A Variety of Causes 9780199251469

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A Variety of Causes

A Variety of Causes Paul Noordhof

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Great Clarendon Street, Oxford, OX DP, 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 © Paul Noordhof  The moral rights of the author have been asserted First Edition published in  Impression:  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  Madison Avenue, New York, NY , United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number:  ISBN –––– Printed and bound in Great Britain by Clays Ltd, Elcograf S.p.A. 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.

Preface and Acknowledgements Causation involves dependency—of one thing being present because another is. The dependency is well expressed using counterfactuals; at its most basic a construction such as ‘If such and such had not occurred, such and such would not have occurred’ (although getting the precise expression right is by no means easy, as we shall see). The dependency is partly to be characterized in terms of raising the chance of something being present and, for causation to take place, the process characterized by the dependency has to be complete. Because causation involves these other things, there is a sense in which it is not fundamental. The metaphysical backdrop to our understanding of dependency, chance, and so on, supports this sense. If dependencies are to be understood in terms of regularities or powers, then these things are fundamental and causation is not. But there is another sense in which causation may be fundamental: it may be a necessary feature of any reality regardless of the particular way in which it is constituted. Readers familiar with the philosophy of mind may find the following a helpful way in. Some philosophers have said that the nature of minds should be understood independent of any particular way in which they are constituted. Computers may one day have minds even if they are made from very different stuff to human beings. It’s the kind of things minds do rather than what they are made of that counts. Likewise the proper understanding of causation is not given by an account of the way in which it is constituted. Outside of solipsism or idealism, not every kind of reality must have minds. So minds are not a candidate for this second sense of how something may be fundamental. Matters may be different with respect to causation. They won’t be different if theories of causation that attribute a rich nature to causation are correct: the richer the theory, the less likely that every reality must conform to this character. However, the more austere the account, the more likely it is that any reality involves causation connecting its elements together. This is the view we will work towards here. Recognizing that causation is something common to very different metaphysical pictures opens up the possibility of a certain kind of defensive move. Objections to a favoured analysis of the dependency in terms of counterfactuals and chance may, in fact, rest upon assuming a certain metaphysical picture. The fault is not the analysis but rather the assumption that only one metaphysical picture can be behind the truth of counterfactuals and chance. This observation can be helpful to both prospective analyses and also the articulation of the various metaphysical pictures, or so I will argue. As the book is large, I hope these preliminary orientating comments are helpful. In brief, and I hope in not too self-undermining a way, it is the kind of book on causation that might be written by somebody who has also been schooled in functionalist approaches to the mental, and applies some of the lessons to the debate

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on causation, although, in fact, I am inclined to reject functionalist approaches to the mental for reasons independent of the framework recommended here. My work on causation, of which this book is the culmination, probably began seriously in  when Murali Ramachandran came to give a paper at the research seminar in the University of Nottingham, where I was then working (although I had done some preliminary work in part of my PhD, supervised by Ted Honderich whose support at the start of my career I would like to recognize and give thanks here). In typical openhearted Murali fashion, he set out his preferred counterfactual analysis of causation and remarked how it was prey to certain counterexamples with which he wasn’t quite sure how to deal. In the slightly unsatisfactory (but not unusual) discussion that followed the participants in the seminar concluded (with a certain amount of intellectual triumph) that the counterexamples to his analysis were indeed counterexamples but no suggestions were forthcoming about how to deal with them. We continued the discussion that night and I think I managed to find another counterexample or so—some of which turned up, redirected, in my ‘Problems for the M-Set Analysis of Causation’ paper in —but we began the investigation into how to provide a better analysis. The early fruit of that discussion was our  Analysis paper ‘Counterfactuals and Pre-emptive Causation’ also co-written with Jonardon Ganeri. At that stage, we conceived of ourselves as offering an improvement on David Lewis’ analysis because ours did not depend upon appeal to the intrinsic similarity of causal processes, in which counterfactual dependence was present, to deal with the late pre-emption problem. The appeal drew on something that was hard to define and seemed to rule out brute singular causation. Yet, brute singular causation had been part of Lewis’ original motivation for adopting a counterfactual analysis of causation over a regularity view. At that point, I wasn’t really considering the metaphysical backdrop to a counterfactual analysis of causation but merely seeking to provide the best analysis possible independent of any such consideration. We heard that there was a causation seminar at Princeton being run by David Lewis going through the literature. A rather daunting prospect! And sure enough, one consequence of this was an early counterexample to our Analysis paper provided by two of its participants, Alex Byrne and Ned Hall. Of course, I should note that the major consequence of this work was the April  issue of Journal of Philosophy and the collection of papers ‘Causation and Counterfactuals’ edited by John Collins, Ned Hall, and Laurie Paul, in part to seek to banish the impression that this is an unduly egocentric story of the generation of the book. In any event, we needed to make a revision to our analysis and the result was our second, and last co-written,  Analysis paper ‘For a (Revised) PCA Analysis’. In spite of the fact that Ned Hall first came into my life as a critic of my work, I am grateful to him for encouraging me to think of putting together a book and his early support at a crucial time for the project. The preliminary exchange I just mentioned was a welcome sign of interest in our endeavours, however, our central focus was attempting to extend the counterfactual analysis to the case of indeterministic causation. It is a standard manoeuvre in the field to focus on the deterministic case and, rather airily, suggest that indeterministic causation may be dealt with by some natural extension of the idea. As we worked on this, we became more and more convinced that this was not the case. Both Jonardon

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and Murali helped me substantially up my game on causation and I want to thank them both. However, it would be an injustice if I did not record, in particular, the wholehearted way in which Murali would both attempt to demolish—and more often than not succeed in so doing—fledgling analyses of causation, as well as assisting in making the formulation of your preferred analysis better. I drew attention to the latter dimension of Murali’s assistance in the  Mind paper ‘Probabilistic Causation, Preemption and Counterfactuals’. The experience of working with Murali—often earning a couple of emails before breakfast, a phone call immediately after, one again at  am and an afternoon discussion on a daily basis while working at different institutions—was probably the most intense of my academic life and assisted significantly in my intellectual development. Unfortunately, the work on indeterministic causation also served to break up the working relationship as the disagreements mounted and, philosophically, we went our separate ways on the issue. ‘Probabilistic Causation, Preemption and Counterfactuals’ is a distant ancestor of part of Chapter  and a little bit of Chapter  in the current work. The analysis is changed because of later issues I saw with the characterization of Probabilistic Σ-dependence, specifically the earlier appeal to ‘at least’ and ‘at most’ rather than mean probability values and dropping a fourth clause for a constraint upon Σ-membership. Another philosopher who was extremely helpful for my further thought on causation, and development more generally, was Hugh Mellor. Hugh made me think much more seriously about the metaphysics that an analysis of causation might capture. Indeed, he was more interested in the metaphysics, than any reductive analysis of causation, in his own work. He had an unfailing knack for making me feel that there were important aspects of the literature—on facts, decision theory, and so on, often to do with Frank Ramsey—my ignorance of which was hampering a successful contribution in the area. I came in as an interloper from philosophy of mind (and the mental causation debate in particular)—with an outdated obsession with analysis at the expense of the development of a metaphysical vision—who he had to convince to get serious. My hope is that Hugh’s exemplary lesson enabled me to get a bit more serious. Naturally, I sought to repay his considerable influence and assistance in developing my own views by criticizing his at length in ‘Critical Notice: Causation, Probability, and Chance, D. H. Mellor, The Facts of Causation’, Mind, October  and a  paper ‘Epiphenomenalism and Causal Asymmetry’ in a Festschrift on his work, edited by Hallvard Lillehammer and Gonzalo RodriguezPereyra, entitled Real Metaphysics. A distant descendant of some parts of this work occurs in the introduction and the end part of Chapter . Mellor got me involved in two activities. The first was a workshop in the London School of Economics organized by Phil Dowe, with Stephen Barker, Helen Beebee, Joseph Berkovitz, Dorothy Edgington, Igal Kvart, David Papineau, and Murali Ramachandran as participants. The workshop was the basis for the later volume of papers Dowe and I edited entitled Cause and Chance. It was at this workshop that I became aware of Edgington’s challenging work on counterfactuals. Up until this point, I had been happy to appeal to reasonable judgements about which counterfactuals were true in the characterization of causal situations, while checking these judgements against the Stalnaker-Lewis semantics for counterfactuals. More specifically I had appealed to Lewis’ account of the similarity weighting of

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possible worlds for the evaluation of counterfactuals, to provide a basis for the distinction between cause and effect. One part of Edgington’s work was to challenge the idea that counterfactuals had truth conditions. My discussion of this element in the book has been relatively brief. The other part was her suggestion that the truth of counterfactuals required prior appeal to causal facts and, thus, could not figure as a vehicle for their analysis. This was obviously a major challenge, which was potentially devastating to my project, and I discussed it in a number of places; first, in the paper for the workshop already mentioned, ‘Prospects for a Counterfactual Theory of Causation’, published as part of the Cause and Chance collection, along with a number of other problems for a counterfactual theory; second in the  Analysis paper ‘Morgenbesser’s Coin, Counterfactuals and Independence’ which was a response to Jonathan Schaffer, who also endorsed Edgington’s scepticism about the suitability of counterfactuals to provide a reductive analysis of causation; and, third, in ‘Counterfactuals, Causation and Humean Supervenience’ (published in Robrecht Vanderbeeken and Bart D’Hooghe’s Worldviews, Science and Us: Studies of Analytic Metaphysics ()) which, amongst other things, also considered later work in support of Edgington’s position by Boris Kment. Chapter  of the book is the final development of this line of discussion making good on unsatisfactory elements in the previous work as far as I can. At the same workshop, I also met Stephen Barker who in his presentations, writings, and comments on my work enabled me to understand the potential difficulties that an appeal to counterfactuals to analyse causation faced both with regard to viewing them as a basis for causal non-symmetry and with the insistence that they are understood in terms of the possible worlds framework. I discuss these issues in the course of the book and Stephen, to my delight, became a colleague at Nottingham whose further contribution I record below. The second activity Mellor got me involved in was the initial meeting, in Lund, of a collection of philosophers interested in Metaphysics in Science organized by Johannes Persson in . Johannes’ resulting invitation came as a delightful surprise, pretty much out of the blue. This was my first experience of going with a group of philosophers to a beautiful place at the invitation of other fine philosophers to discuss topics of mutual interest including, centrally in my case, causation. I am very grateful to Johannes for the invitation. I have often felt a bit isolated from philosophers working on the issues I have worked on and the meeting contributed substantially to reducing that feeling. The meetings continued because Helen Beebee obtained British Academy support for meetings of the Metaphysics of Science group (in Edinburgh, Athens, Reading, Ghent, Birmingham, and Lund again). I am very grateful for the opportunity to get feedback on some of the material of this book from those meetings whose participants at various times included (in addition to Helen Beebee herself) Rani Lil Anjum, Stephen Barker, Karen Bennett, Alexander Bird, Sungho Choi, Peter Clark, Jan Crosthwaite, Phil Dowe, Alice Drewery, Adam Elga, Brian Ellis, Michael Esfield, Philip Goff, Toby Handfield, Jan Hauska, Katherine Hawley, John Heil, Andreas Hüttemann, Joel Katzav, Max Kistler, James Ladyman, Fraser Macbride, Anna Sofia Maurin, Peter Menzies, Stephen Mumford, Robert Nola, Daniel Nolan, David Oderberg, Samir Okasha, Charles Pelling, Johannes

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Persson, John Preston, Stathis Psillos, Don Ross, Markus Schrenk, Rebecca Schweder, Robin Stenwall, Joanna Odrowaz Sypniewska, Emma Tobin, Robrecht Vanderbeeken, Annika Wallin, Erik Weber, and Anne Whittle. The list gives a strong indication of the excellent standard of the comments I received as well as the amount of agreement I faced (not an awful lot). This is probably, in part, due to the fact that I was exploring at the time the consequences of the following two thoughts: first, that the counterfactual analysis of causation is meant to be a necessary truth; second, that the truth or falsity of a Humean metaphysics, that which denies necessary connections between distinct existences, is a contingent matter. I proved to be an inconstant philosophical friend to Humeans and anti-Humeans alike. It was a source of regret to me that my departure from Nottingham to York ended my participation in their later activities under the Arts and Humanities Research Council (AHRC) funding for a project of the same name. Apart from her central role in keeping the Metaphysics of Science meetings going, I would like to single out Helen Beebee for help in numerous ways. First, as she admitted to me much later, she had been one of the anonymous referees for my original Mind paper on probabilistic causation which, she remarked, had ruined a few days of her life. I haven’t managed to make it up to her but I am incredibly grateful to her for both thinking it worth publishing and also for probably the most detailed collection of comments I have received pointing out the inadequacies of a paper I submitted to a journal. She improved the paper considerably. However, our conscious interaction as colleagues only really began during the initial Lund trip and thereafter. Her discussion and work have been instructive of how a well worked-out defence of the Humean position on metaphysics should be conducted. Moreover, she generously shared unpublished work that got me thinking about various issues, for example, whether non-Humean approaches can appeal to counterfactuals in the same way. In addition to the Metaphysics in Science meetings, I was fortunate in being able to present material from the book at research seminars in Aix en Provence (), Glasgow twice (, ), St Andrews (), York (), and Durham (). I thank all the audiences there for their questions and comments. I remember Philip Percival, Daniel Nolan, Robbie Williams, David Bain, Derek Brown, Jennifer Corns, Fiona Macpherson, and Jonathan Lowe for particularly extensive discussion both at and after the meetings for which I am very grateful. Some of these seminars gave me the opportunity to present work that had been supported by two grants I wish to acknowledge here. The first was a Mind Editorial Board Research Fellowship in – that I had to postpone until Autumn . The second was an Arts and Humanities Research Board Research Leave from October  until January  (RLS-AN/APN). The first of these was funding support I received as a result of being an associate editor of Mind from  to , and reviews editor between  and . There was also some money available for research assistance and I’d like to thank Daniel Barnes from Nottingham days (in case Daniel reads this—see, as I promised, though I have kept it much later than I thought) Rosemary Smith, and Owen Hulatt from University of York, who I now have as a colleague. Although it is probably no accident that I have completed the

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book after I completed my lengthy stint as reviews editor for Mind, the support I received from the Mind Association in these ways was certainly invaluable. Three more recent workshops and conferences also proved to be very helpful. I am grateful to Sophie Gibb for inviting me to present at a conference that was part of her AHRC project on the Ontology of Mental Causation. The presentation continued the work that I had initially published as ‘Causation by Content’, Mind and Language, , no. , September , pp. –, and resulted in ‘Mental Causation: Ontology and Patterns of Variation’, in Sophie Gibb, E. J. Lowe, and R. D. Ingthorsson’s Mental Causation and Ontology (), pp. –. Some of the material there has ended up as part of Chapter . I am very grateful to the audience, and other presenters, for enabling me to think more seriously about property realization, the potential for efficacy at different ontological levels, and, indeed, the attractions and drawbacks of a flat one-level structure. I remember thinking about Sophie Gibb, John Heil and David Robb’s work particularly having an impact. The Emergence and Grounding Conference, Glasgow Emergence Project (funded from the Durham Emergence Project), – May , along with an earlier visit to York by Jessica Wilson, enabled me to refine my understanding and, thus, develop my criticism of Jessica Wilson’s important work defending an anti-Humean metaphysics within, broadly, a powers ontology framework. Jessica gave my presentation ‘Two . . . no Three Kinds of Emergence’ the variant title ‘Jessica Wilson Is Wrong about Everything’. Some of the material of that presentation turns up in Chapters , , and . You may notice a theme. Those whose work I find very stimulating, I find the need to criticize as effectively as I can. Who would have me as an admirer? I’m thankful to the good part in which Jessica took this and for her responses to my discussion. On this material, I am sure that reading Umut Baysan’s PhD, his subsequent work, and engagement with my work, also helped me considerably in developing my own thoughts. In the same vein, I was very pleased to be invited to a workshop on Causation by Claudine Tiercelin at the College de France on  December . Apart from Claudine, other participants were Helen Beebee, Sara Bernstein, Christopher Hitchcock, Stephen Mumford, Laurie Paul, Thomas Pradeu, Huw Price, Michael Strevens, and Brad Weslake. For those who are interested, there are videos of the proceedings, my own is here https://www.college-de-france.fr/site/en-claudinetiercelin/seminar----h.htm. As you can imagine, having such people in the audience was both an intimidating experience and also tremendously useful to try out ideas about how a general theory of the type I proposed may be defended. The two departments of which I have been a member while writing this work— University of Nottingham and University of York—have each supported it in a number of ways in addition to study leave. I have presented part of the book in Staff Work in Progress meetings. I am very grateful to my colleagues in York for their comments. Tom Stoneham also organized a very interesting series of Knowledge Exchange seminars on Causal Modelling that enabled me to come into further contact with various major contributors to the field including Stephen Butterfill, Huw Price, Jessica Wilson, and Jonathan Schaffer, meeting the last three for the first time. All the meetings were tremendously helpful. The meeting with Huw Price began my attempt to grapple with his challenging work on causation and the one

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with Jonathan was very important in getting me to think about contextualist approaches. My thanks to Tom and the contributors for these rewarding events. I must single out three particular groups of people for particular thanks. The first were the members of the Metaphysics Group I set up in Nottingham: Stephen Barker, Mark Jago, Penelope Mackie, Harold Noonan, Gonzalo Rodriguez-Pereyra, and the late Michael Clark. Their robust scrutiny was invaluable, it was an intense and engaging group and, in my time in Nottingham, Michael was a very supportive head of department for someone starting out their career. Many happy times with Michael are indelibly etched in my memory, as well as a substantially enhanced appreciation of jazz. The second were the members of the Mind and Reason group I set up in York who include Keith Allen, Ellie Byrne, Nick Courtney, Rob Davies, Dave Ingram, Barry Lee, Mary Leng, Louise Richardson, Tom Stoneham, Ema SullivanBissett, Rob Trueman, along with erstwhile members Chris Jay, Will McNeill, Louise Moody, Christian Piller, Dimitris Platchias, Debbie Roberts, and Rachael Wiseman. I am grateful for all the feedback and discussion they offered along the way. I am grateful to Mary Leng in particular for organizing a small reading group on the book when I was working on the final draft. Some quit from the pressures of having to live a life rather than read my work, I include Greg Currie, Barry Lee, Louise Richardson, and Ema Sullivan-Bissett in this category, although Ema gave loads of helpful philosophical comments on many of the early chapters and read the final proofs while firefighting educational issues arising during the time of Coronavirus. She also had two important influences on the style of writing. First, she removed a slightly wordy diffidence where she could. Where I might be inclined to say, ‘such and such appears to be a mistake’ she would substitute ‘is a mistake’ because, of course, there is a difference between something appearing to be a mistake and it being one. Which do I want to say? Second, where I might want to suggest that a particular objection was familiar, hoping a reader might be indulgent because it was relevant to discuss it in the context, she suggested it was more alienating to those who had not heard the objection before and may feel they were excluded from the club of causation enthusiasts. If, as a result, I come across as more arrogant and self-satisfied, it seems only fair to blame her. Supervising her PhD and, then, continuing to work with her as a colleague, has been a very stimulating and rewarding experience. Some colleagues stuck with the reading group right to the end: Mary Leng and Daniel Molto. They both deserve my immense thanks—they helped to clarify a number of issues and saved me from error—as well as general recognition of their stamina only exceeded by Ema’s feat. Closer to home, Colleen Noordhof also deserves similar recognition and thanks for helping me to improve the text. The two reader reports for Oxford University Press contained many useful criticisms, challenges, and requests for clarification and development. I am very grateful for all their efforts regarding what is a rather long book, including the kind things they said about it. Collectively they expressed views that it was hard consistently to take together. One reader liked the first part of the book (roughly those parts involved primarily in the analysis of causation) much more than the second, although they pointed out matters that needed development. For the other reader, it was the second part of the book on the variety of causation in different metaphysical frameworks that really was of interest. Both united in hoping the book might be a

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bit, or a lot, shorter. My hope was that the analysis kept me honest, while its characterization across different metaphysical frameworks kept things interesting. By keeping both parts of the book in, and attempting to satisfy more successfully their desires for those parts, I unfortunately failed to satisfy their third shared desire. The book became longer rather than shorter. I apologize to them, and any other reader, for this fact. Partly, but not only for this reason, I wish to offer my thanks to the team from OUP who worked hard on the production of the book to try to make the text as good as it could possibly be: Sophie Robinson, Dawn Preston and Chandrakala Chandrasekaran. I am sure that they were sometimes exasperated by me, as well as being impressed by my honesty, but never showed it. Many have spoken of the excellence of Peter Momtchiloff as an editor, as well as his patience and forbearance. I can only echo less eloquently that this is true. He has been quietly suggesting for many years that it was time to finish the causation book, sometimes with an email, sometimes with a quick conversation at one Joint Session or another, or perhaps just a reproachful look. He has always provided the same background quiet encouragement that I needed. Long may Oxford University Press retain his invaluable services to philosophy! I dedicate the book to three people who have waited for it for a long time, one pretty much for all of his life although he did not know of the treat in store for many years: Colleen, Jenny, and Jo. There is a decent chance the book may be published before his next birthday! It is a birthday present rather delayed and, I suspect, not at the top of Jo’s birthday list! But can I persuade you to take more interest and, where I have gone wrong, help out?

 The Analysis of Causation We come across causation in every minute of our waking lives. A child runs across the road without looking. The driver of a car slams on the breaks. The child running across the road caused the driver to slam on the breaks. I put a CD in the CD player and the music of Stan Getz plays soothingly in the background. Putting the CD in the player caused the music to play. I place a pan full of water on the lighted gas ring. Soon after, the water starts bubbling. The heat of the gas ring caused the water to bubble. Obviously, there are many many more examples where those came from. We rely upon causation to get what we want. If I want to hear Stan Getz or boil a pan of water, I put a CD in the CD player or turn up the gas. Nothing could be more important to us than the existence of causation. There is no start to our lives, or changing them, without causation. Though to be clear, I should not be taken to claim that the playing of Stan Getz CDs is essential to life. My answer might be different for David Bowie but I suspect that is an unnecessary diversion to go into here. Is there something general we can say about their nature? David Hume, the father of modern discussions of causation, wrote ‘we may define a cause to be an object, followed by another, and where all the objects similar to the first are followed by objects similar to the second. Or in other words where, if the first object had not been, the second had never existed’ (Hume (), p. ). Following David Lewis, we should note that there are two ideas in play here rather than one (Lewis (b), p. ). The ‘other words’ are certainly not other words for the same thing. The first idea is that causes are part of a regularity: a certain kind of pattern in the universe. The second idea is that effects depend upon causes. The dependence is expressed in terms of a certain kind of conditional, a subjunctive conditional, or, as we have now become used to calling them: counterfactuals. The book is an extended defence of a theory of causation couched in terms of the latter idea. This chapter will focus on preliminary key aspects of the framework. Standard forms of counterfactuals include ‘If it had/had not been that . . . , then it would/would not be that . . . ’ and ‘If it were/were not that . . . , then it would/would not be that . . . ’. The italicized component of these counterfactuals, including the sentences that fill in the . . . , are generally known as the antecedents, the underlined components, the consequents of the counterfactuals. Positive or negative antecedents can be combined with either or both of positive and negative consequents. I don’t propose to go into the controversy over the classification of these conditionals as counterfactuals in an already long book, however, I will briefly discuss the consequent issue over whether they have truth conditions at the end of .. My hope is that the success of the semantics I provide in that chapter provides an implicit defence of the framework adopted. A Variety of Causes. Paul Noordhof, Oxford University Press (2020). © Paul Noordhof. DOI: 10.1093/oso/9780199251469.001.0001

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   

‘Counterfactual’ is a contraction of ‘contrary-to-fact conditional’. Their antecedents describe circumstances presumed to be contrary to fact, their consequents what would (also) hold. Sometimes the presumption is not met. Then strictly speaking they are not counterfactuals but subjunctive conditionals with true antecedents. Contrary to the opinion of some philosophers, it doesn’t seem to be a condition of their truth (as opposed to their utility) that the presumption is met (as Chisholm (), pp. –, and Lewis (a), p. , point out; Mackie (), ch.  and Goodman (), p. , claim otherwise). The presumed contrary-to-factness of the antecedents is not a semantic one—unlike, on some views, the fact that there is a present king of France in ‘The King of France is bald’—that affects the truth value of the counterfactual. I retain the term ‘counterfactual’ to accord with philosophical usage and because there does seem to be a common, counterfactual, presumptive element whether or not it is met. We could call them presumed-counterfactuals but it is unlikely that this would ever catch on. In any event, philosophers have grouped them together and provided a theory to cover both cases. In passing, it is worth noting that not all counterfactuals need to be expressed in terms of subjunctive conditionals. Plausibly ‘No Hitler, no A-bomb’ is a case in point (Lewis (a), p. ). Nevertheless, such cases certainly seem expressible in terms of subjunctive conditionals and I will be setting out my counterfactual theory in such terms. Counterfactuals are well suited to capture the following idea. At root, causes are a means by which things happen. We often say, of a cause, if this hadn’t occurred, that would not have happened. The connection between causation and regularities is not immediately obvious, that between causation and the kind of dependence I have just tried to characterize using a counterfactual is immediately intuitive. Of course, because life is never as simple as we would like, and philosophy reflects this only too accurately, we will, in the discussion that follows, get a long long way from this original intuitive connection. Nevertheless, not far enough to lose the appeal of this original starting point. Counterfactual theories of causation—as all theories that begin at this starting point are called—are probably the most detailed theories of causation ever put forward. They come in many forms and are developed with a considerable amount of technical sophistication. Very often, it is causation understood in these terms that is the default, which philosophers consult, when developing work in other areas. Nevertheless, rather like consequentialist theories in normative ethics, they are often the most reviled too. They are judged to be obviously wrong, to miss out the substance of causation, to be subject to numerous counterexamples. It also appears to be the case that they have never had full monograph defence. The present work is an attempt to rectify the situation. Why have the merits of counterfactual theories of causation escaped so many able philosophers? For some, it seems wholly inadequate, missing the very stuff of causation. One criticism—encountered more in conversation than in print—has rather surprisingly focused on the fact that counterfactuals are pieces of language. Causation has nothing to do with language, this criticism runs, instead it is part of extra-linguistic reality. It is hard to view this as a serious criticism. The counterfactual analysis of causation is not so called because it claims that causation is counterfactuals (those

   



bits of language). Obviously! That would be truly bizarre. Rather the counterfactual analysis claims that the correct characterization of the dependency relation that we call ‘causation’ can be given in terms of counterfactuals. So if you want to say that causation involves powers, or natural necessities, or processes characterized in a certain way, or what have you, you have said nothing that the counterfactual theorist need reject. Indeed, they can accept that the counterfactuals are true because of these other things but insist that these other things are the basis of causation because they make the counterfactuals true. A more substantial reason is that counterfactual theories of causation have often been allied to a particular philosophical research programme, the controversially named doctrine of Humean Supervenience. As we will see in ., a number of different views are often mixed together in the statement of the doctrine but the essential idea that many have in mind is the denial that causation involves necessitation, that causes make their effects occur in this sense. Proponents of counterfactual theories of causation are traditionally taken, following the work of Lewis, to be defenders of Humean supervenience. But, to its opponents, causation essentially involves necessitation. That’s what it is all about! Although I think Humean supervenience may be true, it is no part of my brief to defend Humean supervenience. Indeed part of my argument will be that a counterfactual theory of causation looks in much better shape once it is recognized that its defence does not have to presume that Humean supervenience is true. There is something else going on too, though, related to this. Philosophers are often preoccupied by what they take to be fundamental. Some may criticize this orientation but the issue nevertheless structures their thought (e.g. Schaffer (c)). There is a dominant conception of what is fundamental familiar from another area. Those entities identified by the most basic of sciences—physics—are taken to be fundamental and the issue then becomes whether we need to recognize additional kinds of things, or whether everything else is simply the result of arrangements of wholly physical objects and properties (those identified by current physics, or some constrained development thereof) (Jackson (), pp. –; see . for a relevant sense of ‘result’). There are no doubt many reasons why this conception of the fundamental—call it vertical—is dominant but the most recent explanation is probably focused on the truth or otherwise of physicalism. On this conception, fundamental things are the constituents of the world from which everything else— specifically minds for example—can be constituted. The fact that everything else is constituted from these fundamental things is taken to show something about their nature. In the case of physicalism, that everything is, in a broadened sense, physical. With this dominant picture in place, the corresponding thought is that the proper understanding of causation is revealed in vertically fundamental metaphysics and, thus, it is the commitment to Humean supervenience that shows what causation really is. Perhaps that is another reason why the alliance with this programme of research has been thought so central. But here’s an alternative. There is a second kind of fundamentality. The fundamental as what is common to a variety of different vertical fundamental metaphysical pictures. The fundamental, according to this second conception—call it horizontal— is how the world must be structured. Going back to the question of physicalism, one



   

way of understanding functionalist theories of mind—those that claim that the natures of beliefs, desires, and other mental states are to be understood terms of distinctive causal or functional roles—is that, to understand these states, constitution doesn’t matter, structure does (e.g. Putnam (), Shoemaker ()). If minds aren’t required for worlds, then although minds, according to the functionalist, should be understood structurally, that doesn’t make these structures fundamental. However, suppose there are some structures that should be had by any world to be a world, even though worlds may be constituted in different ways. Then this seems as decent an idea of fundamentality as the first, vertical, sense. Causation has a good claim to be fundamental in this second sense. When Hume wrote of the cement of the universe, he had in mind resemblance, contiguity, and causation (Hume (), p. ). But J. L. Mackie’s coining of the phrase to title his study of causation has indelibly associated it with universe building (Mackie (, ), p. v). Different fundamental things in the first sense must all be cemented together by what is fundamental in the second sense: causation. Counterfactuals are, accordingly, a way in which we might describe a certain modal structure (where ‘modal’ is used as a group term for talk of possibilities and necessities). The work that follows is a defence of this way of delineating the fundamental causal structure of universes. Its principal focus is on how a counterfactual theory of causation may be developed that resolves the main difficulties which have been proposed to face theories in this area. The aim is to restore the counterfactual theory of causation to pole position and situate the contribution of other theories with regard to it. However, there is an implicit secondary goal, the defence of the idea that there is this second way in which something may be fundamental. My feeling is that if this is recognized more generally, a number of issues will look rather different, not least amongst these will be the issue of mental causation, and causation in the special sciences more generally, partly discussed in Chapter . The book breaks down into two parts as a result. The first part focuses on the attempt to give an analysis of the common, causal structure. It sets out the theoretical framework for the particular counterfactual analysis of causation I give, outlines the analysis, defends it, and notes its consequences for issues arising under the general question of ‘what are the relata of causation?’ The second part explains how the variable realization of this common causal structure in different vertically fundamental metaphysical pictures helps the counterfactual theory to provide a satisfactory treatment of causal non-symmetry, and avoid challenges to it derived from the assumption it is committed to the truth of Humean supervenience with regard to laws and chance. It begins by discussing the varieties of causation we may find within a metaphysical framework, for example, causation linked by processes and that which isn’t. This helps to introduce the more general idea. The decision to analyse causation in terms of counterfactuals constitutes a choice that demands justification. It is not an immediate consequence of the idea that causation can be realized in different ways. For example, we could have sought to do this by looking into the various ways that regularities can be captured or in terms of conditional probabilities. The task of the present chapter will be, largely, to summarize the considerations that have been offered in favour of the counterfactual starting point with some additional defensive work of my own. Thus, . explains

   



why we should focus on counterfactual dependency rather than regularities. . sets out in preliminary terms how we should understand counterfactuals, defends the counterfactual approach from the claim that it cannot capture the idea of dependency, and explains the role of appeal to probabilities in the analysis ahead. . sets out the options for counterfactual theories. . explains why it is appropriate to take causation to be a natural relation and discusses some methodological issues about analysis necessary for the theory development ahead, for example appeal to intuitions and the challenge of experimental philosophy. . situates counterfactual theories of causation within the range of other options for understanding causation and closes with a detailed summary of the discussion in the chapters to follow. Those waiting with some impatience for justification of the idea that Humean supervenience may be contingently true will find it in Chapter  and in the final chapter.

. From Regularities to Counterfactuals As I have already noted, the original passage from Hume contained the seeds of two theories of causation. The ‘in other words’ generated the counterfactual approach. The claim that all objects like the first (the cause) are followed by objects like the second (the effect) is a crude statement of a regularity theory. Prior to the rise of the counterfactual theory, it had considerable currency, especially amongst philosophers who looked to experience to justify a particular understanding of causation and law and claimed to find, in experience, nothing but regular succession. I will consider their case in .. Some have persisted in trying to understand causation in terms of regularities, those expressive of laws (e.g. Davidson (b), p. ). I shall briefly discuss law-based theories of causation in . of this book. For many, the counterfactual theory has won out. What are the basic reasons for adopting the counterfactual approach? The first is something upon which I have already touched. The key component of causation is that it is a non-symmetric dependency relation that it is natural to express in counterfactual terms. I accept that, on reflection, we may find that counterfactuals are ill-suited to this purpose and, in the course of the book, I discuss many of the ways in which this has been argued to be the case. My claim is just that the starting position is a very natural one and we need to be persuaded that we should not persist in understanding causation in this way. The secondary importance of regularity is revealed in the apparent possibility of brute one-off causation, that is, causation that is independent of law (see . for more detail). Suppose that I stretch out to touch my host’s favourite glass vase and it crumbles to dust. Was this a fluke? No, let us suppose! If I had not stretched out to touch the vase, the vase would not have crumbled to dust. Is it the case that, in all exactly similar circumstances where I stretch out to touch a vase in an exactly similar way, it crumbles to dust? It seems possible that the answer could be ‘No’ and yet I am the cause of my host’s favourite vase crumbling to dust. I agree it would be amazing if this were the case. But we should keep separate a natural part of an explanation of why there was a causal relationship from what must be present for a causal relationship to be present. Part of the explanation of why the vase crumbled to dust when I touched it may be that there is some law of nature relating the kind of touch I gave



   

with vase crumblings. To think that there must be laws covering the situation is an entirely different matter. Of course, it may be the case that the only way we can ultimately understand causation is in terms of laws. The point is just that we have grounds for giving the counterfactual component of our understanding of causation priority over appeal to law. Second, a successful formulation of the regularity theory has to deal with the fact that two kinds of regularity are not relevant to causation and, concurrently, not counterfactual supporting: accidental and non-accidental regularities that are not laws. Here is a familiar example of an accidental regularity. My life is over and I take stock on my death bed. One of the things that I have noted over my entire life is how many coins I have had in my pocket. Don’t ask me to explain why it interested me. It just did. As things turned out, I never had more than thirty. One generalization would be this: every pocket of PN had no more than thirty coins in it. But a generalization of this kind does not characterize a regularity that supports counterfactual or causal statements. For instance, we would not predict that if I had tried to put a thirty-first coin in my pocket, another one would have fallen out. We would not suppose that if a coin had fallen out, it was caused to do so by adding the thirty-first coin (although, of course, it might have been for other reasons such as the pocket being too full). By contrast, a generalization such as ‘All water heated to  C at . millibars atmospheric pressure boils’ characterizes a regularity that would lead us to predict that if I had heated some water to  C at . millibars atmospheric pressure, it would have boiled. We take the heating of the water to cause the boiling. Thomas Reid provides an illustration of the relevant kind of non-accidental regularity when he objected that a regularity analysis of causation was committed to holding that days caused nights. The regularity holds so long as there is no intervention to disturb the facts about the solar system on which the regularity depends (Reid (), , , p. ). But this is not a peculiarity of non-accidental but non-lawful regularities. No statement of regularity can be formed without a ‘no interventions’ condition such as this. For example, striking a match to light dry grass does not cause a forest fire if a bucket of water is thrown over the flaming grass. The fact that some regularities are counterfactual supporting and imply causal relations, and others do not, has been widely recognized (e.g. Goodman (), pp. –; Mackie (), p. ). The question is: what are we to make of this? One option would be to identify some third feature that these regularities, or the generalizations that characterize them, share and explain how this third feature relates to causation and counterfactual support. Once such feature is that the regularities are laws of nature, the generalizations characterizing them, law statements. Humeans typically understand such generalizations as part of a system of generalizations scientists have formulated to predict how things behave. The generalization about coins does not support counterfactuals, or imply causation, because it is not a law of nature. Similarly, although the regular succession of night upon day depends upon other regularities that are laws of nature concerning the orbiting and rotation of planets, and the position of the sun, it is not a law of nature itself (Mill (), pp. –, Strevens (), pp. –; Psillos (), pp. –).

