductive physicalists take mental properties to be multiply realizable in the first place is that they are, precisely, functional properties. The problem is that, without some restrictions in place concerning what properties are apt for counting as essential properties of events—or, equivalently (I have assumed), concerning what properties can count as causally relevant—counterfactual dependence of the kind identified by differencemaking solutions to the Exclusion Problem, just by itself, is too permissive as a criterion for causal relevance and hence genuinely causal difference-making. And some pretty intuitive considerations indicate that whatever the right restrictions are, functional properties are going to get banned.

5 Role Properties vs Disjunctive Properties Here is a potential objection to my insistence that the Causal Role Problem is a genuine problem that remains even given a counterfactual-style solution to the Exclusion Problem. The first part of the objection runs like this. Sure, our mental concepts are defined in terms of their causes and effects; our concept of pain is the concept of a state that typically has such-and-such causes and effects. But the property that the concept picks out is really a disjunction of the various realizers of that causal role—and that property itself is not, as it were, inherently causally loaded. After all, it’s a substantive empirical claim that a given disjunction of physical properties typically has such-and-such causes and effects. With this move on the table, the Causal Role Problem, if it is still a problem, applies not because mental properties themselves are functional, but because they are disjunctive. And the second part of the objection runs as follows. While, as we’ve seen, Lewis himself bans properties that are ‘too disjunctive’ from serving as essential properties of events because they give rise to spurious counterfactual dependence (as in the example of Jagbir smiling-or-climbing-Everest), there is room for a more nuanced approach: there is a way of ruling out hoked-up disjunctions while making room for the kind we want to allow. Causal Role Problem solved.

HELEN BEEBEE



This objection depends on two claims: the one about the disjunctive (as opposed to functional) nature of mental properties, and the one about distinguishing between hoked-up disjunctions and the ‘nice’ kind, such as the disjunctions that (allegedly) constitute mental properties. I’ll briefly discuss the first claim before arguing that the second is false. The obvious prima facie problem with the claim that mental properties can be identified with disjunctions of physical properties is that in effect it gives up on nonreductive physicalism—the position at issue in this chapter—by identifying mental and (albeit wildly disjunctive) physical properties, which of course is what reductive, type-physicalists do (see §4 above). As Louise Antony (2008) points out, however, we should be wary of the claim that identifying mental properties with disjunctions of physical properties really amounts to an endorsement of reductive physicalism. As she notes, on a conception of properties according to which they are simply sets of possible worlds (so that the property F just is the set of worlds such that at least one proposition ascribing F to something is true at each member of the set), a consequence of the view under discussion is that the mental predicate ‘M’ and the corresponding disjunction ‘P’ do indeed refer to the very same property: M = P. However, she claims that this does not make the view she is defending turn out to be simply a version of the identity theory. Granted a possible-worlds conception of properties, there aren’t really such things as disjunctive properties—a set of worlds is just a set of worlds, after all, and there’s nothing inherently disjunctive about a set of worlds—so there are really only disjunctive predicates. And, given physicalism, any mental predicate is going to pick out some set of worlds describable in purely physical terms. So, on pain of vacuity, we should not think of the truth of M = P, just by itself, as a lapse into the type identity theory—that is, into reductive physicalism. Rather, we should think of what Antony calls ‘strong reductionism’ as the thesis that ‘every mentalistic predicate is necessarily co-extensive with some proprietary predicate of lower-order or lower-level science’ (2008: 173). Since the kind of unwieldy disjunctive predicate that is (on Antony’s view) co-extensive with a given mentalistic predicate will not itself be a proprietary predicate of physical science (even if each disjunct is such a predicate), Antony’s view denies strong reductionism, and hence counts as a version of non-reductive physicalism. Let’s assume, then, that non-reductive physicalism is indeed compatible with taking mental predicates to pick out the same properties as disjunctive physical predicates. Now, according to Antony every higher-order, mentalistic predicate ‘is necessarily co-extensive with some lower-order, possibly infinitely long, disjunctive predicate’ (2008: 170). But the ‘necessarily’ part surely cannot be right. For example, there may well be other possible worlds where human beings evolved in such a way that some proprietary physical predicate ‘P1’ refers to a physical property that realizes pain in that world, but that that physical property is actually a realizer of the mildly pleasurable tickling sensation role. In that case, ‘P1’ cannot be among the disjuncts of our unwieldy disjunctive predicate ‘P’, since if it were, it would follow that an actual



EPIPHENOMENALISM FOR FUNCTIONALISTS

human being with property P1 is in pain rather than undergoing a mildly pleasurable tickling sensation. So, if the view under consideration here is to have any prospects, it looks as though we need to deny what Antony asserts and hold that any mental predicate is in fact co-extensive with some lower-order disjunctive predicate. Or, to put it another way, we need to hold that our mental predicate ‘M’ non-rigidly refers to property P, where ‘P’ is a disjunction of proprietary predicates of some lower-order science. Of course, if the suspicion raised earlier (and endorsed by Lewis), that mental terms that are non-rigid designators of physical properties cannot serve as essential specifications of events, is right, then the same point applies here too. But let’s leave that aside and move on to the second claim that needs to be established, viz., that there is a way of allowing the ‘nice’ disjunctive properties picked out by mental terms to count as causally relevant while banning hoked-up properties such as smilingor-ascending-Everest.10 The first thing to note is that nothing in recent, difference-making attempts to solve the Exclusion Problem helps us to discriminate between hoked-up and nice disjunctions. As we saw in §2, the fact that hoked-up disjunctions can deliver counterfactual dependence, and so ‘make a difference’ in that sense, is part of the problem and not part of the solution. Similarly, nothing in the interventionist solution to the Exclusion Problem will do the trick. In almost all circumstances, intervening on whether or not someone is smiling-or-ascending-Everest generates exactly the same pattern of dependence as does intervening on their smiling alone, since—for almost everyone all the time, and for a very few intrepid people almost all the time—the intervention will proceed by inducing the person in question to smile or not, ascending Everest not being a viable option. So hoked-up disjunctive properties can happily satisfy Woodward’s conditions for causal relevance. This, of course, is not an objection to List and Menzies’ or Woodward’s accounts qua solutions to the Exclusion Problem; it merely makes the familiar point that independent constraints on what can count as a causally relevant factor or an admissible value of a variable are needed in order to rule out spurious cases of dependence. For the most part, we can assume standard restrictions along something like the lines described in §2 above. But of course the point of the Causal Role Problem is precisely that such restrictions throw out mental causation along with the bathwater. Is there such a constraint to be had? Antony argues, in effect, that there is. The question, as Antony puts it, is, ‘what makes it the case that some disjunctive predicates express nomic properties, while others do not?’ (2008: 169). ‘A property is nomic if it participates in lawful objective regularities’, Antony says (2008: 170), which is perhaps not as precise as we might like for current purposes, but nomicity is certainly in the same ballpark as causal relevance; in any case, the basic contrast 10

As we’ve just seen, Antony cautions against thinking in terms of disjunctive properties. I’m doing so here for ease of exposition; nothing hangs on it.

HELEN BEEBEE



Antony is interested in is with hoked-up disjunctive properties (see 2008: 167), which is what I’m interested in here. So let’s take the notion of a ‘nomic property’ to be sufficiently well understood, at least for now. Antony’s answer to the question just posed appeals to Nelson Goodman’s notions of entrenchment and projectibility. First, some definitions: (1) ‘Entrenchment’ is an observable socio-linguistic property... .(2) A predicate will be said to be ‘projectible’ just in case it (a) is entrenched in some community and (b) can in fact be used to state correct predictions and robust (although possibly ceteris paribus) generalizations. (3) A property will be said to be projectible if and only if it is expressed by some projectible predicate, in some language, for some intentional beings. (2008: 170)

With this on the table, Antony says: typically, but not necessarily, entrenched predicates will be projectible. That is, predicates that are entrenched permit and will continue to permit the formulation of correct predictions and robust generalizations...The explanation for the projectibility of a predicate, and hence, in many cases, for its entrenchment, is that the property expressed by that predicate is nomic. Finally, all projectible properties are nomic, but not all nomic properties need be projectible. There may be nomic properties that neither we, nor the members of any other linguistic community, are ever able to express by means of a projectible predicate. (2008: 170)

The basic idea, then, is that mentalistic predicates are (normally) entrenched precisely because they are projectible: they ‘permit the formulation of correct predictions and robust generalizations’. And the reason for the projectibility of mentalistic predicates, in turn, is that the properties they express are nomic. Thus, for example—since we know that some mentalistic predicate ‘M’ (‘pain’, say) is both entrenched and projectible—we can safely infer that the property it expresses is nomic. The corresponding wildly disjunctive physical predicate ‘P’, while co-extensive with ‘M’, is neither entrenched nor projectible: it fails to permit the formulation of correct predictions and robust generalizations. Nonetheless, the property that ‘P’ expresses—being the very same property as that expressed by ‘M’—is nomic. Antony’s implied answer to the question about the distinction between predicates that do and don’t express nomic properties, then, is that the non-nomic properties fail to ‘participate in lawful objective regularities’. But now we face a problem: if properties picked out by functionalist, mentalistic predicates fall on the nomic side of the nomic/non-nomic divide, why should we not say the same for dispositional and causally loaded predicates, and for at least some disjunctive ones? After all, such predicates can in principle be—and many of them are—both entrenched and projectible. Consider predicates like ‘hallucinogen’ and ‘fatal’. These predicates feature in perfectly good robust and stable (if sometimes ceteris paribus) generalizations: people who suffer fatal accidents die, and people who take hallucinogens generally end up hallucinating. So Antony’s view faces a dilemma: if being a hallucinogen and being fatal are nomic properties, then the causal relevance of the mental is secured at the



EPIPHENOMENALISM FOR FUNCTIONALISTS

price of pervasive double-counting. On the other hand, if they are not nomic properties, then the entrenchment and projectibility of a predicate fails to license the inference to the claim that the property the predicate expresses is nomic. My view, unsurprisingly, is that we should accept the second horn of the dilemma. Hallucination and death are things that we are generally interested in—and so it’s entirely sensible to have a general term covering the properties that are liable to cause them, however multifarious those causes might be. (If we weren’t interested in hallucinogenic or fatal properties of things, we wouldn’t have invented the words.) But being fatal is not causally relevant to death: it is a conceptual truth, and not an empirical discovery, that fatal accidents cause death. Similarly for the fact that hallucinogens often cause hallucination: they wouldn’t be hallucinogens if they didn’t. And similarly for mentalistic predicates. Of course, the view under discussion here distinguishes between mentalistic predicates and the properties (expressible in physical terms only by using wildly disjunctive predicates) that they refer to. One might try to argue that it is therefore entirely appropriate to think of the properties that are expressed by the kinds of predicate I’m interested in as genuinely nomic. I think such an argument fails. Suppose we think of being fatal as a property that is expressible in terms that don’t refer to its effects only by using a wildly disjunctive and open-ended predicate: ‘being a head-on high-speed collision, being an airliner crash, being the grabbing of a live electricity cable, being the ingestion of large quantities of cyanide,...’, say (call this property P). P is only fully expressible by actual, finite and non-omniscient human beings by means of the predicate ‘fatal’. Granted, it is not a conceptual truth that P causes death (there are, presumably, distant worlds where drinking cyanide is good for you, grabbing live electricity cables delivers a pleasant tickling sensation, and so on). But that doesn’t make it any more plausible to claim that P is a nomic property. That there are (extremely!) stable generalizations that involve a predicate that expresses P simply doesn’t provide us with any grounds for making that claim, since the stability of those generalizations is explained entirely by the fact that the predicate that determines the extension of P (‘fatal’) is a dispositional predicate. And, again, the same point applies to mentalistic predicates if they are conceived in functionalist terms. I conclude that conceiving mental, functional predicates as co-extensive with physical, disjunctive predicates that refer to physical properties does not deliver a way of granting mental properties causal relevance.

6 Is Epiphenomenalism Really So Bad? The point of this chapter so far has been to justify taking the Causal Role Problem seriously. Doubtless the argument is not decisive, and perhaps the problem can be solved. But suppose it can’t be solved. The result—given our starting assumption, viz., the truth of non-reductive physicalism—would be epiphenomenalism.