   



Appeal to laws of nature may get the regularity theory out of trouble here but creates trouble for cases of causation where there are no laws of nature that seem to cover the types of events mentioned, for example, a stone throwing causing a window to break. Regularity theorists need to find a way of relating such cases to those covered by laws of nature in a way that distinguishes these causal regularities from non-accidental regularities such as that between day and night. This is not impossible but requires some independent motivation given that regularities hold for both kinds of cases, neither of which are laws of nature. If the motivation turned out to be that one kind of regularity was counterfactual supporting and the other was not, then that would be an early victory for the counterfactual theory. Perhaps for this reason, recent regularity theorists have tried to develop an analysis of causal regularity independent of whether or not it is a law. They appeal to different ways in which causes may be conditions for effects than effects conditions for causes. For example, a recent proposal suggests that, in the case of regularities between common effects of a cause, causes and effects display the following structure. D

A

E

C

B

Figure .

Here C is the common complete cause of D and E. A and B are alternative possible complete causes of D and E, respectively, that did not occur. Thus while C is a sufficient condition for D and E, D is not a sufficient condition for C (since A might have been the cause instead), similarly for E, and thus neither D nor E are sufficient conditions for each other (Baumgartner (), pp. –, (), pp. –). A difficulty with the present proposal is that it relies upon the claim that there will always be an alternative possible cause in the circumstances that does not result in a more distinctive version of the effect, say D. For example, my house might be a charred ruin because of a gas explosion or, the alternative possibility, because of a lightning strike. However, we might expect, the way in which it is a charred ruin will differ depending which brought this unhappy circumstance about. The current proposal relies upon it always being the case that there will be two alternative possible causes for which this is not so. Appeals to other conditions are possible. As we shall see, they are an inadequate foundation for all cases of causal non-symmetry and, hence, fail to cover all cases of causal regularities although they have their role in understanding counterfactual non-symmetry to which I appeal later (.). For now, I just note that these problems with placing regularities centre stage in the understanding of causation constitute the second reason for pursuing a counterfactual theory of causation. In fact, focusing on counterfactuals seems the most promising way of getting the relationship between causation and law right. It becomes a matter of identifying the



   

role of laws in the provision of a semantics for counterfactuals. As we shall see in Chapters , , and , the connection is not straightforward. Its articulation provides us with a means of fleshing out the vague idea that causation must be/is often backed by law. Of course, if it were a mistake to seek to understand causation in terms of counterfactuals, then it would be a mistake to try to understand the relationship between causation and law in terms of the semantics for counterfactuals. My claim is simply that the proper account of the relationship will fall out of a successful analysis of causation in terms of counterfactuals. A final reason for finding the focus on counterfactuals attractive relates to my wider project. On the view of laws I mentioned above, those regularities that are laws of nature are described by a certain system of generalizations that enable us to systematize and predict events in the world. Others of a more robust non-Humean metaphysical mentality may talk of generalizations made true by necessities. I think we should keep open the possibility that what unites these different accounts of a certain class of regularities is that they support counterfactuals, one way or another. Having given this, to some extent familiar, defence of my starting point, the rest of the chapter will be concerned with fundamental issues that arise with my approach before we get down to the details of theory construction in subsequent chapters. Many of the chapters that follow will focus on the question of what form a counterfactual theory should take in order to provide a necessary condition for causation as well. By contrast, this chapter will focus on what counterfactualists (that is, proponents of a counterfactual theory of causation) generally agree is a sufficient condition and whether it is plausible to suppose it is sufficient.

. Counterfactuals and Dependency I have claimed that counterfactuals express a certain kind of dependency relation between entities that is, intuitively, causal. The benchmark theory for understanding counterfactuals, the Lewis-Stalnaker possible worlds semantics, presents a potential challenge to this claim. In this section, I outline the semantics, and then discuss the challenge and responses to it. For these purposes, we don’t need to consider a highly developed version of the counterfactual theory of causation. We can, instead, focus on what most would consider a sufficient condition for causation to be present, if a counterfactual theory of causation is defensible at all. The challenge questions whether this is correct.

.. The sufficient condition and the possible worlds semantics of counterfactuals Causes and effects are often events. For instance, the earthquake caused the tidal wave. Later, in ., Chapters , , , and . , I shall consider the range of things that may stand in causal relations and whether there is some particular type of thing which should be counted as the most fundamental causal relata: events, facts, property instances, objects or the like. The discussion to follow will provide justification for my adoption of events now, to fix ideas, since it is a central and essential case. I represent an event by ei where ‘i’ is replaced by a number. Hence, if I want to

  



speak of three distinct events, I might talk of e₁, e₂, and e₃. A candidate sufficient condition can then be put as follows. (SC) For distinct events e₁ and e₂, e₁ causes e₂ if () If e₁ were to occur, then e₂ would occur. () If e₁ were not to occur, then e₂ would not occur. The interest of this condition is that it seems to capture the basic idea of dependence with which a proponent of the counterfactual analysis seeks to work. How are we to understand the counterfactuals? It is common ground that, to assess their truth or assertability, we consider circumstances in which the antecedent is true, that is either e₁ occurs or fails to occur respectively, and whether e₂ occurs or fails to occur as well. It is also common ground that the circumstances to be considered are very like our own. Nevertheless, there may be other differences arising from whether or not e₁ occurs in those circumstances and the treatment of this issue is where the controversy lies. The benchmark way of formulating this understanding of counterfactuals is in terms of the Stalnaker-Lewis possible worlds semantics for counterfactuals (Lewis (a); Stalnaker (), pp. –). Stalnaker and Lewis understood counterfactuals in terms of possible worlds. The assumption that things will remain more or less the same except, perhaps, the change envisaged in the antecedent and what follows from that, becomes a claim about how things are in possible worlds very like our own. Lewis suggests that the following analysis is appropriate. A counterfactual ‘If it were that A, then it would be that C’ is (non-vacuously) true if and only if some (accessible) world where both A and C are true is more similar to our actual world, overall, than is any world where A is true but C is false. (Lewis (), p. )

This should be understood as follows. Suppose we consider a multiverse of possible worlds (for now just think of this as a way of fixing ideas), our universe being one possible world. When we claim that If the dog were to bark, the burglar would run off we are making a claim about how things would be in a world accessible from our world in which the dog did bark. More generally, counterfactuals make claims about a particular subset of the worlds in which the antecedent is true, that is, a particular subset of the A-worlds. The claim is that those A-worlds in which C is true are more similar to our world than any A-world in which C is not true. It is hard to provide a neutral account of what possible worlds are. Consider a complete way in which a universe might be or, indeed, the way our universe is. Lewis takes possible worlds to be instantiations of these complete ways. In other words, possible worlds are concreta just like the actual world (our universe). Others have held that possible worlds are properties. They are ways in which a world might be. Others still have tried to characterize possible worlds in terms of consistent sets of propositions. I do not intend to decide between these accounts here although later, in ., I shall evaluate the impact these accounts have for the successful defence of the doctrine of Humean supervenience. For our present purposes, appeal to possible worlds has two useful features. First, they provide a way of thinking about the consequences of departures from actuality

     and, thus, the significance of features of our universe. Second, they avoid the need to identify the precise collection of laws, or other causal regularities, that are required to evaluate a causal claim and avoid the question of how to handle the ‘no interventions’ requirement of the statement of these laws or regularities. The presence or absence of interventions is all factored in. These are clear advantages over regularity theories of causation. In the analysis of counterfactuals above, the idea of possible worlds being ‘accessible’ to us is used to capture the thought that, for different kinds of necessity, different classes of possible worlds are relevant. It’s not that Lewis had in mind some crossmodal travelling technology. Suppose that we identify ‘it is necessary that p’ with ‘p is true in all accessible worlds’. In the case of nomological necessity, the accessible worlds will be all those which share the same laws as our world. In the case of absolute, or metaphysical, necessity, the accessible worlds are all the possible worlds (Lewis (a), pp. –). The semantics of counterfactuals appeals to the latter notion of accessibility because, if determinism is true, it is plausible that the worlds most similar to the actual world in which the antecedent is true are those with slightly different laws to our world. Given that the antecedent of a counterfactual is not true, a world in which it is would either have to differ in its initial conditions from our world or differ in its laws, perhaps minutely. But if it differs in its laws, it is not a nomologically possible world. The apparent falsity of () If I were to scratch my nose, the past would be very different suggests that we are prepared to consider some worlds in which the laws differ slightly from those in our world to assess a counterfactual rather than allow the changes required to make the antecedent true (given the same laws) ramify back to the initial conditions of the universe. This has been contested and I shall discuss the matter further in .. I satisfy myself at the moment with simply explaining the initial motivation for unrestricted accessibility. The analysis given appeals to the phrase ‘some (accessible) world where both A and C are true is more similar to our actual world, overall, than is any world where A is true but C is false’ rather than ‘C is true in the world in which A is true which is most similar to our actual world’. The latter would require that the following two assumptions are met: first, the Limit Assumption, that there is going to be a closest world as opposed to closer and closer worlds without end; second, the Uniqueness Assumption, that there is going to be only one such closest world (Lewis (a), p. ). The difference between Stalnaker’s development of possible worlds semantics and Lewis’ is that Stalnaker makes these two assumptions (Stalnaker (), pp. –). A consequence of so doing is that Stalnaker can preserve the putative Law of Conditional Excluded Middle. Either if it were that A, then it would be that C or if it were that A, then it would be that not-C. It is not obvious that this is a benefit. Failure to validate conditional excluded middle seems perfectly plausible. One familiar illustration is Either if Bizet and Verdi were compatriots, then Bizet would be Italian or if Bizet and Verdi were compatriots, then Bizet would not be Italian.

  



There are close worlds in which Bizet is Italian and just as close worlds in which Verdi is French. So it is neither the case that Bizet would be Italian nor the case that he would not be. Neither disjunct is true (Lewis (a), p. ). By contrast, Stalnaker accommodates such cases by appealing to the supervaluationist account of vagueness. Although the Limit Assumption is true, it is semantically indeterminate exactly which circumstances are envisaged in which Bizet and Verdi become compatriots. Under some precisifications, Bizet would be Italian, under others, he would not. Since ‘If Bizet and Verdi were compatriots, then Bizet would be Italian’ is not true under all precisifications, the conditional is neither true nor false. Nevertheless, the Law of Conditional Excluded Middle would be true because, whatever the precisification, one disjunct or the other would be true (Stalnaker (), pp. , –). Stalnaker’s approach is alleged to have difficulty in providing an account of conditionals of the form: if it were that . . . then it might be that . . . which gives them different truth conditions to the corresponding would-conditional, on the assumption that ‘If it were that A, then it might be that B’ is equivalent to ‘It is not the case that, if it were that A, it would be that not B’ (Lewis (a), p. ). In ., we shall see that the equivalence is questionable. However, if the equivalence is accepted, then there does seem to be an issue for Stalnaker’s approach. There are two ways in which ‘It is not the case that, if it were that A, it would be that not B’ is true. The first is if the closest A-world (world in which A is true) is a B-world. In that case, ‘If it were that A, it would be that B’ is true too giving rise to the alleged problem: no distinction is made between ‘would’ and ‘might’ conditionals. The second way is if the closest A world in which B is no closer than the closest A world in which not-B because, in A-worlds indeterminism holds, so B has a less than  chance of occurring. When it does occur, the corresponding would-conditional would be true. However, Stalnaker is committed to reinterpreting this worldly-indeterminacy—and apparent failure of the Uniqueness Assumption—as a semantic indeterminacy to preserve his treatment of the Law of Conditional Excluded Middle. This seems to me a cost. Therefore, I shall work with Lewis’ approach in what follows. Nevertheless, I suspect that most of the ideas in this book will be available to the determined proponent of Stalnaker’s approach, perhaps with relevant adjustments. My tentative endorsement of Lewis’ approach to counterfactuals should be situated within a larger framework of options for the treatment of counterfactuals. In outline, the terrain is shown in Figure .. Let me explain in outline why I end up in the bottom left-hand corner. I take counterfactuals to be committed to some kind of dependency relation for their truth. The assumption that counterfactuals can be true in this sense puts me on the realist wing of the chart in Figure .. My response to anti-realism about counterfactuals only becomes clear at the end of Chapter , so I discuss that matter then (.). As we have seen, Lewis appeals to a possible world being more similar to the actual world than any other world which meets a certain condition: a three-place relation of comparative similarity. He uses this to order possible worlds in terms of ‘closeness’ to the actual world. The proper characterization of similarity—which will be the subject matter of Chapter —constitutes, as Lewis notes, a potential solution to the cotenability problem, which first cropped up for metalinguistic approaches to

    

Counterfactuals

Anti-realism

Realism

Possible Worlds

Lewis

Metalinguistic/ Sub regions of Worlds (Goodman, Barker)

Stalnaker

Primitive Modal Facts

Necessitarian (Bird, Armstrong, Ellis)

Past Tense Indicatives (Edgington)

Causal Models (Pearl)

Figure .

counterfactuals. For many counterfactuals, the antecedent does not entail the consequent but the antecedent together with some other statements, characterizing the way the world is, does. The alternative, metalinguistic, approach to counterfactuals explicitly appealed to this, holding that the truth of counterfactuals depended upon the consequent being entailed by the antecedent together with a set of statements individually and collectively meeting a certain (cotenability) condition. The problem was providing a characterization of the condition in question. Consider the much discussed ()

If I had struck the match, it would have lit.

Clearly, we should not include the actually true statement ‘The match is unlit’. However, we should include true statements such as ‘The match is dry’, ‘Matches made of such and such combustible material burst into flame when struck’, and so on. The latter are consistent with the truth of the antecedent but so is the former. So appeal to consistency alone won’t do. The concern was that the correct specification of the condition would turn out to be circular by involving an appeal to a counterfactual itself, viz. all the true statements about the world which would not be false if the antecedent were true (Goodman (), p. ). Lewis’ specification of a comparative similarity ordering of possible worlds promises to settle when true statements about the actual world would be false in counterfactual circumstances. Partly for this reason, I will not consider the metalinguistic alternative much further. Proponents of it could recast my analysis in their terms utilizing the material in Chapter  as my answer to their cotenability problem. Nevertheless, in ., I will discuss the objection that a similarity weighting over possible worlds is the wrong answer to the cotenability question because something more local than a world is needed for

  



our counterfactual reasoning. If that were right, then it might be more conducive to a metalinguistic approach. I explain why it would be a mistake to go down this line. Equally, I don’t seek to resolve the cotenability problem by assuming that the world is indeterministic and, hence, we can keep fixed all the actual conditions except taking the counterfactual antecedent to be true. Our counterfactual reasoning does not seem to make this assumption and we need a semantics for counterfactuals that explains how this is possible. Necessitarian accounts of counterfactuals presume that the truth of counterfactuals should be understood in terms of the recognition of the modal properties of objects and properties in the world. No appeal to possible worlds, for example, is needed. Such ontologies will be discussed in .. Their explanatory capacity in this area will be found wanting. Inevitably, they must take possible world or metalinguistic form. Thus discussion of them at this point is unnecessary. Causal modelling approaches limit their ambitions to counterfactuals to do with causation. Thus, they eschew reductive ambitions and the aim of providing a complete theory of counterfactuals. Such approaches are not appropriate for the project undertaken here. Let us now return to the putative sufficient condition for causation with this preliminary understanding of the semantics of counterfactuals in place. (SC) (SC)

If e₁ were to occur, then e₂ would occur. If e₁ were not to occur, then e₂ would not occur.

Suppose that, as a matter of fact, e₁ and e₂ occur. Then Lewis’ analysis proclaims that (SC) is true because there is no world as similar to the actual world than itself and, in that world, e₁ and e₂ occur (dubbed the Centring Assumption). The analysis proclaims that (SC) is true if, some world in which e₁ and e₂ do not occur is closer than any world in which e₁ does not occur and e₂ does. The dependency expressed by the counterfactuals has been cashed out in terms of co-occurrence at possible worlds meeting the relevant similarity conditions. In .., I will consider the objection that this makes the counterfactuals in question ill-suited to capture the notion of dependence at the heart of our notion of causation.

.. Causal necessity and sufficiency According to the first modern proponent of a counterfactual theory of causation, Ardon Lyon, counterfactual dependence provides us with an unproblematic notion of causal necessity and sufficiency (Lyon (), p. ). Recent discussion has been less favourable. David Ruben and Hugh Mellor have argued that the Stalnaker-Lewis semantics for counterfactuals throw this into question (Ruben (); Mellor (), pp. –). The worry is that for any two actual events, e₁ and e₂, it immediately follows that ‘If e₁ were to occur, then e₂ would occur’ is true because the world most like the actual world is the actual world. Yet they may, intuitively, be entirely unrelated to each other. On the assumption that I drummed my fingers on my desk at . p.m. and Theresa May met the European delegation at  p.m., the following counterfactual is true, ‘If the drumming of my fingers on my desk were to occur, then Theresa May’s meeting the European delegation would occur’. Ruben and Mellor claim that this establishes that the sufficient condition cannot capture the sufficiency of causation. There is no way in which we would say that the drumming

     of my fingers made, or was sufficient for, Theresa May to meet the European delegation. People in government just aren’t responsive to a sign of my impatience. Mellor notes that the same reasoning throws into question the claim that a counterfactual analysis captures the fact that causes are necessary in the circumstances (bracketing overdetermination and pre-emption—issues I’ll discuss later in Chapter ). Suppose it is neither the case that I drummed my fingers on the table nor the case that Theresa May met the European delegation. Then the following counterfactual is true: ‘If the drumming of my fingers on the table were not to occur, then Theresa May’s meeting the European delegation would not occur’. It is unlikely that my inactivity had that kind of impact upon world affairs either. The putative failure to capture independently causal necessity and sufficiency set out above would imply that counterfactuals are ill-suited to capture the appropriate notion of dependency. So, the charge runs, although it is very natural to appeal to counterfactuals to express causal dependency, the correct semantics for counterfactuals shows that this is a mistake. Attempted resolutions of the problem either don’t work or are not cost-free. One suggestion has been that we ought to replace the simple counterfactuals to which the sufficient condition appeals with embedded counterfactuals. For instance, we should characterize the sufficiency of causation by the following. If neither e₁ nor e₂ had occurred, then if e₁ had occurred, e₂ would have occurred (Vihvelin (), pp. –). Unfortunately, according to the Stalnaker-Lewis approach, in order to assess the embedded counterfactual, we go to the closest not-e₁-nor-e₂ world and then consider how things are placed in the closest world to that, in which e₁ occurs. There is no reason to suppose that this won’t bring us right back to the actual world again. In which case the truth of the embedded counterfactual will be settled simply by the fact that, in the actual world, e₁ and e₂ occur. As already noted, the problem arises for the Stalnaker-Lewis semantics because of the centring assumption: no world is as similar to w as w itself (Lewis (a), p. ). We might weaken this to the claim that no world is more similar to w than w itself. This allows for the possibility that there are other worlds that may be counted just as similar to w as w itself in the relevant respects of similarity. If we did weaken the centring assumption, then the counterfactual would only be true if, not only were the antecedent and consequent true in our world, but also in all equally similar worlds. Weakening the centring assumption has clear costs. It is highly intuitive that no world is as similar to w as w itself. There is no guarantee that some of these similarities will prove to be irrelevant. Moreover, we are inclined to conclude that () If I were not to succeed in finishing this chapter by the end of the day, I would be bitterly disappointed is true if I fail to finish the chapter today and am bitterly disappointed. Whereas relaxing the centring assumption would mean that, in the circumstances in which the antecedent is true, we would still hesitate to endorse the counterfactual unless it is true in all the worlds sufficiently like the actual world. If the reply I make below were

  



not available, the option of weakening the centring assumption might be worthy of further examination but given its availability, the cost seems too high. A third response, canvassed by Mellor, is to replace the counterfactuals above with counterfactuals mentioning chances. (M) (M)

If e₁ were to occur, then ch(e₂) would be . If e₁ were not to occur, then ch(e₂) would be  (Mellor (), pp. –).

The thought seems to be that causes are sufficient for their effects if they make the chance of an event  and necessary for their effects if their absence makes the chance of an event . Two issues need to be distinguished. First, there is the question of whether we need to appeal to these chances to capture causal necessity and sufficiency given that there can be both deterministic and indeterministic causation. Second, does such an appeal answer the original concern that the counterfactuals fail to capture the appropriate connection between events? Before we get back to this second issue, we need to be clear about the first.

.. Indeterministic causation: preliminary characterization Here is an actual case in which it seems that causation takes place under indeterminism. Though, if the case turned out to be merely possible, this would still be enough to establish that an analysis of causation should allow for probabilistic instances. Radium and uranium have radioactive isotopes that turn into other elements—decay—when subatomic particles such as α or β particles ‘tunnel’ out of the nuclei of these elements. The decay is not governed by deterministic laws so that, at time t, it is settled that an atom of radium starts to decay given the circumstances which hold. Rather the laws that govern decay give the atom a less than  chance of decaying during a time interval. However, if the nucleus of an atom is bombarded by a subatomic particle, then it is almost certain to decay. For such a case, it seems right to say that the bombardment of the nucleus of the atom is a cause of the decay. Yet, since the chance of decay is not , the bombardment is not sufficient for the decay. And since the decay might have happened anyway without the bombardment, the bombardment is not necessary—that is, it is not even necessary in the circumstances in which we are envisaging. Some accounts that allow for indeterministic causation distinguish between sufficiency and necessity. Causes need not be sufficient for their effects but, bracketing pre-emption and the like, they must be necessary in the circumstances (Mackie (), pp. –; Ramachandran (), pp. –, ; Barker (), pp. –). The asymmetry appears unmotivated. First, there is no reason to suppose that, in an indeterministic world, although positive causes may fail to be sufficient for their effects, negative causes (or their positive surrogates, see ..) will be sufficient for the non-occurrence of these effects. Yet, this is what endorsement of the asymmetry comes down to. If e₁ must be necessary in the circumstances for e₂, then not-e₁ must be sufficient for not-e₂. Later, I shall discuss how we should understand negative causation but it doesn’t touch the point here (Chapter ). Second, adoption of the asymmetry seems to rest upon a tacit retention of a deterministic view of causation.

     A deterministic view of causation can be retained in an account of causation in indeterministic cases in indeterministic cases in one of two ways. (PofC) e₁ is a probabilistic cause of e₂ if and only if e₁ has a certain probability of being a deterministic cause of e₂ (PofC for probability of causation) (Tooley (a), pp. –, is tacitly committed to, at least, the coherence of such an account). (CofP) e₁ is a probabilistic cause of e₂ if and only if e₁ deterministically causes ch(e₂) (Hausman (), pp. –; Papineau (), p. ) (CofP for causation of probabilities). The right-hand side of each biconditional is taken to describe the causal reality. That is, probabilistic causal statements are true because of what is described on the righthand side (see .. for weight of ‘because’ here). At best, the recommendation of the causation of probabilities thesis seems to boil down to that of a preferred terminology. The proper characterization of the relationship between e₁ and e₂ will be untouched by the question of whether the thesis is true. At worst, it is not obvious that such causes will be distinct from their effects. What is the putative caused chance of e₂? If the chance of e₂ is a property of e₁ in virtue of having a certain property, F, say, and a law involving F, then there is no distinct chance of e₂ to be caused by e₁. It is just e having F in the circumstances in question. Tacit commitment to the probability of causation thesis seems the most natural way to understand why some philosophers are prepared to adopt the asymmetry regarding necessity and sufficiency in the circumstances. Someone who argues that, if a cause were not to occur, the effect would not occur, appears to want a sign that a cause has got through to bring about an effect. Here’s an alternative that accepts that causation may be indeterministic. If causes need not be sufficient for their effects, then they are not enough to explain why an effect occurred rather than it didn’t. At that point, things just happen the way they do. There’s no success or failure of the cause to get through to the effect. If there were, then we would have a case of deterministic causation after all. There would be some extra factor to which we might appeal to explain why the effect occurred in the circumstances it did. A cause would have a certain probability of deterministically causing the effect depending upon the probability of the extra factor being present. If there is no extra factor to explain why the effect occurs when it does, then, likewise, there is no extra factor whose absence will ensure that the effect does not occur. Hence, adoption of the asymmetry is most naturally understood in terms of a tacit endorsement of the probability of causation thesis. Some worlds may accord with the probability of causation thesis. The burden of my original example of decay is that there may be causation in worlds for which it is false. Hence, asymmetric accounts should be rejected. In indeterministic worlds, (SC) If e₁ were to occur, then e₂ would occur, (SC) If e₁ were not to occur, then e₂ would not occur, will be of little help in the characterization of causation. It is plausible that there will be some cases of causation in which, because e₁ is not sufficient for e₂, (SC) will not

  



hold, and because e₁ is not necessary for e₂, (SC) will not hold. The most natural way to think of indeterministic causation is in terms of chance-raising. In deterministic worlds, causes raise the chance of their effects to . In indeterministic worlds, causes raise the chance of their effects, it is just not to  (or, more weakly, not always to ). The possibility of indeterministic causation together with Lewis’ semantics for counterfactuals also explains why ‘If e₁ were to occur, then e₂ would occur’ cannot characterize the sufficiency of causes for their effects. If both e₁ and e₂ occur, then the counterfactual is true. If the world is indeterministic, then (say) e₁ may only have given e₂ a . chance of occurring. In those circumstances, the cause, e₁, would not be sufficient for the effect. The counterfactual cannot characterize sufficiency because of the possibility of fulfilled less than  chances.

.. Counterfactual versus conditional chance-raising Two options are available for the characterization of chance-raising: conditional probabilities and counterfactual probabilities. Conditional probabilities are one of the other alternatives identified at the outset by which causation might be characterized in a way that allowed for its variable realization. Appeal to counterfactual probabilities, on the other hand, would make the resulting counterfactual theory a development of two traditions of analysis of causation: the counterfactual approach and the chance-raising approach. Probability counterfactuals attribute chances to the events mentioned in the consequent relative worlds, in which the antecedent is true, closer to the actual world than worlds where these chances don’t hold. It has been more usual to characterize chance-raising in terms of conditional probabilities. I should explain why I don’t adopt this line. Those who appeal to conditional probabilities seek to develop an analysis of causation from the following basic idea. (PC) c causes e iff P(e/c) >> P(e/not-c) or P(e) (Examples of P(e/not-c) include Good (), p. , upon which Good (), Good () develops a quantitative account, Skyrms (), Eells (), p. ; examples of P(e) include Suppes (), p. , Suppes (), p. ; Reichenbach (), p. ). Here ‘P(e/c)’ means the probability of e given c and ‘>>’ means ‘is proportionately very much greater’. P(e) is the unconditional probability of e. Comparing the probability of P(e/c) with either P(e/not-c) or P(e) are ways of focusing on the contribution of c. It is questionable whether, if c induces a proportionately very slight increase in the probability of e, we would be happy to call it a cause. The formula may be changed to appeal simply to ‘>’ (i.e. ‘is greater than’) if this consideration has no weight. In the formulation given, ‘c’ and ‘e’ are token events, ‘C’ and ‘E’, when they occur below, are types of events. Analyses of causation appealing to conditional probabilities often start with causal statements about types of events—for example, smoking causes cancer—rather than token events. It is then, often, mistakenly assumed that the same analysis will work for token events (e.g. Suppes (), p. ). The formulation, (PC), above is the basic idea from which a type analysis is developed characterized for the token case. Accounts appealing to conditional probabilities face various well-known difficulties that inform their development. First, P(e/c) >> P(e/not-c) may hold because both

     are effects of a common cause. So additional constraints need to be introduced to rule this out (Lewis (b), p. ). For example, Patrick Suppes suggests An event c is a spurious cause of e if and only if (i) (PC), (ii) c occurs earlier than e and (iii) there is a partition of events earlier than c such that P(e/c & d), where d is any element of the partition, is the same as P(e/d) (Suppes (), p. , also Reichenbach (), p. ).

This is not the end of the difficulties. More generally, those who appeal to conditional probabilities owe us an account of the partitioning of the space of outcomes that reveals statistical dependencies that are genuine causal dependencies from partitionings in which they are not. Suppose I have smoked on three occasions and that studies have shown that this is enough to increase the chance of heart disease. Suppose, also, that I was so ashamed of so doing that I exercised vigorously on five occasions—being an idle kind of fellow this is something I would not have done otherwise—and studies have shown that even having done this limited amount of exercise during the course of a number of years reduces the chance of heart disease. Then, it may turn out that P(my heart disease/my smoking) < P(my heart disease/my not-smoking). Nevertheless, my smoking was still a cause of my heart disease. This is revealed by the following. P(my heart disease/my smoking and my exercise) > P(my heart disease/my not-smoking and my exercise). These two inequalities formulated in terms of token events would be derived from conditional probabilities concerning the event types specified by the descriptions, estimated by studies in a population. The question is: on what else should we condition in order to reveal whether or not one element upon which we are conditioning is a cause? Nancy Cartwright suggests that we are unlikely to find a solution that will prove satisfactory to proponents of a reductive analysis of causation because it will have to appeal to some thing like a conditionalization on otherwise causally homogenous circumstances (Cartwright (), pp. –; for further developments that don’t change the basic problem, see Eells (), chs –). If we assume indeterminism, the following solution suggests itself (e.g. Kvart (), pp. –). We take the relevant background to be the actual background. Thus we should consider P(my heart disease/my smoking and actual background) > P(my heart disease/my not-smoking and actual background) If there are deterministic elements in the background however, for instance, it is determined that the individual in question is a smoker, this resolution will require further adjustment. What should we take the background to be? We are now faced with a version of the cotenability problem to which Lewis’ similarity weighting was a contribution. The attempt to extend the conditional probability approach to cases with deterministic elements does not present us with a substantial alternative to the counterfactual approach.

  



Determinism also gives rise to a problem given the standard view that conditional probabilities are to be defined as follows. (CP)

P(E/C) = P(E & C)/P(C).

If c caused e then P(e & not-c)/P(not-c) is undefined because its denominator, P(not-c), is zero. Hence P(e/not-c) is undefined, vitiating the characterization of chanceraising. This leads many proponents of conditional probability theories to limit their accounts to indeterministic worlds (e.g. Kvart (), p. ). Clearly it would be desirable to have an account of greater generality. Recent work by Alan Hájek throws into question this last objection. He argues that our intuitive notion of conditional probability has values in the circumstances indicated. Suppose a fair coin is not tossed and determinism is true. Asked what the probability of heads is given the coin is tossed, we would all say .. Similarly we would say that the probability of the coin being tossed given that it was tossed is . Conditional probabilities should not be analysed in terms of unconditional probabilities such as those suggested in (CP). Conditional probabilities are the fundamental ones. Accordingly, probabilities primarily hold relative to particular circumstances. Unconditional probabilities are just abstractions from these circumstance relative chances. Instead of taking (CP) as a definition of conditional probabilities, we should take it to be a constraint that holds when P(C) is positive (Hájek (), pp. –, –). If Hájek is right, then the zero denominator problem falls away because it rests upon taking (CP) to define conditional probability in all circumstances. Nevertheless, this does not mean that we should re-examine conditional probability accounts of causation. Understanding conditional probabilities Hájek’s way renders the conditional probability approach a way of formulating the counterfactual approach since now they are appealing to similar ideas. The similarity might initially seem to benefit further the conditional probability approach. In response to the concern that it needs to appeal to the idea of causally homogenous circumstances, its proponents may say counterfactualists’ account of the similarity weighting for counterfactuals, and the consequent notion of closest worlds, can be used to provide a non-circular characterization of what is involved. The benefit is short-lived. The counterfactualist will point out that they make no assumption that there is one way in which various worlds count as the closest in which the antecedent is true. If proponents of a conditional probability account are happy to start talking of causes conditional probability-raising against a variety of candidate causally homogenous circumstances, I think the counterfactualist should just welcome a friend of their approach rather than a continuing competitor. I suspect that most proponents of conditional probability accounts would be reluctant to go down this line in any event. In which case, the potential for providing a non-circular reductive account of causation still makes probability counterfactuals the preferable means of characterizing the nature of causation.

.. Causal necessity and sufficiency and the tie between events Putting together the point that the non-probability counterfactuals may hold when causes are not necessary or sufficient for their effects (due to indeterminism) with the

     promise that probability counterfactuals will provide a satisfactory way of characterizing chance-raising, we should characterize causal necessity and sufficiency in the way that Mellor recommends, viz (M) (M)

If e₁ were to occur, then ch(e₂) would be . If e₁ were not to occur, then ch(e₂) would be .

This is subject to a qualification in .. Nevertheless, even with the qualification, such a formulation provides no resolution of the original difficulty. The worry was that the non-probability counterfactuals would make any actually occurring event sufficient for any other event and the failure of any event to occur necessary for any other event that fails to occur. The only contribution of (M) and (M) to this issue is to make any actually occurring event sufficient for any other event which has chance  of occurring and the failure of any event to occur necessary for any other event which has chance  of occurring. Under determinism, then, we would be no further forward assuming that all actually occurring events have chance  of occurring and all events that actually fail to occur have chance  of occurring. For example, suppose, as things are, Theresa May has a chance of  of meeting the European delegation. Then the following is true: if the drumming of my fingers on my desk were to occur, then the chance of Theresa May meeting the European delegation is . But just as I don’t think my finger activity settled whether Theresa May met the European delegation, so I don’t think my finger activity gave it the probability of  (the point is made by Edgington (a), p. ; Hinkfuss (), pp. –; and Noordhof (b), pp. –). The same consideration can be run regarding (M) as a characterization of causal necessity. Instead, we must recognize that (M) and (M) do not capture causal necessity and sufficiency taken in isolation. Rather (M) only captures causal sufficiency given that (M) holds and vice versa (Noordhof (b), p. ). My drumming my fingers on the desk is not causally sufficient for Theresa May meeting the European delegation because if I hadn’t drummed my fingers on the desk in those circumstances, then she still would have met the European delegation. The solution will not satisfy some. They will object that, under determinism, just so long as (M) is true, the actual presence of e₁ and e₂ in the actual world is all that causal sufficiency amounts to on this view. The desire for something more intimate—some real necessitation between e₁ and e₂ as it were—is strong. This brings us to one of the central issues for counterfactual theories of causation: their connection with the denial of intra-world necessary connections between distinct existences. I shall devote Chapter  to the discussion of it and offer some further comments upon this objection towards the end of ..

. Types of Counterfactual Theory There are various dimensions by which we may classify counterfactual theories of causation according to the nature of the counterfactuals used, the semantics provided of the counterfactuals, and so forth. These concern the successful development of the counterfactual theory. Setting these aside, though, there are demarcations to be drawn concerning the fundamental metaphysical picture with which we end up in the light of the previous sections relating to the contingency of Humean supervenience and the truth conditions for counterfactuals.

   



Let Reductive Counterfactualism be a counterfactual theory of causation that denies that counterfactuals can be barely true and eschews intra-world modal facts—such as necessary connections—as their truth conditions. Instead, the truth conditions are understood in terms of possible worlds characterized by the kind of similarity weighting provided earlier. Let Concessive Counterfactualism be a counterfactual theory of causation that denies that counterfactuals can be barely true but which allows that there may be some possible worlds, though not all, in which their truth conditions involve intra-world necessary connections. Let Primitive Counterfactualism be a counterfactual theory of causation in which counterfactuals are true but their truth conditions can be specified in no other terms. Finally, let Weak Counterfactualism be a counterfactual theory that claims that counterfactuals provide important insight into the character of causation but recognizes that there are certain elements of causation that will escape the analysis in its terms (Paul and Hall ()). The first three differences of theory don’t touch the character of the basic analysis, the last one obviously does. I represent the theoretical options in Table .. The first column does not concern whether or not the truth of counterfactuals implies the existence of modal facts but rather whether it implies the existence of modal facts under some independent characterization. I have not identified all the options in logical space but just the most significant combinations of these three elements. In what follows, I shall defend concessive counterfactualism and explore the possibility that reductive counterfactualism is true. I note the possibility of primitive counterfactualism for those who deny the existence of possible worlds and hold that facts (actual states of affairs), if anything, are solely responsible for the truth of counterfactuals. Mellor is a candidate example of the latter, as is, perhaps, Marc Lange, though his main focus is laws (Lange (), ()). What is the attraction of concessive counterfactualism? It is an option that is more or less forced on you if you take the doctrine of Humean supervenience to be contingently true and a counterfactual theory of causation to be necessarily true. Although there are intra-world necessary connections in some worlds, causation Table . Type of Counterfactualism

Independently Modally Characterized/Dependently Modally Characterized/ Non-Modal/Mixed

Barely/ Non-barely

Complete/ Incomplete

Reductive (Lewis)

Non-modal

Non-barely

Complete

Concessive

Mixed

Non-barely

Complete

Primitive (Lange, Mellor)

Dependently Modally Characterized

Barely

Complete

Weak (Paul and Hall)

Neutral

Neutral

Incomplete

Non-Reductive (Glymour, Hitchcock, Pearl, Woodward) (see . .)

Modal (causal model)

Non-barely

Incomplete

     does not require the existence of these necessary connections. In worlds in which they are not present, there will still be causation given that the relevant counterfactuals hold in virtue of what is the case in the closest worlds in which the antecedents of the counterfactuals are true. The presence of necessary connections just becomes one way in which the conditions necessary for the truth of the relevant counterfactuals are realized. Those who reject the counterfactual approach on the grounds that it doesn’t capture the necessity of causation or the physical reality of causation—I shall discuss theories which involve these claims later—are therefore to be accused of confusing how causation may be realized from the minimum required for causation to be present. An argument against the well motivatedness of this position is developed in ., . and ..

. Causation as a Natural Relation and the Nature of Analysis The counterfactual analysis of causation developed in subsequent chapters is an analysis of causation as a natural relation. It is not an analysis of our concept of causation (not a piece of conceptual analysis). In this section, I want to make clear the nature of the position to be developed, and offer a preliminary defence of the methodology behind its development. We should assume that all the participants in the debate about the nature of causation and, indeed, most human subjects, display sufficient mastery of the concept of causation that it is legitimate to attribute the concept to us. This may prove to be incorrect but it is a reasonable working assumption that the parties to a substantial discussion about the nature of anything are masters of the concept of it. We don’t have to feign perplexity as to the subject matter, nor check whether we satisfy the basic conditions for possession of the concept. Our earlier conceptual development is replete with such checks. So it can be assumed, at the minimum, that we know what count as cases of causation and what do not. Our appreciation of the basis of such judgements may be less good. We might confidently identify certain things as games or cakes, and others not, without being able to articulate precisely what the basis of these judgements are. On other occasions, though, our confidence that such and such is a case of causation comes along with an account of why: because it has such and such a feature to distinguish it. Mastery of the concept of causation need not be the same for each of us. If Hilary Putnam’s division of linguistic labour is appropriately taken over to our conceptual understanding, then it is possible that we may qualify as masters of a concept while displaying somewhat different capacities (Putnam (), pp. –). If that is right, then a corollary is that legitimate attribution of the possession of a concept does not require knowing all the truths that people may know in virtue of being masters of the concept. Such a view obviously recognizes a distinction between conceptual analysis and an analysis of the nature of causation. By my lights, it is because the different conceptual capacities of subjects are all organized in a certain respect towards developing our knowledge of causation, that these capacities qualify us as masters of the concept of

         



causation. The organization can be displayed by relations of deference to experts or by systematic interdependencies between possessors of the concept where nobody is a full expert but collectively there is expert performance from mutual correction. Focus on providing an analysis of the nature of causation might seem mistaken given the means I adopt to develop my views in what follows. I don’t go out to investigate causation in the wild but stay in my armchair. This concern assumes that any readily available knowledge about causation will become part of our concept of causation. Without empirical investigation as part of the methodology, the charge runs, we can only do conceptual analysis. There is no reason to suppose that this is so. The conditions someone must satisfy to possess the concept of causation are one thing, the everyday knowledge they have of things that fall under that concept another. There will be a relationship of course. Gross ignorance, where one might expect otherwise, is evidence that somebody does not possess the relevant concept. Nevertheless, that does not mean that all the knowledge of which somebody might be grossly ignorant is conceptual knowledge. Equally, everyday knowledge for one subject—which might be part of another subject’s grasp of the concept—may be elevated into conceptual knowledge as the former subject’s understanding develops. Either way, an investigation may have an a priori character not because it simply appeals to our conceptual mastery of a concept but because, while it appeals to both our conceptual mastery and our empirical knowledge, it draws further conclusions without essentially appealing to any further empirical investigation. The starting point may not be a priori but the shift from it to a further state of knowledge may be. It is possible that there is an intermediate level between our possession of a concept and our everyday knowledge of X that some philosophers have called our conception of X (Higginbotham (), pp. –). An analysis of what we take to be X may be an articulation of the conception that we have formed. Depending upon the nature of tacit knowledge, the conception may be tacitly known and analysis may make it explicit. A procedure aimed to articulate our conception of X is prima facie different from one involving the a priori development of an analysis of X by application of our concept of X (to fix what we’re talking about) to our everyday knowledge. The development of an analysis may result in a conception of X but it need not, prior to that, involve tacit knowledge of a conception. Since we may pursue an analysis of X without commitment to whether it is an expression of, or a development of, a conception, we can remain neutral on this issue. Within this framework, there is no immediate entry point for what may be dubbed the challenge of experimental philosophy understood, in this context, to be the application of the methods of social psychology—roughly the controlled application of questionnaires to identify what subjects are inclined to say on a subject matter—to provide insight into the putative intuitions that might be thought to be data against which an analysis of causation should be tested. For one thing, the debate to follow will not make a contested default claim about causation—roughly in the way that some argue we have a default commitment to a kind of free will incompatible with determinism—that needs to be assessed (see Nahmias et al. (), pp. –, Nichols and Knobe (), pp. –, for the concern regarding free will). The earlier discussion of this chapter is a case in point.

     Two claims about causation were identified in Hume: regularity and dependency, arguably neither entail the other. The emphasis on dependency arose because of difficulties in providing a proper characterization of the relevant regularity and relating it to causation. Probably the closest we will come to making contested claims of the same ilk occurs when we consider whether causation must involve necessary connection (Chapter , .) and whether it must involve genuine processes (.). In each case, I grant the plausibility of the contested claim and seek to accommodate it. So no further scrutiny of its foundation is needed in the way required by the free will debate. The other point at which I recognize the findings of experimental philosophy are with regard to the idea that causes are contra-normal conditions. There I consider different models to accommodate our tendency to identify causes in this way and explain how one favours my own position (..). For another thing, the recognition that different subjects may possess a concept of causation in virtue of having different bundles of relevant capacities provides a ready explanation of variation in what subjects are inclined to say about particular cases. Socio-cultural differences, for example, may mean that certain capacities predominate for one group of subjects and others for a second group. In the discussion ahead, we will see that different theorists have placed the emphasis upon different features of causation. The theory developed will try to place these various features in a context that seeks to accommodate all in an appropriate way. If the correct starting position is that we vary in the capacities that constitute the basis for our grasp of the concept of causation, then the claims of others, and the everyday knowledge we have about cases of causation, are the basis for further development of our understanding of the nature of causation. We should be interested in how a particular approach can respond to such information. We will not be in a situation in which there is some key notion—such as, in epistemology, knowledge may be taken to be—about which there are important allegedly rationally intractable differences over what is required for it, with knock-on consequences for how we should go about obtaining knowledge (Weinberg et al. (), pp. –). The residual issue is whether some of the findings of experimental philosophy provide grounds for being sceptical about the method of developing an analysis of causation in part by appealing to whether we have a case of causation in one situation or another: the so-called method of cases (e.g. see Cappelen (), pp. –; Machery (), pp. –). The concern is that such appeal draws on intuitions about whether or not we are faced with a case of causation in the situations envisaged. These intuitions, it is alleged, have questionable epistemic force because of the crosscultural and cross-socio-economic group variation observed, along with apparent contamination of these intuitions by other factors like moral considerations (see e.g. Machery et al. (), pp. –; Machery (), pp. –). To assess this issue, we can remain neutral over whether intuitions are inclinations to judge, judgements, or quasi-perceptual intellectual presentations of something as the case (for discussion, see Chudnoff (), ch. ). Nevertheless, for the reasons outlined above, we should not view them as intuitions drawn from our possession of the relevant concepts alone (an assumption often made, for example, Kauppinen (), pp. –). Some may be but others may be the result of our possession of concepts together with everyday knowledge that we are holding fixed in our consideration of the situation.

         



A preliminary clarification is required concerning the claim that intuitions are evidence that can be used to favour one theory over another. Suppose that we intuit that p. For simplicity, suppose that p implies not-T (some favoured theory of causation). Then it is p that is evidence for not-T. It is not the intuition that p. The point is similar to that in the case of belief. If I believe that p and p implies not-T, then it is p that is the grounds for failing to believe that T. Scepticism over the status of intuitions only raises the question of whether, if we intuit that p, then p. Scepticism raises the question of whether we have evidence by having intuitions, not whether intuitions are evidence. An exception to this point is if the intuitions themselves were seen as expressions of, for example, the concepts we possessed. My intuitions that these or those are cases of causation would then be evidence against which a particular theory of the nature of my concept of causation is tested (Williamson (), pp. – for related discussion). But, as I emphasized, the task at hand is not conceptual analysis but the analysis of causation itself (the latter outstripping anything it might be plausible to think is part of our concept of causation). In that context, when we intuit that p, p is a consideration for or against a particular theory concerning the subject matter of p. Noting that it is an intuition is not meant to close down the question of whether p by ruling out the possibility of considerations against it having more significant weight. The second point to make is that the intuition that such and such is a case of causation draws on everyday capacities to identify, or classify something as falling under a certain concept. There is no special faculty at work in, what some think of as the distinctive activity of, thought experimentation. If I have the intuition that a particular arrangement of lines on a white piece of paper is a rectangle, then there is no different capacity at work intuiting that, if the paper had been yellow, or parallel lines in the shape had been a bit longer, the arrangement of lines would still have been a rectangle (see also Williamson (), pp. –). All that is being envisaged is that different circumstances result in the manifestation of the same intuition that something is a rectangle. Changes in the actual world show that this is the case and, if we possess the capacity to intuit that something is a rectangle, imagined differences can show this is the case too. From this perspective, scepticism about intuitions, drawn from psychological work on thought experiments, threatens to generalize to scepticism about the basis of our judgements in general, which would be unwarranted (a threat acknowledged by Machery (), p. ). As a result, in appealing to claims about whether or not something is a case of causation, we are not appealing to a distinctively philosophical expertise although philosophers, like anybody else who is used to talking about cases of causation, may develop expertise in this area. There are no ‘wildly implausible’ credentials being attributed to the intuitions of Western analytic philosophers, for instance, but rather a recognition of how their practices may assist in the development of general expertise (for the charge Machery et al. (), pp. –). In which case, such philosophers will be more sensitive to little differences between cases that some folk might miss. Such sensitivity, developed through discussion of a range of cases, is implausibly dismissed as seeking to apply the concept of causation beyond its everyday use (Machery (), pp. –). The discussion of atypical or hard cases is the very stuff of developing an expertise in a subject matter.

     It is a mistake to think of the situation—as some experimental philosophers do—as a question of whether it can be established that there is a particular kind of expertise that philosophers have, with the suggestion that empirical investigation is needed to provide evidence that we do. Instead, our starting position is one of prima facie trust in our capacities reinforced by the tendency towards stability in the intuitions that we have found in the field of philosophy (Williamson (), pp. –). Of course we might discover this is misplaced. Expert performance in stock-broking and psychiatry are cited as fields in which expertise has been found wanting and, thus, as a warning against presumptions of philosophical expertise (Weinberg et al. (), p. ; Shanteau (), p. ). However, the implications of this discussion for the presumption of philosophical expertise are by no means straightforward, and provide little support. In the case of psychiatry, there is variation over different aspects of its practice. Training in a checklist of features for a certain personality disorder enables trainees to perform almost as well as experienced psychiatrists, which, in itself, is not high with  per cent accuracy. The ability to reproduce putative expert performance so easily is part of the case against psychiatric expertise or skill. Training did not help at all with other tests, such as Rorschach inkblots, but even here experienced psychiatrists showed no additional predictive accuracy (e.g. Garb (); Camerer and Johnson (), p. ). However, the bearing of this on the case of intuitions concerning the application of concepts such as causation is questionable. First, psychiatrists and trainees are seeking to apply a predictive concept with complex implications for future behaviour. The same is true of stockbrokers’ attempts to identify stock that is likely to rise or fall. Intuitions about whether or not a case with a certain structure is a case of causation, or the truth conditions of counterfactuals, does not have this feature. For one thing, the examples used to elicit intuitions about whether or not we have a case of causation are supposed to contain all relevant features on the basis of which we might arrive at a judgement. If more detail is needed, these additional features can be written into the case. We don’t have a conjecture based upon evidence of which we wish we could have more, for example, in the case of responses to inkblots. Further, while identifying something as a cause does have a predictive element, the conclusion that, if certain conditions hold, then it is appropriate to conclude that c caused e primarily does not. Any link to an underlying regularity will be qualified and, if C-type events failed to cause E-type events in the future, we would expect that the circumstances were in some way different or we had a case of brute singular causation. If the absence of predictive success is not explained in these terms, then an appropriate manifestation of our causal expertise is to withdraw the causal claim because the connection to future activity is one of the conditions causal expertise takes into account. Second, attempts to provide an analysis of causation are one way in which one might identify a checklist of features for cases of causation. Suppose the attempt is successful and provided to trainees allowing them to be as successful as those who generated the analysis in the first place, in identifying cases of causation. Even if this could be taken to establish that intuitions about causation are not the expression of a skill, it could not undermine their epistemic status because they were the basis of the checklist. So the observation that something is not the display of a skill if a subject can

         



be trained in relatively short order to display the competence in question is orthogonal to the question of the role of intuition in evaluating philosophical theories of causation and counterfactuals, say. Third, expertise is acknowledged to be valuable with regard to insight into the likely accuracy of one’s predictions—this is known as calibration (Camerer and Johnson (), p. ). So one might expect that, if the analogy applies, it will imply that philosophers are better able to evaluate the competing claims of intuitions because they will be more accurate in assessing their relative confidence in each. We shall see how philosophical methodology supports this feature. It is also incorrect to say that the competences behind our intuitions are nourished by a slender diet of cases to categorize (Weinberg et al. (), p. ). Certainly for the subject matter of this book, causation and counterfactuals, we are presented with a litany of examples of these every day of our lives. For that reason, the expertise we have on these matters is not highly specialized like, for example, share performance or the identification of specific clinical personality disorders. A more appropriate comparison might be to consider the circumstances in which our intuitions about what counts as a dog or a city are overthrown by noticing that there is, or it has not been established that there is not, some variation across socio-economic groups, or across cultures, on these matters. Although the case against intuitions in, at least, our subject area is not made, I would not want to take the content of immediate intuitions subjects have, those presumably reported in experiments, to have significant epistemic weight in themselves. Instead, they are inputs into a process that involves checking them for consistency, considering whether there are rationales for them, and the construction of theories that seek to describe the nature of that concerning which they are intuitions. The epistemic status of their contents, in part, derives from their robustness through this process (Kauppinen (), pp. – for a version of the same idea). Subjects questioned by researchers in experimental philosophy for the most part do not have their judgements subject to such scrutiny and, thus, the variation observed in the work of experimental philosophers does not touch on the status of judgements used in our context. We don’t have to deny that responses to questionnaires reveal subjects’ intuitions about how cases should be classified although there will be cases in which such a denial is reasonable (e.g. Bengson (), pp. –). Instead, we just need to notice that the status of the intuitions that have gone through the process of comparison, and so forth, have an epistemic status that derives from it. In engaging in this process, we have moved beyond the stage of identifying what intuitions people have about a subject matter. We know the range of things people find intuitive, as is revealed by our professional colleagues just as much as the difference in the claims of the subjects of questionnaires. We are considering the extent to which one intuition or another is due to a misunderstanding of a situation or can be explained away. Often intuitions come in pairs, for example, this is not a cause of an effect because, if it did not happen, then the effect would have happened anyway. The latter element is not the full justification of the former—otherwise it would not be an intuition—but rather is suggested to supply part of the epistemic

     credentials of the first claim. By pointing out that the second claim is not true of some clear cases of causation then leads to a re-examination of the first. There are two further important elements of this process. The first is that part of the defence of a theory of causation, or any other philosophical subject matter, is an explanation of why there may be some recalcitrant intuitions whose contents are, in fact, false. The fact that this is often a central part of philosophical debate, and will have a role in discussing resistance to Humean metaphysics, is one source of scepticism about whether philosophical methodology is successfully characterized as primarily involving intuitive verdicts about cases. The second element is that, in evaluating any theory of a philosophical subject matter, a question arises about whether we have an explanation of its central significance in our lives. Is what we are seeking to understand shown to be important in an appropriate respect? That way we avoid any charge that if different social cultural groups tend to favour different theories, favouring our own is merely parochialism (for the charge Machery (), pp. –). I shall provide an explanation of this kind for causation in what follows. This is not to deny that there may be biases at work in the production, persistence, and evaluation of the content of our intuitions. For example, it has been found that warmth (one facet of extraversion) is associated with compatibilist intuitions in the free will debate for both naïve and expert subjects; although, it is also recognized that expert subjects have more incompatibilist intuitions (Schulz et al. (), pp. –). The presence of other factors resistant to the development of expertise is not altogether surprising considering the intractable nature of the dispute between compatibilists and incompatibilists. It does not undermine the fact that the intuitions of expert subjects, even in this area, have enhanced credentials having been subject to criticism and defence by each party. Nor is it obvious that the data that reveal the biases expert subjects may display really speak to the issue of robustness since the kind of checks that are run to identify expertise are succinct responses to simple questions to check relatively basic knowledge of the field (e.g. Schulz et al. (), p. ). As we shall see, there are biases at work in identifying the relative causal contributions of different factors, relating to our moral disapproval of agents (..) (Machery (), pp. –). However, the discussion of this in the context of the analysis of causation advanced in the present work shows how they may be identified and subject to scrutiny. Indeed, we will find that the identification of biases in this respect actually assists the defence of the analysis offered in the book. A final point to make is that, although it is interesting that a certain personal feature can make somebody more prone to have a particular intuition, this is not really news. It is a familiar fact that differences of intellectual temperament and personality can lead philosophers to have significantly different starting points. Philosophical discussion of these issues has sought to use these differences to further understanding of the issues they concern. In many cases, the results of experimental philosophers reinforce our experience of teaching philosophy, and debate with our colleagues, rather than introduce a new dimension to our understanding of disagreement. And where there is little disagreement about what we should say about a case—quite unlike the question of free will—there is no reason to view our intuitions as tainted.

         



I have said that causation is a natural relation. Its status as a relation has been questioned and will be defended in Chapter . So I will say no more about that assumption here. Talk of causation as natural does require further elucidation. The basic idea is that natural properties and relations constitute explanatorily fundamental resemblances in the world. This is a combination of two strains of thought. First, there is the distinction between sparse and abundant properties (Armstrong (), pp. –; Lewis (a), p. ). Corresponding to every predicate or logical construction of predicates, we may say there is a property in the abundant sense. Intuitively, not every predicate which is true of an object characterizes a way in which it resembles another object. We may count two objects as duplicates even though there will be predicates true of one and false of the other. Sparse properties are those that make for resemblance (for more on duplication, resemblance, and so on, see .). Certain relations may make a contribution to whether one object is a duplicate of another object by holding between parts of objects. The suggestion is that causation is such a relation for causal processes or objects involving causal processes. Second, there is the distinction between those properties and relations that have explanatory value and those that do not. One way that a property or relation may have explanatory value is that it occupies a certain causal role identified by science as part of a theory which best explains how things work. Another way is by being part of the characterization of an explanatory relationship itself. It is clear that causation falls under the second category though, given the existence of iterated causation—e₃ being caused by e₁ causing e₂—that does not rule out it also falling under the first. A related distinction is the distinction between natural and non-natural kinds. The fundamental idea seems to be a difference between kinds of things with explanatory value and those without it but perhaps some other purpose of classification (LaPorte (), p. ). Often, natural kinds have normal distinguishing features held together or explained by underlying mechanisms (Putnam (), p. ). Examples of natural kinds are commonly taken to be: Stuffs: gold, water, carbon. Biological species: elms, horses, tigers. Physical kinds: atoms, electrons, molecules. There are disputes over particular types of cases. For instance, some hold that biological species are individuals: particular evolutionary trees of organisms. A particular horse will be part of the individual biological species horse as well as, maybe, the instantiator of a biological kind, being a horse (Ghiselin (), p. ; Smart (), pp. –; Lowe (), p. ). Debate over particular cases does not mean that the question ‘If causation is a natural relation, is it a natural kind?’ is illegitimate. The immediate answer seems to be ‘no’. It is not a stuff like gold or carbon or a kind of individual like atoms or tigers. Causation does, however, constitute a high-level characterization of a certain kind of process: causal processes. Some processes are plausibly understood to be natural kinds too, for example electrolysis, oxidation, radioactive decay, and so forth. Nor does the high-level characterization that causation provides rule it out from being a natural kind. There are other plausible cases of high-level characterizations which are kinds, for example physical kinds: all those identified by physics or composed from

     things identified by physics. It may be argued that physical kinds so characterized would include telephones and these aren’t natural kinds. Of course, that’s right. Telephones aren’t. But just because something fails to be a natural kind by being a telephone does not mean that it fails to fall under any natural kind, for example, by being physical. So if processes are to count as kinds, then causation is a natural kind by characterizing a certain kind of process of explanatory value. The point about telephones also applies to causal processes. Certain types of processes such as pushings, pullings, smashings, and so on, are not plausibly viewed as different natural kinds. The processes that fall under these kinds will all still be a natural kind by being causal processes. My claim that causation is a natural relation, by characterizing a natural kind of process, is stronger than P. F. Strawson’s claim that causation is a natural relation. He takes causation to be a natural relation because pushings, pullings, and so on, are natural relations. Other causal relations identified by sciences are modelled on them (Strawson (), pp. –). By contrast, I make no assumption that these everyday causal relations are natural kinds. The sciences will identify the different kinds of causal process. My claim that causation is a natural relation depends upon the feature I have identified above concerning its significance, namely it characterizes a certain kind of process of explanatory value and, indeed, as we shall see in Chapter , a dependency relation of explanatory value even when a process is lacking. There is a difference between causation and certain other natural kinds. We do not arrive at a proper understanding of the nature of natural kinds even by a mix of conceptual understanding and everyday knowledge. According to some accounts of natural kind terms, reference of the kind is fixed in the actual world by a stereotypical collection of properties that members of the kind in question may fail to have in other possible worlds, or for that matter, the actual world. Natural kind terms refer to properties that are the typical causal explanatory basis for the stereotypical properties mentioned. Thus, the nature of the property to which our kind term refers is a matter of further empirical investigation (Putnam (), (); Kripke (), pp. –). Theoretical identifications such as water is H₂O, Gold is the element with atomic number , and so forth, if necessary, are a posteriori. Things are different with causation. Although I doubt that my counterfactual analysis of causation is an a priori (as opposed to a posteriori) necessary truth, I do think that, given our everyday knowledge about causation together with our grasp of the concept of causation, it is possible to provide a priori reasons for the account I favour. The point just made does not depend specifically upon the Kripke-Putnam account of the semantics of kind terms. Somebody who holds that a description such as the actual causal source of our stereotype for K (a particular kind) captures the meaning of our term for K (rather than simply playing a reference-fixing role) would still recognize a difference between standard natural kinds and causation (Jackson (), pp. , –). The difference in the types of empirical knowledge (‘everyday’ or more derived from particular scientific investigations subjects may not be aware of) needed to settle the nature of the kind in question remains. We can explain the phenomena either by supposing that we have more everyday knowledge about the nature of causation (as I have suggested) or by supposing that the conditions under which we are prepared to ascribe to someone possession of the

         



concept of causation are more exacting. The probable source of the difference understood either way is a difference in the explanatory role that is played. Standard natural kinds are identified by arriving at a detailed understanding of a certain kind of causal profile that they occupy. We fix upon a subject matter and develop an account of the nature of such kinds as our knowledge of the causal role deepens. By contrast, the causal relation is a natural explanatory relation. Its proper characterization is prior to the development of any explanatory role. It specifies the explanatory target of all the other particular explanatory activities we get up to. Thus it would be no surprise if our everyday knowledge of it is greater or if the requirements for possession of the concept of causation are more exacting. Indeed, even if causation plays a role in fixing the reference of most natural kind terms, with regard to its own reference an exception should be recognized. It is to be expected that subjects will have an understanding of causation that does not defer to whatever is the causal source of our practice of using causal terms on pain of not knowing what they are talking about. Whatever the exact source of the difference, there is no need to question the status of causation as a natural kind. As I have already made clear, the proposed analysis of causation is an analysis of the nature of causation rather than our concept of causation. It is compatible with providing an analysis of causation that the concept of causation is conceptually prior to our concepts of the things in terms of which we analyse causation (e.g. counterfactuals). By this, I mean that, in fact, it may have been that our grasp of the concept of causation enabled us to grasp the concepts of these other things (at least roughly, see .). If an analysis of causation is possible in terms of other things, then it should, in principle, be possible to grasp the concept of causation in terms of the concepts of these other things. That does not mean that, in fact, we grasped the concept of causation in that way nor that every creature could, in principle, do so. For the same reason, my analysis of causation is not meant to be an analysis of our conceptual competence. The full analysis does not lay out what somebody grasps when they grasp the concept of causation. Nor is it committed to being an expression of their conception. If the final formulation is accepted, then it could become a subject’s conception of causation and inform their practice. Indeed, I hope that it is sufficiently plausible that this becomes the case. A consequence of these points is that it is no objection to the analysis to say it is too complicated to be what, in fact, people understand by the concept of causation. Nor, in general, do worries about the triviality of analysis apply (Langford (), p. ). An analysis of the form c causes e iff X requires no equivalence in meaning (apart from picking out the same relation) between the left-hand side and the right-hand side. So there should be no worry that, if they mean the same, then the analysis could not be substantial. There is, of course, going back to Bertrand Russell, a line of scepticism about the significance, and indeed naturalness of, causation. Russell dismissed it as a relic (Russell ()). In part, the detail and development of the analysis is my answer to that objection. However, of particular significance are concerns about the anthropocentric character of causation drawn from the fact that causation seems a non-symmetric relation but the facts in terms of which its dependency may be understood are symmetric. It has been suggested that its non-symmetric character is drawn from our understanding of our own agency. I consider this particular line of

     thought in .–. By my lights, the objection mistakes a plausible story behind the theoretical unity of our concept of causation—and one basis for causal nonsymmetry in the absence of others—for an insight into the nature of causation. Other grounds for denying that causation is a natural relation have focused on phenomena such as the intensionality of some causal discourse—taking it to suggest that causal discourse is a contextual matter—its extrinsic character, or its apparent normative dimension (e.g. Sider (), fn. ). These will be discussed in Chapter  (context dependence and extrinsicality), .., .. (normative dimension), . (context dependence and contrastive character); ... (intrinsicality). In brief, I don’t deny that some causal statements are contrastive and contextual but causation itself is non-contextual and intrinsic. Appeals to context to explain the phenomena are unnecessary and less successful than has been appreciated. The putative normative dimension is an illusion that is the result of biases deriving from our inclination to blame. The full defence of causation as a natural kind must await this discussion. There is a more recent line of scepticism that questions the naturalness of causation by denying that there is any unity in what we call causation: Causal Pluralism. Many claims are grouped under the heading of Causal Pluralism. It is, perhaps, a surprise that for a work entitled ‘A Variety of Causes’ I would not place my own theory in this category. For our purposes, the key question is whether there is one kind of relation that is the causal relation, under which there may be many subcategories. Philosophers have different reasons for denying that there is. Some argue that causation is a cluster concept involving a number of different rough tests for the presence of causation and a number of different relations may satisfy enough of the tests (e.g. Skyrms (), p. ; with qualifications, Godfrey-Smith (), pp. –). Others argue that causation is a minimal family resemblance concept with everyday notions like pushing, pulling, and the like, falling under it due to the resemblances between them but nothing substantially common to them all (Anscombe (), Cartwright (), pp. –; Psillos (), pp. –). Some observe that there is no independent characterization of what causation would involve in each of these cases and, further, no analysing these cases in terms of a general relation of causation plus independently characterized supplementary material to explain how this particular case of causation is a push, a pull, and so on (Anscombe (), p. ; Cartwright (), p. ). A final group of philosophers argue there are some fairly precisely specified, possibly technical, notions of causation and our concept of cause applies, or should apply, to their disjunction (Hall (a); Cartwright (), p. ). My implicit argument against all of these positions is to produce an analysis of causation and explain why we should favour it. I discuss some of the considerations that make people adopt a type of causal pluralism when I appeal to the distinction between hasteners and delayers to develop my analysis in Chapter , the relata of causation in Chapters , , and , and, centrally, the distinction between cases of causation putatively involving substantial processes from those where a simple dependence is in play in .. The claim that there is one kind of relation is compatible with the following theses. First, there is another kind of causal relation that holds at the level of types or

       



properties. The rejection of causal pluralism only holds for token or particular causation. Second, there are many different kinds of particular that may stand in a causal relation: events, objects, facts, and so forth. Third, and finally, within the context of a uniform causal relation between particulars, it is possible to identify different contributions to the relation (Hitchcock (a), pp. –). These are matters we shall discuss further in the chapters on causal relata and property causation. In the final chapter, I will spell out in more detail how the framework I favour recognizes variety in causation compatible with a denial of pluralism.

. Alternative Accounts of Causation and the Discussion Ahead More time is devoted in the pages ahead to developing my own analysis of causation and the surrounding territory than in discussing the many alternative accounts on offer in the literature. To some extent, I regret this because an important component in the proper understanding of a philosophical theory is a detailed appreciation of the alternatives, and the problems they face. One natural way of structuring the discussion would be to devote different chapters to different theories and introduce my own midway through the book. Instead I have adopted a rather different approach. I discuss other theories in the context of particular problem areas. For example, theories that appeal to laws come up in the chapter on the connection between causation and laws (.). Process theories come up when I discuss the difference between substantial causal processes and double prevention cases in which an event enables another event to occur by preventing something from stopping it (.–). Part of the reason for this is that theories are revealed in their best light when we come to the problems that motivated them and their contribution within the framework I am developing is most easily displayed. Probably the main reason, though, for discussing the alternative theories in the context of particular problem areas is that many of the theories are not in the running if a counterfactual theory of causation can properly be defended. Let me try to justify this apparently rash remark. Consider, for example, the very sophisticated, technically accomplished, and highly influential Causal Graphs/Bayesian Networks Approach developed by Judea Pearl, Peter Spirtes, Clark Glymour and Richard Scheines, and championed by Christopher Hitchcock and James Woodward (Pearl (b), (); Spirtes et al. (), Hitchcock (a), (b); Woodward ()). Its proponents take the notion of a causal mechanism as a primitive and claim that the proper semantics of counterfactuals will make ineliminable appeal to such a mechanism, which is represented by what they call Directed Causal Graphs (arrow diagrams with certain conventional properties) (e.g. Pearl (a), pp. –). In Chapter , I discuss whether the semantics for counterfactuals needs to appeal to the notion of causation in its characterization and argue it does not. The semantics, moreover, has the benefit of more general application. If the argument there is correct, then this component of Pearl’s approach is open to question. Similarly, in Chapter , I provide an analysis of a completed causal process in terms of probability counterfactuals and some other conditions. If the analysis there is correct, then while one is at liberty to take causal

     processes as a primitive, it is not necessary. Since my attempt to provide such an analysis is part of a reductive programme, Pearl’s and my theory are operating at different levels. I could use much of Pearl’s technical apparatus and offer my own approach as a further analysis of some features of it. Process theories—that is, those that characterize causation in terms of causal processes involving transmission or conservation of a quantity such as energy— provide another case in point. They are offered, in part, because it has seemed that causation need not involve chance-raising and there are cases of pre-emption that cannot be understood by appeal to counterfactuals or, indeed, by any other means. In Chapter , I explain how a competitor absent chance-raising approach can deal with the problems identified. If I am right, a central motivation for these theories is taken away. Moreover, as we shall see, process theories have commitments of their own that prove to be unattractive and these theories struggle to provide a characterization of a genuine causal process independent of appeal to counterfactuals (.–). Certain of their proponents emphasize that their theories are only empirical claims concerning the nature of causation in our world. Such theories are not even in the same game as counterfactual theories. The general point, then, is that other theories derive their sustenance from perceived failures in the counterfactual theory. Hence the best argument that I can give against these other theories is the full development of such a theory. That is what I seek to do in the pages ahead. The discussion to follow takes a pretty natural structure. Chapter  is devoted to a defence of the theoretical interest of my starting point, namely that causation may, but need not, involve necessary connections between distinct existences. Where Chapters  to  develop an analysis of causation, and related issues, that is compatible with no necessary connection between (wholly) distinct existences, the contribution of Chapter  is to defend the claim that the notion of necessary connection between distinct existences is coherent and, according to the most plausible way of understanding (wholly) distinct existence, cannot be ruled out. I argue that we have experiences of causation and, in specific circumstances, may well have experiences of necessary connection, although our experience mischaracterizes it. I provide an analysis of our cognitive grasp of necessary connection and use this to explain how counterfactuals successfully capture the intimate connection we take to be present between cause and effect that, when there is no necessitation, may be lacking. The defence work is continued in Chapter  by which time the structure of my position has been revealed and the discussion can turn to considerations against necessary connections between distinct existences drawn from the analysis of modality, specifically, the principle of recombination as a principle of plenitude. Chapter  also plays a subsidiary role. In explaining how we may experience causation, and our cognitive grasp of necessary connection, I provide grounds for supposing that there is causation in worlds in which there are no necessary connections between distinct existences. Many of the features of such a world, and the experience of subjects within it, bear comparison with worlds in which there are necessary connections. So, as we shall see in ., it would be a mistake to deny that causation is present in such a world.