HELEN BEEBEE



It’s generally assumed that epiphenomenalism with respect to the mental would be a completely unpalatable result.11 But how bad would epiphenomenalism be, really? Not nearly as bad as one might think, in fact—or so I shall argue. I’ll argue that the kind of epiphenomenalism that the Causal Role Problem points to, while it does undermine the causal relevance of mental properties, leaves much of what we want to say about the mental intact: the causal irrelevance of the mental does not entail that mental properties are explanatorily redundant, nor does it entail that mental events are causally inefficacious. Finally, it does not entail that conceiving the world in terms of mental properties is useless for the purposes of controlling ourselves and others. Let’s start with the explanatory point. Here we can appeal to a Lewisian story about causal explanation (Lewis 1986b): to explain an event is to provide information about its causal history. Functional mental properties can perfectly well satisfy this requirement. When I explain your behaviour B (saying ‘ouch!’ and grimacing, say) by citing the fact that you are in pain, I do provide information about the causal history of B. In particular, I provide the information that B was caused by some event with some physical feature or other that typically plays the pain role—even though that role might well include, precisely, exhibiting B-like behaviour. One might object that such an ‘explanation’ is trivial, since in effect it amounts to no more than explaining some event e by saying that was caused by some event or other of a kind that typically causes e—which hardly sounds like front-page news. Well, our explanation here may not be front-page news, but it is still informative, since B could have been caused by an event with some physical feature that does not typically play the pain role. You might, for example, have wanted to deceive me into thinking that you were in pain because you were looking for sympathy, and said ‘ouch’ and grimaced for that reason. The physical features upon which that desire supervenes do not typically play the pain role. Or you might have been acting in a play that called for pain behaviour at the moment in question, or responding to someone who has just threatened to kidnap your cat unless you say ‘ouch’ and grimace right now. Again, in such cases the physical state in question is not one that typically plays the pain role. So citing the fact that you were in pain rules out all of these possible causal histories, just as it would if being in pain were genuinely causally relevant to B. This is an apt place to compare the kind of epiphenomenalism under discussion here with Jackson and Pettit’s distinction between ‘programme’ and ‘process’

Three exceptions: first, Jack Lyons defends epiphenomenalism in his 2006: §§3 and 4. The point I make below about the causal efficacy of mental events is basically a short version of Lyons’ claim that ‘property epiphenomenalism’ does not entail ‘event epiphenomenalism’. Lyons argues that (property) epiphenomenalism is not only acceptable but a virtue of non-reductive physicalism. I lack the space to discuss this interesting suggestion here. Second, Segal (2009) also makes the point about the event/property distinction and adds his own defence of epiphenomenalism in response to a version of the Exclusion Problem. Finally, Frank Jackson (2012: §VII) argues that objections to epiphenomenalism from introspection, evolution, and knowledge are unsound. 11



EPIPHENOMENALISM FOR FUNCTIONALISTS

explanation. According to Jackson and Pettit’s original account, ‘properties may be causally explanatory properties without being causally productive or efficacious ones. These properties programme the result to be explained, rather than actually bringing it about, and are the properties appealed to in what we called programme explanations’ (1988: 400). And the kinds of property that Jackson and Pettit want to count as being ‘causally explanatory’ without being ‘productive or efficacious’ include functional properties. Jackson and Pettit’s 1988 view is, I think, compatible with epiphenomenalism about mental properties. Indeed, some of what they say about programme explanations seems to suggest that at least some properties that can crop up in programme explanations are genuinely epiphenomenal. Thus they say: We may explain the conductor’s annoyance at a concert by the fact that someone coughed. What will actually have caused the conductor’s annoyance will be the coughing of some particular person, Fred, say; when we say that it was someone’s coughing that explains why the conductor was annoyed, we are thinking of someone’s coughing as Fred’s coughing or Mary’s coughing or Harry’s coughing or..., and saying that any of these disjuncts would have caused the conductor’s annoyance—it did not have to be Fred. (1988: 394, my italics)

The implication here is that someone’s coughing did not cause the conductor’s annoyance, despite the legitimacy of the explanation described above. So it looks as though we can have genuine (programme) explanation in the absence of causal relevance on Jackson and Pettit’s 1988 view. So far, so good. In later work, however, Jackson and Pettit (1990) distinguish not just between those properties that feature in programme and process explanations, but between ‘causally efficacious’ and ‘causally relevant’ properties—where their response to the Exclusion Problem is roughly to argue that the problem trades on the assumption that causal efficacy is the only kind of causal relevance there is, and that this assumption is false. It is this further move that I think needs to be rejected: to say that a property is causally relevant is, it seems to me, to ascribe a distinctively causal, and not merely explanatory, role to it. And, as I’ve argued, no such role can be ascribed to functional properties. In his contribution to this volume, Pettit attributes a ‘distinct-existences assumption’ to List and Menzies’ account of mental causation: ‘higher-level [multiplyrealized] properties—or more strictly, their instances—are distinct existences... from the properties or property-instances to which they bear [significant law-like] relations’ (this volume, 233). Pettit here clearly has in mind the Problem of Metaphysically Necessitated Effects—a problem which, as we saw in §3, connects with concerns about the failure of the principle that causes and effects are distinct. (Thus: the disposition to dissolve in water ‘is not a distinct existence from the dissolving and not capable, for example, of bearing a causal relationship to it: that is, a contingent relationship that might not have obtained, even under presumptively suitable conditions’ (this volume, 234).

HELEN BEEBEE



Pettit further claims that the ‘distinct-existences’ assumption is, in fact, made in his and Jackson’s earlier work with respect to functional properties. In a footnote, he says: While we discussed the application of the model to cases of dispositions, where the distinctexistences assumption does not apply, we used that application only to illustrate how the programming relationship need not add to our causal understanding. Notice that the distinctexistences assumption does apply, however, with functional as distinct from dispositional states. Unlike dispositions these are not characterized by just one manifesting connection but by the fulfilment of a number of conditions—usually, typical rather than invariable conditions. When the existence of the state requires a number of conditions to obtain, then even if they invariably include the connection with the effect to be explained, invoking the state in the explanation directs us to a connection between the other conditions required for the state to obtain and that effect. (Pettit, this volume, 235 n. 7)

Pettit’s point here, then, is that, thanks to differences between dispositional and functional properties, the latter properties (or perhaps instances thereof), but not the former, are distinct from their effects. Thus, while the ‘view that dispositions can be differencemakers and causes’ is ‘utterly implausible’ (this volume, 234, n. 6)—and hence, I take it, the view that dispositions are bearers of causal relevance is similarly implausible—the same cannot be said of functional properties. In fact, this point is similar to the point made in §3 that PMNE doesn’t really apply to functional properties (or at least not the ones that non-reductive physicalists take to be mental states). But of course that all still leaves the Causal Role Problem in the running, since many of the properties that lead to double-counting are ones such that are ‘distinct existences’ from their putative effects in Pettit’s sense: the putative causal relationship between them and their effects is ‘a contingent relationship that might not have obtained, even under presumptively suitable conditions’. The sending of an invitation to the speaker, for example, was a potential cause of the seminar going on next door, e (call this property F), since it was an actual cause of e; but the relationship between the cause-event’s being F and the occurrence of e is contingent: a last-minute train cancellation might have prevented the speaker from turning up, for example. Similarly, the relationship between disjunctive properties and events that counterfactually depend on them is not one where the distinct-existences assumption fails; the contingency of the relationship between Jagbir’s smiling-orascending-Everest and Jake’s smiling is every bit as contingent as the relationship between Jagbir’s smiling and Jake’s smiling. So we are still left with the conclusion that functional properties cannot, pace Pettit, be bearers of causal relevance. That said, it seems to me that the general spirit of Jackson and Pettit’s account is, in places, closer to the epiphenomenalist position currently under discussion than Pettit now wants to accept. For one thing, several of the cases of programme explanation that they mention seem to me to count as genuinely explanatory, for the reasons they give, independently of whether or not they fall within the ambit of the Causal Role



EPIPHENOMENALISM FOR FUNCTIONALISTS

Problem: for example, ‘the property of a group that it is cohesive; of a mental state that it is the belief that p; of a biological trait that it maximizes inclusive fitness’ (1990: 112). For another, Jackson and Pettit do not seem fully committed to the claim that a merely ‘causally relevant’ (as opposed to efficacious) property really is distinctively causal; indeed, at one point they describe such a property as ‘perfectly inert’ (1990: 114). So to my mind one can read Jackson and Pettit’s position as an argument for the explanatory usefulness of functional properties, even assuming that they are genuinely epiphenomenal. Indeed, Jackson is an unashamed epiphenomenalist: ‘functional properties do not do any causing’, he says (2012: 278). The second reason why epiphenomenalism is not as bad as it may seem at first blush is that it is entirely consistent with the causal efficacy of mental events. Take your having been in pain just now. According to the general Lewisian story described in §2, and indeed—as we saw in §4—according to the view explicitly endorsed by Lewis in the particular case of mental events, there is no event that is essentially your being in pain; however, that property is a perfectly good accidental property of some event whose essential properties are physical. That event is a perfectly legitimate cause of your pain behaviour, and it is a mental event in the sense that it is correctly describable in mental terms. So mental events can—and very often do—cause things. When people ingest hallucinogens, their doing so really does frequently cause them to hallucinate, notwithstanding the fact that the events we’re quantifying over are only accidentally ingestions of hallucinogens. Thirdly and finally, it is not a consequence of epiphenomenalism that mental properties are useless for the purposes of manipulating and controlling ourselves or our environment. By way of a contrast, consider some pair of properties P1 and P2, such that we are perfectly well able to identify and intervene on instances of both P1 and P2, and such that each of P1 and P2 (but no other property—and we know this) is causally relevant to some other property Q. Now suppose that we define a new property, P*, such that to have P* is to have some property or other that typically causes Q. P* is, it would seem, a pretty useless property for practical purposes (though the predicate ‘P*’ might be a convenient linguistic shortcut in certain circumstances). Our conceiving of the world in terms that invoke P* does not really help us to bring about or avoid Q, in the sense that we can perfectly well intervene on either P1 or P2 themselves in order to bring about or avoid Q. (And of course if we can’t intervene on P1 or P2 for some reason, we aren’t going to be able to intervene on P* either.) The practical situation with respect to mental properties, however, is different. By and large, we cannot (as things currently stand, at any rate) intervene on subvenient physical properties directly, and in at least many cases it would probably be immoral to do so even if we could. Our only option is to intervene on their supervening mental cousins. Sally currently believes that the train doesn’t leave for another half hour, and her being in the physical state that realizes this mental property is causing her to get ready too slowly. I know that the train leaves in twenty minutes, and, since I want her

HELEN BEEBEE



not to miss it, I need to cause her to be in a physical state that realizes that mental property. I am able to do this in a variety of ways that, fortunately, require no knowledge of the physical state of Sally’s brain beyond which relevant mental states it is realizing: I point at the clock, show her the train timetable, or whatever. In other words, I intervene on her physical state by intervening on her mental state (or rather, strictly speaking, by doing something that, for all practical purposes, is just like intervening, intervention being a causal notion, and mental properties being just as unsuited to the role of effect as they are to the role of cause). This is, of course, a very common pattern in our manipulation and control of ourselves and others. Nothing in this story requires us to conceive of mental properties themselves as bearing causal relevance to the behaviour in question. If I urgently need a writing implement—say because I’ve just witnessed a hit-and-run and I’m in danger of forgetting the car’s registration number—I might reasonably request something to write with. I don’t care whether it’s a fountain pen or a biro or a pencil or... .You satisfy my request by handing me a pencil, and I successfully write down the car’s registration number. We can make sense of the fact that this episode comes to a satisfactory resolution without having to conceive being a writing implement as itself causally relevant to my writing down the registration number. Nor must we commit ourselves to the view that an event that has passing me a writing implement as an essential feature has occurred. Similarly, if epiphenomenalism is true, for the mental case. We need not conceive of mental properties as causally relevant, or as essential features of any events, in order to make sense of our manipulation (or perhaps ‘manipulation’) of them in achieving our ends. My aim here has merely been to point out that epiphenomenalism—of the kind that is engendered by a commitment to non-reductive physicalism, or so I’ve argued—is not obviously a crazy position. Our common-sense theory of the mental plainly assigns explanatory status to mental properties (‘Jack ate the chocolate because he was hungry’) and causal efficacy to mental events (‘Jill’s thumping headache caused her to turn the lights down’). And it’s a plain fact of life that we routinely control our own and others’ mental states and ensuing behaviour by intervening (or at any rate by doing things that for practical purposes are just like intervening) on the mental properties we and others instantiate. Epiphenomenalism, I have argued, allows the non-reductive physicalist to keep all of this. So what, exactly, doesn’t it allow us to keep, that we really care or ought to care about? This, I think, is the question that those philosophers who reject epiphenomenalism out of hand need to answer.

References Antony, L. 2008. ‘Multiple Realization: Keeping it Real’, in Being Reduced: New Essays on Reduction, Explanation, and Causation, ed. J. Hohwy and J. Kallestrup. Oxford: Oxford University Press, 164–75.



EPIPHENOMENALISM FOR FUNCTIONALISTS

Bennett, K. 2007. ‘Mental Causation’, Philosophy Compass, 2: 316–37. Bird, A. 2007. Nature’s Metaphysics: Laws and Properties. Oxford: Oxford University Press. Block, N. 1990. ‘Can the Mind Change the World?’ in Meaning and Method: Essays in Honor of Hilary Putnam, ed. G. Boolos. New York: Cambridge University Press, 137–70. Jackson, F. 2012. ‘Leibniz’s Law and the Philosophy of Mind’, Proceedings of the Aristotelian Society, 112: 269–83. Jackson, F., and Pettit, P. 1988. ‘Functionalism and Broad Content’, Mind, 97: 381–400. Jackson, F., and Pettit, P. 1990. ‘Program Explanation: A General Perspective’, Analysis, 50: 107–17. Kim, J. 1989. ‘The Myth of Nonreductive Materialism’, Proceedings and Addresses of the American Philosophical Association, 63: 31–47. Lewis, D. K. 1980. ‘Mad Pain and Martian Pain’, in Readings in the Philosophy of Psychology, vol. I, ed. N. Block. Cambridge, MA: Harvard University Press, 216–22. Lewis, D. K. 1986a. ‘Events’, in his Philosophical Papers, vol. II. Oxford: Blackwell, 262–9. Lewis, D. K. 1986b. ‘Causal Explanation’, in his Philosophical Papers, vol. II. Oxford: Blackwell, 212–40. List, C., and Menzies, P. 2009. ‘Nonreductive Physicalism and the Limits of the Exclusion Principle’, Journal of Philosophy, 106: 475–502. Ludwig, K. 1994. ‘Causal Relevance and Thought Content’, The Philosophical Quarterly, 44: 334–53. Lyons, J. C. 2006. ‘In Defense of Epiphenomenalism’, Philosophical Psychology, 19: 767–94. McLaughlin, B. 2007. ‘Mental Causation and Shoemaker-Realization’, Erkenntnis, 67: 149–72. Molnar, G. 2003. Powers: A Study in Metaphysics, ed. S. Mumford. Oxford: Clarendon Press. Prior, E. W., Pargetter, R., and Jackson, F. 1982. ‘Three Theses about Dispositions’, American Philosophical Quarterly, 19: 251–7. Raatikainen, P. 2010. ‘Causation, Exclusion, and the Special Sciences’, Erkenntnis, 73: 349–63. Rupert, R. 2006. ‘Functionalism, Mental Causation, and the Problem of Metaphysically Necessary Effects’, Noûs, 40: 256–83. Segal, G. 2009. ‘The Causal Inefficacy of Content’, Mind and Language, 24: 80–102. Shoemaker, S. 2001. ‘Realization and Mental Causation’, in Physicalism and its Discontents, ed. C. Gillett and B. M. Loewer. Cambridge: Cambridge University Press, 74–98. Weslake, B. Forthcoming. ‘Exclusion Excluded’, International Journal for the Philosophy of Science. Woodward, J. 2008. ‘Mental Causation and Neural Mechanisms’, in Being Reduced: New Essays on Reduction, Explanation, and Causation, ed. J. Hohwy and J. Kallestrup. Oxford: Oxford University Press, 218–62.