       



In Chapter , I develop a semantics for counterfactuals, building on Lewis’ theory and similarity weighting, with two principal aims. The first of these will be to resist those who argue that appeal to counterfactuals in the analysis of causation is circular because their semantics must appeal to causal facts (specifically, in the similarity weighting for worlds). The second of these will be to secure the semantics for counterfactuals for a possible account of causal non-symmetry in terms of counterfactual nonsymmetry. As a result, my focus, to begin with, will concern the weight that Lewis rightly places on perfect match, although I moderate it in certain respects to deal with an indeterministic version of Fine’s Future Similarity Objection and develop a more precise understanding of the role of approximate match. There will be further developments of the semantics when I discuss the nature of causal non-symmetry in Chapters – and laws in Chapter , its final form is set out in .. In Chapter , I outline my counterfactual analysis of causation and explain how it deals with the standard problem cases that are meant to motivate other accounts. Although the development takes the form of a consideration of difficult cases of causation and attempting to tease out, expressed in counterfactual and probabilistic terms, the dependency involved in causation, the leading idea at which we end up has some independent motivation and simplicity. It is that causes of a target event are those which (independently of its competitors) both make the mean chance of an effect, e₂ say, very much greater than its mean background chance, and actually influence the probability of the effect in this way, at the time at which the effect occurred via a complete causal chain. There are grounds for thinking that this is an important relation for us, some of which will be explored in the subsequent chapters. I compare it with related approaches and also the claim that causation is a contextsensitive contrastive relation. I deny that it is. Part of the case against is made in . but the discussion is continued in Chapter , ., Chapter , and .. One consequence of my analysis is that causation is non-transitive. In Chapter , I justify this verdict against attempts to defend the claim that causation is transitive and compare it with accounts that seek to capture the non-transitivity of causation in another way. Where I think the key move to understanding causation is to consider whether there is a certain kind of chance-raising involved after subtracting competitor processes, fixing accounts fix the values of the other processes in order to detect chance-raising dependencies between the target cause and effect. This alternative manoeuvre is seen to engender problems. I explain how the nontransitivity of causation drops out of my characterization of cause described in italics above rather than, for example, the idea that causes are difference-makers (in a specified sense) or, in the kind of cases considered, switchers by interaction with a process. The analysis of causation proposed in Chapter  has two immediate consequences regarding causal relata. The first is that the analysis will be satisfied by both an element in some causal circumstances for an effect and also by the causal circumstances taken in toto for that event, sometimes called the total cause of the effect. The second is that the analysis does not distinguish between elements in the causal circumstances, characterizing some as causes, others as enabling conditions, to take one alternative. Chapter  focuses on these consequences and defends them against

     those inclined to reject them and, thus, inclined to reject my proposed analysis altogether, or insist that it requires supplementation. I explain how the idea of causes as contra-normal conditions either derives from certain biases at work in our attributions of causes or can be the basis for a pragmatic explanation of why we favour elements in the causal circumstances as causes over others. It is a mistake to take contra-normality to be part of the nature of causation. Chapter  focuses more specifically on the ontology of causal relata aside from the question of their relationship to causal circumstances. A distinction is drawn between what kinds of entities may be causes and what entities are the fundamental causal relata. Arguments to settle the latter question, which is the main focus of the chapter, either arise from the nature of the causal relation itself or more general ontological issues, for example, whether the nature of reality is ultimately given by truth-makers: ‘the world is the totality of facts, not of things’ (Wittgenstein (), .). I explain the theoretical motivation for identifying events as one fundamental causal relata, namely they are needed to be triggering causes, and argue against recognizing other fundamental relata than properties (which is the subject matter of Chapter ). Recognition of facts is neither required to capture the nature of causation nor for their truth-making role since no such role is required. The particular theory of events developed is that they are temporally limited particulars involving the instantiation of all the properties required for the instantiation of a particular determinate property. I explain why more finely individuated events, involving the instantiation of perhaps just one property, are unnecessary. They are not needed to capture the truth of various causal claims or make the analysis of causation I favour work. Indeed, the analysis removes an argument for these other ways of understanding events. Chapter  completes my defence of my rejection of truth-making—and, hence, of facts as causal relata—by focusing on the issue of negative causation, and the attendant question of whether causation must always involve a relation between cause and effect. Indeed, some writers have denied that causation ever involves a relation between cause and effect because of the case of negative causation (e.g. Mellor (), p. , Martin (), p. ). I explain how statements may have truth-bases without truth-makers and argue that statements of negative causation have, as truth-bases, causally related positive events. The plausibility of this treatment provides further support for the rejection of truth-making in Chapter . My discussion of property causation in Chapter  plays a number of roles. One is simply to develop an account of properties, and their instances, in causal relations, since I have said that properties are the other fundamental relata. It is an important part of my approach to emphasis in causal statements—that sometimes are taken to favour implicitly contextualist views—and denial of essential properties to events. The approach is developed in the context of a certain challenge. If one set of properties supervenes upon another set of properties, then do the former properties have causal powers illegitimately ascribed to them by a counterfactual theory? I argue the attribution is legitimate if the following is the case: first, the superveniencebase properties minimally metaphysically necessitate the supervening properties; second, part of the minimal supervenience-base causes the target effect; third, instances of the supervening properties would all cause certain target effects in

       



the right kind of circumstances, as a result of this. When these conditions are met, it is legitimate to suppose that the causal relationship holds not only in virtue of the supervenience-base properties but also the supervening ones. I identify two further explanatory virtues that citing property causes may display. The first is when a property has a distinctive causal profile: there are some circumstances in which it makes a causal contribution that no other property would. The second is when an instance of the property supplies the precise contribution required for a certain effect, that is, there are no redundant elements to its contribution. Pragmatic appeal to the second explanatory virtue is used to explain away our tendency to hear certain explicitly contrastive statements as true when, in fact, they are false. I draw on this framework to assist in dealing with the issue of Chapter . A counterfactual analysis of causation only works if counterfactual dependencies that characterize causal dependencies can be distinguished from those that hold because of logical or metaphysical necessities, for example, in the case of relational properties or identity. As it turns out, the simple claim that the relevant causally characterizing counterfactual dependencies are those which hold between distinct existences doesn’t work, in part because there can be dependencies between distinct existences that hold in virtue of logical or metaphysical necessities and, in part, because there can be causal relations between existences that aren’t distinct. My solution is to argue that, when counterfactuals hold concerning entities with properties that stand in some kind of loose existential dependency relation, we should only count the counterfactual dependence as indicative of causal relationship too if part of their corresponding minimal supervenience-bases satisfies the analysis of causation. I explain how this idea will apply if properties are understood in ways proponents of a powers ontology recommend. I also develop an analysis of intrinsic properties in this chapter, appealing to three features—External Independence, Duplication Characterization, and Recombination Maximisation—each of which, by itself, doesn’t quite work to demarcate what we have in mind. This is the basis for some of the discussion in Chapters , , and . The counterfactual approach I favour classifies a motley crew of relations as causal relations, those involving substantial causal processes as well as those that don’t. Some will judge this a source of weakness. They hold that understanding causation in terms of a substantial—and not simply counterfactual—characterization of causal processes better captures the intuitive differences between various cases of causation, the intrinsicality of causation, what is involved in action at a distance, and avoids the danger of proliferating causes by recognizing lots of negative cases. . will deal with the last issue. In Chapter , I argue that my more inclusive analysis of causation is compatible with allowing that there are ways to distinguish the variety that falls under it. I can appeal to the same characteristics as those who take causation to involve substantial causal processes without having to insist that these characteristics themselves serve to characterize causation. This proves to be an advantage because the theories that make an appeal to substantial processes in understanding causation face considerable difficulties that I devote the first part of the chapter to explaining. I go on to explain why the attempt to tie causation to the presence of substantial causal processes between cause and effect fails to be justified by appeal to responsibility, or by its

     capacity to make sense of causal locality and the intrinsic character of causal processes. In the light of the discussion, I consider the approach that the counterfactual theory would take to the Bell phenomena. Some claim that it closes off certain options and forces certain conclusions. I explain how this is not the case. In Chapter , I turn to the question of the distinction between cause and effect. This is often discussed under the heading of causal asymmetry but I argue that causation is a non-symmetric rather than asymmetric relation. Different bases have been identified for causal non-symmetry. Within the counterfactual framework, this has included an asymmetry of overdetermination, the independence condition, and an appeal to agency. Proponents of non-reductive approaches to causation have suggested that causal non-symmetry may be independent of all three. I argue that causal non-symmetry can be rooted in one or more of these three, defending the appeal to some of them against recent attacks, and accommodate the non-reductive approach by recognizing a fourth non-symmetry appealing to a primitive nonsymmetric chance-raising. Each counts as an appropriate basis for causal nonsymmetry because it may be the realization of non-symmetric chance-raising. Key moves in this chapter involve a refinement of how to understand the way in which the asymmetry of overdetermination works, and how it interacts with the revised similarity weighting I provide, the contribution of the independence condition to a proper understanding of the transition period (the point of departure from our world to realize the truth of a counterfactual antecedent), the role that appeals to primitive non-symmetric chance-raising should play in the treatment of problem cases, the circumstances in which an appeal to an interlevel non-symmetry of agency may be appropriate, and the priority ordering of these various realizations of causal non-symmetry. Agency or manipulability theories of causation claim that key to understanding the nature of causation is that causes are means to ends for agents. A principal problem with such theories is that they are circular, appealing to causation in order to understand the relationship between agents and the actions they use as means to the ends, and in the characterization of means to ends. Chapter  begins by discussing agency theories of causation in order to isolate two potential contributions to the analysis of causation developed up until that point. The first is the characterization of effective means, both in terms of evidential decision theory and in causal decision theory. Successful characterization of effective means in terms that don’t make primitive appeals to causation provides a more detailed understanding of the third source of causal non-symmetry, mentioned in Chapter , based on agency. A successful characterization of effective means in terms of evidential decision theory clearly satisfies this requirement and I outline how this may be developed. However, there is a problem with the proposed development of evidential decision theory that reveals the importance of causal thinking—captured in causal decision theory—in characterizing when an action fails to be the most effective means to a certain end. I discuss the implications of this for my analysis and argue that it does not undermine the appeal to the non-symmetry of agency I propose. The influence of agency approaches to causation is also displayed in current non-reductive analyses of causation that appeal to the idea that causes are to be understood in terms of interventions. I explain the extent to which the similarity weighting for

       



counterfactuals I propose is a successful characterization of the notion of intervention and question the motivation for approaches that take the idea of intervention to be primitive. I close the chapter by explaining how my approach to causal nonsymmetry can explain the fact that, metaphysically necessarily, causes usually precede their effects. My answer is that temporal direction is preponderant causal direction. I explain how this idea relates to two asymmetries of agency, an asymmetry of intervention and knowledge. I turn to the issue of the relationship between causation and laws in Chapter . I defend the claim that laws are potential patterns of causation characterized by the counterfactual analysis. I explain how the various accounts of law in the literature—or refinements of them—are not properly thought of as accounts of law but rather ways in which laws may be realized. The various potential counterexamples to Humean accounts of laws are best seen as appealing to worlds in which laws are not realized in the Humean way, rather than showing something about the nature of law. This point is particularly salient bearing in mind the intellectual difficulties of non-Humean accounts of law—such as independent necessitation between properties accounts or the powers ontology—and the fact that their virtues have been rather overstated. In particular, I bring this out with regard to counterfactual support and their alleged superiority in providing a basis for the rationality of induction. An outstanding issue in the discussion so far is the nature of chance. In Chapter , I argue that just as laws are variably realized so are objective chances: in the patterns identified by the best system analysis and in propensities. I focus on two problems, first the problem of undermining that is alleged to afflict Humean accounts of chance and, second, the relationship of chance to frequencies and, thus, to successful action. Although some propensity accounts can avoid undermining, they do so at the expense of the second relationship. More concessive propensity theories, I argue, make some headway with regard to the second problem but start to suffer from the first problem. The perceived advantage for agents in conforming their beliefs to chances, understood as propensities, is rooted in the same mistake about induction identified in Chapter . So the successful treatment of chance does not tell in favour of one theory of the laws that support them than another. In Chapter , I close by considering whether the position defended in the pages ahead—specifically taking the distinct existences principle to be a contingent truth (at best)—undermines attempts to provide a reductive account of modality. Is a coherent development of a reductive account of modality even possible within the present framework? I explain how this option is still open, down-peddling the significance of my approach for the principle of recombination, and explaining why the principle of recombination is unlikely to play successfully its role as a principle of plenitude in any event. If I am right, this failure is no particular problem for the reductive project. I defend the distinct existences principle against an argument that it is necessarily false and suggest, by comparison, we have more reason to believe in the possibility of worlds in which Humean supervenience is true and there is causation than in physicalism. The counterfactual theory of causation, and surrounding framework developed in the preceding pages, explains

     why this is the appropriate verdict at which to arrive. My hope is that, when you reach this point, you will agree with me. The close of the chapter outlines the ways in which we should understand the varieties of causation and sketches some implications for other metaphysical debates. Causation is one horizontally fundamental metaphysical category but there may be others. It would be good to find out.

 Humean Supervenience and the Possibility of Necessitation For some, the relationship between causation and necessary connection (or necessitation) between distinct existences is essential. There is no causation without necessary connection. For others, the whole idea of necessary connection between distinct existences is incoherent. Those who combine the view that our idea of causation essentially involves that of necessary connection and that such a notion is incoherent, often put forward revisionist analyses of causation. They remove the incoherent element and put something in its place. My own approach, drawn from Lewis, is to allow that such necessary connections are coherent but claim that whether or not they hold is a contingent matter (Lewis (b), pp. –). It is very natural to think of causation as involving necessary connection but it needn’t do so. A refined counterfactual analysis that allows for the possibility that causation is variably realized supplies all that we need. In some worlds there might be necessary connections between distinct existences in virtue of which the counterfactuals hold, but this should not lead us to suppose that there can be no causation in worlds in which this is not the case. While subsequent chapters will involve a defence of the claim that causation need not involve necessary connections between distinct existences—specifically, the success of the analysis of causation (Chapter ), the defence of sources of causal non-symmetry not derived from primitive non-symmetric chance-raising (Chapters , ), the defence of the best system analysis of laws as a realization of laws (..) and the Humean supervenience of chances (Chapter )—the present chapter is primarily a defence of necessitation accounts of causation against the claim that we have no coherent idea of necessitation and it is not possible between distinct existences. In Chapter , we considered the objection that counterfactual dependency was inadequate to capture our intuitive notions of causal necessity and sufficiency. The objection did not question the extensional adequacy of the account of causal necessity and sufficiency but rather whether the materials used were adequate to the task of capturing our intuitive notion of causal necessity and sufficiency. One way in which the account could be supplemented is to look for some further connection between cause and effect. For instance, it might be argued that causes must be spatiotemporally proximate to their effects or that there should be a certain kind of continuity of property. In Chapter  and ., I will argue that such accounts do not supply what is required. We should not insist upon spatiotemporal proximity because it is possible to develop an analysis of causation that does not require it. We should not

A Variety of Causes. Paul Noordhof, Oxford University Press (2020). © Paul Noordhof. DOI: 10.1093/oso/9780199251469.001.0001

        appeal to continuity of property because, first, this is compatible with a failure of the appropriate kind of causal dependency, second, causation may be present without it, and third, such an account appeals to the idea of transmission of a particular that either cannot be understood independently of causation or proves redundant (for the latter, see .). I reject straight appeal to laws in Section .. Aside from spatiotemporal continuity, these are all candidate-distinguishing features of causation that Mackie called somewhat misleadingly ‘necessity₁’ (Mackie (), pp. –). In the present chapter, I’m going to focus on the direct answer: what is missing is that causes necessitate their effects. I defend the coherence of this response but deny that this implies the inadequacy of the appeal to counterfactual dependency. I explain how the dependency is related to our grasp of the notion of necessary connection and argue that this explains why, in worlds for which Humean supervenience is true, we conceive of causes as necessitating their effects when, in fact, there is causation without this feature (.). For that reason, I start with the question of the relationship between what has come to be known as the doctrine of Humean supervenience, the denial of necessary connections, and the counterfactual theory of causation. In ., I will describe the thesis I wish to defend—the, at best, contingent truth of Humean supervenience and the denial of necessary connections between distinct existences— and contrast it with stronger theses. I note that what distinguishes my position from that of late-period Lewis is whether we have a coherent notion of necessary connections between distinct existences. . and . are addressed to this issue. In ., I argue that there are good grounds for supposing that we experience causation and we may, also, have experiences of necessary connection, albeit inaccurate or incomplete ones. So Humeans can’t appeal to the failure of our experience to reveal either as part of a defence of Humean approaches to causation. Our experience is not only compatible with the truth of necessitarian theories, it may provide evidence of their truth in this world. Having said that, the view of our experience of causation I set out in . also supports the claim that there might be causation in a world for which a Humean metaphysics is true. In such a world, there may be subjects who experience causation, possess the concept of necessary connection, and make what they take to be interventions in it. It would not seem radically different from a world in which a non-Humean metaphysics is true. So there is no easy argument for the claim that causation would be absent from such a world. Our causal talk would have ready application within it. Our experience of causation, and necessary connection, cannot be the basis for either a concept of causation or necessary connection. There are features of both that cannot be derived from experience even if experience provides grounds for their application. I explain what is involved in these concepts in . partly to show why this is the case and partly, also, to demonstrate that attributing an idea of necessary connection to subjects is coherent. The answer I provide explains why counterfactuals of the form I have discussed are the appropriate way in which to capture causal necessity and sufficiency, the point I adverted to earlier. The counterfactuals allow for the possible truth of a Humean metaphysics and explain why we feel we should want more.

       



As we shall see, our concept of necessary connection is neutral over whether it captures interworld resilience of patterns (e.g. Humean laws) or intra-world necessary connections between distinct existences upon which interworld resilience of patterns are based. So, finally, I turn to the question of whether any support for the denial of necessary connections between distinct existences is to be derived from a proper understanding of distinct existence. I argue that nothing in the proper understanding of distinct existence rules out intra-world necessary connections between distinct existences and there may be other theoretical considerations in their favour. This will conclude my preliminary defence of the claim that it is coherent and, as it will prove, attractive to develop a theory that insists on nothing stronger than the possible realization of causation in necessitations in nature.

. Humean Supervenience and the Denial of Necessary Connections The counterfactual theory of causation was developed by Lewis to explain how the existence of causation was compatible with the doctrine of Humean supervenience expressed as follows. All there is to the world is a vast mosaic of local matters of particular fact, just one little thing and then another . . . We have geometry: a system of external relations of spatio-temporal distance between points . . . And at those points we have local qualities: perfectly natural intrinsic properties which need nothing bigger than a point at which to be instantiated. For short: we have an arrangement of qualities. And that is all. There is no difference without difference in the arrangement of qualities. All else supervenes on that. (Lewis (b), pp. ix–x)

He names it in honour of Hume as the great denier of necessary connections (Lewis (b), p. xi). In a nutshell, we can formulate it as the claim that ‘Any world which is a minimal duplicate in terms of the qualities instantiated and their spatiotemporal arrangement of our world is a duplicate simpliciter of our world’ (cf. Jackson (), p. ). In other words, a duplicate of our world in terms of the qualities instantiated and their spatiotemporal arrangement which stops right there—by having no extraneous material—is a duplicate of our world. Qualities are relatively intrinsic properties that occupy spatiotemporal regions of relatively small extent. Thus the typical image proponents of Humean supervenience have in mind is of newspaper photographs made of filled in and empty pixels. In ., I will provide an account of intrinsic properties that serves to articulate further the motivation behind the doctrine and, in .–, I shall return to its proper formulation and assessment. Following on from the passage quoted above, Lewis writes I concede that Humean supervenience is at best a contingent truth. Two worlds might indeed differ only in unHumean ways, if one or both of them is a world where Humean supervenience fails. Perhaps there might be extra, irreducible external relations, besides spatiotemporal ones; there might be emergent natural properties of more-than-point sized things; there might be things that endure identically through time or space, and trace out loci that cut across all lines of qualitative continuity. It is not, alas, unintelligible that there might be suchlike rubbish. Some worlds have it. And when they do, it can make differences between worlds even if they match perfectly in their arrangements of qualities. (Lewis (b), p. x)

        My proposed formulation accommodates this point by allowing for the possibility that there might be other worlds, which aren’t minimal duplicates of our world, for which Humean supervenience fails. Strictly speaking, the doctrine of Humean supervenience should not be formulated in terms that imply that it is true of our world, if the compatibility of causation with Humean supervenience is all in which we are interested. A formulation that is neutral upon this point would be as follows. Humean supervenience holds of a world w when Any world which is a minimal duplicate of w in terms of the qualities instantiated and their spatiotemporal arrangement is a duplicate simpliciter of w. The counterfactual theory of causation may then be used to show that there is causation in w and, hence, the presence of causation in our world does not imply that Humean supervenience is false. It is a common presumption that if Humean supervenience is true, then there are no necessary connections between distinct existences (hereafter, the Distinct Existences Principle). The argument is rarely made explicit which is slightly puzzling. After all, in principle, nothing has been said to rule out the possibility that it is a relation between distinct existences that is supervenient upon arrangements of perfectly intrinsic natural properties. Probably, this option is taken as ruled out because, if necessary connections exist, they are an example of irreducible external relations. They could not hold in virtue of the entities—for example, the instances of qualities—they relate. I shall accept this assumption for now (see .., ., . for further discussion). A necessary connection between distinct existences would have the following character. A is necessarily connected to B iff either it is not possible that A exists and B does not or it is not possible that B exists and A does not (here ‘A’ and ‘B’ stand for distinct entities). Metaphysically necessary existents are necessarily connected because they exist together in all possible worlds. Unless it is denied that metaphysically necessary existents can be distinct—consider God, mathematical and logical entities as possible candidates—the principle is focused on contingent existents. Or, in a Necessitist framework in which all objects are necessary existents, its focus is on concrete existents and their necessary co-concreteness (i.e. spatio-temporal character) rather than existence (cf. Williamson (), pp. –). If there were necessary connections between distinct contingent or concrete existences, then, although these two entities fail to exist or be concrete in some world, and although they are distinct existences, at least one cannot fail to exist or be concrete when the other exists or is concrete. The necessity and possibility used to characterize the definition of necessary connection should be entirely unrestricted. That is not to deny that there is a possible definition which restricts our attention (say) to merely nomologically possible worlds and holds that if A is nomologically necessarily connected to B, then it is not nomologically possible for A to exist without B or vice versa. It is just that Humeans have not been interested in this more restricted characterization of distinct existence (unless, for reasons we shall discuss in ..–, and .. nomological necessity is a kind of metaphysical necessity). Thus Hume himself writes

       



There is no object, which implies the existence of any other if we consider these objects in themselves, and never look beyond the ideas we form of them. Such an inference wou’d amount to knowledge, and wou’d imply the absolute contradiction and impossibility of conceiving anything different. But as all distinct ideas are separable, ‘tis evident there can be no impossibility of this kind. (Hume (), pp. –)

If two objects, A and B, were nomologically necessarily connected, it would not be the case that looking at object A in itself (independent of the laws), it would imply the existence of B or vice versa. So the passage doesn’t commit Hume to the denial of nomological necessary connections. The denial concerns objects that imply the existence of each other and here the notion of a metaphysically necessary connection is relevant. In his initial list of ways in which Humean supervenience may fail, Lewis does not mention the existence of necessary connections. Indeed, he suggests that the denial of necessary connections between distinct existences is a necessary truth because it is ruled out by his principle of recombination, viz. any number of duplicates of anything coexists with any number of duplicates of other spatiotemporally distinct things size and shape permitting (Lewis (c), pp. –). He uses the principle to specify the extent of possible worlds. He writes ‘It is no surprise that my principle prohibits strictly necessary connections between distinct existences. What I have done is to take a Humean view about laws and causation, and use it instead as a thesis about possibility’ (Lewis (c), p. ). Lewis also makes his opposition to metaphysically necessary connections clear in his opposition to David Armstrong’s theory of law. I find its necessary connections unintelligible. Whatever N may be, I cannot see how it could be absolutely impossible to have N(F, G) and Fa without Ga. (Unless N just is constant conjunction, or constant conjunction plus something else, in which case Armstrong’s theory turns into a form of regularity theory he rejects). (Lewis (a), p. )

The second passage reveals that Humeans don’t object per se to calling something causal or nomological necessity and taking it to capture the tie between cause and effect. However, they want to know what people have in mind. The objectionable element is the claim that, if a potential cause necessitates an effect in circumstances C, then metaphysically necessarily, if the cause is present in those circumstances, the effect occurs. The Humean wants to know how, if the effect is a distinct existence from the cause, it cannot fail to occur in those circumstances. Lewis’ position seems to have softened by  in his discussion of the occupants of what he calls the ‘biff ’ role, that is, the intrinsic relation between distinct events that is associated with probabilistic counterfactual dependence. Lewis writes ‘It might be a Humean supervenient relation. Or it might be a relation posited by some antiHumean metaphysic of nomological necessity . . . Myself, I’d like to think that the actual occupant of the biff role is Humean supervenient, physical and at least fairly natural’ (Lewis (b), pp. –). He makes clear in a footnote that he has Armstrong’s position in mind (Lewis (b), p. , fn. ). The passage suggests that while, in the actual world, he hopes that the occupant of the biff role will be Humean supervenient, in other possible worlds there might be different occupants

        for which a denial of necessary connections between distinct existences would be false. At its most basic, Humean opposition to necessary connections between distinct existences in causation can come in at two levels and two strengths. At the level of ideas, the claim is that metaphysically necessary connections between distinct existences is incoherent. At the level of contingent entities, the claim is that metaphysically necessary connections between distinct existences are impossible. This gives rise to map of the main options in Figure .. The passage I have already quoted from Lewis’ earlier work indicates why it is legitimate to put him in the ‘Yes-No’ combination right-hand box. Here is a familiar passage from the Treatise that justifies placing Hume there. ‘These ideas [of necessity, of power, and of efficacy] . . . represent not anything, that does or can belong to the objects, which are constantly conjoin’d’ (Hume (), p. ). There is a substantial body of scholarship that questions Hume’s commitment to anything that might be classified as Humean in the sense specified above and below. However, the

Causation: Necessary Connections between Distinct Existences

Incoherent?

Yes Possible?

No Possible?

Yes

Figure .

No Empty Position A?

No Hume/Early Lewis

Powers Ontology

Yes -Actual/Necessary ‘New Hume’

Late Lewis Favoured Position in Book

Yes - Only Possible Empty Position B

       



widespread characterization of the principle on which we are focusing as Humean would render any eschewal of this title as unnecessarily distracting (e.g. as well as the passages above, Lewis (c), p. , Armstrong (), pp. , , –; Wilson ()). There are also good grounds for supposing that Hume was a Humean so it would be a shame to abandon the name in any event (Millican ()). The placing of Late Lewis in a left bottom box is both controversial and of particular interest because it is close to the position adopted in this book. We differ over whether there is any incoherence at all. I shall discuss it after I have examined the motivation for the other positions. I know of no philosopher who combines the claim that it is coherent, or only contingently incoherent, that there should be necessary connections between distinct existences with the claim that, necessarily, there are no necessary connections between distinct existences (Empty Position A). Nevertheless, it seems to me that this combination of views is tenable for anyone who allows that if something is a conceptual possibility, then it need not be a metaphysical possibility. Such a thinker allows that subjects may have concepts of things that do not fully reveal their natures. In which case, we may have concepts of causes and effects that leave open the possibility of a necessary connection between these distinct existences. Nevertheless, it may still be the case that necessary connections between distinct existences are not possible. The combination of necessary incoherence with the contingent truth of there being necessary connections between distinct existences seems structurally similar to the position that some people attribute to Hume in the Enquiry (e.g. Wright (), ch. , pp. , –, ; Craig (), ch. ; Strawson ()). There are, however, important differences. First, according to this view, although Hume emphasized that we could not form an idea of necessary connections in nature, he did allow that we might form a ‘relative idea’ of items in the external world (of which necessary connection may be one) (Hume (), p. ). Also he did not consider the question of whether it is possible to form an idea of necessary connections between distinct entities but only considered whether we could. According to this alternative reading of Hume, although he allowed that there were necessary connections between distinct existences, he did not think we could know them. Presumably, though, if he is prepared to allow that there are necessary connections between distinct existences, he is also prepared to allow that there might be worlds in which there are no necessary connections between distinct existences. It is just that he had little interest in them. If he is prepared to allow that there might be such worlds, then given his view about our ignorance about necessary connections in our world, it is a short step to concluding that, as a matter of contingent fact, there are no necessary connections in our world although we naturally suppose that there are. That would give us apparently Empty Position B. My own position is a development of late-period Lewis’ position. Where we differ is that I deny that there is any incoherence in the idea of necessary connections between distinct existences. For me the question is: have we any grounds for recognizing their presence? To establish the coherence of necessary connections between distinct existences, I shall begin by discussing whether we have an experience of necessary connection or a concept of necessary connection. Lack of

        both would threaten both the coherence of the claim that there may be necessary connections between existences and remove the grounds for supposing that there are. I shall argue that, in fact, we have both. Nevertheless, that does not mean that there are necessary connections between distinct existences. So I then turn to the question of whether there are more direct grounds for supposing that there are not because of what is involved in distinct existence. I argue that the only plausible accounts of distinct existence don’t rule out the possibility of necessary connections between distinct existences. As noted earlier, I postpone the question of whether a successful analysis of modality requires the necessary truth of the denial until .–. I end by noting how my account of the concept of necessary connection provides an explanation of how the counterfactual theory of causation may avoid the charge that it doesn’t capture our intuitive notions of causal necessity and sufficiency: the matter hanging over from ...

. Experiences of Causation and Necessary Connection Perception is factive. If I perceive O being F (or that O is F), then it is the case that O is F. The issue of present concern is not whether we perceive causation, and necessary connection, but rather whether we experience either of them and the relationship between these experiences. Experiences of causation and necessary connection may be perceptions but it is possible that they are not. For example, we might experience e₁ causing e₂ but it is an illusion that e₁ is causing e₂. Indeed, as we shall shortly see, the most famous experimental work on the experience of causation plausibly falls under this category. The question of whether we have an experience of necessary connection is in principle distinct from that of whether we have an experience of causation. If necessary connection, in fact, is no part of causation, then this is more or less uncontroversial. However, even if necessary connection is an essential feature of causation, it doesn’t follow that, in order to experience causation, we should experience necessary connection. It may be an essential feature of me that I have the parents that I do and an essential feature of gold that it has the atomic number  (Kripke (), pp. , –). Experience of either does not require experience of these features. The point is important because it is generally assumed that Hume’s fundamental claim was a denial that we experience causation and that, in pointing out that Hume was wrong about this (or about the observability of particular types of causation like pushings and pullings), we have exhausted the interest of the issue (e.g. Ducasse (); Anscombe (), pp. –; Strawson (), pp. –; Mellor (), p. ; Armstrong (), p. ; Menzies ()). We have not if there is a separate issue of whether we experience necessary connection. We might fail to experience the latter and yet it is still appropriate to characterize our experiences as experiences of causation. To fix ideas, let us stipulate that the phenomenal content, or character, of an experience, at least partly, specifies what it is like to undergo the experience. One target thesis, which we may call the Causal Phenomenal Content, holds that

     



some experiences have a phenomenal content that is correctly characterized either by (a) particular types of causal relations e.g. pushes, pulls, stops, supports, etc. or (b) the causal relation expressed by ‘–causes–’ itself. The Necessary Connection Phenomenal Content thesis holds the equivalent for necessary connections. This characterization of the issue is meant to be neutral over various accounts of the phenomenal content of experience, for example representationalist or relationist (i.e. whether the phenomenal content is determined by representations or brute relations of awareness) (Tye (), chs , ; Dretske (), chs , ; Martin (), Fish (), pp. , , and so forth). Indeed, it is compatible with allowing that these phenomenal contents are determined by qualia that characterize a particular way in which relations between events are experienced: the causal or necessary connection way respectively (see Block for such a view of qualia, e.g. Block ()). It also brackets the issue of whether any phenomenal contents should be characterized by the causal relation in general as opposed to specific causal relations like pushing and pulling. Some philosophers allow for the latter but not the former (e.g. Fodor (), p. ). When one ball strikes another and the other moves off, when we flick a switch and the light goes on, when we drop a book into water and the pages become soggy, our experiences are correctly described as having a phenomenal content involving causation. It may be that these experiences are mistaken. The second ball would have scooted off anyway. Somebody else flicked the light switch. The pages are water resistant but happen to undergo a similar physical transformation for other reasons. Nevertheless, our experiences aren’t neutral on the issue. These phenomenological observations accord with the experience of many philosophers writing on the issue, for example those mentioned above and Susannah Siegel (Siegel (), pp. –). It has also been empirically investigated, most famously by Albert Michotte (Michotte ()). To give one central illustration of Michotte’s empirical work, Michotte investigated what he dubbed launching (Figure .). A square A is displayed on a screen travelling towards another square B. On A becoming coincident with B, B moves off. Most subjects described their experiences as seemingly involving A causing B to move. This experience vanishes if A stops short of B before B moves off, there is a time lag between A’s becoming coincident with B and B moving off, or B moves off at a significantly different speed, etc. The fact that subjects describe their experiences in this way doesn’t mean that the phenomenal content of their experiences includes causation. An alternative is that they arrive at a rapid judgement. However, there are considerations that speak in favour of the causal phenomenal content thesis. First, phenomenal content involving causation displays the two distinctive features of phenomenal content involved in the experiences characteristic of perception: nonneutrality but non-subject committing. It makes a claim about the way the world is— that there is causation in it—and hence is not neutral on this subject. This feature distinguishes it from thought and imagination. Nevertheless, unlike the case of judgement, just because the content has this feature, it doesn’t follow that the subject having the state with this phenomenal content is committed to the world containing causation between the entities so characterized, for example, the moving squares. Indeed, the subject may be aware of the fact that the entities aren’t causally related.

       

Figure .

These two features should not be taken to be a feature of all experiences. Sensuous imaginative experiences—for example, visualizing something to be such and such a way—do not display non-neutrality. Sensuous imaginings are neutral on how the world is. The features are characteristic of experiences that may fall short of perceptions by failing to be factive e.g. hallucinatory experiences. Certain kinds of relationists about experience may be unhappy about putting the matter this way because they deny that hallucinatory experience has content. Nevertheless, they may concede that hallucinatory experiences are subjectively indiscriminable from (genuine) perceptions in part because hallucinatory experiences seem non-neutral and yet the subject of experience is not committed to the truth of what is experienced. Second, a distinctive feature of at least some perceptual processes is that they are relatively informationally encapsulated, and hence, modular (Fodor (), pp. –). The experiential states that arise as a result of them aren’t affected too much by the beliefs we have. That’s why we continue to experience the Müller-Lyer illusion even when we know that the two lines are equal.

Figure .

So, similarly, subjects know that Michotte’s moving squares aren’t actually causally related to each other. Nevertheless, they experience the movement of the squares to be causally related. Moreover, there is evidence that such experiences are present prior to any plausible time at which subjects may be attributed the concept of cause, at six months of age (Leslie and Keeble (), p. ). For ease of reference, let’s dub the claim that there are states with causal contents that are the outcome of modular processes the Modularity Hypothesis.