16 The Consequence Argument Disarmed An Interventionist Perspective Peter Menzies

1 Introduction Peter van Inwagen’s Consequence Argument is often said to provide the most compelling argument in favour of incompatibilism.1 Van Inwagen summarizes the argument in these words: If determinism is true, then our acts are the consequences of the laws of nature and events remote in the past. But it is not up to us what went on before we were born, and neither is it up to us what the laws of nature are. Therefore, the consequences of these things (including our present acts) are not up to us. (1983: v)

I examine a full statement of the modal version of the argument in a later section.2 But for now its import is clear: our present actions are not up to us by virtue of the fact that we cannot do anything other than what we are predetermined to do by the laws and events in the remote past. The Consequence Argument is thought to be an argument in favour of incompatibilism because it supports the first premise in what has been called the Basic Argument for incompatibilism:3 If determinism is true, I do not have the ability to do otherwise. I have free will only if I have the ability to do otherwise. Therefore, if determinism is true, I do not have free will.

1 Peter wrote this paper in the southern winter (northern summer) of 2014 and shared it with several colleagues. He intended to revise it, but unfortunately did not have the time to do so. The present version has been edited by Christian List. Any substantive editorial changes are clearly marked. Christian is very grateful to Helen Beebee, Chris Hitchcock, Catriona Mackenzie, Eddy Nahmias, and Daniel Nolan for helpful comments and advice. 2 Van Inwagen presents three versions of the Consequence Argument in his 1983, the first of which is the modal version that has received most attention. I shall follow tradition and focus on the modal version in this chapter. 3 The terminology ‘Basic Argument for incompatibilism’ is due to Kadri Vihvelin (2013: 2).



THE CONSEQUENCE ARGUMENT DISARMED

One way to side-step the conclusion of this argument is to deny that the Consequence Argument establishes the first premise. Another way is to reject the second premise. Some compatibilists have sought to do this by appealing to Frankfurt-style examples to argue that one can have free will even though one lacks the ability to do otherwise. Their rejection of the second premise allows them to accept that the Consequence Argument establishes the truth of the first premise or, at least, to remain neutral on this issue. The literature on the subject of whether the second premise is true is vast.4 It would take another long chapter to say anything worthwhile on this subject. Nonetheless, what one can say is that if the second premise is accepted as true, the force of the Basic Argument for incompatibilism depends to a large extent on how well the Consequence Argument supports the first premise. This is the question that this chapter takes up. In the chapter I scrutinize the Consequence Argument by recasting it in terms of the interventionist causal-modelling framework developed by Judea Pearl and elaborated by James Woodward and Christopher Hitchcock.5 I believe that this recasting of the argument is justified because the interventionist framework offers a more psychologically realistic setting for assessing the causal reasoning involved in the argument, where ‘causal reasoning’ is understood broadly to include reasoning about laws, causation, counterfactuals, and abilities. Traditional discussions of the Consequence Argument presuppose that we reason causally by thinking about how total states of the universe evolve over time. For example, the original formulation of the argument understands determinism as the thesis that for any two instants of time t and t', there is a proposition P that expresses the state of the world at instant t and a proposition Q that expresses the state of the world at instant t' such that the conjunction of P together with the laws of nature entails Q. By contrast, the interventionist framework assumes that we engage in causal reasoning typically by thinking about how local, small-scale systems evolve over time in accordance with causal generalizations that often fall short of being laws. It also assigns an important role to interventions thought of as external causal influences that intrude on the workings of a system and disrupt the causal generalizations that apply to it. When the Consequence Argument is recast in terms of this psychologically more realistic framework, its error is more easily discernible. I argue that the error in the argument lies in a premise that has hitherto been taken universally to be true. Further, I argue that by extrapolating the kind of causal reasoning employed in the interventionist

4 For the original Frankfurt counterexample to the Principle of Alternate Possibilities, see Frankfurt 1969. This principle states that the ability to do otherwise is a necessary condition for moral responsibility rather than free will. For discussions of whether moral responsibility and free will require the ability to do otherwise in the context of Frankfurt-style counterexamples, see Fischer 2010; Haji 2011; Widerker 2011; and Widerker and McKenna 2003. 5 See, for example, Pearl 2009 [2000]; Woodward 2003; Hitchcock 2001; Woodward and Hitchcock 2003; and Hitchcock and Woodward 2003.

PETER MENZIES



framework from the local to the global scale, we can see that the diagnosis of the flaw in the argument applies also to its original formulation.6 My plan of action is as follows. In section 2, I outline the basic features of the interventionist framework developed by Pearl, Woodward, and Hitchcock. In section 3, I explain how we should understand an agent’s ability to do otherwise. I defend the currently unpopular view that this ability should be understood in counterfactual terms, showing how the arguments that have been taken to refute this view fall well short of their mark. In section 4, I recast the Consequence Argument in terms that enable its evaluation within the interventionist framework and argue that while the argument is valid, it is unsound because of its reliance on a false premise. In section 5, I argue that this diagnosis can be extended to the original formulation of the argument. Section 6 (added by the editor) addresses an objection.7 Finally, in section 7, I discuss whether my response to the Consequence Argument is a form of local miracle compatibilism, comparing and contrasting it with Lewis’s version of this view.

2 Interventionist Causal Modelling Causal modellers claim that models mediate our mental representations of causation, counterfactuals, and dispositions. This may seem a controversial claim, but it simply amounts to saying that our thinking and reasoning about these subjects presuppose some background theory—a theory that may be very rudimentary in form. It is hard to avoid making this assumption if one believes that causal relations, counterfactuals, and dispositions require covering generalizations. Given the mediating role of models, the interventionist framework delivers truth conditions for statements about causation, counterfactuals, and dispositions that are relativized to a model. Unrelativized truth conditions can be obtained by positing a unique correct model— a model that determines the conditions under which statements about causation, counterfactuals, and dispositions are true or false tout court.8 6

Other philosophers have employed the interventionist framework to discuss the tenability of incompatibilism. However, their purposes and approaches differ from this chapter’s. Adina Roskies (2012) draws on interventionist theories of causation to capture compatibilist notions of self-authorship and control. Jennan Ismael (2007, 2011, 2012) employs interventionist modelling to correct some pretheoretic misconceptions about time, causation, and laws occurring in the free will literature. Oisin Deery and Eddy Nahmias (2014) draw on causal modelling to discuss Frankfurt cases and manipulation arguments. None of these authors uses the interventionist framework to critically scrutinize the Consequence Argument in any depth as their concerns lie elsewhere. 7 This sentence has also been added by the editor. The rationale for adding the new section is explained in note 27 below. 8 A statement of relativized truth conditions of the form ‘p is true in model M iff such-and-such conditions hold’ should be read as a conditional statement of the form ‘If M is the correct model, then p is true iff such-and-such conditions hold’. By supposing that some model is indeed the unique correct model, one can detach from this conditional to obtain unrelativized truth conditions. Whether it makes sense to think that the adequacy conditions on models determine a unique correct model is a complex question requiring more extensive discussion than is possible here.



THE CONSEQUENCE ARGUMENT DISARMED

The causal modelling tradition depends on a distinctive understanding of the nature of the background theories. It supposes that a background theory takes the form of a model M formally identified with an ordered pair , where V is a set of variables and E a set of structural equations. Let us consider these concepts in turn. A variable is simply a property or quantity that is capable of taking at least two different values. The set of variables of a model constitutes the basic language used to describe the states of the target system. It is common to think that causal relations, counterfactuals, and dispositions are concerned with property-instances or events. This thought can be accommodated by taking the relevant variables to be two-valued, with the values corresponding to the presence or absence of the properties or events. Variables are divided into exogenous variables (whose values are determined by factors outside the model) and endogenous variables (whose values are determined by factors inside the model). Structural equations are generalizations that guide our causal reasoning. I shall focus on the deterministic case, in which each endogenous variable Y is written as a function of other variables X1, ..., Xn: Y = fY(X1, ..., Xn). In this case, the variables on the right-hand side are said to be parents of the variable on the left-hand side. Side matters in the structural equations for endogenous variables as it encapsulates a direction of determination: the values of the right-hand-side variables determine the values of the left-hand-side variables and not vice versa. From the fact that Y = fY(X) it doesn’t follow that X = fY–1(Y).9 The structural equation for an exogenous variable consists in a statement of the actual value of the variable. We are now in a position to introduce the concept of an intervention.10 Definition 1: An intervention on a variable X that sets it to value x is an occurrence that (i) causes X to take the value x; (ii) disrupts the link between X and its direct causal antecedents (its parents); but (iii) does not disrupt any other causal link.11 An intervention is an idealization of the kind of manipulation used in scientific experiments to test causal hypotheses. A prime example is a randomized experiment in which test subjects are assigned to two groups by a randomizing device, and one group of subjects—the treatment group—is treated with the putative cause, and the other group—the control group—is not so treated. The manipulations involved in this kind of experiment are paradigmatic interventions because they set a variable to a value corresponding to whether the test subject is treated with the putative cause or not, and they do so in a way that decouples the value of this variable from its normal causes but does not affect any other causal relations among the variables. In this example, interventions 9

Indeed, the function fY need not be invertible [added by the editor]. The next two paragraphs have been shortened by the editor, and the opening sentences of both paragraphs have been suitably adjusted (i.e. ‘We are now in a position...’ and ‘It is helpful to give... Consider...’). The rest of the wording is Peter’s. The editor thanks Chris Hitchcock for comments. 11 This definition of an intervention is less stringent than that given by Woodward (2003: chapter 3) and is closer to the weaker definition offered by Pearl (2009: 70), which is more suitable to my purposes. 10

PETER MENZIES



are human manipulations. But interventions are not, in general, restricted to human actions: so-called ‘natural experiments’ in which a natural occurrence changes the trajectory of an otherwise isolated system can count as an intervention. It is helpful to give a simple example of how structural equations can describe typecausal relations that go beyond mere associations or correlations between variables. Consider a common-cause situation in which a virus causes a person, Jones, to get a high temperature and a rash. We can construct a simple model M1 = of the situation in these terms: Set of variables V1: V = 1 if Jones has virus, 0 otherwise. HT = 1 if Jones has a high temperature, 0 otherwise. R = 1 if Jones has a rash, 0 otherwise. Set of structural equations E1: V = 1. HT = V; R = V. The structural equation for the exogenous variable V is written on one line and those for the endogenous variables HT and R on a line below. The structural equations for HT and R say that an intervention that changes the value of the variable V from 1 to 0 will also change the value of each of these endogenous variables. There is no structural equation linking HT and R because an intervention that changes the value of one of these variables will not affect the value of the other. Given a plausible definition by Woodward of type-causation, when a variable X is a parent of another variable, X is a direct type-cause of Y.12 Accordingly, these structural equations tell us that V is a direct type-cause of each of HT and R, and that neither HT nor R is a direct type-cause of the other. One can represent the causal structure of this model using a causal graph. In the graph, the nodes represent variables and an arrow from one node to another represents the fact that the variable represented by the former is a parent of the variable represented by the latter. Given Woodward’s definition of type-causation, the arrow between two variables represents a direct type-causal relation between them. The causal graph for the model M1 just described is depicted in Figure 16.1. HT

R

V

Figure 16.1 A causal graph 12 Woodward (2003: 55) defines direct type-causation in these terms: X is a direct cause of Y with respect to some variable set V iff there is a possible intervention on X that will change Y when all the other variables in V besides X and Y are held fixed at some value by interventions.



THE CONSEQUENCE ARGUMENT DISARMED

R

HT

V

Figure 16.2 A causal graph

The concept that will be of most use in our discussion below is the concept of an interventionist counterfactual, which is defined in these terms: Definition 2: The interventionist counterfactual ‘If it were the case that X=x, then it would be the case that Y=y’ is true in model M iff ‘Y=y’ is true in the submodel MX=x that is obtained by replacing the structural equation for X in the model M by the new equation X = x. For example, the counterfactual ‘If Jones had not had a high temperature, he would still have had the rash’ is true in the model M = described above. This represents the fact that an intervention that changes the value of HT from 1 to 0 will not change the value of R. This is modelled by replacing the equation HT=V by the equation HT=0 and then solving the remaining equation to determine that the value of R remains 1. Modelling the intervention in this way has the effect of cutting off the variable HT from the normal causal influence of its parent V, or breaking the causal arrow between HT and V, as depicted in Figure 16.2. The concept of breaking causal arrows in causal modelling is similar to Lewis’s (1979) concept of a miracle used in his explanation of how the antecedent of a non-backtracking counterfactual is realized in a deterministic setting. By comparison with the standard possible-worlds semantics for non-backtracking counterfactuals, the present account of interventionist counterfactuals is a more psychologically realistic account of our understanding of counterfactuals, certainly in the context of scientific experimentation. Instead of representing the content of counterfactuals in terms of the way in which laws govern the evolution of the entire universe, it represents their content in terms of the way in which causal generalizations or structural equations, which typically fall well short of being laws, apply to typically localized, small-scale systems. The knowledge required to reason about interventionist counterfactuals is the kind of knowledge possessed by ordinary people engaged in causal reasoning. This discussion of interventionist counterfactuals reveals a crucial feature of structural equations: a structural equation of the form Y = fY(X1, ..., Xn) must be understood as being qualified by a proviso to the effect ‘Provided no interventions occur on the left-hand-side variable Y’. For, as the truth conditions for interventionist counterfactuals make evident, any structural equation for an endogenous variable can be disrupted by an intervention. Such an intervention disrupts the equation by setting the variable on the left-hand side of the equation (here Y) to a value that is not identical to the value generated by the function on the right-hand side (here

PETER MENZIES



fY(X1, ..., Xn)). Consequently, in order for the equation to hold true in the model, it must be read as qualified by a proviso of this kind. This observation will be central to our discussion of the Consequence Argument in later sections.13

3 Defence of the Counterfactual Analysis of the Ability to Do Otherwise In order to evaluate the Consequence Argument, we need to understand the concept ‘the ability to do otherwise’. To play its role in the Basic Argument for incompatibilism, the concept must be understood as referring to one of the abilities required by free will. I use the expression ‘the ability to do otherwise’, rather than ‘can do otherwise’, because the latter is ambiguous in several ways. First, it is ambiguous between epistemic and ontic readings. Second, even in its ontic reading, it is ambiguous between a ‘possibility’ construal and an ‘ability’ construal. Under the ‘possibility’ construal, ‘Agent x can do A’ is true even when x does A by a fluke. For example, ‘I can win the lottery’ is true if it is possible for me to win the lottery by the fluke of drawing the right ticket. Clearly, this ‘possibility’ reading of ‘can do otherwise’ is not relevant to the discussion of free will, and so it is best to focus on the ‘ability’ construal from the outset.14 The ability to do otherwise is one among many abilities involved in free will. It in turn consists of many simpler abilities, including the ability to choose in response to reasons, the ability to form intentions on the basis of choices, and the ability to perform an action on the basis of intentions. I believe that all these abilities are to be understood in terms of counterfactuals, more specifically interventionist counterfactuals. G. E. Moore (1912) first articulated the view that the abilities involved in free will should be understood counterfactually. But this view has fallen out of favour because it faces a number of seemingly powerful objections. In this section, I shall defend the view against the three principal objections that turned many philosophers, both compatibilists and incompatibilists alike, against the view. In section 4, I shall show how a counterfactual understanding of the ability to do otherwise enables us to detect the fallacy in the Consequence Argument.15 13 There are two ways in which the proviso qualifying a structural equation can be interpreted. On the first interpretation, the proviso is part of the content of the structural equation with the equation taking the form of a conditional. On the second interpretation, the proviso is not part of the content but states a precondition for the application of the (unconditional) equation to a particular system. For discussion of these two ways of reading ceteris paribus generalizations, see Woodward 2003: chapter 6. The ambiguity in the interpretation of provisos can be seen in Hempel’s classic paper (1988), though he seems on balance to favour the second interpretation. The question of which interpretation is correct is tied up with the vexed question of how to interpret the qualifying clauses of ceteris paribus laws. I plan to side-step this issue by interpreting the proviso qualifying a structural equation in a way that is neutral between these interpretations. 14 However, see Christian List (2014) for an ingenious defence of the thesis that physical determinism is compatible with the ability to do otherwise when this ability is given a modal or ‘possibility’ reading. 15 I am indebted in this section to Vihvelin (2013: chapter 6) for her discussion of the objections to the counterfactual account of ‘the ability to do otherwise’. While I differ from her in my responses to these



THE CONSEQUENCE ARGUMENT DISARMED

3.1 Broad’s Objection C. D. Broad (1952) raised an early objection to the counterfactual analysis of the ability to do otherwise. He argued that the sentence ‘I have the ability to do A’ is equivalent in meaning to ‘If I were to choose to do A, I would do A’ only if it is assumed that I also have the ability to choose to do A. In this case, the counterfactual analysis of ‘The agent had the ability to do A’ needs to be completed by an analysis of ‘The agent had the ability to choose to do A’. But it would not do to try to analyse this ability claim in terms of counterfactuals since doing so would generate a vicious infinite regress. Though often repeated in the literature, I believe that this objection rests on a serious conceptual confusion. In asserting the counterfactual ‘If I were to choose to do A, I would do A’, it may be reasonable to assume that I also have the ability to choose to do A. For the ability to do an act is frequently accompanied by the ability to choose to do the act. But it is important to bear in mind that these abilities are distinct existences, and this means that one may occur without the other. Indeed, we can expect double dissociations between the abilities to exist because the abilities are subject to different kinds of impairments. For example, I might have the ability to choose on the basis of reasons but lack the ability to act on these choices because I am paralysed. Conversely, I might have the ability to act on my choices but lack the ability to make choices on the basis of reasons because I am subject to some compulsion. The fact that the abilities are distinct existences means that there is no logical connection between them. Accordingly, in the absence of a logical connection, there is no reason to think that the counterfactual analysis of ‘I have the ability to do A’ stands in need of completion by an analysis of ‘I have the ability to choose to do A’. This latter ability should, I suggest, also be understood in counterfactual terms, but there is no reason to think that the counterfactual analysis of the former ability is somehow incomplete or deficient without it.

3.2 Chisholm’s Objection The second objection to the counterfactual view of the abilities involved in free will is due to Roderick Chisholm (1964). The objection takes the form of a counterexample to the analysis of ‘I am able to do A’ in terms of the counterfactual ‘If I were to choose to do A, I would do A’. The counterexample goes roughly as follows. Suppose that I am offered a bowl of red candy but I cannot choose to take one because I have a pathological aversion to red candy. Nonetheless, it is consistent to suppose that if I had chosen a red candy, I would have taken it.16 So we seem to have a straightforward counterexample to the counterfactual analysis: the counterfactual is true while the corresponding ability statement is false. objections, I agree with her assessment that they have considerably less merit than they are usually thought to have. 16

This example is an adaptation of one given by Lehrer (1968).

PETER MENZIES

R

C



A

P

Figure 16.3 A causal graph

It is useful to construct an explicit causal model to guide our reasoning about the example. Let M2 be a model consisting of the following variables V2 and structural equations E2: Set of variables V2: R = 1 if I have sufficient reason to choose red candy, 0 otherwise. P = 1 if I have an aversion to red candy, 0 otherwise. C = 1 if I choose to take a red candy, 0 otherwise. A = 1 if I take a red candy, 0 otherwise. Structural Equations E2: R = 1; P = 1. C = R & ~P; A = C.17 The resulting causal graph is depicted in Figure 16.3. This model represents the pathological aversion to red candy as affecting my ability to make a choice on the basis of reasons rather than my ability to act on the basis of my choices. For it is natural to interpret the example as suggesting that the aversion does not impede my ability to carry out my decisions, as say a bodily paralysis would, but rather hinders my decisionmaking by overriding or bypassing the reasons I have for making a choice. The representation afforded by the model enables us to see more clearly where Chisholm’s counterexample to the counterfactual analysis of abilities fails. The counterexample is supposed to work by highlighting a contrast. On the one hand, I lack the ability to take a red candy because I lack the ability to choose to take one due to a pathological aversion. On the other hand, it is true of me that if I had chosen a red candy, I would have taken one. But now observe that the expression ‘I lack the ability to take a red candy’ is ambiguous between (a) I lack the ability to take a red candy in response to reasons; and (b) I lack the ability to take a red candy in response to choices. It is certainly true that I lack the first ability, because I lack the constituent ability to choose on the basis of reasons. (Note that the counterfactual ‘If I were to have sufficient reason to choose a red candy, I would choose to take one’ is false.) But I have the second ability since I am not paralysed, nor do I suffer any impairment in my capacity to translate my choices into action. It is this second ability that

17

Informally, these equations say the following: R and P each take the value 1; C takes the value 1 iff R takes the value 1 and P takes the value 0 (so that C takes the value 0 iff R takes the value 0 or P takes the value 1); and A takes the same value as C. This footnote has been added by the editor.



THE CONSEQUENCE ARGUMENT DISARMED

corresponds to the true counterfactual ‘If I were to choose to take a red candy, I would do so’. Accordingly, once we are careful to distinguish the abilities that are referred to by the expression ‘I lack the ability to take a red candy’, we can see that the counterexample fails. When this expression is read as referring to the ability to take a red candy in response to reasons, then it is surely true that I lack this ability because I lack an ability that is a constituent of it (the ability to choose on the basis of reasons). But when the expression is read as referring to the ability to take a red candy in response to choices, then it is just as surely true that I possess this ability, in accord with the counterfactual that we take to hold in the example.

3.3 Lehrer’s Objection The next objection, due to Keith Lehrer (1968), is the most cogent of the objections raised against the counterfactual analysis of the abilities involved in free will. Even so, philosophical treatments of abilities and dispositions, given since Lehrer first raised the objection, provide a very plausible response to it. Lehrer argues that ‘I can do A’ cannot be equivalent in meaning to any conditional of the form ‘If conditions C were to obtain, then I would do A’ because the following three propositions are logically consistent: (i) If conditions C were to obtain, I would do A; (ii) Conditions C do not obtain; and (iii) If conditions C do not to obtain, I cannot do A. Propositions (ii) and (iii) entail that I cannot do A. But if ‘I can do A’ means (i), we obtain a contradiction. What reason is there for thinking that these three conditions are consistent? Here is a modification of an example given by Lehrer (1968) that appears to demonstrate their consistency: The example involves two stages. First stage: suppose, that, unknown to myself, a demonic being has implanted a small monitoring device in my brain so that when I choose not to raise my hand, he reads this off his monitor and presses button A, which causes my arm to become temporarily paralysed. Let us suppose that I choose not to raise my hand, the demon presses button A, and my arm is paralysed. Second stage: suppose that if I change my mind and choose to raise my arm, the demon will press button B and release me from my paralysis. The following three propositions are true of this example and appear to be consistent: (i0 ) If I were to choose to raise my arm, I would do so (because the demon would now reverse my paralysis); (ii0 ) I choose not to raise my arm; and (iii0 ) If I do not choose not to raise my arm, then I cannot do so (because the demon will paralyse my arm).

PETER MENZIES

C



A

P

D

Figure 16.4 A causal graph

From (ii0 ) and (iii0 ), we can infer that I cannot raise my arm. But if the sentence ‘I can raise my arm’ means (i') ‘If I were to choose to raise my arm, I would so’, we have a contradiction. Once more it is instructive to provide an explicit model of this situation to guide our reasoning about it. Let M3 be the model that consists of the following sets of variables and structural equations: Variables: C = 1 if I choose to raise my arm, 0 otherwise. D = 1 if the demon pushes button B, 0 if the demon presses button A. P = 1 if my arm is paralysed, 0 otherwise. A = 1 if I raise my arm, 0 otherwise. Structural Equations: C = 0. D = C; P = ~D; A = C & ~P. The resulting causal graph is shown in Figure 16.4. This example turns out to be quite complicated in its structure.18 Using terminology that has become current since the time Lehrer presented his counterexample, we can say that the example involves two stages: a first stage that involves a finkish disposition and a second stage that involves a finkish absence of a disposition. A case of a ‘finkish’ disposition is one in which an object loses a disposition when the disposition is put to the test. Here is an example of a finkish disposition due to Lewis (1997): Finkish disposition: A sorcerer takes a liking to a fragile glass. If ever this glass is dropped, he quickly casts a spell that changes the crystalline structure of the glass, rendering it no longer fragile and thereby aborting the process of breaking. In this example, the disposition is finkish because putting the fragility of the glass to the test makes the fragility disappear. The first stage of Lehrer’s example involves 18 I am indebted to Vihvelin (2013: 200–1) for the point that Lehrer’s example is an instance of a finkish lack of disposition, though her analysis of the example’s structure and her treatment of the example differ from those presented here.



THE CONSEQUENCE ARGUMENT DISARMED

something like a finkish disposition since my choosing not to raise my arm makes my ability to act on my choices disappear (by inducing the demon to paralyse me).19 A case of a finkish absence of a disposition is one in which an object gains a disposition when the stimulus condition of the disposition is realized. Here is an example due to Martin (1994): Finkish absence of disposition: A sorcerer likes to break glass. A particular piece of molten glass is viscous and not fragile. However, if the molten glass were struck, the sorcerer would intervene to make the molten glass cool and solidify quickly so that it would break a short time later. Martin’s example illustrates a finkish absence since striking the molten glass causes the glass to become fragile. Likewise, the second stage of Lehrer’s example illustrates a finkish lack of disposition because my choosing to raise my arm causes my ability to act on my choices to reappear (by causing the demon to reverse my paralysis). Examples of finkish dispositions and finkish absences of dispositions were constructed as counterexamples to a simple counterfactual analysis of dispositions along the following lines: Simple Counterfactual Analysis: x is disposed to give response R to stimulus S iff, if x were to undergo stimulus S, it would give response R. A finkish disposition shows that the analysis is not necessary because the disposition may obtain even when the corresponding simple counterfactual is false. A finkish absence of a disposition shows that the analysis is not sufficient because a disposition may fail to obtain even when the corresponding simple counterfactual is true. While most philosophers agree that these examples demonstrate the inadequacy of the simple counterfactual analysis of dispositions, most would also agree that an amendment of the simple analysis proposed by Lewis (1997) provides a satisfactory account of these examples. Lewis’s analysis relies on the thesis that dispositions supervene on the intrinsic properties of the objects possessing the dispositions. A simplified version of his analysis states: Lewis’s Counterfactual Analysis: x is disposed at time t to give response R to stimulus S iff, for some intrinsic property B that x has at t, for some time t' after t, if x were to undergo S at t and retain the intrinsic property B until t', then x would give response R. Applying this analysis to the standard examples of finkish dispositions and finkish absences of dispositions yields the right answers. Thus, the glass in Lewis’s example is fragile because it has an intrinsic property—its crystalline structure—such that if it 19 As Chris Hitchcock has pointed out, the first stage of Lehrer’s example does not perfectly match the case of a finkish disposition, because choosing not to raise my arm is not the stimulus condition for the disposition; choosing to raise my arm is. This footnote has been added by the editor.