     



The Modularity Hypothesis has been challenged. There are individual differences over the extent to which subjects report experiencing causal relations in these circumstances. Some subjects appear to take a more analytic approach to their experiences and are less inclined to characterize what they experience in causal terms (Gemelli and Cappelini ()). Higher intelligence has also been found to be related to a failure to report experiencing a causal connection (Beasley ()). In experimental work in which the apparent support of a model bridge is removed, with the bridge subsequently collapsing, the extent to which subjects report experiencing causality, as the time lag between removal and collapse increases, often depends upon imaginative engagement and their experience of longer or shorter delays before collapse, in between the assessment periods (e.g. Gruber et al. (), Powesland ()). The suggestion is that, if perceptual processes giving rise to experiences of causation were modular, there would not be this variation. These observations are inconclusive. The changes to the threshold beyond which spatiotemporal discontiguity removes the experiences of causation can probably be explained by sensory adaptation and, thus, don’t undermine the case for modularity (Schlottmann and Anderson (), p. ). It is plausible that we can explain individual differences due to analytic attitude, or intelligence, by noting that such subjects may well be considering whether the experience of causation is an experience of necessary connection. We will come to this shortly. Variation may also arise due to the relative impoverishment of images putatively suggestive of causality in the experiments and the experimental prompts/verbal requests the subjects receive (White (), p. , see Gemelli and Cappelini (), Beasley (), for illustrations of different verbal prompts). In any event, individual differences don’t rule out the modularity hypothesis. Modular processes need neither be innate nor uniform (Scholl and Tremoulet (), p. ). They can be tuned in different ways during the course of development (Scholl and Leslie (), p. , see Schlottmann (), for a more sceptical note). Further support for the modularity hypothesis stems from a variation on launching experiments that shows that experiences of causation are dissociated from judgements of causation (Schlottmann and Shanks ()). In a preliminary experiment, the time lag between A becoming spatially contiguous with B and B’s motion was varied. However, a colour change of B, from red or blue to black, always occurred temporally prior to B’s motion in one set of cases. Even so, subjects’ experiences of causality were dependent upon the time lag between the spatial contiguity of A and B and B’s motion in spite of the fact that the colour change of B always predicted whether B would move in that set (Schlottmann and Shanks (), pp. –). This demonstrates that the dependency of experiences of causation on particular features of the causal situation is not significantly altered if there is another feature, which is unrelated to taking A as colliding with B, that is a better predictor of the effect, even when subjects might reasonably take this other feature to support a causal judgement that the effect will occur. In a second experiment, this fact was drawn to the subject’s attention. Subjects were asked whether spatial contiguity of A to B was necessary for B to move and how convincing particular launch events looked. It was pointed out that the display was the result of a programme that might make colour change rather the spatial

        contiguity necessary. It was found that launch events looked convincing cases of causation for the smaller delay in the movement of B whether or not B’s movement was contingent upon A’s. By contrast, in response to the question of how necessary the movement or the colour change was for B’s movement, subjects’ judgements varied depending upon whether the movement was contingent upon A’s movement or colour change. These were taken to be causal judgements. As a result, Schlottmann and Shanks observed a dissociation between subjects’ experience of causation and judgement of causation. This supports the claim that experiences of causation are informationally encapsulated (noted by Menzies (), p. , although, puzzlingly, he takes the judgements to be judgements of correlation not causation). Of course, the evidence is contestable. Woodward argues that the dissociation of experiences of causation from causal judgements just mentioned is the basis for two distinct conceptions of causation: causation involving mechanical processes and causation as difference-making (Woodward (), pp. –). The latter conception of causation is targeted by questions like ‘Would B’s movement occur without A moving?’. If two conceptions are at work, then there is no particular reason why judgements about causation in the difference-making sense should have any impact upon the judgements we make about how we experience launching, or, indeed, other, effects and vice versa. In which case, the dissociation would not be evidence that our experiences of causation are the outcome of modular processes. Since experiences of causation arising from cases of launching are present in mature subjects, the success of the two conceptions response depends upon such subjects plausibly failing to integrate their experience of the continuities indicative of mechanical processes with the idea of difference-making. Like Woodward, I think that there are little grounds for supposing that this is the case. The integrated account I develop during the course of this book constitutes my full defence of this claim. For now, I just highlight three elements. First, the discussion of pseudo-processes, and the implicitly causal notion of transfer, explains why continuities indicative of mechanical processes cannot provide an independent basis for causation (see .). Second, there are cases of causation that don’t involve such continuities (see .). Third, those cases that are said to motivate a process account of causation in fact cannot make good on these claims but can provide supplementary materials for the successful development of the counterfactual approach (see .. and .). For this reason, the modularity thesis retains support from Schlottmann and Shanks’ work. There are two further grounds for supposing that we experience causation. The first is that experiencing a certain sequence as causal has been found to generate illusory ‘causal’ crescents. In this case (Figure .), a circle moves from the left into the centre of the display, covering a circle in the centre to a certain degree and stops. The degree may be varied and includes completely covering it. The circle in the centre moves off when the target degree of coverage is reached, travels to the right, returns, and covers the circle stopped in the centre to the same degree, the circle returns to the left and the cycle is repeated. If subjects take the movement to be noncausal and one circle travels until completely covering the other, then the circle is seen as passing over the other in spite of the fact the circle passing is seen as changing colour (Scholl and Nakayama (), p. ). The context in which this cycle occurs

     



Figure .

varies. A key one involves lower down, synchronous with one circle covering another, a standard case of launching. Subjects are asked to estimate the size of the crescent still revealed of the covered circle. It was found that the size of the crescent was overestimated when the sequence, it is hypothesized, is experienced as causal due to the launching context. Even when one circle completely covers the other, if the sequence is experienced to be causal, then a small crescent is seen. When this context is not present, the size of the crescent is more accurately identified although still overestimated (Scholl and Nakayama (), pp. –). It is hard to deny this is an experiential effect given the properties experienced. There is also evidence that the effect is due to the workings of our sensory apparatus rather than a result of at least some types of cognitive penetration. The launching context does not give rise to a judgement that there is causation between the launching and launched event. The effect of the context seems to be a consequence of a state that is both non-neutral but not subject committing. As subjects in this experiment aren’t asked for their verdicts as to whether or not they are experiencing causal connections, there is further reason for not supposing that a thought about causation is in play. Instead, it seems that when the visual system treats one item as the cause of another, it makes assumptions about what is physically possible. Total overlap, or for that matter significant overlap, seem either impossible or less plausible if the first is the cause of the second. This suggests that it is the visual system that is identifying something as a cause of something else and not a judgement we make on the basis of experience that, in itself, does not attribute causation to the entities it concerns (Scholl and Nakayama (), pp. –, Macpherson (), p. , for a similar response in other alleged cases of cognitive penetration). The final reason for supposing that we experience causation is that it displays the characteristic features of categorical perception. Speech perception is a good example of the latter. Although auditory signals may vary in properties in various dimensions in a host of small ways, our speech perception is extremely sensitive to certain of

        these changes—the changes in frequency involved in the shift from ba, to da, to ga for example—presenting it as a difference in phonetic categories even though they are no more different than other shifts along the dimension in question. Difference of context, such as the speaker’s dialect or rate of speech, also has a distinctive role in determining which phonetic gesture—as it is dubbed—a particular speaker is perceived to make, for instance, ba (Butterfill (), pp. –). Similarly, Stephen Butterfill notes, the presence of spatiotemporal contiguities and the context effect noted in the case of illusory causal crescents gives rise to experiences of causation where other, no lesser, differences in these features lack similar striking presentation (Butterfill (), pp. –). The best explanation of features of our experience, then, is that it involves a species of categorical perception relating to causation. Although there are good grounds for supposing that we experience causation detailed above, there is no doubting that philosophers have denied it. Here is Hume: ‘No object ever discovers, by the qualities which appear to the senses, either the causes which produced it, or the effects which will arise from it’ (Hume (), p. ). How is this possible? Do people have genuinely different experiences? In the absence of strong evidence that this is so, a better explanation is that philosophers feel compelled to deny that we experience causation for one of two reasons. First, if causation is an extrinsic matter, then it seems we should not be able to experience it when we focus on things that do not reveal the extrinsic character of causation. Suppose, for the sake of argument, that if there is causation, then there is a regularity, that is, if c causes e, then Cs cause Es. Then how might we experience that c causes e just as a result of currently experiencing c and e? It might just seem impossible (for an expression of this line of thought, though not agreement with it, see Beebee (a), pp. –). Second, if causation is an intrinsic matter, then, it might be argued, we would have to experience the necessary connection between cause and effect. But we don’t experience that. The second reason helps to explain why the issue of whether we experience causation has been conflated with the issue of whether we experience necessary connection. The first reason fails to withstand scrutiny. The fact is that there are cases in which we do experience something to have extrinsic properties as a result of sensory stimulation by its intrinsic properties. When somebody talks to us in a language we understand, we generally experience that their words, phrases, and sentences have the meanings that they have. We needn’t experience the referents of those words, if they have them, but we do experience them to be referring to this or that (O’Callaghan (), pp. –). The phenomenal content we undergo as a result— which may be auditory, something common to auditory and the visual experiences we have on reading words, or some extra-sensory content—displays the distinctive characteristics of a phenomenal content of perception. It is both non-neutral and non-subject committing. It is not neutral about whether or not the words, phrases, or sentences have meaning. It claims that they do. Yet, subjects may appreciate they are undergoing an illusion. They may know that the noise is not an utterance of a language they understand but some other language, or the sound of running water, or whatever. Indeed, it is very hard to hear the sounds to be shorn of meaning. The observation that we experience meanings in this way doesn’t imply that we should distinguish between auditory experiences of utterances we understand, and

     



ones we don’t, in terms of meanings. As Casey O’Callaghan points out, there will be other ways in which we can distinguish the distinct phenomenal contents of our auditory experiences, in particular, the language-specific phonological attributes of spoken utterances to which speakers of the language are sensitive, and others may not be (O’Callaghan (), pp. –). It is rather that a certain mental state must be recognized—an experience of meanings having the distinctive phenomenal contents of perceptions—regardless of whether it should be classified as an auditory experience. O’Callaghan’s point that our auditory experience of homophones—like bank (money/river); pole/poll (rod, place on earth, vote)—does not differ regardless of which meaning we hear an utterance to have does not undermine, nor does he envisage it to undermine, this claim. We can be neutral over whether the additional meaning content is part of the auditory experience or a distinct state (for similar considerations that would apply to this case in favour of the former, Noordhof (), pp. –). The key point is that, however the matters above are resolved, the meaning of the words depends upon extrinsic facts such as how they are used in a whole variety of situations. Presumably we can have such experiences because our perceptual processes make general assumptions, perhaps partly as a result of previous experience, about these extrinsic matters in interpreting sensory input. Thus in order to experience that c causes e, we don’t (now) have to be picking up information about the matters of fact which must hold in order for causation to be present. The assumptions in play in our perceptual processing of causation need not be correct. We are focused on the question of whether we have experiences of causation, not whether these experiences are perceptions of causation, which, thereby, place us in a position to arrive at knowledge. Nevertheless, although our experiences of causation may be less reliable than our experiences of some other things, it should not be assumed that when experiences of causation are perceptions of causation, their capacity to confer knowledge is much reduced compared to perceptions of other things. There is a temptation to claim, as Christopher Peacocke does, that experiences of causation can only be a basis for knowledge if the subject has grounds for taking his or her experiences of causation to be reliable indicators of the presence of causation in the world, which may come down to whether the relevant laws hold (Peacocke (), pp. –). However, if we require confirmation of the assumptions made by our perceptual systems here, it is hard to see why this would not undermine the claims for perception to be a basis for knowledge everywhere. Perceptual mechanisms make assumptions about the world to generate most perceptual experiences. Most of these assumptions would be equally hard to justify. If the assumptions of our perceptual systems are generally true, and thus sufficient to make our experiences reliable, and, perhaps, there is an evolutionary story to tell about why these assumptions are generally true, then this may provide a basis for taking our perceptions to put us in a position to arrive at knowledge. If that’s right, then there is little reason to view our experiences of causation as particularly suspect. The line of response does raise a new difficulty. It might seem that if we do perceive causation, we are in a position to answer inductive scepticism. The inductive sceptic claims that, if I am presented with a C, I have no reasonable grounds for supposing that an E will follow (just because, for instance, previous Cs caused Es). If, amongst

        the extrinsic facts required for c to cause e, is a regularity such as all Cs cause Es, then a perception that c caused e will entail that future Cs cause Es. In which case, perceiving one of those future Cs, will give me grounds for supposing that an E will follow (Beebee (a), pp. –). The worry is that our putative perceptions of causation are too slender a basis for a victory over the inductive sceptic. One response to this concern is to allow that perception provides knowledge of causal relations in certain contexts but not those in which inductive scepticism is raised. The same reasons that we have for claiming that we don’t know that a certain causal regularity will hold are reasons to hold that we don’t have a perception of an instance of that regularity (Beebee (a), pp. –). The response just given extends to all dogmatist responses to scepticism. They hold a version of the following thesis. (D) If it seems to S that o is F, then S is entitled, or prima facie justified, to judge or believe that o is F. Perceptions of causation provide perceptual seemings to which this thesis would apply. In which case, they are not undermined by sceptical contexts but provide an answer to such a challenge. The argument would proceed as follows. () c causes e (remembered content of perceptual seeming). () If c caused e, then all C-events are regularly associated with E-events (conceptual truth about causation). () There is a C-event (now) (content of perceptual seeming). Therefore, I am entitled to believe that () There will be an E event. Other sceptical issues would still arise, for example, relating to memory to which appeal is made in (). But the argument provides a response to inductive scepticism using general resources to which a dogmatist may appeal. Although I don’t want to support a dogmatist position here, I think that a satisfactory response to the concern raised should not rest upon the unacceptability of the dogmatist response to scepticism in general. Moreover, the fact that the reasons for rejecting candidate-inductive knowledge like there will be an E are reasons for rejecting the claim that it seems that c causes e, does not imply that we have no entitlement to believe that there will be an E. In contexts in which inductive scepticism is raised, I may have reason to doubt that I perceive causal relations but, if I perceive them, then I have reason to believe that inductive scepticism is false. It is just that I cannot justify this claim appropriately, or answer the sceptic. The worry is that we shouldn’t even be able to say that somebody perceiving a causal relationship has reason to believe that inductive scepticism is false. A better response is to note the following. Even when we experience a causal relationship, we often have no idea of the generality which it supports: how extensive it is, for instance, whether it extends into the future; the required background conditions; and which of the many features of the cause are relevant. Of course, we

     



may have some idea, but not of all the factors that would allow us to conclude that things will behave in such and such a way in a new case. So prior perception that c caused e plus a future perception of a C would give no grounds for supposing that an E will occur. Of course, knowing all the rest of this stuff would, when coupled with a perception of a C, give us grounds for believing an E will follow. However, it is this latter knowledge (call it B) that the inductive sceptic will challenge. In brief, just because our perception that c caused e depends upon prior assumptions, in some way approximating to B, it doesn’t follow that we have grounds to believe B on the basis of perceiving that c caused e. Moreover, there is the possibility, which cannot be ruled out, that c caused e is a case of brute singular causation. In which case, there will be no B to cover this case even if it was only perceived to be a case of causation because of standard assumptions made by the perceptual system. So the problem with the argument lies finding a version of premise () that is untouched by inductive scepticism. I hope to have taken away one reason for rejecting the claim that we perceive causation, and a putative consequence of it, its provision of a response to inductive scepticism. I noted that the second was that it is assumed that, if we experience causation, we should experience necessary connection. Those who take themselves to experience causation mostly reject this assumption. Those who deny that they experience causation make it. Of course, if our experience of causation does not require that we experience all properties that causation may have, then the same may be true for necessary connection. In this sense, experiences of causation may be experiences of necessary connection, without experiencing the necessitation involved as part of the phenomenal content of experience. However, their putative failure to have such an essential part of necessary connection threatens their status as experiences of it. By contrast, experiences of causation have many other features that incline people to believe they are experiencing it. I have already explained why experiences of causation don’t involve experiences of necessary connection. Now I want to go on to explain why people mistakenly deny that they experience necessary connections at all. It is plausible that they may do on some specific occasions. Hume speaks for many, I think, when he writes When we look about us towards external objects, and consider the operation of causes, we are never able, in a single instance, to discover any power or necessary connexion; any quality which binds the effect to the cause and renders the one an infallible consequence of the other . . . we could foresee the effect, even without experience; and might, at first pronounce with certainty concerning it, by mere dint of thought and reasoning. (Hume (), p. )

This suggests that he makes a second, supporting, assumption (Fales suggests something similar (), p. , Mackie dubs it necessity₂ (Mackie (, ), p. ). If we experience a C necessitating an E, then our experience of a C would provide a priori indefeasible grounds for concluding that an E will occur. The appeal to the a priori in the characterization of this second assumption might seem to be an obvious mistake. What it is meant to indicate, though, is that given an experience of C, we need no further experience in order to have indefeasible grounds for concluding that E will occur. For instance, we need no experience of a constant conjunction between previous Cs and Es.

        We can see the assumption at work in Hume’s discrediting of the most natural examples to give the experience of necessary connection: our experience of our will over our own bodies and our experience of pressure upon or resistance to us. In the first, it seems very natural to say that we experience exerting ourselves in trying to do certain things—especially things that are proving difficult to achieve physically. In the second, that we experience bodies pressing upon us, or resistant to, what we are trying to do. The experiences in each case point to a certain outcome. Our experience of our exertion seems to convey to us a direction of activity and our experience of resistance or pressure upon us seems to convey to us that a certain outcome is being resisted or that a certain outcome is being forced upon us. Hume writes of the effect of our will on our bodies: ‘the effect is there distinguishable and separable from the cause, and cou’d not be forseen without the experience of their constant conjunction’ (Hume (), p. ) and of resistance to us: ‘This sentiment of an endeavour to overcome resistance has no known connexion with any event: What follows it, we know by experience, but could not know it a priori’ (Hume (), p. , fn. ). In both, Hume emphasizes that we could not foresee a priori what would follow. We may will our arm to move, experience our exertion (especially if somebody is holding the arm down), and yet it is always conceivable that the effect does not follow. It is easy to understand why the assumption is a natural one to make. If I experience e₁ as necessitating e₂, it would seem that I should experience that e₂ must occur. It is conceivable that e₁ occurs without e₂ occurring but, when it fails to occur, that’s because e₁ no longer necessitates e₂ and hence the necessitation is not there to be experienced (bracketing issues about indeterminism). Yet, it is hard to see how to square this with the phenomenological facts of our candidate experiences of necessary connection. They might not supply us with an experience that shows how e₂ must occur but they certainly are not neutral over whether or not e₂ occurs. As we already noted, things appear to point in the direction of its occurrence. Even some of those who come down on Hume’s side regarding our experience of necessary connection, acknowledge the naturalness of this way of putting things with our experience of a force vector such as pressure (Armstrong (), pp. , –). Evan Fales suggests that our experience of necessary connection does not provide a priori grounds for the putative effect because it does not rule out the possibility that some required background conditions are not met. To take his example, suppose that somebody is pushing your head with their hands. If your head had imperceptible support, it would not move back. So you could not conclude from the experience of pressure that your head must move back. Nevertheless, the experience of pressure is an experience of necessary connection. If you exclude the possibility of imperceptible support, then the transition from our experience to a belief that the head will move is indefeasibly a priori justified (Fales (), pp. xi–xii, –, esp. , ). Fales’ conclusion misrepresents what our experience is like in the other direction to Hume. What we experience—the pressure—does not appear to make alternatives impossible given the right background conditions are met. For all that pressure inclines things to go in a certain direction, it still seems not ruled out a priori by our experience of it that something else happens instead. Moreover, it is not at all clear why we should experience any inclining towards an outcome if the background

     



conditions aren’t met. If what we are experiencing, when somebody is pressing upon our forehead, is the resultant force, then, when our heads are imperceptibly supported, we should experience no force for movement. Putative causes are necessitating given certain circumstances. They don’t have a circumstance-independent necessitation that we can experience come what may. Alternatively, if we are experiencing the contribution of one force, which may be offset, then we are not experiencing a necessary connection at all but just whatever one particular cause brings to the circumstances: what we might call a necessitation-determiner. Interpreting our experience of a force as a necessitation-determiner rather than the resultant force has, as a consequence, that our experience of a cause’s contribution given the circumstances is incomplete. There is empirical support for this. Peter White has pointed out in his psychological work on our perception of forces that, by Newton’s Third Law, when subjects push a body along the ground, an equal and opposite force is exerted on them by the body they push. However, what they experience when pushing the body is that the body resists, rather than exerts a force on them, and the resistance is experienced as overcome by the force they are exerting. The force they are exerting on the body is experienced to be greater (White (), pp. , ). In fact, what is greater is the force they are exerting on the body compared with force on the body that is the result of the friction supplied by the ground. White’s work shows how this incomplete perception of the forces involved in agency is taken across to subjects’ experience of forces in launching events by drawing on their responses to rating scales about the forces and resistance involved (White (), pp. –). These observations may incline the unwary to suppose that, in fact, we never experience causal necessitation and, perhaps, conclude that there is no such thing to be experienced. However, there are considerations on both sides. In the circumstances in which we successfully act, overcome resistance, or are forced to move in a certain way, there is, in fact, no failure in the background conditions required for the outcome to occur. In that context, the operative cause determines that the outcome occurs and our experience of no impediment, or an overcome impediment, testifies to the presence of the appropriate background conditions, as well as the cause, for the cause to necessitate the effect. Yet, on the other hand, as I noted, it does not seem as if we are experiencing necessitation. This leads me to entertain an alternative. We experience causal necessitation while misrepresenting, or not fully representing, its character. We experience a cause as bringing about an effect but not in such a way that it is sufficient for the effect to occur. In Anscombe’s terms, we experience it as enough for, but not determining, the effect. This might suggest that that our putative experience of necessary connection is better thought of as a veridical representation of probabilification rather than an experience of necessitation (e.g. as making the chance of the cause over .).¹ However, important differences between necessitation and probabilification are reflected in our experience.

¹ I’m grateful to Steve Barker for raising this possibility.

        First, when something presses upon our bodies, the connection between the impinging item and ourselves is experienced to be complete. By contrast, one event can probabilify another event even though, in fact, the causal chain between them is incomplete. Our experience can be neutral on completeness while presenting probabilification. So, in the case of our experience of pressure, we don’t simply have an experience of probabilification. Second, probabilification involves the idea that there is no causal redundancy. For instance, if there exist competitor causal chains that would cause the effect to occur, even if the actual cause were absent, there is no probabilification. It is no part of our experience of pressure that there is no redundancy (and hence probabilification). For these reasons, our experience is better characterized as an experience of necessitation whose character is, in some way, not fully represented or misrepresented. One development of this thought would suggest that our experience fails to represent the highly probabilifying character of the cause as , another would suggest that our experience misrepresented the cause as failing to probabilify the effect with probability  (or giving it a probability less than ). The former development is maybe more plausible partly because it involves less commitment to what is represented in experience and partly because the content of experience is that the cause is enough for the effect but with no representation of the effect’s probability as a result of the cause. The points will be clearer when I develop the analysis of causation in Chapter . However, taken together they suggest that our experience may present causal necessitation but fail to represent its probabilifying character of, in the case of deterministic causation, . Further support for my attribution of content is provided by the distinction I drew in . between the conditions under which it is appropriate to attribute a concept of some item in the world and what is required to understand the nature of the item in question. Once it is appreciated that experience need not supply the latter, and indeed that the latter can be given a characterization independently of experience, then there is no motivation to deny that experience in some way inadequate to what is experienced cannot be an experience of the thing in question: causal necessitation. A consequence of my proposal is that our experiences of necessary connection may provide defeasible a priori justification for beliefs in the existence of effects. They just don’t provide indefeasible justification. This is quite compatible with, in fact, causes failing to necessitate their effects. Recognition that our experiences have this content, which may, in part, explain why many find Humeanism so implausible, does not imply that the content is veridical. We could have non-veridical experiences of something whose character is not fully represented. The proposal is also compatible with the existence of a certain kind of inductive scepticism. For one thing, the experiences of necessary connection I have identified are limited, for example, experiences of pressure or the will. Moreover, while, in experiencing a necessary connection, we may have defeasible a priori grounds for supposing that a certain effect will occur, it does not provide us with such grounds regarding the pattern of events that will hold in the future. A necessary connection between types of events need not persist. I shall discuss this matter further in the chapter on causation and law (..).

    



. The Concept of Necessary Connection One way of seeking to resolve the question of whether we have the concept of necessary connection is to identify its origin a priori or in experience. Given what I have argued in the previous section at the end, its origin in experience is problematic. Suppose that we have a concept of necessary connection in the following sense. When we have experiences involving necessary connections, we are inclined to make certain judgements with a common conceptual constituent C. Although this may be sufficient to attribute to a subject the concept of necessary connection, it would not imply that they had the appropriate understanding of the concept as involving a connection invariable across changes in circumstances. This is a natural consequence of experience’s failure to represent the appropriate probabilification in even the most favourable circumstances such as pressure upon our bodies or our actions. It also supports scepticism about any attempt to arrive at a concept of necessary connection a priori. As Hume remarks, ‘When we reason a priori, and consider merely any object or cause, as it appears to the mind, independent of all observation, it never could suggest to us the notion of any distinct object, such as its effect; much less, show us the inseparable and inviolable connexion between them’ (Hume (), p. ). Any concept of the connection between distinct objects we derive from experience will not be something which, reflecting upon it a priori, reveals an inseparable and violable connection. Our understanding of certain entities, though, may supply the relevant notion of necessary connection independent of those aspects of their character revealed in experience. One would be God and his actions. A second would be powers and their manifestations. In the case of God, it follows from his omnipotence that, metaphysically necessarily, if he wills that e occurs, then e occurs (Malebranche (), p. ). Because God is the only omnipotent thing, there is no necessary connection between any other entity and its candidate effects. In which case, even if we have a concept of necessary connection, a question arises over whether it correctly characterizes the connection between those entities typically thought of as cause and effect in daily life. Moreover, the omnipotence of God is a slender basis upon which to justify one’s claim to possess a concept of necessary connection since an equally plausible question may arise over the claim to understand God’s omnipotence. The case of powers and their manifestations provides a different problem. The standard picture of powers is that they are to be understood in terms of a trigger (to their manifestation), T, which, in circumstances C, results in an object, O, possessing the power, P, to manifest it in the appropriate ways, M. In brief, then, metaphysically necessarily, if T in C and O has P, then O has M (where M is characterized in terms of an effect caused by O in O* (where O 6¼ O*)) (Bird (a), p. ). For example, one might think that water (O) has the power to dissolve sugar (O*) because, metaphysically necessarily, if sugar is placed in water, then it dissolves. If water failed to dissolve the sugar, it would not have that power. We possess the concept of necessary connection by reflecting upon the connection between an object’s possession of a power in the specific circumstances and triggering required, and its manifestation.

        This connection between powers and their manifestations has come under pressure. The objection is that it is always possible that there might be interference in the process giving rise to O having M (Schrenk (), pp. –). In which case, the claim goes, there is no metaphysically necessary relationship between T in C and O having P on the one hand, and O having M on the other. The natural response to this objection is to have a non-interference condition. Indeed, it might be suggested that this is implicit in the proper characterization of C. The worry is that if the ‘noninterference’ condition is just some global state of the world that rules out the possibility of interference, or is just the trivial ‘and there is no interference’, then we can’t base our understanding of necessary connection on understanding P, T, and M. Instead, we are drawing upon a prior understanding of what is involved in a necessary connection. We have no better claim to have identified the a priori source of our concept of metaphysically necessary connection than God’s omnipotence. We’ve just substituted P’s uninterfered-with potence for necessary connection. We can take some solace in the following thought, though. Discussion of whether or not there is a plausible origin of our concept of necessary connection is, at best, an indirect means of resolving the question of whether we possess it. Showing that experience or a priori reflection may provide us with some basis for possessing the concept does not show that we do possess it. If we consider what is involved in the possession of the concept of necessary connection then we can provide a direct means to assess whether or not attribution of it is coherent. From that perspective, a promising suggestion may be drawn from Frank Ramsey’s work on our belief in causal generalizations, discussed recently by Mark Sainsbury. In brief, it is that somebody believes that Cs cause Es only if they are in the grip of a certain kind of belief regularity. If the person were to come to believe that a C has occurred, then the belief would cause them to believe that an E has occurred—call this the C-E belief regularity (Sainsbury (), pp. , –; Ramsey (), pp.  or ). The idea that we may draw from this is that being in the grip of such a belief regularity partly constitutes our possession of the concept of causal necessitation. If the idea is to bear fruit, we need to be able to distinguish being in the grip of a C-E belief regularity from believing a universal generalization relating Cs to Es. A subject may believe a universal generalization without supposing that there is any necessitation between Cs and Es. It may just be accidental that all Cs are succeeded by Es. The proper analysis of believing a universal generalization is not straightforward. For instance, (UG) For all x, S believes that if x is C, then x is E is no good because it suggests that, in order to believe that all Cs are Es, one has got to have a belief about every item in the universe (over which the quantifier is ranging) (Sainsbury (), p. ). (UG) For all x, if S believes that x is C, then S believes that x is E seems compatible with failing to believe that all Cs are Es. For example, I may not believe that all dogs are fierce. Nevertheless, if every dog I have come across and

    



about which I have formed a belief, I have believed to be fierce, (UG) is satisfied (Sainsbury (), p. ). (UG)

For all x, if S were to believe that x is C, then S would believe that x is E

might seem to resolve the problems with the other two. Unlike (UG) we wouldn’t just focus on every object that I, in fact, believe to be the dog but also consider what I would believe about the others. Unlike (UG) we don’t suppose that I have a belief about every object in the universe. Nevertheless, there are clear problems with (UG). It seems unlikely that we are cognitively so busy that we would form a belief that x is E about everything that we would form the belief that x is C. Moreover, there are ways in which we can come to believe that x is C in which we would abandon the generalization rather than conclude that it was E. Here is an example. Suppose that I have two general beliefs. First, that all the people in the room are journalists. Second, I will never encounter an honest journalist (all honest journalists are such that I will never encounter them). If I am introduced to Tom in the room, described to me as a professional philosopher, I would not believe that he is a journalist (unless I took the description to be a joke). Nevertheless, it does not follow that I failed to have the first general belief prior to being introduced to Tom. The example might seem to suggest that a more minimal way for the object to be introduced is required. Following standard terminology, let me call the way in which an object or property is presented or introduced, the object or property’s mode of presentation. A mode of presentation serves to characterize how we conceive of an object. To deal with related difficulties, Peacocke proposed that the appropriate characterization of the mode of presentation of an object, under which a general belief is manifested, is the next one to be encountered (Peacocke (), pp. –). If my thought of Tom had been that the next one encountered (rather than a philosopher) is in the room, then I would conclude that Tom is a journalist. Nevertheless, as Sainsbury points out, this manoeuvre doesn’t always work. Suppose I meet Honesty Blaise, a manifestly honest journalist under the mode of presentation, the next one encountered. If I were to believe that the next one I have encountered is an honest journalist (as I do in this case because of her manifest honesty), then I would not believe that I have not encountered her (Sainsbury (), p. ). But, once more, this does not imply that I did not have the second general belief. The minimal mode of presentation strategy doesn’t work. We need some constraint to rule out cases in which I don’t display the required regularity in belief because I cease to have the general belief rather than never had it. Something like the following seems appropriate (Means to Belief) The counterfactual dependency between the belief that x is C and the belief that x is E should hold just so long as the means by which the subject arrives at the belief that x is C does not result in the belief that x is not-E (Sainsbury (), p. ). The problem now is that (UG) with this constraint seems no different from our original analysis of what is involved in being in the grip of the regularity. If I were to believe that x is C and this does not result in the belief that x is not-E, then (on the

        assumption that I believe that all Cs are Es) I would be caused to believe that x is E (or that x being E has occurred). In which case, we have no distinction between general beliefs and, specifically, beliefs involving causal generalizations. The solution to this problem is to recognize that being in the grip of a regularity is not simply a matter of there being a causal connection between our beliefs but this connection being more resilient than any causal connection associated with belief in a simple universal generalization (Sainsbury (), pp. –, makes this suggestion, which I develop below). The question is how to characterize the resiliency required. My proposal is that this is the same task as seeking to characterize the similarity weighting for counterfactuals (a matter I shall turn to in detail in Chapter ). The resiliency of causal generalizations is captured by the fact that, when we envisage changed circumstances, we consider these circumstances more similar to the actual circumstances, if we retain the actual laws as much as possible. Our grasp of the concept of causal necessitation is thus displayed by the fact that there are certain generalizations, those that express laws, which we retain in a wide variety of different circumstances. In so doing, causal generalizations that might not be laws, but are a consequence of laws holding, are retained as well. Those generalizations that we take to express causal necessitation are retained to a much greater degree than those merely recording accidental associations. As we shall see later, the similarity weighting for counterfactuals has to be adjusted to accommodate the fact that not all cases of causation involve law. Nevertheless, the accommodation will also be resilient in the same fashion (.). If we believe that Cs cause Es, then, it is not just that were we to have a belief that a C has occurred, we would believe that an E has occurred, if we consider the question. Rather, this counterfactual dependency between a belief that a C has occurred and a belief that an E has occurred will persist through changes in our other beliefs about the world to a much greater extent than dependencies corresponding to accidental generalizations. Moreover, in those precise circumstances, abstracting from the existence of competing generalizations, we will not simply have the counterfactual dependency between the beliefs but between the absence of the belief that C occurred and the absence of the belief that E occurred (something to which Peacocke appeals (), pp. –). These twin mental dependencies, either of which might be manifested, given what we learn about the occurrence or non-occurrence of C, provide good grounds for attributing to ourselves (and others who do likewise) the concept of causal necessitation. The Means to Belief principle still has a role to play. It moderates the resilience of the grip a causal generalization has on us, and can favour an accidental generalization. Similarity of cognitive worlds is not just to be modelled by the similarity weighting of possible worlds because of the special role of how we arrive at beliefs. Let me illustrate this by a couple of cases. First here is one involving an apparently resilient accidental generalization. Suppose I believe that Mark is the model of sobriety. Take Mark to a party, he doesn’t get drunk. I form the belief that everybody at a certain party was drunk. I am informed that Mark was at the party. If my belief in the universal generalization was formed by inspection of all the individuals at the party (one of whom I did not recognize to be Mark) then I don’t retain the causal generalization that Mark never

    



gets drunk at parties. Rather I abandon this belief in favour of the accidental generalization that everybody at the party was drunk (Sainsbury (), p. ). Here, the means by which I discover that Mark was at the party provided me with evidence against the claim that he was not drunk. The abandonment of the causal generalization is explained by the Means to Belief principle. Second, there are the cases of non-resilient causal generalizations. Suppose I believe that plants of kind K do not survive in temperatures under freezing. Then I will hold that if such a plant is planted in Iceland, it will die. Nevertheless, if I learn that these plants were reared in Iceland and are being planted out, I would question the causal generalization. I would not use the causal generalization to conclude that the plants would die (Peacocke (), pp. –). Once more the Means to Belief principle explains this. The means by which I learnt that the plant was planted in Iceland undermined the belief that it would die. I have just focused on qualifications to the resilience of causal generalizations that result from the means by which we arrive at the antecedent belief. There is also a way in which belief in causal generalizations is undermined, or blocked, because of the circumstances in which a particular association between Cs and Es is observed, that does not have the same impact on the corresponding non-causal generalization. Indeed, some of these circumstances may be responsible for the transition from causal generalizations to corresponding non-causal generalizations. One experimental set up that illustrates these points involves subjects pressing the space bar on the computer (A) with the outcome (when it happens) of a triangle flashing on the screen for . seconds (O). It is observed that the larger the difference between P(O/A) and P(O/not-A), the more inclined subjects are to rate A as a cause (e.g. Wasserman et al. (), pp. –, the precise set up described in Shanks and Dickenson (), p. ). If the difference between P(O/not-A) and P(O/A) is relatively small, subjects do not judge that causation is present. Note here that the truth of the generalization ‘As are followed by Os’ is unaffected by the value of P(O/not-A) or indeed its relationship to P(O/A). Even if there is no difference of value, and so A-ing apparently makes no contribution to O, the generalization remains true when Os invariably follow As. Equally, should it be observed, before or afterwards, that Os occur without As, indeed frequently without As, then observation of Os following As does not result in Os being rated a cause of As or, in the case of the observation of Os occurring independently afterwards, subjects’ judgements that As are causes of Os are undermined by the subsequent observations. In this experiment involving a video game, O and A were more complex: the destruction of a tank and the firing of a shell, respectively. The prior or posterior observation of the destruction of tanks was attributed to the presence of mines in the game environment (Shanks and Dickenson (), pp. –). Again these observations concerning what occurs prior and posterior to the firing phase doesn’t touch on the truth of the corresponding generalizations. My suggestion is that these further dispositional properties of resilient generalizations are part of what makes them the expressions of necessary connections. The resilience must be tempered not just by how we discover whether the antecedent of a conditional is true—as spelt out by the Means to Belief Principle—but also by additional commitments involved in the idea of causal necessitation, namely that the

        candidate causally necessitating element must normally make a difference. I say ‘normally’. As we shall see later, there may be redundant cases of causation whose recognition adds additional complexity to the disposition but does not give rise to further difficulties. Up until this point, I have focused on how our grasp of the concept of causal necessitation is constituted by our treatment of causal generalizations. The link with the provision of a similarity weighting for counterfactuals later shows how this treatment may be extended to the singular case (see .; .). Taking a certain co-occurrence between particulars to be resilient in changed circumstances also constitutes part of our grasp of the concept of causal necessitation. The development of the similarity weighting in the chapters that follow is thus a further contribution to the treatment of the subject matter of this section (Chapter ; .). Applied to the task at hand, it articulates a complex dispositional structure true of subjects as a result of which those subjects have a, perhaps primitive, representation of a certain kind of dependency that holds between those entities mentioned in the antecedent and consequent of the counterfactual. If the dispositional structure identified represents a necessary connection, this is in prima facie conflict with a Humean account of causation. The dispositional structure present in us represents a necessary connection between putative distinct existences—the candidate cause and effect—that a Humean account denies. It would seem that Humeanism could only be true of our world if all our causal beliefs were false (Beebee (), pp. –, –, for further discussion of this issue with respect to Hume). The response to this challenge is to recognize that the putative necessary connection is taken by the Humean to be an interworld resilience of patterns rather than an intra-world presence of necessity between distinct existences. Corresponding to resilient causal generalizations are patterns of coinstantiation of properties that persist in possible worlds close-by to our world. The Humean claims that the dispositional structure represents the fact that there is this interworld resilience of patterns. The non-Humean insists that intra-world necessity in some way influences this interworld resilience (see .). The dispositional structure is neutral between them. We can now return to the objection that counterfactuals fail to capture the intimate tie between causally related events. Consider again our target counterfactuals: () If e₁ were to occur, then e₂ would occur. () If e₁ were not to occur, then e₂ would not occur. While one of the two counterfactuals about the events may be true just if the antecedent and consequent is true, prior to a subject’s learning which is the case, the corresponding belief counterfactuals capture two sides of the same mental dispositional structure with regard to representation of the relationship between the events in question. The link between resilience and counterfactuals explains how counterfactuals successfully capture our ideas of causal necessity and sufficiency. The counterfactual expresses the fact that the connection between these two events is a resilient one. Recognition of the resilience need involve no further tie, though, between the events in this world. Their presence as part of a pattern that is, in fact,

    



resilient in close-by worlds is enough. By the Humean’s lights, that means any further story about the connection will draw on claims about laws and probabilities understood in Humean terms, not necessities. By the same token, it is open to nonHumeans to appeal to necessities in the way sketched above. The proper response to the claim that there is an intimate connection between events that fails to be captured by counterfactuals is to say that they reflect the different ways that the Humean and the non-Humean can capture the connection. Possession of the concept of causal necessitation is not itself possession of the concept of necessary connection. A necessary connection between A and B is one in which it is metaphysically not possible for A to exist without B existing or vice versa. Causal necessitation does not involve any such thing. If A’s existence causally necessitates B’s existence, it is still possible that B not exist in worlds in which the laws are different (for example). There is a necessary connection, though, between A’s causal necessitation of B and B. Thus somebody who possesses the concept of causal necessitation will display a grasp of the concept of necessary connection. If our possession of the concept of causal necessitation is revealed by the resilience of causal generalizations, then it is plausible that our concept of necessary connection is revealed by even greater resilience. It is tempting to put this point by saying that we believe that, metaphysically necessarily, if A exists, then B exists only if there is a counterfactual dependency between a belief that an A exists and a belief that a B exists no matter what other beliefs a subject may have. However, this cannot be right. We can give up metaphysically necessary truths in the face of evidence without throwing into question whether we took them to be metaphysically necessary. Even in this case, resilience is moderated to some degree. Nevertheless, the possibility doesn’t arise for the metaphysically necessary connection between an A’s causal necessitation of a B and a B. We are not going to give up the claim that metaphysically necessarily, if an A causally necessitates a B, then a B. Rather we would give up the claim that an A causally necessitates a B. Thus, in these particular cases, our possession of the concept of causal necessitation can be the basis for a partial characterization of the concept of a necessary connection. If a subject believes that As causally necessitate Bs, then no matter how the subject’s beliefs change compatible with an A causally necessitating B, the subject will still believe B occurs. Of course, if an A occurs, there might be something that intervenes to prevent a B from occurring (as we discussed earlier). In that case, an A does not causally necessitate a B. Our focus was on what followed if it did. Equally, although an A causally necessitates B requires that a B occurs, the claim is not that causally necessitating is a relation between an A and a B. Causal necessitation is what an A brings to make a B occur. A B’s occurrence is not required as it would be if it were a relation between As and Bs. An A’s causal necessitation of a B is a particular B-directed property of As that, if an A possesses it, a B occurs. Causation is not causal necessitation. Rather the latter is a putative necessary condition of the former in the deterministic case. The question of whether it is coherent for there to be a necessary connection between distinct existences, thus, comes down to this. Is it possible for the counterfactual dependence between a belief that an A exists and a belief that a B exists to display the dispositional structure I have identified when (i) an A and a B are

        conceived to be distinct existences in the world and (ii) the dispositional structure represents an intra-world relationship between an A and a B? At least prima facie, there seem no grounds for ruling this out. The only reason for rejecting the possibility will stem from how a subject conceives of distinct existence. So I will turn to that question. In focusing upon it, we examine direct arguments in favour of the denial of necessary connections between distinct existences.

. Distinct Existence If there is a necessary connection between contingent existences, an A and a B, then either it is not metaphysically possible that an A exists and a B does not or vice versa. The question for us now is what rules out such a connection between distinct existences (if anything). The most natural understanding of distinct existence is just denial of numerical identity. Under this characterization, there are immediate counterexamples. Consider the connection between the property of being rectangular and that of being square (Stoljar for further discussion (), p. ). These properties are numerically distinct and yet it is not possible that the property of being square can be instantiated without the property of being rectangular being instantiated. Water molecules have oxygen atoms as essential parts according to many accounts of natural kinds. That implies it is not possible for a water molecule to exist without a constituent oxygen atom. To such cases, there are three typical responses. According to some, while the properties might be distinct, the instances are the same (e.g. Macdonald and Macdonald (), p. ). According to others, only the most determinate properties exist so there are no instances of the property of being rectangular (Gillett and Rives ()). According to a third group, the principle formulated in terms of numerically distinct entities is a mistake. We should reformulate the principle in terms of wholly distinct entities (e.g. Armstrong (), p. ; see also Wilson (), p. ). Later discussion will undermine the plausibility of the first two responses. In .. I suggest that the most natural development of either a theory of universals or of tropes is to deny instance identity. This receives further support from the account of intrinsic properties developed in .. In ..., I explain why we should allow determinable properties to exist. In what follows, we shall see that the third line of response fails to save the denial of necessary connections between distinct existences as a necessary truth (.., ..). The issues raised concerning numerical identity, and distinctness, dramatizes the fact that we are looking for a basis for claiming that two entities are uncontestably distinct from each other. The basis will be something that helps to characterize the contingent realm. The question is whether, having found it, it rules out the possibility of necessary connections between distinct entities so understood. If it did, we can allow that there are necessary connections between numerically distinct entities. It is just that some numerically distinct entities are not distinct existences in the identified sense (or senses). I shall argue that there are three accounts of distinct existence in this sense. The first, modal, characterization makes the denial of necessary connections between distinct existences a trivial truth but is useless for the purposes to which it is put. The

 



spatial and distinct arrangement characterizations capture important features of our idea of distinct existence but lend no support to the claim that the denial of necessary connections between distinct existences is a necessary truth. Unlike Jessica Wilson, I don’t limit these accounts of distinct existence, and the corresponding formulation of the distinct existences principle, to intrinsically typed entities for two reasons (Wilson (), p. , and subsequent formulations). First, the conclusions that those who appeal to the principle are trying to draw are entirely general (relating to all contingent existences) and not to just a particular—intrinsically typed—kind of entity. Second, intrinsically typed entities may have natures that are essentially extrinsic in some way. Intrinsic typing is just a certain way of characterizing these entities. In which case, any conclusion about these entities in virtue of their intrinsic typing doesn’t even establish that there are no necessary connections between these entities and other entities.

.. Modal characterization of distinct existence A modal characterization of distinct existence would claim that a and b are distinct existences iff it is possible for a to exist/be instantiated (with its parts unchanged) without any actual part of b existing/being instantiated and it is possible for b to exist/be instantiated (with its parts unchanged) without any actual part of a existing/being instantiated (Armstrong (), p. ; cf. Stoljar (), p. ; Wilson (), pp. –, a necessitist version could be formulated in terms of concreteness). a and b are not distinct existences if either (i) metaphysically necessarily, if a exists/ is instantiated then b exists/is instantiated or metaphysically necessarily, if b exists/is instantiated then a exists/is instantiated or (ii) metaphysically necessarily, if a (or one of its parts) exists, one of the actual parts of b exists or if b (or one of its parts) exists, one of the actual parts of a exists. We need to consider parts of a and b given that the identity of these parts is not essential to a and b. Suppose that we did not and that a and b share a part. Then we might conclude that it is possible for a to exist without b, and vice versa, because, in the possible circumstances in which they did, a no longer had an actual part of b or b no longer had an actual part of a. Yet, intuitively, a and b would not be distinct existences. Although proponents of the modal characterization don’t often say it, talk of parts of a, and so on, shouldn’t be understood to limit the characterization to mereological accounts of parthood or, for that matter, exclude other forms of construction. Elucidation of distinct existence relevant to Hume’s principle need not involve commitment to only certain kinds of construction being allowed even if proponents of Hume’s principle often are so committed. Other candidate constructive relations include: Non-mereological composition: states of affairs have as non-mereological parts objects and the properties they possess. Constitution: objects have as constituents their matter and the form the matter takes e.g. the lump of bronze that is a statue. Set Membership: an object, x, is a member of its singleton set {x}.

        Structural properties: Properties are constructed from other properties which do not figure as a part because, otherwise, multiple cases of a property would be needed e.g. CH₄. Object formation: Objects are bundles of properties at time (cf. Bennett (), pp. –, (), pp. –, for further discussion Noordhof ()). In each of these cases, entities that overlap with any of the constructive elements mentioned would not be wholly distinct. For example, hydrogen is not a mereological part of the structural property of methane and yet hydrogen is not wholly distinct from methane. We don’t have to allow for the legitimacy of any, or all, of these constructive relations. The important point is that to the extent they exist, we would need a more nuanced understanding of part in the original formulation, or replacement of part in the formulation by something like ‘constructive element’. We can set aside these details for the main argument. The modal characterization of distinct existence allows for the possibility that two things, which fail to be distinct existences, don’t have a metaphysically necessary connection holding between them (as opposed to their parts). If there is a metaphysically necessary connection between them, though, then they cannot be distinct existences. This provides immediate support for the denial of necessary connections between distinct existences but it trivializes the principle. Suppose that e₁ causally necessitates e₂. The principle does not rule this out because e₁ and e₂ are distinct existences. It is not true that metaphysically necessarily if e₁ occurs then e₂ occurs. On the other hand, the principle does proclaim that e₁’s necessitation of e₂ is not a distinct existence from e₂. However, that doesn’t make necessitation problematic. Apparent counterexamples to the distinct existences principle are reclassified rather than ruled out. The principle doesn’t say that e₁’s necessitation of e₂ doesn’t exist but that if it does, it is not a distinct existence from e₂. Given the modal characterization of distinct existence, many would be prepared to accept this (e.g. Stoljar (), p. , takes a similar principle to be analytic, probably for this reason, Ayer (), p. , takes it to be trivial). The point is entirely general. Any of the putative non-Humean ontologies discussed in Chapters  and  would be ruled as Humean with adjusted claims about what are the distinct existences in these ontologies. To avoid triviality, there must be an independent account of distinct existence than that which appeals to modality.

.. Spatial characterization of distinct existence A spatial characterization of distinct existence holds that a and b are distinct existences iff the spatiotemporal location of a is wholly distinct from the spatiotemporal location of b (Armstrong (), pp. –). a and b have, in this sense, no overlap in spatiotemporal extent (Gendler and Hawthorne (), pp. –; Wilson (), p. ). A spatial characterization of distinct existence provides some support for the truth of the denial of necessary connections between distinct existences but it is hard to see how it could establish its necessity. If the spatial location of one thing is wholly distinct from the spatial location of another thing, then it seems that the first portion

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of space could exist without the second and, hence, that there is no metaphysically necessary connection between them. Nevertheless, although necessary connections in such circumstances would be puzzling, it is difficult to rule out their possibility completely, especially when there are potential candidates. Entirely predictably, one would be e₁’s causal necessitation of e₂. The location of this might well be thought to be e₁’s location. e₁’s location, we may suppose, is distinct from e₂’s location. Yet, there is a putative necessary connection between them. Other candidates would be instances of powers or dispositions, together with their triggers and a ‘no interventions’ condition, if a powers ontology were true (discussed in Sections . and ..–). Proponents of the spatial characterization of distinct existence may insist that these candidate counterexamples to the principle are, in fact, legitimately ruled out by the plausibility of the principle. As I have noted, necessary connections between entities in spatiotemporal locations wholly distinct from each other are puzzling. However, this puzzlement must be set against the potential explanatory virtues of postulating such relations discussed later in Chapters  and . Endorsing this version of the distinct existences principle is taking a pre-emptive view about the explanatory costs versus benefits of this evaluation which is, at best, premature. Proponents of this version of the distinct existences principle are also unable to find support for their position from the claim that their candidate principle is based upon a unitary conception of what constitutes distinct existence. The spatial characterization of distinct existence fails to capture certain intuitive cases of distinct existence involving states of affairs. Let ‘a’, ‘b’ stand for particulars and ‘F’, ‘G’, their properties. Thus one state of affairs would be Paul has two legs, represented: Fa. Other states of affairs would be Paul has two arms (Ga) and Jo has two legs (Fb). Intuitively, Fa and Ga are distinct states of affairs, as are Fa and Gb compared with Fb and Ga. Nevertheless, the spatial characterization would deny that these are wholly distinct existences because, in the first case, the particular, a, is common to both, and in the second case both particulars and properties are common to both (Armstrong (), pp. –, ). Nor is this point irrelevant to our subject matter of interest. The simplest form of Armstrong’s account of laws of nature takes them to be secondorder necessitation relations between first-order properties that he represents as follows: N(F, G). It is a consequence of his position in this form that, in simple cases, metaphysically necessarily, if Fa and N(F, G), then Ga. Philosophers have questioned such an account on the ground that it postulates necessary connections between distinct existences. However, the spatial characterization of distinct existence would not legitimate this charge because Fa and Ga share a particular. In which case, many putative necessary connections would not infringe a denial of necessary connections between distinct existences drawing upon this notion of distinct existence. We need a notion of distinct existence that promises to capture this dimension of the debate.

.. The distinct arrangement characterization of distinct existence and distinct existence pluralism The Distinct Arrangement characterization of distinct existence holds that

        a and b are distinct existences if and only if either (i) neither a nor any of its parts is a part of b nor b nor any of its parts is a part of a or (ii) although there is overlap of parts, the parts are differently arranged. The state of affairs Fa is a distinct existence from the state of affairs Gb by the first clause. The states of affairs Fa and Ga, or Fa and Gb compared with Fb and Ga, are distinct existences by the second clause. Although it captures when states of affairs are distinct existences, it generates less happy verdicts regarding ordinary objects. For instance, suppose that conjoined twins share a heart. I would say that their problem was that they weren’t distinct existences. The distinct arrangement characterization would proclaim otherwise by clause (ii). That suggests that there is no one characterization of distinct existence. The account will vary for spatiotemporal objects subject to mereological composition and for states of affairs (and structural universals like N(F, G)). The spatial characterization is appropriate for the first type of case. By contrast, the distinct arrangement characterization is appropriate for the second type of case involving states of affairs and properties. Different ways in which entities are constituted result in different accounts as to when their existence is wholly distinct. It might be thought that the first clause of the distinct arrangement characterization can be taken to cover cases of mereological composition and there is no need to recognize an independent account of distinct existence in terms of spatiality. However, this is not correct. It relies upon the assumption that, for any two spatiotemporally overlapping entities, there will be parts that they share. This does not follow for spatially extended partially overlapping simples or for terduring objects. According to terdurantists, physical objects have temporal extent. They are not endurantists who hold that physical objects are wholly present at each temporal instant of their existence. However, terdurantists deny that simple physical objects have temporal parts (Parsons (); Miller (), pp. –). Consider an event involving a particular simple terduring object for some portion of the object’s existence. The event won’t be a temporal part of the object and the object won’t be a part of the event if the object’s temporal extent runs beyond the event. So the distinct arrangement characterization would take them to be wholly distinct. Yet, intuitively, there is a way in which their existences are not wholly distinct from each other. The spatiotemporal characterization captures this. The case of spatially extended partially overlapping simples illustrates the same point. There is spatial overlap but because neither of these simples has a proper part and neither is wholly located where the other is, the distinct arrangement characterization would take them to be wholly distinct. Recognition of this second type of distinct existence does not change matters with regard to the denial of necessary connections between them. If the arrangement of one entity is different from the arrangement of another entity, then it is prima facie puzzling why there should be a necessary connection between them. The arrangement of the first would seem insufficient to determine the arrangement of the second. Nevertheless, although puzzling, it is hard to rule out and, as we saw at the end of .., Armstrong’s account of law provides possible cases in which a necessary connection does exist between distinct existences, as does the powers ontology. As

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a result, the plausibility of the distinct existence principle so understood rests upon a prior assessment of the explanatory virtues of non-Humean approaches to laws (amongst other things).

. Concluding Remarks In the first section of the chapter, I identified a position the implications of which have gone relatively undiscussed, namely a counterfactual theory of causation that allows for the possibility of both Humean and non-Humean realizations. Prior to helping ourselves to the resources of such a position, we needed to consider the preliminary arguments Humeans offered in favour of denying necessary connections between distinct existences. First, we looked at what they said about our experience of causation and necessary connection and found it wanting. It is plausible that we experience both, though our experience fails to characterize fully the nature of necessary connection. In . we turned to the question of whether we had a concept of necessary connection between distinct existences that might characterize the nonHumean realizations of causation. I provided an analysis of what this involved, however, the analysis was neutral over whether it captured an interworld resilience of patterns or an intra-world necessary connection between distinct existences. Thus, we turned to conditions under which we might conclude that two things were distinct existences in the relevant sense. We found that there are two such forms of distinct existence and that neither ruled out the possibility of necessary connections between them. The grounds for postulating that there is a necessary connection would result from explanatory considerations that we shall discuss in Chapters , , and . As we saw earlier, Lewis’ position changed from the rejection of the possibility of necessary connections between distinct existences to denying that there was a need to allow for them. There is no guarantee that Lewis’ change of position is the right approach. In ..–, I shall consider the role of the principle of recombination and whether it provides us with a theoretical reason to reject necessary connections between distinct existences. I shall argue that it does not because the principle is either not needed to satisfy the aims Lewis had in mind for it or the aims appear unachievable. I will also consider Wilson’s argument for the necessary falsity of the distinct existences principle, given a certain assumption, and explain why it is unsound (.). Before I get to the final skirmish over whether the distinct existences principle is necessarily true or necessarily false, I shall develop a counterfactual theory of causation that takes into account the fact that, in some possible worlds, the denial of metaphysically necessary connections between distinct existences is false. It has quite radical, and positive, implications for the development of a semantics for counterfactuals and the success of a counterfactual theory in its treatment of suggested difficulties with it. Starting with a fixed view of whether necessary connections between distinct existences are possible has distorted the evaluation of the counterfactual theory. On the one hand, opponents of the Humean metaphysic have taken it to be committed to Humeanism and, thus, facing certain counterexamples. Drawn to talk of necessities, its opponents have overlooked the merits of appeal to

        counterfactuals in providing an analysis of causation. On the other hand, proponents of the counterfactual theory have felt constrained to answer objections to counterfactual theories within the commitments of a Humean metaphysic that obscures its merits. The book, then, up to the last chapter, will provide an implicit case for the merits of taking the denial of necessary connections between distinct existences to be contingent, at best, before we consider the residual case for taking its truth value to be necessary.

 Counterfactuals and Closeness A counterfactual theory of causation relies upon a successful semantics for counterfactuals. In Chapter , I endorsed Lewis’ development of the Stalnaker-Lewis possible worlds semantics in which A counterfactual ‘If it were that A, then it would be that C’ is (non-vacuously) true if and only if some (accessible) world where both A and C are true is more similar to our actual world, overall, than is any world where A is true but C is false (Lewis (), p. ).

I postponed the proper characterization of similarity between worlds to this chapter. Counterfactual theories of causation are in difficulty if the characterization either involves ineliminable appeal to causal facts in characterizing the similarities that matter or fails to explain causal non-symmetry. My principal aim in the present chapter will be to defend a modification of Lewis’ account of the relevant similarity between worlds that avoids these problems. We will have to wait until Chapters  and  to see whether it successfully avoids the second. Lewis’ fully developed theory—the combination of the analysis and the account of similarity between worlds—involves the defence of a number of choices in the proper understanding of counterfactuals. His appeal to similarity is neither a primitive nor some general intuitive understanding of similarity. Instead, it involves the articulation of a number of different factors weighted against each other (thus dubbed a similarity weighting). At its heart is a view about the relative weight of differences of law and particular matters of fact, the latter being understood as the arrangement of objects and properties that make up a possible world. After I have outlined the grounds for allowing that there is some trade-off between laws and particular matters of fact in evaluating similarity—a trade-off outlined in Lewis’ similarity weighting—I shall discuss the position of those who insist that no trade-off should be envisaged (.). The laws should be taken as fixed, that is, invariant, in the assessment of counterfactuals. This is, in effect, a discussion about the status of the perfect match condition of the similarity weighting. Taking laws to be invariant has the consequence that, plausibly, any attempted counterfactual theory of causation will struggle to distinguish between cause and effect within the theory and, indeed, fail to keep the causal circumstances fixed against which causal dependencies are revealed. I shall question the motivation for insisting upon invariance, laying the foundation for the further development of an understanding of causal non-symmetry in Chapters  and . As we shall see, though, the appeals to both perfect and approximate match in particular matters of fact, in the similarity weighting, have their price. One issue is whether recognizing the importance of these dimensions of similarity requires us to envisage changes in laws that fail to yield the intuitive truth values for counterfactuals. A Variety of Causes. Paul Noordhof, Oxford University Press (2020). © Paul Noordhof. DOI: 10.1093/oso/9780199251469.001.0001

    It has been argued that, rather than think in terms of worlds, and areas of match between worlds, we should think of more local regions of match to which we apply whatever laws seem to be at work, in the circumstances about which we are engaged in counterfactual reasoning. Apart from its threat to any attempt to provide an account of causal non-symmetry in counterfactual terms, I argue that this approach is both undermotivated by the kind of case that favours it and also has difficulties accounting for other counterfactuals we find it very natural to assert (end of .). Where the perfect match condition really gives rise to a difficulty is shown by a development of what is called the future similarity objection under indeterminism. In . and ., I argue that some adjustment to Lewis’ similarity weighting is needed. I consider alternatives that have been offered—for example, an adjustment to the analysis of counterfactuals or an appeal to considerations of typicality or fit—and argue that they either don’t work or have unacceptable consequences of their own. Instead, I propose a limitation to the perfect match condition. The precise characterization of this is assisted by discussion of a case that is alleged to threaten the capacity of counterfactuals to provide a non-circular analysis of causation. The objection is that we should only appeal to perfect match in those facts subject to the same causal explanation (Kment (), p. ). As we shall see, this is unnecessary. In ., I turn my attention to the proper articulation of the approximate match condition. Some have argued an appeal to causal notions is also required here. I explain why this isn’t the case and suggest an alternative. If perfect and approximate match in particular matters of fact are important contributions to similarity between worlds, then there will be a point of divergence, from the particular matters of fact of the actual world, that develops into the conditions under which the antecedent of the counterfactual is true (given that the presumption of its falsity is met). This is known as the transition period. Various approaches have been taken to the transition period. Most broadly, though, the division is between those who argue for a substantial miracle very close to the point at which the circumstances described in the antecedent have to be realized, such as Frank Jackson, and those who urge a more graceful transition, such as Lewis (Jackson (), p. ; Lewis (), p. ). Strictly speaking, Lewis’ preferred similarity weighting seems to provide support for the former but, in fact, he has always suggested that the transition period will be graceful, implying a particular way of understanding his similarity weighting. My adjustment to the similarity weighting makes this approach to the transition period more obvious. Perhaps, here more than anywhere, errors of characterization in the similarity weighting may show up in erroneous attributions of truth or falsity to counterfactuals. Both the substantial miracle and the graceful transition understandings of the transition period threaten to give rise to such artefacts. If the transition is effected by a substantial miracle—coming from nowhere as it were—then there will be lots of counterfactuals implausibly made true or false by the impact of such a miracle. For example, to consider a variant of a nice case due to Jonathan Bennett: If nobody had been on the beach when the tidal wave struck, the local community would not have been devastated by the loss of loved ones (Bennett (), pp. –). Imagining all the beach walkers suddenly disappearing before the tidal wave struck, would make the counterfactual false. The local community would be mourning the inexplicable

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disappearance of their loved ones, which they might put down to the tidal wave. The intuitive truth of the counterfactual clearly depends upon a graceful transition to the antecedent in which lots of people decided not to walk on the beach that day. Even if the transition period involves graceful transition, there are problem cases. In . I will address concerns that still arise on this understanding of the transition period. The approach to counterfactuals that I am seeking to develop further in the current chapter contrasts with approaches that deny that they have truth conditions and see their assertion as intimately related to future indicative conditionals. Consideration of this alternative approach deserves more space than I can devote to it in a book on causation. Nevertheless, it is helpful to indicate how the recommended approach can defend itself against the alternative. This is a matter I touch on in the conclusion to this chapter. I leave the discussion to the end because part of the case for support of my approach is that it provides a plausible account of the truth conditions of counterfactuals, dealing with some of the problems opponents to the approach cite in favour of an alternative.

. Lewis’ Similarity Weighting and the Status of the Perfect Match Condition Initial discussions of Lewis’ semantics for counterfactuals assumed that he was just appealing to an intuitive notion of similarity to characterize similarity between possible worlds. It is not quite clear why this assumption was made given that, in his original presentation of his theory, he argued that similarity of laws should be given particular weight as a result of which, for instance, future similarities in particular matters of fact may be discounted (Lewis (b), pp. –). In any event, by , it was manifestly clear that Lewis’ account of similarity between worlds involved a weighting of several different factors. His preliminary characterization ran as follows. (A) It is of the first importance to avoid big, widespread, diverse violations of law. (B) It is of the second importance to maximize the spatiotemporal region throughout which perfect match of particular fact prevails. (C) It is of the third importance to avoid even small, localized, simple violations of law. (D) It is of little or no importance to secure approximate similarity of particular fact, even in matters which concern us greatly (Lewis (), pp. –). The similarity weighting was derived from considering our verdicts concerning the truth or falsity of certain counterfactuals. For example, Nixon never pushed the button which would have launched a nuclear strike against the Soviet Union (as then was) and brought down a nuclear holocaust on us all (Fine (), p. ). Call this w₀ (the actual world). Consider the counterfactual () If Nixon had pressed the button, there would have been a nuclear holocaust.

    Assume the world is deterministic. Let w₁ be a world in which a tiny miracle occurs just prior to Nixon pressing the button—that is, a little violation of (as in, departure from) the actual laws not the laws of w₁—so that Nixon presses the button. Holocaust ensues. Let w₂ be a world in which the actual laws are never violated and Nixon pressed the button. The past of w₂ would have to be rather different from that of w₀ in order that Nixon pressed the button as a result of the actual laws. Let w₃ be a world like w₁ except that shortly after Nixon presses the button another tiny miracle occurs which stops the button’s signal transmitting to the launch pad so that there is no holocaust. However, all the other effects of pressing the button remain: ‘Nixon is still trembling, wondering what went wrong . . . His gin bottle is depleted. The click of the button has been preserved on tape. Light waves that flew out the window, bearing the image of Nixon’s finger on the button, are still on their way to outer space. The wire is ever so slightly warmed’, and so on (Lewis (), p. ). Let w₄ be a world like w₃ except that a large miracle has taken place so as to cover up all these other effects as well. Lewis argues that our commitment to the truth of () rests on the following judgements. First, we judge that w₁ is closer than w₂ hence perfect match (B) is more important than avoiding small localized law violations (C). Second, w₁ is closer than w₃, hence avoiding small localized law violations, (C), is more important than securing approximate match, (D). Third, w₁ is closer than w₄ hence perfect match (B) is not as important as avoiding big, widespread, diverse violations of law. I shall follow Lewis’ practice in the remainder of the chapter. I shall consider our intuitive verdicts regarding certain counterfactuals and, where Lewis’ similarity weighting does not secure them, adjust the similarity weighting. One issue is whether this can be done in a well-motivated economical way without undermining the prospects of an analysis of causation in terms of counterfactuals. A second issue is whether the range of verdicts support Lewis’ attempt to provide a relatively uniform account of similarity, with context of utterance simply settling with what things should be similar, or whether standards of similarity varies with context. One context sensitivity Lewis recognized relates to so-called backtracking counterfactuals. Let ‘c’ stand for a cause and ‘e’ stand for the effect of which c is a cause in the counterfactual If c were not to occur, then e would not occur. The counterfactual is foretracking because the cause is mentioned in the antecedent and the effect is mentioned in the consequent. The counterfactual If e were not to occur, then c would not occur is backtracking because the effect is mentioned in the antecedent and the cause is mentioned in the consequent. It is tempting to take foretracking counterfactuals to go from past to future and backtracking counterfactuals to go from future to past. Indeed, this is how Lewis originally puts it (Lewis (), p. ). However doing so sits badly with taking backtracking counterfactuals to be generally false except in special contexts. Cases of backward causation wouldn’t involve the special context and yet we want the relevant future-past counterfactuals to be true. Lewis’ similarity weighting is developed so that foretracking counterfactuals come out true and backtracking counterfactuals come out false given certain contingent facts about

 ’     



the world, in particular, that the cause has many consequences apart from the effect whereas the same does not hold of the effect in the direction of the cause. I shall discuss this further in .. Characterizing backtracking counterfactuals as running from effect to cause does not introduce a circularity already into the eventual picture I defend. As we shall see, an independent characterization can be given of the standard way of evaluating counterfactuals. This together with the analysis of causation can be used to introduce the idea of a backtracking counterfactual. I have just characterized the difference in causal terms at this point for ease of exposition. The recognition of backtracking contexts aside, the semantics of counterfactuals is relatively free of factors set by context. Suppose I utter the counterfactual ‘If it were that A, it would be that C’. In addition to the facts about context that settle the content expressed by A and C—for example, if A contains ‘I’ who ‘I’ refers to or if A contains ‘water’ what the extension of ‘water’ is—the context of utterance will settle the actual world similarity with which is relevant for the assessment of the counterfactual. The similarity weighting takes the perhaps context-determined content of the antecedent as input and provides the relevant worlds of evaluation as output. The counterfactual will be true if the worlds of evaluation in which A, C are true are more similar to the actual world than those in which A, not-C are true. No further variation in content, due to the counterfactual construction, is introduced by pragmatic factors such as the speaker’s intention and the background knowledge of the utterer or audience. Lewis, initially a friend of further context sensitivity due to the counterfactual, ended with a theory less hospitable to it when he set out a specific similarity weighting (see Lewis (a), pp. –, (), pp. –, –). Those fond of contemplating whether Caesar would have used the A-bomb or catapults had he been in command in Korea might conclude that more widespread changes in laws and particular matters of fact would have to be envisaged to make catapults readily available as a viable strategy rather than update Caesar of the merits of a nuclear arsenal. Nevertheless, even if I am wrong about this, so long as there is a certain type of context which does not ineliminably appeal to causal facts, but which enables us to formulate a counterfactual analysis in terms of counterfactuals used in this context, the needs for the analysis are met. As I have already noted, the similarity weighting allows for a trade-off between match in particular matters of fact and differences of law. This can be made to feel very counterintuitive. Suppose that, in fact, I do not snap my fingers and the world is deterministic. Consider the counterfactual ()

If I were to snap my fingers, then the laws would be different.

If no weight is given to perfect match, then we can pronounce () false. Instead of the laws being very different, the snapping of my fingers would have occurred because the past was very different. As a result of this different past, and the laws that hold, I snapped my fingers. If perfect match is valued, it seems that () is true. Surely I am not so powerful as to change the laws merely by snapping my fingers! To generalize the last point, it is urged that laws are counterfactually invariant for counterfactuals whose antecedents are logically consistent with what is nomologically necessary (i.e. with the laws) (Lange (), p. ).

    Lange utilizes the idea of counterfactual invariance to provide an analysis of laws. For him, the truth of counterfactuals may be taken as primitive. The idea undergoes sophisticated development in order to avoid the circularity currently present by the idea of ‘consistent with the laws’. We do not need to consider this in order to assess the implications for Lewis’ similarity weighting. The reason why () appears false is that we have the intuition that we cannot make the laws false. Lange suggests that it is part of our intuitive notion of law that particular matters of fact are governed by law but do not govern what laws hold (Lange (), p. ). In .., I will discuss whether it is essential for something to be a law that it governs in this sense. For the moment, I will focus on the weaker claim that particular matters of fact do not govern the laws that hold. Suppose that it is a candidate law that all Fs are Gs and that there is some last thing that is an F (all the other F things having been Gs). Put at its simplest, the claim is that I cannot make the candidate law a law by causing the F to be a G and stop it from being a law by causing the F to be not-G but something else. But now consider () () If I had snapped my fingers, then the past would have been different. Lange accepts that counterfactuals like this would be true, although, in foretracking contexts, takes them not to be (Lange (), pp. –, (), pp. –). He can strike this balance because he adopts the position, which we shall discuss later, that counterfactuals are evaluated relative to a smaller class of propositions than those needed to specify a whole possible world and, thus, takes the implications for the past to be offstage. In any event, () seems just as implausible as the counterfactual concerning laws in all but special cases. It is certainly no more plausible than the corresponding counterfactual concerning laws when thinking through the implications of determinism (cf. Lange (), p. ). If backward causation is a possibility, then there may be cases in which () is intuitively true, even taking it to have a causal connotation. Outside of these, we seem no more able to affect the past than we are able to affect the laws. There is a further consequence of being much more concerned about the difference to laws if I acted in a certain way than the difference in the past, under determinism. If the past would be very different if I acted in a certain way (because the laws are kept fixed), then the causal circumstances in which my action operates will be very different too as a result. Suppose I am considering what would happen if I struck a match in a room with a suitable proportion of methane to oxygen (methane should be between – per cent of the air in the room I gather). Let’s say the methane level has just reached  per cent and the other facts are propitious. I take it that the counterfactual ‘If I were to strike a match, there would be an explosion’ is true. However, under determinism, my counterfactual action would be the result of many changes in the past (given that the laws must be kept fixed). Who knows whether those changes would occur without changing the methane level currently in the room as a consequence? So we lose the intuitive truth of the counterfactual and undermine the validity of our counterfactual reasoning about the future. Accepting the truth of many backtracking counterfactuals relating to the past affects the truth of many foretracking counterfactuals about the future (Downing (–), Lewis (), pp. –).

 ’     



If determinism is true, though, then the following (it seems) must be true. () If I had snapped my fingers, then it would be the case that either the laws are different or the past is different. Placing the perfect match condition above the no local violation of laws condition provides one way of balancing the past against the laws. Placing the no local violation of laws condition above the perfect match condition provides another way, favoured by Lange. Given that Lange takes () to be false, he must hold that there is a noncausal sense in which changes in my behaviour relate to changes in the past (e.g. Lange (), pp. –). Why should we suppose that the connection between my behaviour and changes in law is any different? It seems perfectly plausible to reason as follows (a) If I were to snap my fingers and the past were unchanged, then the laws would have to be different. There is a non-causal sense in which, if there were changes in our behaviour, there would be changes in the law just as in the case of the past. The ‘would have to be/ have’ construction implies ‘would have’ although it suggests something stronger in which other options are ruled out, not necessarily by causal means of which () is a case in point (cf. Lange (), p. ). Similarly we might reason (b) If I were to snap my fingers and the laws were unchanged, then the past would have to be different. Those who are inclined neither to take the laws or the past as fixed aren’t, by their moderation, committed to a causal reading of how the laws and the past would be different. Lewis’ similarity weighting should not be taken to be balancing causing changes to the laws with changes in perfect match. The similarity weighting just involves a judgement about the relative weight of two kinds of difference in the evaluation of counterfactuals. Whether or not this involves causing changes in one or the other involves appeal to additional considerations (e.g. satisfying the analysis offered later in the book). Recognition of the distinction is independent of one’s theory of law. For example, even if laws don’t supervene upon particular matters of fact, the distinction is necessary so long as the following holds. ()

Metaphysically necessarily, if it is a law that all Fs are Gs then all Fs are Gs.