PETER MENZIES



were struck and retained this property, it would break. Similarly, the molten glass in Martin’s example is not fragile because it has no intrinsic property such that if it were struck and retained this property, it would break. Up until now, our discussion has operated under the assumption that abilities are to be understood in terms of simple counterfactuals. But the examples of finkish dispositions and finkish absences of dispositions show that this assumption is untenable and that we must adopt something like Lewis’s amended analysis. So let us apply this analysis to Lehrer’s example. The crucial point of Lehrer’s example is that we assert at its second stage that I cannot raise my arm (due to the paralysis induced by the demon) while asserting that if I were to choose to raise my arm, I would do so (because the demon would reverse my paralysis). If the counterfactual ‘If I were to choose to raise my arm, I would do so’ were equivalent in meaning to ‘I can raise my arm’, then we would be entangled in a contradiction. But, as we have seen, ability and disposition propositions must be understood in terms of more complex counterfactuals. For example, the proposition that I can raise my arm at time t (at the second stage when I am already paralysed) must be understood in terms of a counterfactual such as (iv') There is some intrinsic property B of mine at time t and there is some time t0 after t such that if I were to choose to raise my arm at t and retain this intrinsic property B until t0 , I would succeed in raising my arm. But of course this counterfactual is false, matching the falsity of the proposition that I can raise my arm at t. In general, if Lehrer’s counterexample to counterfactual analyses of dispositions and abilities is to be effective, it must show that the counterfactual (iv') is true when the proposition ‘I cannot raise my arm at time t’ is also true. But in the present type of example involving a finkish absence of a disposition, my not being able to raise my arm at time t will rule out my possession of an intrinsic property that would make the existential proposition (iv') true. There are other objections to the counterfactual analysis of the ability to do otherwise.20 But it suffices for our present purposes to have rebutted the three principal objections that have held sway for so long in the literature.

4 The Consequence Argument Locally Applied Let us turn now to consider the modal version of van Inwagen’s Consequence Argument. It is helpful to be able to formalize the argument. For this purpose, As well as examples involving finkish dispositions and finkish absences of dispositions, there are other counterexamples to the counterfactual analysis of dispositions involving so-called masks and mimics. For discussion of these other kinds of counterexamples, see Bird 2007: chapter 2. Lewis’s amended counterfactual analysis does not handle these kinds of counterexamples, and separate treatments must be offered for them. 20



THE CONSEQUENCE ARGUMENT DISARMED

I shall use this symbolism: L symbolizes the proposition expressing the conjunction of all the laws of nature; H symbolizes a proposition expressing the state of the world in the remote past; A symbolizes a proposition describing a particular action I will perform; □ symbolizes logical necessity; and N(p) symbolizes the proposition ‘I am not able to do anything to render p false’. I shall adopt the simple formulation of the argument proposed by Finch and Warfield (1998), which uses a rule of inference—Rule β*—which is less controversial than the rule van Inwagen originally employed—Rule β: Rule β: From N(p) and N(p ⊃ q) infer N(q). Rule β*: From N(p) and □(p ⊃ q) infer N(q). In this simple formulation, the argument runs: Premise 1: □(L&H ⊃ A) (Thesis of determinism) Premise 2: N(L&H) (Fixity of past and laws) Conclusion: N(A) by Rule β*. The first question that needs to be settled is whether the argument is valid. Some compatibilists have argued that the inference Rule β* employed in the argument is invalid. But this claim is, I believe, false if, as seems reasonable, we interpret N as a necessity operator. From the standard possible-worlds semantics, we know that, for every necessity operator, there exists an accessibility relation that restricts quantification over worlds. So let us say that N(p) is true in world w iff p is true in all the worlds that are N-accessible to w. To see that Rule β* is valid we need to consider the three cases in which □(p ⊃ q) is true: (i) □(p ⊃ q) is trivially true because □(~p) is true; (ii) □(p ⊃ q) is trivially true because □(q) is true; and (iii) □(p ⊃ q) is nontrivially true in the cases where (i) and (ii) fail to hold. The validity of the rule β* is easily established in the trivial cases (i) and (ii). So let us focus on the non-trivial case (iii). In Figure 16.5, the shaded circle is the set of N-accessible worlds to world w. The figure illustrates that when N(p) and □(p ⊃ q) are true in w, N(q) must be true in w.21

p

q

w

Figure 16.5 Possible worlds

It is presupposed here that □ (which, as noted, stands for logical necessity) is a stronger necessity operator than N. Thanks to Chris Hitchcock for highlighting this point. This footnote has been added by the editor. 21

PETER MENZIES



So, the Consequence Argument in its present form is valid, since the only inference rule it employs is valid. Consequently, the compatibilist can challenge the argument only by disputing one or both of its two premises. Most of the critical attention has focused on its second premise. Recall that it says that I am not able to do anything to render false the conjunction of the law proposition L and the history proposition H. I believe that from an interventionist perspective this premise is impeccable. Rather the questionable premise is, I suggest, the first premise to the effect that the law proposition and history proposition logically imply the action proposition A. This premise is used in every version of the Consequence Argument, but it is rarely questioned. Nonetheless, the interventionist must regard it as false. To see this it is best to evaluate the argument in the context of its application to a localized, small-scale system. This is appropriate because the argument, if sound, should be cogent whether it is applied to the whole universe or to a small-scale system. For the argument purports to show that my present actions are not up to me by virtue of the fact that I am not able to do anything other than what I am predetermined to do by the laws and events of the past, whether these laws and past events are those belonging to the whole universe or a small-scale system. So let us consider a very simple small-scale system of an agent’s decision-making, which is modelled in terms of the following variables and structural equations: Variables: R = 1 if there is sufficient reason for me to perform A1; 2 if there is sufficient reason to perform A2; 3 if there is sufficient reason to perform A3. D = 1 if I decide to perform A1; 2 if I decide to perform A2; 3 if I decide to perform A3. A = 1 if I perform A1; 2 if I perform A2; 3 if I perform A3. Structural Equations: R = 1. D = R; and A = D. The resulting causal graph is shown in Figure 16.6. We can reformulate the Consequence Argument as applying to this small-scale system as follows. Let R = 1 stand in place of the history proposition H; let the conjunction of the structural equations D = R and A = D stand in place of the law proposition L; and let A = 1 stand in place of the proposition A. Then the argument purports to establish the conclusion that, given the history and the ‘laws’, I am not able to do anything to render false the proposition A = 1, or in other words, I am not able to do anything other than do A1. But the interventionist should claim that this conclusion is false. On the compatibilist reading of ‘ability to do otherwise’ proposed above, I am able to perform some R

D

Figure 16.6 A causal graph

A



THE CONSEQUENCE ARGUMENT DISARMED

R=1

D=2

A=2

D=2 □➞ A=2

D=1

A=1

D=1 □➞ A=1

D=3

A=3

D=3 □➞ A=3

Figure 16.7 Logically possible trajectories

action other than A1. For the ability-backing counterfactuals are true: D=1 □➞ A=1, D=2 □➞ A=2, and D=3 □➞ A=3. (Since abilities involved in this simple model are not finkish dispositions or finkish absences of dispositions, we can revert to the simple counterfactual renderings of abilities.) The falsity of the conclusion means that one of the argument’s premises must be false. It is not difficult to see that it must be the first premise—the seemingly innocuous thesis of determinism. This thesis is false because interventions may occur that disturb the evolution of the system from its predetermined course. Consider Figure 16.7, which shows the logically possible trajectories of the simple system. A horizontal line represents the trajectory or evolution of the system from one state to another when there are no interventions. A heavy diagonal line represents that an intervention has taken place to change the value of a variable. The counterfactual in a box beside each horizontal line represents the counterfactual that is true of that trajectory. Given the actual initial state of system consisting in R = 1, the system evolves to state D = 1 and then to state A = 1. But it is possible that interventions change the value of D = 1 to D = 2 or D = 3 with the result that the system follows different trajectories.22 This figure shows clearly that the history proposition (R=1), taken in conjunction with the proposition expressing the conjunction of the structural equations (D=R & A=D), does not logically imply the proposition A=1 (where, crucially, the structural equations are each understood as being qualified by a no-interventions proviso, as explained earlier).23 The only logical implication is this: the actual values of the exogenous variables, taken in conjunction with the structural equations, logically imply the corresponding variables of the endogenous variables only if no interventions take place in the system. This means that the first premise of the argument—the unqualified thesis of determinism—is false. Its falsity provides us with a neat explanation of why the conclusion of the Consequence Argument is false: each intervention

22 What kind of interventions can change the decision I make? Two kinds of interventions suggest themselves as being feasible. One kind of intervention could result from the action of another agent, who offers inducements to me to make a different decision from the one that my own reasons would dictate. Another kind of intervention could result from my own resolution to decide on the basis of the outcome of a randomizing device independently of any reasons I may have. 23 The parenthetical remark has been added by the editor.

PETER MENZIES



that gives rise to a possible trajectory of the system corresponds to a true interventionist counterfactual supporting the claim that I have the ability to perform an action other than the one I actually perform. The possibility of an intervention giving rise to a trajectory diverging from the actual trajectory depends on the fact that the intervention overrides the structural equation linking the intervened-on variable with its parents. (All other structural equations continue to hold since they are robust under interventions on the right-hand side variables.) For this reason, as was noted in section 2, the structural equation of an endogenous variable must be read as affixed with a qualifier thus: ‘Provided no interventions occur (on the left-hand-side variable), then Y = fY(X1, ..., Xn)’. So understood, a structural equation is literally true in a model even when the functional dependence implied by a structural equation is overriden by an intervention.24

5 The Consequence Argument Globally Applied A possible objection to my argument in the preceding section is that I have not answered van Inwagen’s original version of the Consequence Argument, which is formulated with a particular understanding of determinism in mind. More specifically, van Inwagen formulates the thesis of determinism in this way: Thesis of determinism: For any two instants of time t and t', there is a proposition P that expresses the state of the world at instant t and a proposition Q that expresses the state of the world at instant t' such that the conjunction of P together with the laws of nature entails Q.

Furthermore, it could be argued that my critique of the Consequence Argument, formulated in terms of states of small-scale systems that allow for external interventions, will not carry over when the argument is formulated in terms of the states of the whole universe that leave no room for external interventions. Indeed, the question may reasonably be asked whether my critique of the argument gets any grip whatsoever when the argument is formulated in global terms. Interventionists have registered concern about whether it makes sense to apply causal modelling to the whole universe. For instance, Pearl writes: ‘If you wish to include the whole universe in the model, causality disappears because interventions disappear—the manipulator and the manipulated lose their distinction.’25 24

A structural equation with qualifying proviso is true in its model whether we interpret the proviso as part of the content of the equation or a condition of application of the equation that is not part of its content. (These two interpretations are described in note 13.) Clearly, under the first interpretation, a structural equation is to be read as a conditional with the proviso as antecedent: such a conditional can be true in the model even when its antecedent is false. Likewise, under the second interpretation, when its proviso is not met, a structural equation can be true in a model: the failure of the proviso simply signifies that the equation is not applicable to the particular system at hand. 25 Pearl 2000 (349–50). Woodward expresses similar concerns in his 2007 (90–3).



THE CONSEQUENCE ARGUMENT DISARMED

Notwithstanding Pearl’s concerns, I believe that the proposed diagnosis of the flaw of the Consequence Argument applies even when the argument is formulated in global terms. To explain this, let us suppose that we have a model of the whole universe where the structural equations are genuine laws that apply to global states of the universe. In order to address Pearl’s point that the concept of an intervention as an exogenous influence from outside a system does not make sense when the system is the whole universe, we need to define the notion of an intervention in a different way: Definition 3: A miracle that fixes the value of X at x is an uncaused occurrence that (i) makes true X=x; (ii) disrupts the links between X and its causal antecedents; but (iii) does not disrupt any other causal link. On this definition, a miracle is not caused at all and so a fortiori not caused by causal influences outside the model. The concept defined here is very similar to the concept of a miracle that Lewis uses in his account of non-backtracking counterfactuals. Indeed, it is natural to think that Lewis’s concept of a miracle, like the concept of an intervention, is a development or extension of the concept of a human manipulation: a miracle is, so to speak, the work of the hand of God.26 Once more, I claim that the thesis of determinism, as originally formulated in the Consequence Argument, is false, i.e. □(L&H ⊃ A) is false. In order to recognize its falsity, consider the following logically possible world—call it the determinismfalsifying world. The world agrees in its laws with the actual world throughout its evolution (so L is true); further, it agrees in its history with the actual world up to the time to which H refers (so H is true); but then the world diverges from the actual world due to a ‘divergence’ miracle that gives rise to a trajectory in which A is false. How is this possible? How can the determinism-falsifying world agree with the actual laws throughout its evolution when a divergence miracle occurs? I suggest that there is no contradiction here if we think of the laws governing the evolution of the whole universe as qualified by a ‘No miracles proviso’. As we saw earlier, a structural equation such as Y = fY(X1,..., Xn) is violated when a miracle or intervention fixes the value of Y, but the corresponding law is not broken if it is understood as described by the statement ‘Provided no miracles or interventions occur to fix the value of Y, then Y = fY(X1, ..., Xn)’. Even when the structural equation is violated by a miracle or an intervention, this statement of law is true. I use this understanding of ‘law’ in the description of the determinism-falsifying possible world.

26 The concept of a miracle may seem illegitimate from a scientific point of view. But any account of counterfactuals about whole states of a deterministic universe will have to invoke some such concept to explain how deterministic worlds can agree with respect to laws and to history up to a certain point and then diverge thereafter.