Suppose there is an F; then if it is not a G, the law doesn’t hold. The connection between the presence or absence of a G in those circumstances and the law is a noncausal one. Events can make a law fail to hold in this sense but they can’t make a law a law (if laws don’t supervene upon what patterns of properties are instantiated). For further discussion, see ..–. There are two immediate consequences of this point. The first is that it does not follow from the fact that, if I were to do A, the laws would be different, that I am able to break the laws. You might think that the laws rule out me doing A and, yet, if counterfactually, I did A, the laws would be different. The second is that taking the laws to be invariant, in the circumstances in which I snap my fingers, is distinct from

    taking them to govern what goes on, or denying that we are able to break the laws. We have just seen that this is so in the case of denying that we are able to break the laws. The claim in () that there is a metaphysically necessary connection between the law that all Fs are Gs and all Fs are Gs is a plausible characterization of laws governing particulars. Nevertheless, it is compatible with this claim to note that the laws would be different, in the non-causal sense, if different particular matters of fact were to hold, perhaps as a result of what we do. Proponents of invariance are in no position to resist the non-causal reading, concerning how differences in particular matters of fact would imply differences in law, given what they must allow about the past. Invariance, by their lights though, is an insistence on laws being held fixed even on the non-causal reading. It is their insistence upon this point that makes invariance distinct from, and not required by, these other notions of governance or inability to break the laws. The motivation for taking laws to be invariant is, thus, the success or otherwise of so doing for providing an analysis of law. The discussion of laws in Chapter  together with the counterintuitiveness of backtracking, and its consequences for foretracking counterfactuals, constitute my reasons for resisting invariance and the changes to the similarity weighting it would imply. Moreover, the role of laws in the similarity weighting attributes a more modest invariance to laws. While this might not be as neat as Lange’s preferred invariance for laws, there is no reason why it could not be the basis for an analysis and, indeed, it is. As we shall see, though, a key element is an appeal to causation (.). Let me consider three objections to the position sketched here. The first is that, under determinism, even if I did not snap my fingers, I am able to snap my fingers. If I am able to snap my fingers, then I am able to do something that, if I did it, would make a law, which actually held, fail to hold (given the past is held fixed). This is unacceptable. In response, we should distinguish between the ability to make this or that the case and the ability to do something which, if one did it, other things would be the case in a non-causal sense. Even if I do have the ability to snap my fingers in the situation envisaged, the ability to change the past or laws that this implies is ability in a weaker sense, one that does not imply causing these changes. I remain neutral over whether we are able to snap our fingers in a deterministic world in the situation envisaged. Let me underline the point in another way. Alvin Goldman argued that our basic acts level-generate other acts in various ways due to the context in which they occur. In a case of simple level-generation, for example, Alvin’s dangling a line in the water levelgenerates Alvin fishing (Goldman (), p. ). My snapping my fingers, though, does not level-generate my either making the laws or the past different. If I snap my fingers, then in that context, either the past or the laws are different to the way they are if I don’t snap my fingers. But that doesn’t imply that my action is making either the past or laws different. Suppose I don’t, in fact, snap my fingers. Let the past be P and the laws be L. In circumstances in which I do snap my fingers, let us suppose that both are different. Thus we have L* (≠ L) and P* (≠ P). Then my snapping my fingers is a doing of something in an L* & P* context. It is not changing an L & P context to an L* & P* context. If I snap my fingers, I was never in an L & P context. In contrast with Lewis’ position, I don’t allow that there are law-breaking events, which would lead up to the (counterfactual) finger snapping, but that we just don’t

 ’     



cause them (Lewis (a), p. ). Even if my decision going one way rather than another is the point of divergence from the actual world to lead to my snapping my fingers, all that has happened is that the decision has occurred in a world with different laws and/or past. The issue of whether I have an ability to snap my fingers in a deterministic world remains to be decided (in this I agree with Helen Beebee’s rejection of the helpfulness of the distinction Lewis makes, although for different reasons) (Beebee (b), esp. pp. –). The second objection is that allowing perfect match a weight over local law violations cannot yield the appropriate verdicts regarding certain counterfactuals. One recent example is as follows. Let L be a simple true deterministic law that Frank, a philosopher of physics, has devoted his life to studying, that he has not been given a glass of water for his latest talk on the subject and that Nancy, in a public debate, is (wrongly) arguing that there are isolated exceptions to certain generalizations that follow from L, contrary to what Frank has always argued, and thus the law is wrong (Dorr (), p. ). Consider () If we had given Frank a glass of water, his whole career would have been devoted to a mistake. The charge is that prioritizing perfect match would render this counterfactual true but it is clearly false. A key assumption of this case is that there is just a single simple deterministic law that impacts upon it. Suppose there are two ways in which the past could diverge in appropriate ways, to maximize perfect match, and yield the truth of the antecedent, appealing to laws L₁ and L₂ respectively. Then it is not the case that Frank’s whole career would have been devoted to a mistake but only may have been devoted to a mistake. This is nowhere near as counterintuitive. Further ‘his whole career would have been devoted to a mistake’ has a certain amount of rhetorical force behind it. Although the law is wrong, if the exception is minor, just enough to result in Frank being given a glass of water, then the law is likely to be very nearly right. ‘If we had given Frank a glass of water, his whole career would have been devoted to something that, at least, contains a minor error’ lacks the same intuition tweaking counterintuitiveness. Finally, while it is implausible that subjects have detailed commitments concerning the complexity of laws, or for that matter, the integration of the past, in their evaluations of counterfactuals, it is plausible that the intuition that () is false rests on the implicit assumption that there is a complex of factors that give rise to the way things are and that the contrary to fact antecedent of a counterfactual may come about in any of a number of different ways. Cian Dorr suggests () is the kind of counterfactual in which everyday folk are interested, as opposed to claims like if such and such were the case, it would have to be the case that either the laws or the past are different, which are only of interest to philosophers (Dorr (), p. ). Unfortunately ordinary folk have the tendency to be remarkably interested in such counterfactuals about the past of the general kind when the topic of determinism comes up. So I resist the claim that, when faced with () If we had given Frank a glass of water, his whole career would have been devoted to a mistake

    and () If we had given Frank a glass of water, the past would have been somewhat different (right back to the initial conditions of the universe), ordinary folk say () is clearly more counterintuitive. But rather than debate over the capacity of ordinary folk to have conviction about the relative plausibility of abstractions, consider the following () If I had given Frank a glass of water, much of what I remember about my past life would be a little different and many of my actual memories systematically false. This is very counterintuitive but seems to be a consequence of Cian Dorr’s argument that contrary to fact antecedents come to be true by changes to the past right back to the initial conditions of the universe that, at least, preserve approximate match (Dorr (), pp. –). In the case of my decision to give Frank a glass of water, the relevant changes would include changes in my life and these would be the basis of the claim that () would come out true. If we have an explanation of why (), at least, seems false, based upon our implicit empirical commitments, and there are other counterfactuals whose intuitive falsity is supportive of the weight we have given to perfect match in the past, then we have no grounds to revise the similarity weighting. Certainly we lack the crispness of the verdicts about Nixon and the holocaust that generated Lewis’ similarity weighting in the first place. The third objection targets an assumption upon which I traded in the reasoning. It is that, we need to evaluate a counterfactual with regard to a complete set of circumstances: a possible world. The assumption is in play in forcing us to consider the relative weighting of perfect match and various law violations. As I noted, Lange abandons the assumption to retain the counterfactual invariance of laws without having to endorse the consequences of the truth of lots of backtracking counterfactuals in evaluating a foretracking counterfactual (since trade-off with perfect match is no longer required) (Lange (), pp. –, in earlier work he retained the laws even though they were violated Lange (), pp. –). The plausibility of there being trade-offs between past and laws, rather than wholesale changes of the former to keep the latter fixed, is a point against Lange’s position. It may be that we can overlook what made a certain counterfactual antecedent true in most cases because it is indeterminate and our focus is elsewhere. Nevertheless, there are circumstances in which this is highly salient and, then, it is quite clear that we assume that circumstances are similar in relevant respects to the actual world in the way the similarity weighting seeks to articulate. For example, if I were to announce to my family now that I am an extra-terrestrial visitor, we would not predict that they would inquire about interstellar travel and life on other planets, as opposed to display condescension and concern. This is presumably because the circumstances we consider are ones in which I have had the kind of life which would make such an utterance rather surprising rather than one which involved the fact that I stepped from a rocket, took off my space helmet, and gently insinuated myself into their lives. Yet, presumably, such an announcement would involve the breaking of some laws given standard assumptions about my mental stability and grip on reality.

 ’     



b2 h2

b1

W h1

h3

p

Figure .

A challenge for my defence of the orthodoxy would be cases in which, it seems, the possible worlds approach cannot capture the counterfactuals we are inclined to assert. Here is a candidate case due to Stephen Barker (Figure .). We are to imagine a cylinder with three holes, one in the top (h₂), two in the sides (h₁, h₃). If a ball, b₁, is fired in way W, it will pass in through h₁ and out through h₃. In fact, no such ball is fired, and a ball, b₂, drops through h₂ to be lodged on a pillar (p) which would be on the flight path from h₁ to h₃ (Barker ()). Barker suggests that the counterfactual ()

If b₁ had been fired in way W, it would have passed through h₃

is false because of the other ball blocking the flight path. However, if b₂ had not dropped, then () would be true. Thus, the following is true. () If b₂ had not dropped through h₂, then if b₁ had been fired in way W, it would have passed through h₃. The problem for the proponent of the possible worlds approach is that, to keep perfect match, we must suppose that there is some violation of the laws to deflect b₂ from going through h₂. In those circumstances, who is to say that the laws in question—for example the gravitational laws—might not affect the flight path of b₁? Barker concludes that the possible worlds approach fails to capture the intuitive truth values of counterfactuals such as these. A response to Barker’s challenge is that his suggested way in which the antecedent might be true—that is, a significant and highly general law violation—would violate the perfect match condition since it would have many implications for past events as well as the subsequent events which are the subject matter of the target nested

    counterfactual. As a result, a small localized law violation, perhaps involving a change to the dropping ball to disturb its flight or an intervention, for example a collision with something not present in the actual world, is the most natural way in which the truth of the antecedent will be realized. This presents no difficulty for obtaining the correct truth values for () and (). Barker’s answer to a response of this kind seems to be that small localized violations of a law—for instance, the counterfactual world involving a putative law that doesn’t hold in a certain spatiotemporal region—would result in something which shouldn’t be counted as a law at all because, otherwise, we’d have a law which gives significance to a physical particular, such as a spatiotemporal region. On the other hand, identifying some general characteristic that explains why there is a disruption in the flight path in the spatiotemporal region would ramify and, thus, reduce perfect match so that it becomes unclear whether the envisaged circumstances would hold at all (Barker (), pp. –). The challenge is overstated. Of course, it is possible to argue that there is some deep connection between various laws and/or too many exact duplications of particular types of circumstances so that a small miracle can’t produce the desired upshot of the antecedent being true without radically undermining perfect match because of the implications elsewhere. However, we have no particular reason to believe that this is the case for the circumstances in which we have firm intuitions about the counterfactuals that hold. So long as there is some property that distinguishes the circumstances envisaged, from all other past circumstances (say), this can be built into a different law that allows for the relevant exception. If there is not, we can suppose that some novel entity has an impact in those, now slightly changed, circumstances. Alternatively, we can suppose that some law is minimally indeterministic, rather than deterministic, and stipulate that it fails at this moment. Since this would allow us to preserve perfect match without law violation in all other circumstances there is no reason to suppose that this will ramify. The options considered above don’t trade upon the laws of nature being lossy but this is another option. The idea is developed by analogy with data-compression techniques. The law statements, which are part of the best system of laws, provide the most effective means of data compression regarding the particular matters of fact in a world. They are rough generalizations capturing as much information as possible given certain limitations and are not meant to be exceptionless (Braddon-Mitchell (), pp. –). The laws are the patterns picked out by these law statements. Lossy laws, plus the initial conditions of the universe, allow us to reconstruct a good approximation to the subsequent particular matters of fact. They are compatible with the world being deterministic so long as you don’t assume that laws govern the development of the world as opposed to constitute a pattern described by a law statement. If lossy laws were to be thought of as governing worldly development, then the pattern of events could not display an exception to the law unless the law was indeterministic (Barker (), p. , for this assumption). That is not the picture proposed. If the laws are lossy, then the need for a miracle to bring about the truth of the antecedent does not require that, in the counterfactual world, different laws hold. The same lossy laws may hold. So no, alternative, allegedly peculiar laws are required. If an exception to the law statement holds, what should we say about the truth of the

     



law statement given that it is of the form ‘All Fs are Gs’ (i.e. no exceptions are catered for)? On one view, it is a false law statement but still part of the best system of laws. On another view, the truth of the law is settled by the fact it is part of the best system of laws even if the generalization, which the law statement expresses, is false (Braddon-Mitchell (), pp. –). We have enough to conclude for now that the appeal to possible worlds remains a plausible articulation of our commitments in the case of counterfactuals. Contrary to what is suggested, there are no insuperable difficulties to them providing the intuitive truth values we assign to counterfactuals. However, consider the proposed alternative. The idea is that, rather than generate whole worlds, we envisage holding fixed smaller classes of propositions against which we evaluate the counterfactual by appeal to the actual laws. The rest is offstage (Barker (), pp. –). This misidentifies an important feature of our counterfactual thought. The rest is offstage not because it is not part of our evaluation of counterfactuals but because it is thought to be irrelevant. There will be ways in which the antecedent would be true without radically altering the set up against which one wishes to evaluate the counterfactual. If we see that we are mistaken about this, we would adjust our evaluation of the counterfactual. This is easiest to establish if there are convincing supernatural truths. Thus, for example, if I am later convinced that there is a malicious demon out to thwart my attempts to pass a ball through the cylinder, then I would be inclined to deny the embedded counterfactual and claim that something else would have got in the way, the ball would have changed, whatever. This is regardless of what pragmatic factors served to fix the collection of propositions held fixed at the time to which the actual laws were applied. Assumed irrelevance of large tracts of the worlds—which assumption may well be mistaken—is not evidence in favour of something more local being all that is relevant to determining the truth of a counterfactual. Other illustrations are given towards the end of .. The next section seeks to put pressure on the significance of the perfect match requirement from another direction. Instead of there being a conflict with laws, we will face a situation in which absence of conflict makes its application completely unchecked.

. The Future Similarity Objection under Indeterminism Let us return to Nixon and the holocaust. The counterfactual ()

If Nixon had pressed the button, there would have been a nuclear holocaust

was advanced by Kit Fine as a problem for Lewis’ position on the understanding that Lewis was appealing to an intuitive understanding of similarity between worlds. On the assumption that our world will not have a nuclear holocaust, it is going to be very unlike any that does and very like any that does not. Hence, Fine suggested, we should conclude the counterfactual is false (Fine (), p. ). This became known as the Future Similarity Objection. Lewis’ similarity weighting discussed above was

    fashioned to deal with the difficulty as it stands. However, it appeals to two contingent facts in order to succeed. The first is that a cause will have many consequences. The second is that in order to cover these up we will have to violate the actual laws. It is no surprise that the future similarity objection is resuscitated when these facts come under question. I will discuss failure of the first contingent fact more in .. For now, I will focus on the second. The treatment recommended here will also assist in dealing with the first issue. The original future similarity objection worked under the assumption of determinism. If the world is indeterministic, then all the effects of Nixon pressing the button can be covered up without law violations. For instance, if it is a law that, for all x, if Fx, then chance (Gx) = ., it is no violation of this law if Fa and not-Ga. Indeed, a certain proportion of instances of Fa and not-Ga are explicitly expected by the law. Therefore, Lewis’ similarity weighting would proclaim () false. By itself, this might not seem to be too counterintuitive. In spite of the fact that we are inclined to utter lots of would-counterfactuals in a world we take to be indeterministic, it might be thought that, strictly speaking, none of them are true. Moreover, we can still truly say () If Nixon had pressed the button, then a nuclear holocaust would have been very likely. The real problem is that Lewis’ similarity weighting proclaims that () If Nixon had pressed the button, then there would not have been a nuclear holocaust is true. The closest world to the actual world will be one in which there is a complete cover-up since this will involve no law violation and secure the maximal amount of perfect match. The Indeterministic Future Similarity objection is not met by altering Lewis’ analysis of counterfactuals in any obvious way, for instance, by holding that ‘“If A were the case, then C would be the case” is true if and only if (i) the vast majority of closest A-worlds are worlds in which C (ii) in the actual world, if A, then A and C’ (canvassed in Bennett (), pp. –, though I have made one adjustment since Bennett seems to overlook the possibility that the counterfactual is true when not-A and (i) is met). The intuitive line of thought behind such an alteration would be that, if C has only a high, but not equal to one, probability of being true given the antecedent is the case, C won’t be true in every close-by A-world. Nevertheless, it will be true in most close-by A-worlds. Unfortunately, this approach cannot be maintained with Lewis’ account of the similarity weighting of worlds, and the proposed adjustment below vitiates the need to change the analysis. If we can obtain more perfect match without law violation, then no close-by A-world will be a C-world. All close-by A-worlds will be worlds with perfect cover-up and so no holocaust. Strengthening the first condition of the similarity weighting—the no widespread miracles condition—does not seem to work either, for example, by requiring that there should be no widespread occurrence of improbable events or a remarkable coincidence (a ‘quasi-miracle’, Lewis (b), pp. –). Lewis rightly identifies that the problem with the first suggestion is that it threatens to make the actual world less similar to itself than, according to the similarity weighting, another possible world.

     



The problem is that the actual world plausibly contains many improbable events whose replacement by more probable events in a counterfactual world would make that world more similar to the actual world (by the similarity weighting). This is unacceptable. However, it is hard to see how Lewis’ favoured approach avoids a similar difficulty: remarkable coincidences also occur in our world. Moreover, appeal to quasi-miracles has two further problems. First, it introduces a questionable level of anthropocentricity in the assessment of counterfactuals (McDermott (), pp. –). According to Lewis, remarkable coincidences are what we count to be remarkable, for instance, monkeys managing to produce the collected works of Shakespeare by random typing. Monkeys typing an equally improbable particular random letter sequence with few apparent words, the same spaces, and the same length as the works of Shakespeare would not seem remarkable and, hence, not count as a quasi-miracle. Second, as John Hawthorne pointed out recently, we are in danger of unfortunate trade-offs between the remarkable and improbable. For instance, we have to accept that () If I were to toss a coin a million times, it would not come up either all heads or all tails is true but () If I were to toss a coin a million times, I would not get a sequence S (where S is a particular random sequence of heads and tails) is false (Hawthorne (), pp. –). Yet P (all heads or all tails) is higher than P(S). This last point underlines the significance of the point about anthropocentricity. While we might initially think that it is remarkable rather than improbable coincidences which are to be avoided, it is pretty clear that we don’t think that an acceptable price of avoiding the remarkable can be a favouring of the less probable over the more probable in one’s view of what may occur. Regarding the first of these problems, it might be suggested that we could just stipulate that the actual world is most similar to itself. However, the fundamental problem is the havoc this proposal plays with the purpose behind the perfect match condition. Suppose that our past contains many improbable or remarkable events and we are considering the truth of a counterfactual. Then the closest world will have stripped out all these improbable or remarkable events with resultant loss of perfect match. Now the conditions holding when the truth of the antecedent is realized will be very different. Who is to say whether the consequent will be true? In any event, even if its truth or falsehood is clear, the truth values assigned to the counterfactual will depart radically from what we assume is the case. What would happen if I criticize the current government? Perhaps I would be shot because stripping out the remarkable and improbable events may have resulted in Nazi Germany winning the Second World War and ruling in the United Kingdom. Or perhaps I would be thrown to a herd of tyrannosaurus rexes to eat kept especially for the purpose of eradicating awkward opponents, given that the dinosaurs had not been wiped out by an improbable event. A more promising approach is to look to our understanding of laws under indeterminism to provide the solution to the indeterministic future similarity objection. As we shall see in more detail in .., and as we touched on earlier, Lewis’

    conception of laws is of those patterns that are expressed by general statements that form part of the best system for characterizing the overall pattern of events in the world. ‘Best’, here, is understood in terms of simplicity and strength. There is a tradeoff between having the fewest number of generalizations (formulated in some favoured vocabulary) (simplicity) and their joint capacity to entail all the particular matters of fact of the world (strength) (Lewis ()). The existence of indeterminism introduces a new factor, since indeterministic laws cannot entail all the particular matters of fact of the world: fit. In the case of finite worlds, indeterministic laws fit one world more than another if they make the events of the first world more probable than the events of the second world. In the case of infinite worlds, this measure does not serve to differentiate between worlds since the probability of any infinite sequence of events, each of which having less than  probability, is . To deal with this case, it is proposed that we move to evaluating the probability of certain test propositions concerning the character of the sequences in the worlds given the laws. These test propositions concern the typicality of the sequences, for example, the limiting frequency of a certain type of event (e.g. heads from tossing a coin); the probability of one pattern occurring as much as the other, and so on. Indeterministic laws fit one infinite world more than another if they make the test propositions of the first more likely than the test propositions of the second (Elga (), pp. –). With this refinement in place, Robbie Williams puts forward the following adjustment to Lewis’ similarity weighting. (WA) It is of the first importance to avoid atypicality of the world as a whole, by the lights of the chancy laws of nature of w₀. (WC) It is of third importance to avoid even small, localized, atypicalities by the lights of the laws of w₀ especially when the atypical region is one that contains the salient location (Williams (), p. , my italics, discussed below). Typicality is the extended notion of fit detailed above. (WA) and (WC) are Williams’ versions of condition (A), the no widespread miracles condition, and condition (C), the avoid local miracles condition, respectively. Although I shall discuss problems with Williams’ formulation particularly, the difficulties have general application to this type of approach. The first problem is that, again, these conditions threaten to make the actual world less similar to itself, if it is atypical. Remember that patterns of particular matters of fact can be atypical without implying that the law statements, which pronounce them atypical, are not the best set of law statements. Issues of strength and simplicity come into play. Once more, this isn’t a problem that can be resolved by stipulating that a world is most similar to itself. The issue concerns what worlds are counted as closest to this world for assessing a counterfactual. There is no guarantee that the conditions, which it is natural to presume will hold if the antecedent were true, would in fact hold given this similarity weighting. Thus the verdicts concerning the truth of counterfactuals promise to be highly revisionary. The second problem is that it doesn’t deal with the indeterministic future similarity objection. The kind of cover-up required subsequent to Nixon pressing the button would not amount to a less typical world. All the consequences of the button

     



pressing might be eradicated by what, in the broader scheme of things, may be a single miniscule exception to one of each of a number of laws. This could easily be counterbalanced elsewhere, if it is even necessary. This seems to be accepted by Williams who mentions (WC) as what would deal with the occurrence of locally improbable events, those that might provide the cover-up of the indeterministic future similarity objection (Williams (), p. ). However, (WC) ranks after the perfect match condition. It was the perfect match condition that gave rise to the difficulty in Lewis’ similarity weighting and its retention of its rank in Williams’ adjusted similarity weighting leaves the problem unaddressed. A third worry concerns Williams’ qualification ‘especially when the atypical region is one that contains the salient location’. It is addressed to a slightly different point that we shall consider in . but which I can introduce in preliminary form here because it assists in the development of my own position. Suppose there are n coins each flipped ⁶ times. As n gets large, then, statistically, one coin, ni, will produce a sequence of ⁶ heads. Consider two worlds: one in which my flipping produced a sequence of ⁶ heads, one in which this occurred as a result of someone else’s flipping. Suppose in the actual world, I didn’t toss the coin. Consider the counterfactual () If I were to flip the coin a million times, it would not have landed heads each time. Without ‘especially when the atypical region is one that contains the salient location’, this counterfactual is false. One of the closest worlds is one in which I do produce the sequence. If I may produce the sequence then it is plausibly not true that I would not have produced the sequence. With the ‘especially when the atypical region is one that contains the salient location’, the closest worlds are ones in which the sequence occurs elsewhere and, hence, () comes out true. This takes the desire to secure ‘would’ conditionals in indeterministic worlds a step too far. When told the world is indeterministic, we are prepared to hedge our commitment to the ‘would’ conditionals we standardly assert. Thus, it is not counterintuitive to claim that, in fact, it is not the case that something would have happened, it was just extremely likely. By contrast, consider the following counterfactual () If I were a member of a ,, strong team and each of us tossed a coin a million times, it wouldn’t have been any of us who got ,, heads. In circumstances in which there are so many such teams that statistically one member of one of the teams would get this sequence, it takes a peculiar brand of pessimism to suppose that a member of one’s own team would not be the lucky tosser. Yet, Williams’ adjustment appears to have this result. Better to lose the ‘would’ conditionals than build pessimism into our semantics. A third response to the indeterministic future similarity objection is to weaken the perfect match condition or do away with it altogether. Doing away with the perfect match condition altogether does not deal with the issue. The focus just turns to the equivocal ‘approximate match’ condition. If approximate match is of some significance, then the same problem arises. A world in which there is no holocaust after the button pressing has a greater area of approximate match than a world in which there

    is a holocaust. If approximate match has no significance, then we would have no circumstances in which to assess whether the consequent followed from the truth of the antecedent given the laws. Some match is required. So let us look at weakenings of the perfect match condition instead. In earlier work, Bennett suggested that all the assessment of counterfactuals requires is perfect match at the time of the truth of the antecedent (Bennett (), pp. –). In later work, Bennett supplied two good reasons for not going down this route. First, when we assert counterfactuals, we typically assume that the circumstances at the time of the antecedent will be a little different guided by how the world might have evolved to arrive at the truth of the antecedent. His nice example concerns the evaluation of () If the German Army had reached Moscow in August , it would have captured the city. In assessing the counterfactual, we don’t assume that the city would remain sparsely populated, defended by inexperienced troops, while the more experienced ones remain where they are fighting since-departed German troops that, we are supposing in the counterfactual scenario, reached Moscow. Instead, we assume that the German troops had fought more successfully and the Soviet troops had retreated (Bennett (), pp. –). Second, we also assert counterfactuals where we assume that the past leading up to the antecedent is more or less in place. Again, Bennett provides a nice example. () If that hill outside Syracuse had not been levelled last year, it would have been a superb site for a memorial to the Athenian soldiers who starved to death in their marble quarries. The counterfactual is only true because, in fact, Athenian soldiers did die in   in the way described (Bennett (), p. ). Thus, there seems no escape from a version of the perfect match condition that looks at total world histories and not just a portion of time around the time of the antecedent. However, this is not the only way in which the perfect match condition may be weakened. In ., I set out my preferred alternative.

. Antecedent-Relative Potential Chance-Raising The indeterministic Nixon case reveals that we don’t attach weight to perfect match in particular matters of fact that is obtained at a certain cost. Consider a counterfactual world in which the antecedent of a counterfactual is true. As a result, some events distinct from those mentioned in the antecedent will be less probable than they would be if the antecedent were false. If a more extensive area of perfect match is secured by events whose occurrence in that world has been made less probable by the antecedent, then the more extensive area of perfect match has no value. This only applies to antecedents that are actually false. We do not wish to undermine the status of the actual world as ‘closest world’ in the circumstances where, as things turned out, a string of events made less probable by those mentioned in the true antecedent actually occurred. Otherwise a counterfactual could end up false in spite of the antecedent and consequent being true simply in virtue of another world, with the less probable events being excised,

-  -



being counted as ‘more similar’. Nixon’s pressing of the button makes the holocaust more probable than it would otherwise be and, thus, the absence of a holocaust less probable. If this is so, it is not appropriate to retain perfect match with regard to this feature. Thus, it is taken out of the calculation. As a result, () If Nixon had pressed the button, then there would not have been a nuclear holocaust is false. As we shall see, probability raising or lowering is insufficient for causation and, so, such an appeal does not make counterfactuals depend upon an analysis of causation. There may be events leading up to those involving truth of the antecedent that end up being less probable than they would be if the antecedent were false. The perfect match condition would not apply to these either. This is entirely appropriate and introduces no features not already present in Lewis’ original similarity weighting, which relied upon small miracles to give rise to the truth of the counterfactual antecedent. These components of perfect match that don’t matter lie in the transition period. It is easy to explain why we don’t value perfect match in this regard. We engage in counterfactual reasoning to consider what differences there would be to the world if certain things were to happen, a subset of which we can affect. The perfect match condition reflects the fact that we are interested to evaluate this in circumstances that, otherwise, are very similar to our own. Inoculating against the consequences of changes to the world envisaged in the antecedent, by valuing perfect match in events made less probable by events mentioned in the antecedent, vitiates the purpose of such reasoning. Although the general idea is clear, it unfortunately needs an adjustment. Consider the following case. There is an indeterministic lottery draw which you set going by pressing a button. A signal travels into a box which, when it reaches point r, randomly goes down either a path leading to a randomizing device r or another leading to a randomizing device r. Each gives the same chance to each possible outcome of the lottery. The paths reconverge and lead out of the box to a display. The box is totally impenetrable and isolates the causal processes going on within it from all other events in the world. In fact, the signal travelled down the path to r resulting in the display of the winning number: .

r2

17 r1

r3

Figure .

Consider the counterfactual

    () If the random process at r had turned out differently and the signal had travelled from r to r rather than r, ticket number  would still have won. Intuitively () is not true in the situation described. Yet, Boris Kment (whose example this is) claims that we might secure more perfect match, if we retained the winning number as  (Kment (), p. ). The changes consequent upon the different path travelled by the signal have no repercussions for the future because the box is totally impenetrable. So a more extensive perfect match, rather than just some approximate match, can be secured by keeping the winning ticket fixed. The point applies to Lewis’ original similarity weighting but it applies just as much to the proposed revision I am discussing since the truth of the antecedent does not make the winning ticket number, , more or less probable. Kment suggests that the moral to draw from this case is that only certain kinds of perfect match matter: perfect match for those items with the same causal history (or no causal history in the default case) (Kment (), pp. –). Applied to the lottery case, the ticket number being  would not be a relevant case of perfect match because its causal history is different in the two cases. As Kment acknowledges, appeal to causal history faces a counterexample of its own. Certain differences in causal history do not undermine an event’s contribution to perfect match. For example, suppose that there are two qualitatively identical cell phones, CP and CP, randomly varied day by day for Susie’s use, the lottery administrator. The following counterfactual seems intuitively true without a special story. () If Susie had used CP rather than CP for that day, the outcome of the lottery draw would have been the same. Nevertheless, the phone counts as a difference to the causal history of a particular outcome (Kment (), pp. –). Instead of appealing to a potentially irrelevant causal history, we should appeal to the notion of making more probable, in the absence of the alternative path. Using a mechanism I discuss further in .–. as part of the toolkit for providing an analysis of causation, we may define a notion of making less Σ-probable as follows. e₁ makes e₂ less Σ-probable iff there is some (possibly empty) Σ-set of actual positive events such that, for some time of assessment t, (i) if e₁ were to occur without any of the events in Σ, it would be the case that the mean value of ch(e₂) is x; (ii) if neither e₁ nor any of the events in Σ occurred, it would be the case that the mean value of ch(e₂) is y; where x < y. We put events in Σ to see how our target event, e₁, lowers the chance of e₂ in the events in Σ’s absence. I discuss the need to appeal to mean value in general in .., so set it aside for now. The chances of an event fluctuate over time. The phrase ‘for some time of assessment t’ seeks to acknowledge this. The idea is that one event makes another less probable if at some time its presence or absence influences the chance of the other event occurring. We would then formulate the restriction on (B), the perfect match condition of the similarity weighting as follows.

-  -



(B*) It is of the second importance to maximize the spatiotemporal region throughout which perfect match of particular fact prevails unless, in so doing, we fail to minimize the occurrence of distinct events (or their absences) that the counterfactual events required for the truth of the antecedent of the counterfactual make less Σ-probable, given that the antecedent is actually false.¹ Appeal to Σ-probability retains the result we want regarding the Nixon case since Σ can be the null set. In the lottery case, we would put in Σ the event of triggering randomizing device r. In circumstances in which this failed to occur, the failure of the signal to travel to r would lower the chance of the result, , and, indeed, any other result. No result would be generated. Since the antecedent mentions this Σ-probability lowering event for the result, , a world which extends its perfect match to our world by including the result counts as no closer than a world that fails to include that result. In which case () is false as desired. The winning number may be  but it is not the case that it would still be . By contrast, which cell phone is used does not affect the Σ-probability of the result being the same. So, for (), the lottery result, , can be an additionally significant component of perfect match. The most striking feature of the proposal is that it appeals to a counterfactual in its characterization of making less Σ-probable. An obvious concern is that such an appeal is circular. We need to understand the semantics of these probability counterfactuals in order to understand the semantics of counterfactuals generally. As a special case, we need to appeal to a prior understanding of the probability counterfactuals in order to understand these very counterfactuals. One response to this concern is to note that the perfect match of particular matters of fact that is discounted by the revision to (B), (B*), does not touch, for our present purposes, the key values given to the probabilities, namely those values which hold just as a result of those events mentioned in the antecedent, without whatever events there are in Σ, at the time t at which this is reflected. Subsequent values may be altered by the extent of perfect match allowed but this does not affect the role of the probability conditionals in the perfect match condition. Indeed, these values can be read off from the laws given the events mentioned in the antecedent. A second point is that the appeal to counterfactuals in the similarity weighting can be cashed out in other terms. The appeal is just to provide the most perspicuous characterization of the idea. The underlying thought is that an initial similarity ordering of worlds may be revised as a result of local interworld comparisons ¹ I should acknowledge that my earlier proposal ‘It is of the second importance to minimise differences of particular fact from the actual world which are improbable (here I mean something vague but certainly less than  %)’ (Noordhof (), p. ) doesn’t work. It will only yield the right result in the Nixon case if we allow that a difference of particular fact may just be difference in some relational fact dependent upon the presence or absence of the antecedent. The improbable departure from the actual world is a failure of memory, or a failure of the signal to be transmitted. These both advert to the fact that the button was pressed. It is no departure from the actual world that there is no memory or signal transmitted since, in the actual world, there wasn’t either. But now consider all the improbable particular matters of fact which occur prior to the button pressing. They would all have the relational property of occurring prior to the button pressing which, since they were very improbable, would constitute an improbable departure from the actual world. In which case, the past would look very different if we tried to minimize improbable departures. Who is to say what would happen then if the button were pressed?

    concerning Σ-probability lowerings. Thus, suppose we have three indeterministic worlds: w@: the button is not pressed, there is no holocaust; w₁: the button is pressed, there is a holocaust; w₂: the button is pressed, there is no holocaust. Lewis’ similarity weighting ranks in order of closeness w@ > w₂ > w₁. However, if we compare the Σ-probability of there being no holocaust in w@ with the Σ-probability of there being no holocaust in w₂ and w₁, we find that the value has lowered. So, by (B*), we discard the ordering between w₂ > w₁ and judge them on a par with respect to w@. As we shall see later, there are other local multiworld properties to which we may appeal in the proper understanding of counterfactuals in different worlds relating to non-Humean accounts of law and probability (see Chapters  and ). (B*) does not make ()

If Nixon had pressed the button, there would have been a nuclear holocaust

true. It just makes () If Nixon had pressed the button, then there would not have been a nuclear holocaust false. This seems to me to be the key result. Our fundamental conviction is that it is wrong to say that there wouldn’t have been a holocaust not that, in an indeterministic world, there would have been one.

. The Approximate Match Condition and the Appeal to Causal Independence The least satisfactory component of Lewis’ similarity weighting for counterfactuals is his characterization of the approximate match condition. Approximate match is said to have little or no importance. There is evidence that this is overstated and that certain kinds of approximate match are important. The question is ‘What kinds?’ One suggestion, which has received a lot of support, is that approximate match in particular matters of fact which are causally independent of the truth of the antecedent is important, approximate match in other matters of fact is not (Edgington (a); Bennett (), pp. –; Schaffer ()). Its supporters claim that this is, at least, potentially threatening to counterfactual analyses of causation. They usually go much further. In this section, I shall explain why the suggestion is incorrect. I will also note that, even if it were correct, the threat is overestimated. The motivation for the claim is nicely revealed by a case put forward by Michael Slote who credits it to Sydney Morgenbesser (Slote (), p.  fn. ). The winning number of a lottery is . I bought a ticket with a different number. I truly assert ()

If I had , I would have won the lottery.