PETER MENZIES



One way to see that the determinism-falsifying world is logically possible is to compare it with the ‘divergent worlds’ that Lewis invokes in his (1979) account of non-backtracking counterfactuals. Lewis says that if we are evaluating the counterfactual P □➞ Q in the actual world, a divergent world is one which agrees in its history with the actual world up to the time of P, contains a miracle that realizes P, and thereafter evolves in accordance with laws that are exactly like the actual laws. Few philosophers have thought that Lewis’s divergent worlds are logically impossible. Still they are not quite like the determinism-falsifying world described above. One evident difference follows from Lewis’s claim that the divergence miracle is a miracle with respect to the actual world but not with respect to the divergent world: in other words, it ‘breaks the laws’ of the actual world but not those of the divergent world. Since for Lewis a law is, at least, ‘an absolutely unbroken regularity’, the laws of the divergent world cannot be the same as the actual laws (Lewis 1979). In this respect, a divergent world is different from the determinism-falsifying world, which must agree with the actual laws throughout its course of evolution. However, let us consider whether Lewis was too hasty in thinking that the divergent worlds cannot have the same laws as the actual world. For a start, observe how strange the laws of Lewis’s divergent worlds are. These laws agree with the actual laws in their application until just before the divergence miracle. Then there is an apparent singularity or ‘blip’ in one or more laws of the divergent worlds allowing the miracle to take place. Thereafter all the laws agree completely in their application with the actual laws. These laws are surely highly unusual dog-legged constructions! Now suppose, as an alternative hypothesis, that the actual laws are complex functional dependencies with the qualifier ‘Provided no miracles occur’ affixed. Then the laws of the divergent worlds and the actual world could be identical. The proviso would allow the same laws to apply to the actual world and the divergent worlds throughout their histories, even though some of the functional dependencies are violated by miracles in the divergent worlds. It is interesting that Lewis went part of the way towards envisaging this in his discussion of the similarity relation for non-backtracking counterfactuals, where he wrote: ‘Indeed, a version of the violated law, complicated and weakened by a clause to permit the one exception, may be simple and strong enough to survive as a law [in a divergent world]’ (1973: 75). Here he says that the miracle-allowing law of the divergent world could be a simple modification of the actual law though he does not go as far as saying that the laws would be identical. Nonetheless, if Lewis had taken this extra step by construing these laws as qualified by a ‘No miracles or interventions’ proviso, he would have a more streamlined account of the laws involved in non-backtracking counterfactuals. When laws are understood in this way, the apparent difference between Lewis’s divergent worlds and the determinism-falsifying world evaporates. Consequently, there is reason to think that one kind of world is just as logically possible as the other.



THE CONSEQUENCE ARGUMENT DISARMED

6 An Objection (Editorial Addition) It is worth considering the following objection.27 The denial of the first premise of the Consequence Argument, so the objection goes, simply misses the target as a response to van Inwagen’s claim that free will is incompatible with determinism. Surely, van Inwagen would grant that, if we deny the thesis of determinism, as expressed by the statement □(L&H ⊃ A), then the Consequence Argument no longer rules out free will (perhaps other arguments still do, but those are not our topic here). And so it seems that the present chapter does not disarm the argument for the incompatibility of free will and determinism, but rather bypasses it altogether, by denying determinism. However, there is a possible response to this objection. The rejection of the first premise of the Consequence Argument is still compatible with another, qualified version of determinism—which is arguably the version of determinism that best fits the interventionist picture of causation adopted in this chapter. To explain, suppose, as before, that we have a model of the whole universe where the structural equations are genuine laws that apply to global states of the universe. We can now distinguish between two variants of that model. In one variant—call this the qualified variant—every structural equation is qualified by a ‘no miracles’ proviso, so that the corresponding law is of the form: ‘Provided no miracles or interventions occur to fix the value of Y, then Y = fY(X1,..., Xn)’. In another variant of the model, none of the structural equations is qualified by such a proviso. Call this the unqualified variant. It should be evident that the system of laws in the unqualified variant may well satisfy the first premise of the Consequence Argument, □(L&H ⊃ A), even when the system of laws in the corresponding qualified variant does not. Indeed, this chapter deals precisely with a system of laws in the qualified form. As should be clear from section 5, the laws imply a strictly deterministic evolution of the universe only if we set aside miracles and determinism-falsifying worlds. But crucially, the laws no longer imply a strictly deterministic evolution once we acknowledge the logical possibility of miracles and of determinism-falsifying worlds. 27

This section has been written by Christian List on behalf of Peter Menzies, partly in response to an objection that Daniel Nolan had raised in correspondence with Peter. Christian subsequently learnt that Eddy Nahmias had independently raised a similar objection in correspondence with Peter. Peter himself wrote the following in an email to Daniel Nolan: ‘I’ve had the worry in the back of my mind for some time that van Inwagen and others might reply that my “unless an intervention occurs” laws are not properly deterministic. I will clearly need to amplify my comments to substantiate my claim that they are properly called deterministic. I think that in many scientific disciplines, including many areas of physics, scientists use models that appeal to laws that are said to be deterministic even though they are known to be falsifiable by interventions. (The label “determinism” seems to characterize the functional form of the law rather than its status as exceptionless.) I suppose this is partly what Cartwright [means] when she says that all laws are ceteris paribus. I think that there are no laws, or very few, that are deterministic in van Inwagen’s sense.’ Unfortunately, Peter did not have the time to implement the revisions of the chapter that he had wanted to make. The present short section is an attempt to capture the idea that the proviso-qualified laws discussed in this chapter can indeed be called ‘deterministic’ in an appropriately qualified sense. Christian List is grateful to Daniel Nolan and to Eddy Nahmias for sharing the relevant emails and for helpful comments on the section itself.

PETER MENZIES



On the standard definition of determinism—which we may call determinism simpliciter—the qualified variant of our structural-equations model obviously counts as indeterministic, and only the unqualified variant counts as deterministic. If we use this standard definition of determinism, then this chapter’s denial of the first premise of the Consequence Argument does indeed amount to a denial of determinism. However, if we redefine determinism in a suitably qualified form, then the denial of the argument’s first premise need not amount to a denial of determinism—now suitably qualified. In particular, suppose we define qualified determinism such that our qualified model can count as ‘qualified-deterministic’, on the grounds that, without the provisos, its structural equations imply a deterministic evolution. Formally: Definition 4: Consider a system of laws which are each of the form ‘Provided no miracles or interventions occur to fix the value of Y, then Y = fY(X1,..., Xn)’. This system is qualified deterministic iff its proviso-free counterpart is deterministic simpliciter. (The right-hand side of this biconditional says that the equations of the form ‘Y = fY(X1,..., Xn)’ jointly imply a deterministic evolution in the absence of any provisos.) It then follows that qualified determinism is compatible with the negation of the first premise of the Consequence Argument, and so the present chapter establishes that qualified determinism is consistent with free will. Furthermore, if one accepts the interventionist theory of causation, it is arguable that qualified determinism is a more plausible version of determinism than its unqualified counterpart. From the perspective of the interventionist theory, the term ‘determinism’ refers to the functional form of the laws—i.e. of each of the structural equations of the form ‘Y = fY(X1,..., Xn)’—rather than to the status of these laws as exceptionless or proviso-free. If the functional form of the laws is the key feature that the term ‘deterministic’ is meant to convey, then it seems appropriate to adopt the qualified redefinition of that term.

7 Comparison with ‘Local Miracle Compatibilism’ My response to the Consequence Argument in its global application emphasizes the role played by the concept of a miracle; and this may suggest that it is a version of what has come to be called Lewis’s ‘local miracle compatibilism’ (Beebee 2003). Lewis does not explicitly articulate this view, but the main features of the view can be reconstructed from his articles (1973, 1979, 1981, and 1997). On this view, even though our actions are predetermined by the laws and history, we are free, at least in part, because we can do otherwise. The local miracle compatibilist understands the expression ‘we can do otherwise’ in a distinctive fashion. It means that in certain ‘divergent worlds’ we or our counterparts perform different actions from the actual ones. Figure 16.7, which was introduced to represent the possible trajectories of a



THE CONSEQUENCE ARGUMENT DISARMED

simple decision-making system, can be seen as representing ‘divergent worlds’. Just think of these trajectories as possible worlds with the central trajectory as the actual world and the upper and lower trajectories as non-actual worlds. The latter worlds agree in their histories with the actual world up to the time of decision, but then diverge from the actual world at the time of decision due to a small, local miracle that realizes a different decision D2 or D3. Perhaps, in these worlds, neurons in my brain miraculously fire, realizing decision D2 or D3, which then lead to action A2 or A3. It is because we (or our counterparts) perform these actions in the divergent worlds that we can be said to be able to do otherwise. When local miracle compatibilism is described in these terms, the view elaborated in preceding sections is a version of it. But underlying this similarity, there is an important difference regarding the conception of laws between the version Lewis advocates and the version advocated here. The view developed in this chapter takes the actual world and the ‘divergent worlds’ to be governed by the same laws, whereas Lewis assumes that these worlds are governed by different laws. The difference does not arise because we disagree over whether laws can be broken. On both views, a generalization cannot be a law if it has a falsifying instance. (A law is not falsified, on my view, if its proviso is not met.) Nor does the difference arise from a difference in the way laws are conceived. On both conceptions, we might suppose, for the sake of argument, that the Ramseyian conception of laws is true: laws are contingent generalizations that appear as theorems (or axioms) in each of the true deductive systems that achieves a best combination of simplicity and strength (Lewis 1973: 73).28 Rather the difference in position arises because of a disagreement about the form that laws must take. Lewis assumes that a law has the form of a universal generalization (with an unrestricted domain of quantification) that contains no proviso. On the other hand, on the view I am proposing, a law is a universal generalization qualified by a proviso. This can be interpreted in two ways: either the law takes the form of the conditional with the proviso as its antecedent, or the law is a universal generalization with a domain of quantification restricted to those systems that meet its proviso. (Accordingly, on the present view, we need to accept, at most, that the world is qualified-deterministic, not that it is deterministic simpliciter.29) I have argued that it would considerably simplify Lewis’s account of non-backtracking counterfactuals if he were to adopt the present, alternative conception of the form of laws. This point of disagreeement between the two versions of local miracle compatibilism may seem a very small one. Yet it has broader consequences since it affects the diagnosis of the Consequence Argument’s error. Although Lewis does not directly address the modal version of Consequence Argument, he does address a different counterfactual version: 28 29

I do not in fact endorse Lewis’s Humean conception of laws. This remark has been added by the editor; compare section 6 above.

PETER MENZIES



I have just put my hand on my desk. That, let me claim, was a free but predetermined act. I was able to act otherwise, for instance to raise my hand. But there is a true historical proposition H about the intrinsic state of the world long ago, and there is a true proposition L specifying the laws of nature that govern our world, such that H and L jointly determine what I did. They jointly imply the proposition that I put my hand down. They jointly contradict the proposition that I raised my hand...What if I had raised my hand?...If I had raised my hand, the law proposition L would not have been true. (1981: 123)

It is reasonable to extrapolate from his response to this version of the argument that he would deny the second premise in the modal version of the Consequence Argument. More specifically, he would deny that there is nothing I can do to render false the conjunction of the history proposition H and the law proposition L. On his view, there is something I can do to render false the law proposition L. Lewis’s diagnosis of the error in the argument is different from mine. The difference stems from a disagreement over an assumption explicit in the quote above. Lewis assumes that the conjunction of the history proposition H and the law proposition L logically implies the proposition that I do not raise my arm. On the other hand, I have been at pains to argue that the conjunction of L and H can imply the action proposition only if the proviso of the law proposition is met, which is to say that no miracle has occurred in the system at hand. Moreover, it is natural for a local miracle compatibilist to say that this proviso is not met—because a miracle must have occurred if some action other than my actual action had occurred. The right response for a local miracle compatibilist to give to the question ‘What if I had raised my hand?’ is not that a law would have to have been broken, but that a miracle would have to have occurred. To be sure, this might invite the same kind of sceptical response that Lewis considers in his (1981) article: ‘You claim to be able to perform miracles. A marvellous power indeed! Can you also bend spoons?’ But I reply to this sceptical challenge by appealing to the distinction Lewis draws himself: the distinction between being able to do something such that, if I did it, a miracle would have occurred and being able to do something such that, if I did it, it would cause a miracle or be a miracle itself. The local miracle compatibilist is committed to the first, weak claim and not the second, absurdly strong claim.

References Beebee, H. 2003. ‘Local Miracle Compatibilism’, Noûs, 37: 258–77. Bird, A. 2007. Nature’s Metaphysics. Oxford: Oxford University Press. Broad, C. D. 1952. ‘Determinism, Indeterminism, and Libertarianism’, in his Ethics and the History of Philosophy. London: Routledge & Kegan Paul. Chisholm, R. D. 1964. ‘Human Freedom and the Self ’, The Lindley Lecture. Reprinted in G. Watson (ed.), Free Will. Oxford: Oxford University Press, 1982. Deery, O., and Nahmias, E. 2014. ‘Causal Modeling and Free Will: A New Approach to Old Problems’. Paper presented to 2014 meeting of the Society for Philosophy and Psychology.



THE CONSEQUENCE ARGUMENT DISARMED

Finch, A., and Warfield, T. 1998. ‘The Mind Argument and Libertarianism’, Mind, 107: 515–28. Fischer, J. M. 2010. ‘The Frankfurt Cases: The Moral of the Stories’, The Philosophical Review, 119: 315–36. Frankfurt, H. 1969. ‘Alternate Possibilities and Moral Responsibility’, Journal of Philosophy, 74: 423–40. Haji, I. 2011. ‘Obligation, Reason and the Frankfurt Examples’, in R. Kane (ed.), The Oxford Handbook of Free Will, Second Edition. Oxford: Oxford University Press. Hempel, C. G. 1988. ‘Provisoes: A Problem Concerning the Inferential Function of Scientific Theories’, Erkenntnis, 28: 147–64. Hitchcock, C. 2001. ‘The Intransitivity of Causation Revealed in Equations and Graphs’, Journal of Philosophy, 98: 273–99. Hitchcock, C., and Woodward, J. 2003. ‘Explanatory Generalizations, Part 2: Plumbing Explanatory Depth’, Noûs, 37: 181–99. Ismael, J. 2007. ‘Freedom, Compulsion, and Causation’, Psyche, 13: 1–11. Ismael, Jennan. 2011. ‘Decision and the Open Future’, in Adrian Bardon (ed.), The Future of the Philosophy of Time. Oxford: Oxford University Press. Ismael, Jennan. 2012. ‘Causation, Free Will, and Naturalism’, in H. Kincaid, J. Ladyman, and D. Ross (eds), Scientific Metaphysics. Oxford: Oxford University Press, 208–35. Lehrer, K. 1968. ‘Cans without Ifs’, Analysis, 29: 29–32. Lewis, D. K. 1973. Counterfactuals. Oxford: Blackwell. Lewis, D. K. 1979. ‘Counterfactual Dependence and Time’s Arrow’, Noûs, 13: 455–76. Lewis, D. K. 1981. ‘Are We Free to Break the Laws?’ Theoria, 47: 112–21. Lewis, D. K. 1997. ‘Finkish Dispositions’, Philosophical Quarterly, 47: 143–58. List, C. 2014. ‘Free Will, Determinism, and the Possibility of Doing Otherwise’, Noûs, 48: 156–78. Martin, C. B. 1994. ‘Dispositions and Conditionals’, The Philosophical Quarterly, 44: 1–8. Moore, G. E. 1912. Ethics. London: Williams and Norgate. Pearl, J. 2000. Causality: Models, Reasoning and Inference. Cambridge: Cambridge University Press. Pearl, J. 2009. Causality: Models, Reasoning and Inference, Second Edition. Cambridge: Cambridge University Press. Roskies, A. 2012. ‘Don’t Panic: Self-Authorship without Obscure Metaphysics’, Philosophical Perspectives, 26: 323–42. Van Inwagen, P. 1983. An Essay on Free Will. Oxford: Clarendon Press. Vihvelin, K. 2013. Causes, Laws, and Free Will. Oxford: Oxford University Press. Widerker, D. 2011. ‘Frankfurt-Friendly Libertarianism’, in R. Kane (ed.), The Oxford Handbook of Free Will, Second Edition. Oxford: Oxford University Press, 266–87. Widerker, D., and McKenna, M. (eds). 2003. Moral Responsibility and Alternative Possibilities. Burlington, VT: Ashgate. Woodward, J. 2003. Making Things Happen: A Theory of Causal Explanation. Oxford: Oxford University Press. Woodward, J. 2007. ‘Causation with a Human Face’, in H. Price and R. Corry (eds), Causation, Physics, and the Constitution of Reality. Oxford: Oxford University Press, 66–105. Woodward, J., and Hitchcock, C. 2003. ‘Explanatory Generalizations, Part 1: A Counterfactual Account’, Noûs, 37: 1–24.

Index activity 6, 80, 82, 87, 132, 133, 134–5, 137–40, 143–4, 148–50, 176, 281 Adams, E. 2, 35 Adams’ thesis 2–3, 33–45, 54 agency 5, 102, 116, 122–3, 128, 271, 277, 278 analysis of causation 1, 5, 14, 19, 25, 30–1, 33, 60, 74, 76–8, 80, 103, 105–6, 111, 116 118, 122–3, 128–9, 142, 153–5, 206, 215–17, 220–1, 223–5, 227, 228–9, 238, 245, 278, 288 antecedent time 15, 16, 19, 21, 22, 23, 24, 26, 27, 28, 29 anthropocentricism 3, 74, 81–5, 90–1, 96–7, 105 Antony, L. 287, 297–300 Armstrong, D. 277 Atran, S. 112 Austin, J. L. 137, 138 Ballung 6, 134, 136–7, 139 Baron, S. 153 Baumgartner, M. 256–7 Beebee, H. 11, 184, 327 Bennett, J. 19, 22, 24, 27 Bennett, K. 294 Bernstein, S. 271 best deserver theory 100, 105, 108–9, 113 bicycle helmet 125–8, 129–30 Bird, A. 290, 319 Bjornsson, G. 154, 159 Blackburn, S. 76 Blanchard, T. 7, 118, 121 Block, N. 287 Bloom, P. 269 Bontly, T. 59, 61–4, 228 Braddon-Mitchell, D. 4, 101, 105, 106, 112, 215 Braun, D. 216 Briggs, R. 2–3, 14, 158, 182, 267 Broad, C. D. 314 Byrne, R. 188, 210 capacity 133, 139, 140, 143, 145, 146–7, 150, 151, 181, 315 Carpenter, C. 125 Cartwright, N. 6, 117, 118, 123, 132, 135, 136, 137, 140, 142, 146, 151, 326 causal closure 216, 217, 227, 252, 270, 272, 275, 286 causal exclusion 61, 63, 215, 251–3, 260 causal judgement 3, 65, 99, 154–5, 161–2, 163, 170–2, 184, 198, 217, 222, 228

pragmatics of 86, 175, 187–8, 194–5, 207–12 causal model 3, 25, 26, 48, 67, 91, 104, 155–9, 163–4, 184, 190, 207, 211, 212, 223, 315, 323 aptness of 7, 175–83, 192–206 structurally isomorphic 153–4, 185–8 causal process 20, 75, 89, 101–2, 103–4, 111, 135, 147, 168, 263 causal relata 58, 64–7, 71, 117, 287–9 causal relevance 9, 11, 60, 134, 157, 240–2, 244–5, 247–8, 286–7, 288–91, 292, 294, 296, 298, 299, 300, 301–5 Causal Role Problem 287–91, 292–3, 294–6, 298, 300–1, 303 causal-source thesis 270, 272, 274, 276, 281 causal structure 1, 14, 15, 47–8, 52, 122, 125–6, 132–3, 139, 142, 143, 146, 154, 157, 178, 181, 183, 186, 198, 199–200, 201–2, 204, 211–12, 232, 233, 247, 248, 249, 257, 311 causal sufficiency 9, 10–11, 216–17, 225–7, 229, 239–40, 247, 272, 273, 275–6, 278, 295 causation, causality actual 5, 6, 7, 116–18, 120–3, 124, 128–9, 154–5, 157, 159, 163–5, 166, 168, 171, 172, 175–6, 178–80, 181–2, 183–5, 186–7, 188–90, 194, 195, 196, 198, 199, 200, 202, 203, 205, 206, 207–12 agency view/theory/account of 5, 73, 74–83, 88, 89–90, 91, 94, 96–7, 116, 122–3, 128 backward-looking 89, 117–18, 121, 124 contrastive 3, 58, 67–70, 71, 111, 176, 181, 191, 205, 209–10, 211, 222, 224, 229, 238, 255 efficacy vs. relevance 66, 302–4 forward-looking 117–18, 124 as glue 4, 100–1, 107–10, 111, 112, 113–14 in sensu stricto 99–100 locality 103, 110 mental 7–8, 10, 11, 71, 215, 238, 251, 256–7, 270–1, 277, 278, 284, 286, 287–8, 295, 298, 302 neural 280–4 and norms 129, 188, 192–5, 207, 209, 211–12 by omission 103, 134, 184–5, 195–8, 205, 224 pluralism about 4, 101–5, 109, 110–11, 113, 136 production 4, 100–1, 103, 104, 105, 106, 107, 108, 110, 111, 113–14, 135, 216, 238, 240, 241, 277–8, 279, 295 as symmetrical 100, 104–5, 107, 108, 109, 110, 111, 140



INDEX

cause vs. background condition 5, 165, 180, 192, 234 unmanipulable 80–1, 88–90 chance 22, 23, 30, 47–54, 110 chaos theory 21 Chisholm, R. D. 314–16 circularity objection 49, 74, 76–80, 96 clamping 120–1, 127 closure under conditionalization 37–8, 44 coarse-grained events 65, 276 Collingwood, R. G. 73 Collins, J. 153 Colyvan, M. 33, 153 conditional concept 101–2, 106, 110–14 conditional probability 33, 40, 43, 275–6 ratio formulation of 53 Consequence Argument 11, 307–9, 313, 319–22, 323–5, 326–7, 328–9 context-dependence 3, 4, 17, 19, 25–6, 37, 38–9, 43–5, 47, 54–5, 64–7, 69–70, 84, 136, 192, 226, 236 contrastivism 3, 58, 67–70, 71, 191, 205, 209–11, 222, 229, 238, 255–6 conversational implicature 61–2 corporate responsibility 242 counterfactual dependence 6–7, 118–20, 124, 180, 203, 223–4, 225, 288–91, 292, 295, 296, 298, 303 dependence, spurious 199, 289–90 ideal-conditions 167–8, 169–72, 190–1 Interventionist 6, 9, 25–6, 67, 105, 134–6, 143, 155–9, 222, 223–5, 309–13, 321, 322–3, 326–7 isomorphs 154, 159–62 non-backtracking 4, 15, 158, 312, 324, 325, 328 Stalnaker semantics for 1–2, 3, 5, 15, 16–18, 28, 33–4, 35, 36, 38–9, 42, 45–55 Test 163–9 counterpossible conditional 2, 17 Cover, J. 271 Craver, C. 6, 132–3, 134–5, 136, 137, 138, 139, 143–4 crystals 107–8 Daly, H. 67 Danks, D. 153 Darden, L. 6, 132, 133, 134, 136, 137 decision theory causal 41, 123–4, 125–6 Deery, O. 309 default 4, 5, 6, 86, 93, 95, 112, 116, 180, 191, 192–200 vs. deviant 7, 121, 167, 175–6, 179, 183–90, 203, 205, 207–12 Dennett, D. 242

determinables vs. determinates 58, 59–61, 63, 65, 68, 69, 71 determinism 11, 12, 22, 23, 24, 27, 28, 45, 107, 269–71, 272, 275, 307–9, 313, 320, 322, 323, 324, 325, 326–7 Deutsch, D. 110 Diaconis, P. 194 difference-making 9, 30–1, 168–9, 172, 215–17, 218–20, 221–5, 227, 228, 229, 233, 236–7, 238–41, 242–4, 245–9, 271, 272, 275, 277–84, 286, 289, 295–6, 298 dispositional essentialism 234, 290–2, 295, 302, 318–19 dispositions 30–1, 74, 75, 76, 78, 81, 111, 234, 235, 290, 291, 295, 302, 303, 309, 310 analysis of 318–19 finkish 316–19, 322 Dorin, A. 125 double prevention 103, 154, 166, 172 Dowe, P. 101, 102 Dunaway, B. 112 Eberhardt, F. 153, 254 Edgington, D. 39–40, 42, 44, 47 Edmonds, A. 112 Eells, E. 117 Efstathiou, S. 136 Ehring, D. 101, 117 empiricism 75, 78–80, 95, 96, 111, 113, 114, 193 enabling condition 166–72 entailment within the consequent 38, 45, 55 entrenchment 299–300 epiphenomenalism 11, 270, 286–7, 291, 300–5 events 5, 21, 23, 60, 61, 63, 65–7, 69, 71, 74, 81, 82, 96, 99, 103, 117–18, 119, 121, 135, 138, 139, 154, 157, 161, 166, 168, 175, 179–80, 181, 182, 183, 184, 194, 198, 201–2, 208, 210, 211, 212, 215, 216, 220–1, 241, 251, 269, 271, 272, 275, 287, 288, 289, 290, 291–3, 294–5, 298, 301, 303, 304, 305, 307, 310, 321 exclusion 222, 227, 232, 234, 239, 243–5, 248–9, 280–4 argument 9, 10, 251–3, 257, 258, 259, 260, 263–6, 269, 270–1, 272–4, 275–7, 278 argument against free will 10, 269, 270–1, 272–4, 275–7, 278, 279, 281 causal 215–17, 220, 278–9 downward 8–9, 10, 220, 227, 266, 283–4 principle 8, 10, 215, 217, 222, 232, 234, 239, 242–5, 248, 270, 271, 273, 277, 278, 279, 281, 282, 283, 284 problem 1, 7–8, 11, 33, 61, 63, 233, 286–7, 291, 294, 295–6, 298, 301, 302 explanation 9, 64–7, 67–70, 95, 264, 299

INDEX

causal 6, 99, 102–4, 108–9, 117, 118, 218, 227–9, 238, 243, 276, 277–8, 301–3 process 6, 132–3, 143–4, 152, 302–3 program 232, 233–7, 241, 242, 245, 302–3 explanatory value 228–9 Finch, A. 320 Fischer, J. M. 308 Forrest, P. 104 Frankfurt, H. 270, 308, 309 Fraser, B. 207, 211 free will 1, 309 ability to do otherwise 307–9, 313–19, 321–2 alternative possibilities 223, 226 incompatibilism 10, 269–71, 272–4, 276–7, 278, 280–4, 307–8, 326–7 incompatibilism, Basic Argument for 11, 307–8, 313 local miracle compatibilism 309, 327–9 Frith, C. 281 functionalism 11, 291, 293, 300 role-vs. realizer 286, 294–5, 296, 297 Funkhouser, E. 59 Fyhri, A. 126 Galison, P. 149 Gärdenfors, P. 45 Gasking, D. 73 Gazzaniga, M. 280 Gibbard, A. 35, 37, 123 Giere, R. 155 Gilbert, S. 281 Glymour, B. 153 Glymour, C. 122, 135, 153, 175, 176, 267 goal-directed reasoning 5, 124–8, 129 graph 4, 260 causal 153, 157–8, 160, 161, 162, 163, 193, 194, 198, 199, 201, 203, 204, 254, 255, 257, 258, 263, 311–12, 315, 317, 321 directed acyclic (DAG) 119, 177–8 Grice 61–2 Hájek, A. 14, 26 Haji, I. 308 Hall, N. (E.J.) 4, 22, 35–6, 37, 38, 100, 103, 104, 105, 120, 121, 153, 154, 161, 166, 167, 168, 175, 182, 183, 184, 185–6, 197, 202, 204, 205, 277 Halpern, J. 120, 121, 129, 153, 154, 159, 167, 168, 175, 176, 179, 181, 182, 183, 184, 185–6, 188, 190, 192, 193, 195–6, 197, 199, 200, 202, 204, 206, 211–12, 223, 227 Hardie, J. 146 Harper, W. 37, 123 Harris, S. 269, 271, 280 Hart, H. L. A. 5, 184, 190 Hawthorne, J. 101, 105



Haynes, J. D. 281 Hempel, C. G. 313 Heuristics and biases 206–11 Hiddleston, E. 154, 161, 185 hierarchical architecture 101, 233, 236, 240, 244, 246–7 Hitchcock, C. 5, 64, 67, 99, 120, 121, 123, 129, 153, 154, 155, 157, 159, 161, 163, 167, 168, 175, 176, 179–92, 193, 196, 197, 199, 200, 202, 204, 206, 207, 209, 212, 223, 224, 227, 228, 276, 308, 309 Holmes, S. 194 Honderich, T. 215 Honoré, A. M. 5, 184, 190 Horgan, T. 67 Horwich, P. 76 Hyttinen, Antti 130 ideal condition 6–7, 154, 165–8 imaging 3, 34, 45–6, 47–8, 50–5 impossible worlds 2, 12, 17, 18, 26, 27, 28, 29, 30 impoverishment 198–200 Independent Fixability of Values of Distinct Variables (INF) 254, 255 indexicals 86, 87, 90 interactionist dualism 274 intervention intervention variable (IV) 254–5 interventionism 3, 6, 9, 10, 11, 25, 67, 86, 89–90, 99, 100, 101–2, 103, 104, 105, 109, 110, 122, 123, 132–3, 134–5, 143, 148, 158, 222, 223, 225, 226, 227–8, 229, 238, 251, 253–6, 257, 258, 263–5, 267, 298, 308–9, 312, 313, 321–3, 326–7 intrinsicality 103, 105, 109, 110, 166 invariance 132, 135, 138–40, 142–3, 144, 145–6, 148, 233–6 Ismael, J. 309 Jackson, F. 9, 232, 235, 240, 241, 242, 244–5, 248, 278, 286, 288, 291, 301, 302, 303, 304 Jeffrey, R. 46 Joyce, J. 123 Kahneman, D. 187, 189, 208–9, 210 Kaufmann, S. 3, 34, 39–41, 42–5, 46, 47, 48, 50–5 Kim, J. 8, 9, 65, 215, 216, 233, 234, 238, 239, 240, 241, 242–5, 246, 247, 248, 249, 251–2, 255, 256, 257, 258, 263–5, 270, 271, 273, 276, 277, 279, 294 Knobe, J. 121, 129, 188, 207, 210, 211, 212 Ladyman, J. 71 laws of nature 2, 18, 19, 20, 21, 22, 24, 25, 26, 27, 54, 107, 151, 290, 307, 308, 320, 323, 329



INDEX

Lehrer, K. 314, 316, 317, 318, 319 Lepore, E. 216 levels of causation 58, 69, 70–1, 232, 233–4, 238, 240, 244–8, 282 Lewis, D. 1, 2, 4, 5, 12, 15, 17, 19, 20, 22, 23, 24, 27, 30, 35, 36–7, 39, 44, 45, 46, 48–50, 65, 66, 100, 103, 117, 118, 119, 120, 135, 153, 154, 156, 158, 166, 179, 180, 182, 184, 219, 235, 242, 257, 267, 288, 289, 291, 292, 294, 295, 296, 298, 301, 304, 309, 312, 317, 318, 319, 324, 325, 327–9 Libet, B. 280–1 List, C. 11, 12, 242, 249, 269, 270, 271, 276 List, C. and Menzies, P. 7, 8–9, 10, 33, 215, 216, 218, 219–23, 227, 229, 232, 233–6, 238, 239, 240, 242, 243–5, 246, 247, 248, 265–6, 267, 271, 277, 278, 282, 286, 295, 296, 298, 302, 313 Livengood, J. 125, 184, 212 Loewer, B. 216 Ludwig, K. 292 Lyons, J. C. 287, 292, 301

Merricks, T. 271 Metaphysically Necessitated Effects, Problem of 287, 291–3, 303 Mill, J. S. 133, 183–4 Miller, D. 187–8, 189, 208, 210 mind-body problem 60, 63 miracles 2, 12, 14, 20–1, 23, 24, 25, 26, 27, 29, 119, 120, 135, 158, 257, 309, 312, 324–5, 326, 327, 328, 329 modal semantics 84, 85, 86, 88, 242, 307, 313, 319–20, 328–9 modularity 141–2, 143, 146–7, 148, 149 modus ponens 38, 45, 55 modus tollens 43 Molnar, G. 290 Montgomery, R. 194 Moore, G. E. 37, 313 Moore’s paradox 37 Morton, A. 39 multiple realization/realizability 10, 276, 286–7, 294, 296 Musallam, S. 218

Macaulay, D. 136 Macdonald, C. 237 Macdonald, G. 237 Machamer, P. 6, 132, 134, 136–7 Mackie, J. L. 192 Mackintosh, N. 269 manipulation 73, 80, 81–4, 85, 86–7, 88–91, 92, 94, 97, 122, 132, 135–6, 138, 158, 238, 242, 254, 258, 260, 261, 304, 305, 309, 310, 311, 323, 324 Manley, D. 112 Marcellesi, A. 132, 135, 142, 256 Marras, A. 223 Martin, C. B. 318–19 Maslen, C. 3, 58, 67, 120, 209, 224, 229 Maudlin, T. 104, 121, 184 McCloy, R. 210 McDermott, M. 159, 197 McGee, V. 39, 46 McGrath, S. 184 McKenna, M. 308 McLaughlin, B. 294 mechanism 6, 78, 100, 126, 132–5, 137, 138, 139–40, 142, 143–4, 146, 149–50, 151–2 Medin, D. H. 112 Mellor, D. H. 122, 166 mental causation 10, 71, 215, 238, 251, 256, 270–1, 277, 278, 295, 298, 302 problem of 11, 286, 287 Menzies, P. 1, 2, 3, 4, 5, 6, 7, 11, 12, 25, 26, 33, 67, 68–9, 74, 99, 104, 116, 118, 120, 121, 122, 123, 133–6, 137–40, 141, 142, 143–8, 150, 151, 152, 175, 179, 184–5, 188, 190–2, 209, 212, 232, 236, 244, 251; see also List & Menzies

Nahmias, E. 269, 271, 280, 281, 284, 309, 326 neuroscience 10, 269, 270, 271, 280, 284 Nolan, D. 1–2, 12, 17, 28, 29, 326 norm 38, 96, 122, 184, 188, 195, 206, 207 Normality 5, 16, 20, 23, 61, 69, 75, 76, 80, 89, 116, 121, 129, 135, 136, 160, 175, 183, 184, 185, 187, 188–91, 192–5, 196, 202, 206 Northcott, R. 209, 212 O’Connor, T. 271 O’Leary-Hawthorne, J. 271 overdetermination 6, 8, 118, 164, 179, 194, 235, 252, 272, 273, 274, 276–7, 278–9, 295 symmetric 154, 172, 177–8, 180, 185–6, 199–200, 201 Papineau, D. 216 Pargetter, R. 291 Passingham, R. E. 281 path-specific effect 5, 116, 120–2, 124, 126–8, 129 Paul, L. A. 22, 103, 153, 168, 182, 212 Pearl, J. 1, 4–5, 25, 73, 97, 99, 118, 120, 122, 127, 135, 142, 153, 157, 159, 163, 168, 175, 176, 179, 182, 186, 197, 223, 227, 278, 308, 309, 310, 323, 324 Perry, J. 87 Pettit, P. 9, 10, 11, 232, 235, 237, 240, 241, 242, 244, 248–9, 278, 288, 291, 301–4 Phillips, R. O. 126 physicalism 7–8, 233, 242, 270, 271, 274, 275 reductive 8, 270, 276, 297 non-reductive 8, 232, 251, 252, 253, 259, 261, 271, 273, 276, 286–7, 291, 294, 296, 297, 301, 303, 305

INDEX

Pollock, J. 39 pragmatic explanation 61–2, 63, 64, 65, 66, 67, 70, 85, 184, 227, 229 pre-emption 6, 118, 124, 179, 278 early 154, 163, 172, 198–9, 201, 203, 204, 206 late 154, 172, 199–200, 201, 206 prevention 103, 134, 154, 166, 172, 185–6, 200–6 Price, H. 1, 3–4, 67, 73, 74, 75, 76, 78–9, 81, 83, 85, 89, 94, 116, 122, 130, 138 Principal Principle 50 Prior, E. W. 291 probabilistic validity (probabilistically valid) 35 probability 2, 11, 33, 35, 36–9, 40, 42, 43–6, 49, 51, 53, 55, 123, 126, 135, 140, 149, 175, 208–11, 235, 236, 254, 255, 272, 275–6, 277, 278 problem of metaphysically necessitated effects (PMNE) 287, 291–3, 303 projectible predicates 299 properties causally loaded 289, 290, 296, 299 disjunctive 224, 289, 296–300, 303 dispositional 234, 235, 289–91, 299, 300, 303 functional 11, 235, 287, 289, 290, 291, 292, 296, 297, 300, 301, 302, 303, 304 nomic 298–300 proportional difference maker 265 Proportionality 8, 10, 64–7, 113, 219, 221, 228, 247, 265 constraint 3, 58, 59–61, 62, 63, 68, 69, 70, 238 qualia 101, 105, 106 Raatikainen, P. 271, 279, 286 Ramsey, F. P. 2, 33–5, 39, 73, 122 Ramsey, J. 153 Ramsey test 2, 33–5, 39 realization-sensitivity 8, 219–21 reductionism, strong 294, 297 Rees, G. 281 representativeness heuristics 208–9 responsibility 86, 133, 178, 248–9, 271, 279 legal 5, 117, 118, 129, 137, 188 moral 5, 117, 129, 137, 188, 308 Reuter, S. 284 Richardson, Thomas 126 Robinson, D. L. 125 Rommeswinkel, Hendrik 130 Roskies, A. 271, 276, 284, 309 Ross, D. 71 Rupert, R. 287, 291–2 Sagberg, F. 126 Sakai, K. 281 Salmon, W. 264 Sartorio, C. 184, 205



Schaffer, J. 7, 67, 118, 121, 181, 184, 191, 209, 210 Scheines, R. 122, 135, 153, 175, 176, 254, 260 secondary quality 73, 75–6, 79, 81, 82, 87, 92, 93, 94, 138 Segal, G. 287, 301 Sellars, W. 93, 94, 95, 96 set selection function 45–6, 53 Shapiro, L. A. 221, 223 Shepard, J. 284 Shoemaker, S. 58, 290 Shulz, K. 182 Skyrms, B. 39 Smith, M. 232 Smith, N. J. 46 Sobel, J. H. 45 Sober, E. 223 Spirtes, P. 73, 97, 122, 135, 175, 176, 268 Stalnaker, R. 1–2, 3, 5, 15, 16–18, 28, 33–4, 35, 36, 38–9, 42, 45–55 Stehr, M. 125 Sternberg, E. J. 269 Strangeness of Impossibility Condition (SIC) 28, 29 strategy 5, 29, 37, 38, 42, 45, 54, 81, 103, 104, 121, 123, 127, 128, 129, 134, 164–5, 168, 188, 189, 205, 207–11, 260 Strevens, M. 100 structural equation 11, 132–4, 137, 139, 140–2, 143–4, 145, 146–8, 150, 151, 152, 153, 154, 155–9, 160–2, 163, 170, 171, 172, 175, 176, 178, 182–3, 184, 188, 189, 190, 192, 199, 200, 310–12, 313, 315, 317, 321, 322, 323, 324, 326, 327 model (SEM) 4, 6, 116, 118–20 subjectivity 2, 3–4, 86, 87, 92, 93, 128, 209, 212 supervenience 8, 9, 30, 62, 91, 102, 109, 110, 215, 216, 220–1, 234, 239, 241–2, 243, 244, 245, 247, 253, 318 mental-physical 7–8, 10, 251–2, 254, 255, 256–7, 258–60, 261, 262–5, 270, 271, 272–4, 275, 276–7, 279, 282–3, 295, 301, 304 Swanson, E. 227 Szalavitz, M. 269 Teng, C. M. 153 Thomason, R. 17 transitivity 134, 141, 142, 143, 144–6 weakened 38, 45, 55 Tversky, A. 208–9, 210 van Fraassen, B. 46, 100 Van Inwagen, P. 11, 271, 307, 319–20, 323, 326 van Rooij, R. 37 Vander Laan, D. 29



INDEX

variable endogenous 11, 156, 157, 158, 176, 186, 188, 190, 201, 203, 225, 226, 254, 310, 311, 312, 322, 323 exogenous 119, 121, 122, 156, 157, 158, 176, 177, 186, 190, 192, 198, 203, 225, 254, 310, 311, 322, 324 intervention 254–5 Vihvelin, K. 307, 313, 317 von Wright, G. 73, 81–2 Walker, I. 126 Warfield, T. 320 Weslake, B. 8–9, 10, 11, 159, 161, 179, 205, 221, 223, 227, 228, 286 Widerker, D. 308 Williams, M. 76

Williamson, T. 58 Wilson, J. 271 Wimsatt, W. 137 Woodward, J. 3–4, 10, 11, 25, 60, 68, 69–70, 73–4, 75, 76–8, 79, 80, 81, 82, 83, 84, 85–6, 87, 88, 89–91, 92–5, 96–7, 99, 119, 120, 122, 123, 132, 134, 135–6, 140, 141, 142, 144, 148, 153, 155, 157, 158, 159, 163, 179, 197, 209, 218, 223–4, 225, 226–7, 228, 236, 253, 255, 257, 262, 265, 276, 278, 286, 296, 298, 308, 309, 310, 311, 313, 323 Yablo, S. 3, 8, 58, 59–61, 63, 65–7, 68, 218–19, 221, 238 Yli-Vakkuri, J. 223 Zhang, Z. 153