Lewis’ similarity weighting would proclaim () false. If we roll back the world to the time at which a lottery ticket is assigned to me, the chances of the winning ticket

   



being  are vanishingly small. Hence it is certainly not the case then that I would have won the ticket with that number, given that the truth or otherwise of the consequent is determined by the laws which hold and the particular matters of fact at the time of the antecedent. Simply requiring approximate match as a matter of fourth importance does not seem to alter the verdict. We secure approximate match no better by keeping the winning lottery ticket as  than we do by keeping me not the winner. Dorothy Edgington compares the lottery case with cases like the following provided by Pavel Tichy (). When Fred goes out and it’s raining, he always takes his hat. When he goes out and the weather is fine, it is – he takes his hat. At the moment it is raining and he takes his hat. Edgington, following Tichy, claims that ()

If it had not been raining, he would have taken his hat

is false. Yet what is the difference between the lottery case and the hat case? Certainly if we were trying to retain approximate match, we should conclude that () is true. Appeal to the importance of approximate match in causally independent facts seems to provide the answer. The reason why we should bring across the winning lottery ticket number is that the winning lottery ticket number is quite independent of whether or not it is mine. The reason we should not bring across Fred wearing his hat is that it is not causally independent of the absence of rain. Edgington argues that, if her diagnosis is correct, then attempts to analyse causation in terms of counterfactuals are doomed. The diagnosis is questionable for a number of reasons. First, as we shall see in Chapter , the counterfactuals upon which my analysis rests do not require, for their truth, application of the approximate match condition of the similarity weighting. The cases above used to establish that some approximate match is significant are ‘hindsight’ counterfactuals. They involve varying the past, knowing how things actually turned out, to make a claim about how things would have been then. Both antecedent and consequent are envisaged to be prior to the time of utterance. By contrast, a counterfactual analysis of causation can be given in terms of counterfactuals in which either or both the antecedent and the consequent may occur after the time of utterance. They are not tarnished by what is required to get the truth conditions of hindsight counterfactuals right. So, even if I am wrong that the approximate match condition should not be characterized in terms of causal independence, the prospects for an analysis of causation would not be undermined. Second, the plausibility of the appeal to causal independence rather turns on how it is characterized. One natural formulation would be that e₂ is causally independent of e₁ iff neither (i) if e₁ were to occur, e₁ would cause e₂ nor (ii) e₁ were not to occur, not-e₁ would cause not-e₂.

Suppose that the world is indeterministic and the causal chain between the rain and, in fact, Fred taking his hat has fizzled out. Fred is just not particularly alert to it raining that day because it has been raining a number of days before and so he takes his hat more or less automatically. Let e₁ be it raining and e₂ be Fred taking his hat. Then, as required, the first clause of the characterization of causal independence is not met. Moreover, suppose that Fred may not take notice of the fine weather

    although he is more likely to do so because it would represent a change in the weather. The second clause is not met either. It is not the case that it failing to rain would cause Fred not to take his hat. So () comes out true. Yet this is implausible in the circumstances described. We don’t think we can take across the fact that he did not take his hat because he may have noticed that it wasn’t raining. The account of causal independence may be strengthened to read e₂ is causally independent on e₁ iff neither (i) if e₁ were to occur, e₁ may cause e₂ nor (ii) e₁ were not to occur, not-e₁ may cause not-e₂.

to avoid this conclusion. I have no objection to such an account. I just question whether it is essential to characterize the approximate match condition in terms of it. Instead, I propose that the proper development of the approximate match condition is as follows. (D*) It is of fourth importance to maximize approximate similarity of particular fact which Σ-probabilistically independent of the truth or falsity of the antecedent. Σ-probabilistic independence is defined as follows. e₂ is Σ-probabilistically independent of e₁ iff it is not the case that e₁ makes e₂ more or less Σ-probable (.). Here if anything is a member of Σ, it will be an actual positive event. e₁ makes e₂ more or less Σ-probable if there is some Σ for which e₁ makes e₂ more or less probable. So if e₁ does not make e₂ more or less Σ-probable, then there can be no Σ for which e₁ makes e₂ more or less probable. Equally, e₁ makes e₂ more or less Σ-probable if there is some time at which e₁’s occurrence makes e₂’s occurrence more or less likely. So if e₁ does not make e₂ more or less Σ-probable, there is no time at which the former’s occurrence makes the latter’s more likely. The importance of this last point is revealed by the case of Fred. There is some time, namely after the causal chain fizzles out, when e₁’s occurrence does not make e₂’s occurrence more likely. Nevertheless, this does not mean that the latter is probabilistically independent of the former by the characterization provided. In the case of the lottery, the winning number being  is Σ-probabilistically independent of my having the ticket number  (on standard assumptions). Approximate match in this respect is important. My having a losing ticket number is not Σ-probabilistically independent of my having ticket number . So approximate match in this respect is not important. Let me explain how the account deals with two potentially problematic cases. Suppose Lucky bets heads when the coin is mid-air, the coin comes up tails and we are invited to consider the following intuitively true counterfactual. ()

If Lucky had bet tails, he would have won.

The fact that the coin comes up tails is probabilistically independent of whether or not Lucky bets. So it should be brought forward. However, the outcome of the bet— Lucky losing—might also seem intuitively probabilistically independent of the bet since it is – whether Lucky wins or loses given he bet tails (Schaffer (), p. ). In response, two points are relevant. First, by betting tails, Lucky has increased his chance of losing from  to  per cent since if he had not bet at all,

       



he would have had no chance of losing. Second, in any event, Lucky losing is not Σ-probabilistically independent of Lucky betting tails with the positive actual event of Lucky betting heads in Σ. Lucky betting tails certainly raises the chances that he will win given that the comparison is now with him not placing a bet at all. The second case is due to Edgington. I am considering whether to get on a plane and decide against it. The plane crashes with no survivors. The crash occurs because the devil spun a spinner and the arrow pointed to crash. Consider the counterfactual ()

If I had got on the plane, I would now be dead.

Edgington argues that our intuitive verdict on this counterfactual differs depending upon the following background information. In the first version, the devil has one spinner to determine whether it will crash with a one in a million chance of coming up heads. In the second version, the devil has two spinners. He uses spinner A if I don’t get on the plane, spinner B if I do. Both give the chance of crash as one in a million. Edgington argues that if the situation was as described in the first version, we would be inclined to say that the counterfactual was true. Whereas, if the situation was as described in the second version, we would be inclined to say the counterfactual was false. According to Edgington, the basis of the difference in verdicts is that, in the second case, my going on the plane is a cause of the devil selecting the second spinner. It can’t be probabilistic independence because the probabilities remain the same whichever spinner is used (Edgington (a), p. ). However, the plane crash is not Σ-probabilistically independent of my going on the plane if we put the spinning of the first spinner in Σ. In those circumstances, the use of the second spinner is a necessary condition of the crash.²

. Match and the Causal Circumstances of the Antecedent: Issues with the Transition Period The appeal to both perfect and approximate match is meant to do two things: first, broadly keep fixed the causal circumstances in which we are supposing the events mentioned in the antecedent to hold; second, avoid building into the semantics for counterfactuals a certain temporal asymmetry. Thus, in appealing to perfect match, Lewis does not say perfect match prior to the antecedent holding. In characterizing it as perfect match, rather than similarity of causal circumstances, Lewis does not appeal to the notion of cause in providing the semantics for counterfactuals. One question was whether the perfect and approximate match conditions manage to do just this or whether, by this self-denying ordinance, they create artefacts: true verdicts for counterfactuals that intuitively aren’t true. A second question is whether these conditions even manage to keep fixed the causal circumstances around the antecedent in the way that we require. This brings us to the second potential trouble spot in Lewis’ theory, namely the transition period: that point from when a counterfactual world starts to diverge from the actual world in order to result in the truth of the antecedent of the counterfactual to the conditions described in the antecedent being realized. ² I’m grateful to Philip Percival for a discussion that led to my rethinking of the treatment of this case.



  

I shall focus upon three issues: first, whether we need an explicit appeal to causal considerations in the characterization of the circumstances; second, whether maximizing perfect match can lead to a bias towards lateness; and third, on which the last two subsections of this section are focused, whether the insistence on perfect match can result in a reduction of the similarity of the circumstances at the time at which the events in the antecedent occur.

.. Backtracking and the threat of circularity We have already seen (and resisted) one way in which backtracking counterfactuals would end up more widely true in .. Another line of criticism, put forward by Daniel Hausman, has been that assessment of backtracking counterfactuals is needed to identify the causal structure behind the truth of an antecedent of a foretracking counterfactual and that we need to identify the causal facts that led up to its truth in order to evaluate whether the consequent holds. If this is right, there is a potential threat to counterfactual analyses of causation because, it now seems, we need causal facts upon which to base the truth of counterfactuals rather than the other way around (Hausman (), ()). Here is one of the cases Hausman provides to illustrate his point. Engineers are trying to predict what would happen if a particular steam pipe were to burst (where the steam pipe is part of a functioning nuclear reactor). Hausman urges that the answer depends upon how the bursting occurs. The pipe may be faulty or a girder may fall on it or there may be an earthquake or sabotage or the pressure may become too great (Hausman (), p. ). The reactor would shut down (let us suppose) if the pipe were faulty or the pressure had become too great. It may not if there were sabotage or an earthquake. So we need to consider the question, if the pipe were to burst, how would it come about (a backtracking counterfactual), in order to work out what would then happen. Hausman claims that Lewis’ similarity weighting counsels ignoring the cause of the bursting and merely considers what would happen if a miracle occurred as a result of which the pipe burst. He understands this in the following way. ‘In considering what would happen, if c occurred, one possibility is that c happened inexplicably, as if by intervention or miracle, but it would be irresponsible to suppose that that’s the only way c might happen’ (Hausman (), p. , (), p. ). It is puzzling that he should write this bearing in mind that he appreciates the details of Lewis’ position described at the outset (Hausman (), pp. –). In Lewis’ sense of miracle, c—in this case the pipe bursting—does not happen inexplicably but explicably due to a difference in the laws that hold. Indeed, it is not as though, in Hausman’s scenario, there would be no miracle. Given that the world is deterministic—something Hausman must be supposing in order to talk of Lewis’ need for a miracle—there will be a small miracle just before whatever Hausman takes to be the sequence of events that led up to the pipe bursting. Our world, after all, is one in which the pipe did not burst. The issue of whether or not a reactor would shut down boils down to the question of whether or not it would shut down in worlds in which the laws are slightly changed so that, what would actually have been the most conservative way in which the pipe’s bursting is caused comes about. The perfect match condition does not require that we

       



leave the change, leading up to the pipe bursting, until the last possible moment, since it can be outweighed by the size of the miracle required for the change. The total effect of the perfect match condition plus the importance of avoiding widespread and diverse miracles, is to keep the counterfactual causal structure, in which the antecedent is true, very close to the actual causal structure. This observation does not rule out considering how the various ways in which the pipe-bursting comes about influences what happens next, for instance: what would have happened if the pipe-bursting were caused by high water pressure, what would have happened if the pipe-bursting were caused by sabotage, and so on. In engaging in counterfactual reasoning, we are not restricted to thinking about what would happen if the pipe burst due to the most conservative way in which it may be caused. The expanded antecedents of the foretracking counterfactuals specifying how the event was caused need not be explicit but may be taken for granted by two participants in a conversation or by the individual counterfactual reasoner. In that case, they would be unexpressed antecedents. There is, thus, no need to adjust the similarity weighting we use to assess such counterfactuals. Hausman’s conviction that such thinking cannot be accommodated by Lewis’ semantics for counterfactuals partly depends on his view about what the perfect match condition requires and partly on his view about the essential role of backtracking in discerning the right causal structure (Hausman (), pp. –, (), pp. –). I’ve discussed the former, let me close this section by briefly focusing on the latter. First, backtracking reasoning is not ruled out by Lewis’ semantics. As we have seen, he just takes it to involve a special context because otherwise we would have no explanation of all the times we ignore backtracking considerations. Second, it is not clear that we do need backtracking would-counterfactuals to discern the right causal structure. Instead we may think, if the pipe were to burst, it may be caused by. . . . We would then engage in foretracking counterfactual reasoning to assess which was the most conservative of the various potential causal paths leading to the truth of the antecedent. So, where Hausman envisages there to be an exploration of the causal structure behind a certain outcome, the present proposal either writes it into the antecedent, leaves it inexplicit as part of an assumed conversational context, or substitutes foretracking may-counterfactuals. Where there is no such exploration, then the proposed similarity weighting provides the appropriate evaluations for the standard would-counterfactuals Hausman discusses. Since the introduction of miracles at some point is common to Hausman’s approach as much as one inspired by Lewis, there is no reason for Hausman to demur at this point.

.. A tendency to lateness? If we are to maximize perfect match, then it may seem as if there is an inbuilt bias in favour of late divergence from the actual world to the world in which the antecedent of the counterfactual is true. John Pollock has provided the following nice case initially reported by Donald Nute and updated and glamorized by Bennett (Nute (), p. ; Bennett (), pp. –). Suppose that there are two opportunities in which a subject’s coat may have been stolen from the restaurant, an earlier one and a later one. If the coat is stolen at the later time, then a certain fence



  

preferred by the later thief would be used. In fact, the coat is not stolen. It seems to be a consequence of the similarity weighting favouring the maximization of perfect match that ()

If the coat had been stolen, it would be at the fence of the later thief

is true. This seems an implausible outcome. Whatever determines when the coat was stolen, it shouldn’t be seeking a greater extent of perfect match with the actual world. Of course, on some occasions, there will be contextual factors that settle that the antecedent picks out an event at one time rather than the other. Both participants in a conversation may have in mind the earlier opportunity. The issue concerns whether, when this is not the case, the truth of () is an implication of the similarity weighting. The first point to make is that even though the case describes two opportunities, there can be other considerations, to which the similarity weighting is sensitive, which favour the earlier opportunity. For instance, one opportunity might involve more disruption of the laws that led to the absence of the thieving than the other. Nute himself implicitly suggests that there may be considerations of this type that swing things one way rather than another when he writes ‘In fact, my experience is that when things are left unattended they tend to be removed earlier rather than later’ (Nute (), p. ). We would not want to disrupt the multitude of laws that make this unfortunate observation correct. It is mainly for this reason, I suspect, that the truth of () seems so implausible. Similarly, the new perfect match condition discounts match that would be obtained by distinct events (or their absences) that the truth of the antecedent of the counterfactual makes less probable. If leaving the coat made the absence of acts of thieving the coat more improbable, then more extensive match obtained by supposing a later act of thievery would be discounted. A second point is that this kind of example may trade, for its plausibility, on an implicit backtracking context. Although the consequent is not a cause of the coat being stolen, at which fence the coat is to be found depends upon which thief stole the coat. So the counterfactual is an expression of the result of a piece of reasoning from the effect to the cause. Backtracking reasoning keeps the laws fixed to ascertain how the particular matters of fact may vary. () seems implausible because, if it were true, the suggestion is that we will always find variation in later rather than earlier particular matters of fact (for further discussion of backtracking see ..).

.. Miracles against match There are alleged to be cases in which the combination of giving first ranking to the no widespread miracles condition and second ranking to the perfect match condition seems to require an untoward reduction in the similarity of the causal circumstances, in which the event or events required for the truth of the antecedent occur, to those that actually hold. Suppose that Nixon, in fact, pressed the button but there was no nuclear holocaust because the Soviets had implanted , cable cutters on the circuit to the missile launch pad. Alexander Pruss argues that the following counterfactual would be true. () If none of the Soviet cable-cutting devices were activated, a nuclear holocaust would have ensued (Pruss (), p. ).

       



Yet, the charge is, Lewis’ similarity weighting (and my revision of it) would proclaim the counterfactual false. One way in which the antecedent would be true is if Nixon had not pressed the button. A second way is that each cable cutter failed to cut in. The first would involve a single miracle just before Nixon’s pressing of the button. The second would involve , miracles. Hence, given that the no widespread miracles condition is ranked above the extent of perfect match, the similarity weighting would pronounce the counterfactual false. In this case, the causal circumstances around the time that the cable cutters might have been activated differ in an important respect from the actual causal circumstances, namely that in the latter Nixon pressed the button. The intuition that the counterfactual is true is insecure. It rests upon two different readings. The first places the emphasis on none of the Soviet cable-cutting devices being activated. Their activation requires a signal travelling down the cable. The similarity weighting favours the signal being absent because Nixon did not press the button. If one focuses on the activation reading, () expresses a bit of backtracking reasoning as in the case of the coat thief and () is intuitively false. If none of the Soviet cable-cutting devices were activated, that must have been because Nixon did not press the button sending the signal. In which case there would have been no nuclear holocaust. The second reading places the emphasis on the Soviet cable-cutting devices not working. Understood this way, we do need , miracles to bring about the antecedent and the similarity weighting would not rule otherwise. For the cablecutting devices not to work, the , miracles are unavoidable. When we hear () in the ‘not working’ sense, of course it is true. Indeed, their failure to work indicates that the signal was travelling down the wire but that they did not cut it off. So what is going on in this case is that we are hearing the activation reading when assessing the most parsimonious way in which the antecedent might hold but switching to the not working reading when evaluating the counterfactual. Once we keep track of these, we hear () as obviously false or obviously true, respectively.

.. Similarity of causal circumstances There are possible worlds involving backward causation in which a certain combination of laws and particular matters of fact mean that an insistence on maximizing perfect match reduces similarity of causal circumstances in which we are envisaging the truth of the antecedent of a counterfactual. Michael Tooley has provided such a case (Tooley ()). Suppose that the following laws hold. Law : For any location x, and time t, if location x has both property P and property Q at time t, then that state of affairs causes a related location x + Δx to have property P, and to lack property Q, at the later time t + Δt. Law : For any location x, and time t, if location x has both property P and property Q, at time t, then that state of affairs causes a related location x Δx to have property P, and to lack property Q, at an earlier time t Δt. Here Δt and Δx indicate small differences in temporal and spatial distance respectively. In brief, law  is a P and not-Q producer at a later time and law  is a P and notQ producer at an earlier time. Each does so in circumstances in which P and Q hold.



  

Now suppose that w₀, has the following characteristics. World W₀ Table . Times

T

t + Δt

States of affairs

Not-Px, Qx

Not-P(x + Δx), Q(x + Δx)

Consider the counterfactuals () If location x had had property P at time t, then location x + Δx would not have had property Q at time t + Δt. () If location x + Δx had had property P at time t + Δt, then location x would not have had property Q at time t. It is natural to consider that both counterfactuals are true and to do so because we have applied, in straightforward fashion, the laws to the circumstances which we presume to hold at t and t + Δt respectively. That is, to look at the application of each law in isolation from the other. However, now we should focus on what would make the antecedent true in each case. One way in which P may be brought about at place x, time t is by the application of law  and one way in which P may be brought about at place x + Δx, time t + Δt is by the application of law . If either of these constitute the preferred way in which P may be brought about, then the causal circumstances around the truth of the antecedent will be different from what we intuitively envisage for the counterfactuals to be true, namely the presence of Q. Our conviction that each of the two counterfactuals is true suggests that, in evaluating each, we simply assume that Qx will be present. It is an unexpressed antecedent of each counterfactual that takes us to different possible worlds, engendered by the context in which we are given the table and the laws. When we don’t make this assumption, then one or the other of the counterfactuals is false. If this is the case, no revision is needed to the similarity weighting put forward. The similarity weighting is meant to capture our default evaluation of counterfactuals and not reflect the impact of special contexts. We can evaluate whether the unexpressed antecedent approach succeeds in dealing with the case by considering whether there are contexts that undermine our tendency to take the relevant presence of Q for granted. Suppose I ask you to evaluate the two counterfactuals by considering carefully the operation of both laws together and, in particular, how P will be instantiated. In those circumstances, I think it is natural to be more circumspect in asserting the counterfactuals. For each, we are inclined to say that they may not be true because P may have been instantiated in virtue of the operation of the other law. Can the similarity weighting endorsed so far capture this verdict? Initially it might seem as if it can’t; that it is committed to the first counterfactual, (), being false and the second, (), being true (e.g. Noordhof (a), p. ). We can maximize perfect match by supposing that there are no changes up until time t, when P is instantiated, due to the instantiation of P and Q at x + Δx at t + Δt. But, in fact, this is far from clear.

       



It is helpful to consider two types of case, one in which the putative causes have multiple consequences and one in which they just have the single consequence detailed in Tooley’s scenario. If they have multiple consequences, then in either direction there will be an extensive cover-up operation required. If the instantiation of P at x, t is due to P and Q at x + Δx at t + Δt, then all the other consequences of P at x + Δx at t + Δt in the direction of t must be covered up to secure perfect match up until time t. The similarity weighting will pronounce the cost too high and favour other ways in which P may occur than by the operation of these laws. So () would come out as true, as would () in a different possible world in which a miracle occurred just before t + Δt rather than t. Suppose that the putative causes only have the single consequence detailed by Tooley. Then while P at x + Δx at t + Δt may be the best way to secure perfect match up until time t, it is similarly plausible that P at x at t might be the best way to secure perfect match into the future from t + Δt. The alternatives to P at x + Δx at t + Δt being instantiated as a result of P at x at t are either that there is a small miracle just before or just after t + Δt. If just before t + Δt, there will be untold consequences in the future apart from P at x + Δx at t + Δt and no addition in perfect match which would already have been lost at t + Δt. If there is a small miracle just after t + Δt because P at x + Δx at t + Δt is instantiated due to backward causation, there would be less perfect match in the future. So, whichever way we look at it, both counterfactuals would then seem false. I have explained how the intuitive verdicts for the counterfactuals can be obtained either by taking Q to be an unexpressed antecedent or by appealing to the standard motivation for the similarity weighting in the first place, namely that causes have multiple effects. Examining the consequences of this assumption not being met will be a matter for Chapter . Nevertheless, there may be the residual concern that what the current example has brought out is that the similarity weighting fails to retain the appropriate level of similarity of circumstances, against which the antecedent of a counterfactual is true, to yield the intuitive truth value of the consequent. However, this seems questionable. We standardly accept that the conditions under which an antecedent may be true will alter, in various ways, the circumstances under which the consequent is subsequently evaluated.

.. Closing remarks The discussion of this section has inevitably been fragmentary. Various challenges have been considered regarding the workings of the similarity weighting in the transition period. These challenges have been case-driven. It is my hope that by discussing them in some detail, it is clearer how the favoured similarity weighting can be applied and the resiliency of the analysis it offers. We found that the adjustment to the similarity weighting recommended underlined Lewis’ emphasis on a graceful transition and that properly understood the cases presented no difficulty to the favoured approach. Doubtless there will be other cases—indeed we will discuss some further issues raised by them in Chapter —but the basic structure of the responses available should be clear. Confidence should be increased about the security of our foundation of the analysis in counterfactuals.



  

. A General Defence of the Approach The discussion of this chapter has led to the following account of the similarity weighting for counterfactuals. (A) It is of the first importance to avoid big, widespread, diverse violations of law. (B*) It is of the second importance to maximize the spatiotemporal region throughout which perfect match of particular fact prevails unless, in so doing, we fail to minimize the occurrence of distinct events (or their absences) that the counterfactual events required for the truth of the antecedent of the counterfactual make less Σ-probable, given that the antecedent is actually false. (C) It is of the third importance to avoid even small, localized, simple violations of law. (D*) It is of fourth importance to maximize approximate similarity of particular fact which Σ-probabilistically independent of the truth or falsity of the antecedent. I will use this similarity weighting to assess counterfactuals in the subsequent chapters with one further revision to be discussed in Chapters –, its final formulation occurring in .. The explicit appeal to Σ-probability rather than causation shows that we don’t need to appeal to causal models in order to arrive at a proper semantics for them, contrary to what has been suggested by, for instance Pearl ((b), pp. –). The analysis, together with the similarity weighting, provides the conditions in which counterfactuals are true. At the beginning of the chapter, I noted I would end by considering an argument against them having truth conditions put forward by Edgington. It begins with some observations about a case involving future indicative conditionals. Suppose that if you’ve had vaccine A and you go on to get disease D, you get side effect S. If you’ve had vaccine B and you go on to get disease D, you don’t get side effect S. If you’ve had both A and B, you don’t get D and hence don’t get S. Observer X knows that Pete has had vaccine A and hence is justified in believing that if Pete gets disease D, he will go on to get side effect S. Observer Y knows that Pete has had vaccine B and hence is justified in believing that if Pete gets disease D, he or she will not go on to get side effect S. At best, only one of these conditionals can be true because, on the supposition that Pete gets the disease, their consequents contradict each other. Yet, all of the facts do not decide between them since Pete had both vaccines and hence will not develop the disease. Edgington concludes that they don’t have a truth value (Edgington (b), pp. –). To move from these future conditionals to counterfactuals, Edgington appeals to Would-Will Correspondence ‘If X had . . . he would have . . . ’ expresses at a later time what ‘If X does . . . X will . . . ’ expressed at an earlier time (Edgington (b), p. ). She invites us to consider what X and Y should say if Pete had been run over by a bus before there was any chance of him getting disease D. She reasons, X will be justified in believing that if Pete had got disease D, he or she would have gone on to get side effect S and Y will be justified in believing that if Pete had got disease D, he or she would not

     



have gone on to get side effect S. For the same reason, she thinks that such counterfactuals lack a truth value. As Edgington is well aware, the rejection of truth conditions for future-directed indicative conditionals is not mandatory. Robert Stalnaker, Brian Weatherson, and Daniel Nolan have all defended the application of possible worlds semantics to indicative conditionals which involve a relativization to the speaker’s epistemic situation (Stalnaker (); Weatherson (); Nolan ()). None of the work in this chapter touches on the viability of this position and I do not propose to discuss it further. I mention it as one plausible way of resisting Edgington’s argument. Instead, let me focus on the extension to counterfactuals. It is causally impossible for Pete to get disease D. Nevertheless, the similarity weighting developed in this chapter allows for counterfactuals with causally impossible antecedents to be true or false. In the present case, we might consider a slightly different world in which having both vaccines doesn’t completely rule out the possibility of getting the disease. Does Pete go on to get the side effects? If it is not the case that he would or that he wouldn’t, then the similarity weighting would pronounce both counterfactuals false (Morton (), p. ). Edgington’s response is that, given that we know the facts, this verdict should mean that we have zero confidence that Pete would go on to develop the side effects and zero confidence that he would not (Edgington (b), p. ). But we don’t. Either seems to have some non-zero probability. There is no reason why we should accept that the observers know all the facts if the Stalnaker-Lewis approach to counterfactuals is correct. Specifically, they don’t know what holds at each world in which Pete goes on to develop the disease. Moreover, Edgington’s connection principle—Would-Will Correspondence—is questionable. When the antecedent is causally impossible the counterfactual may record a substantial truth whereas the corresponding future conditional is empty. This is not the only type of case. There are no circumstances in which it would have been proper for someone to assert in the lottery case we have already discussed ‘If X does choose , he will win’ yet there will be for ‘If X had chosen , he would have won’ (Bennett (), p. ). In response to this, Edgington suggests that a does-will conditional can be right in virtue of the fact that it is rational to assert, afterwards, a had-would-have conditional (Edgington (b), pp. –). This seems to build an unexplained asymmetry into our treatment of these conditionals. Why is it that the later rational assertability of a had-would-have conditional makes an earlier does-will conditional right and not that the latter’s failure earlier to be rationally assertible make the later had-would-have conditional wrong? I know what the answer is if the had-would-have conditional is ascribed truth conditions, but Edgington’s view is that it does not have truth conditions but only conditions under which it would be rational to assert them. All of this suggests that the counterfactual simply does not express the same thing at a later time as the future conditional expresses at an earlier time. I conclude that the direct argument against the approach to counterfactuals defended here is inconclusive. The revisions of the similarity weighting I have defended provides grounds for supposing that the approach is legitimate and may provide an appropriate analytic basis for the development of a counterfactual analysis of causation. It is time to turn to its development.

 A Counterfactual Analysis of Causation In this chapter, I set out a counterfactual analysis of causation. I develop it by discussing some difficulties that have plagued previous accounts of this type with regard to indeterministic causation, early and late pre-emption, and hasteners and delayers. To an extent, then, the theory developed is counterexample driven and, in my experience, this can give rise to dissatisfaction. First, there is the worry that the intuitive verdicts about whether something is or is not a cause, to which I appeal, aren’t robust or have questionable validity. Second, even if agreement can be reached about what we are intuitively inclined to say in different cases, the interest of an analysis based upon these intuitive verdicts can be questioned. Why should something be identified precisely like that and, even if there is something that fits this picture, maybe there is a slightly different one of greater significance? Third, it may be wondered whether there is one kind of thing that is causation or whether there are a plurality of different kinds of thing responsible for the proliferation of the literature. My response is that, at first glance, there are many different kinds of relation that might, and indeed, have been taken as causation or, at least, as essential to causation. For instance, some insist that a cause must raise the chance of an effect (Mellor (), p. ; Beebee (a), pp. –); others insist that causes must be linked by genuine causal processes to their effects and rule out preventers of preventers as causes (Salmon (); Dowe ()); and so on. Each of these requirements has some plausibility and each has been strongly resisted. It is perfectly possible to argue that a kind of thing that had one of these elements would be of great significance, and herein lies the problem. Arguments about the significance of a certain kind of thing are often rather easy to find and can obscure the possibility that a closely related but distinct kind of thing is also of considerable significance. Thus rather than rush too early to some theoretically motivated dismissal of intuitive verdicts as to what we count as cause and fail to count as a cause we should examine quite closely what these intuitive verdicts reflect. The recommended examination will give us traction upon the issue of whether there is a plurality of kinds of causation or simply one. If there are a number of different kinds of candidates for causation each of which clash with some of our intuitive verdicts about what counts as a cause, and none of which does significantly better than the others, then the suggestion that there is a plurality of kinds of causation becomes rather plausible. On the other hand, if we find out that we can characterize something as causation which does rather better than the others, it is

A Variety of Causes. Paul Noordhof, Oxford University Press (2020). © Paul Noordhof. DOI: 10.1093/oso/9780199251469.001.0001

    



more plausible to take this to be causation and the others to be related kinds, perhaps subkinds, but not themselves causation per se. In this chapter, and Chapters –, , I will consider whether there are various kinds of causation in play and allow for two, causation between particulars and property causation. I resist the extension of this further although note that negative causation requires special treatment to fit into this framework (Chapter ). It is quite compatible with my conclusion here that we may recognize a variety of different kinds of cause where by that I mean causes from different ontological categories such as objects, events, facts, and so forth. This will be a subject upon which I focus in Chapter . On the matter of whether our intuitive verdicts are robust and defensible, with some adjustments, I shall suggest that they are. A principal part of my defence of this claim will lie in the characterization of causation I develop from the cases I discuss in the chapter. The interaction between intuitive verdicts and theory comes to a reflective equilibrium with the theory formulated (Goodman (), pp. –; Rawls (), p. ). It is not that my theory accords with absolutely every intuitive verdict about what is a cause and what is not but I explain how, where departures do occur, the departures have clear and principled motivation. Moreover, the intuitive verdicts are at their weakest in these cases. The theory is shown to capture something of substantial practical significance making it entirely plausible that we should have developed and should retain a notion of it to pick out a particular feature of reality with the contours causation possesses. Many of the intuitive verdicts are captured by subcategories of the general notion. So the theory has the advantage of being maximally sensitive to our intuitive verdicts while at the same time suggesting ways in which certain verdicts should be adjusted (often in minimal fashion). I shall argue that causes are entities, for example, an event e₁, which (independently of its competitors) both makes the mean chance of an effect, e₂ say, very much greater than its mean background chance and actually influences the probability of the effect in this way at the time at which the effect occurred via a complete causal chain. No counterfactuals occur in this formulation of the nature of causation. My commitment to a counterfactual theory of causation stems from my conviction that counterfactuals are well suited to capture this general kind of dependency relation. My discussion of the problem cases to follow is, in effect, a discussion of how various counterfactual formulations fail to capture this dependency relation and what should be put in their place. Much of the discussion below is more specifically focused on the problem of characterizing the circumstances in which there is a complete causal chain from cause to effect. Pre-emption, and even more sharply, indetermistic pre-emption is the natural way to deepen one’s understanding of what is required. In such cases, we have two causal chains, one gets to cause the effect and the other does not because the causal chain leading from the pre-empting cause completes whereas the chain from the preempted candidate cause does not. The first section of this chapter introduces the problem and discusses inadequacies of previous solutions, in particular the benchmark theory provided by Lewis. In the second, and largest section of the chapter, a mechanism is introduced by which we can scrutinize the counterfactual dependency at work, in pre-empting and pre-empted chains respectively, and the analysis of completeness is developed. A natural proposal—developed first with regard to



    

deterministic causation—is that an incomplete causal process is one in which there is a missing, required event (..). There are difficulties with this idea though. One line of difficulty concerns cases of immediate causation in which the process just completes at different times or as a result of different factors external to the process (..). A second line of difficulty concerns how we are to understand that there is a missing required event in indeterministic causation (..). A third line of difficulty is that additional redundancy in a causal set-up might obscure whether or not an event is required for a particular causal chain to complete (..). While the last concern can be dealt with by a modification of a detail of the analysis in terms of missing events, the other concerns motivate appeal to the idea of a cause raising the chance of the effect just before the time at which it occurs (rather than just after the cause occurs) (..). However, this proposal faces a difficulty with regard to hasteners and delayers. This is used to motivate a development of the chance-raising idea (..). The mechanism used to isolate the pre-empting and pre-empted processes involves us in considering counterfactual circumstances, and characterizing completeness in that context. The failure of the ‘absent events’ account of incompleteness implies that there are other ways in which a pre-empted process may be counterfactually complete but actually incomplete. .., .., and .. focus on aspects of the timing of the process and show how we can deal with this matter. .. and .. discuss situations in which either there seems to be some theoretical motivation for a competing sign of completeness or the materials—specifically the probabilities—seem to give out ways of dealing with them. Having developed the analysis, I examine how it relates to contextualist contrastive accounts of causation in .. The analysis identifies a non-context-dependent characterization of causation that, initially, might not be apparent from some of the theoretical development of it in .. In the concluding remarks of the chapter, I state the full theory and compare it with a theory rather like it, offered by Michael Strevens, and some clear competitors that approach the issues in a different manner. I identify a problem that they face with respect to the discussion in this chapter. I should make clear at the outset that I am going to be concerned with causal relations between particulars—specifically events. In Chapters  and , I will consider issues relating to their individuation and whether they are the primary relata of causation. I don’t believe that the details of my analysis will be affected by the resolution of these issues. As should become clearer in what follows, one of the advantages of my own approach is that it involves few commitments on this front.

. Indeterministic Causation and Pre-emption: A Devastating Combination In his treatment of indeterministic causation, Lewis put forward an account of probabilistic dependence which may be formulated as follows Event e₂ probabilistically-depends on a distinct event e₁ iff it is true that: if e₁ were to occur, the chance of e₂’s occurring would be at least x, and if e₁ were not to occur, the chance of e₂’s occurring would be at most y, where x is much greater than y (Lewis (b), pp. –).

   -



The phrases ‘at least’ and ‘at most’ have been introduced to try to accommodate Lewis’ point that in the closest e₁-worlds—and also in the closest not-e₁-worlds—the chance of e₂ may fluctuate so that there is no precise chance that e₂ has. The chances mentioned are objective, single-case chances as opposed to frequencies, features of the world and not credences (Lewis (b), pp. –). He remarks that ‘much greater than’ is to be understood here as ‘by a large factor’ not ‘a large difference’ because both of the probabilities may be small (Lewis (b), pp. –). Lewis then defined causation by taking the ancestral of the relation of probabilistic dependence. As a result, we have For any distinct actual events e₁ and e₂, e₁ causes e₂ iff there are events x₁ . . . xn such that x₁ probabilistically depends upon e₁, x₂ probabilistically depends upon x₁ . . . xn probabilistically depends on xn , e₂ probabilistically depends on xn (Lewis (b), p. ). I have suppressed, for the moment, Lewis’ reformulation to deal with late preemption. Lewis himself took the present account to deal with early pre-emption— of which Figure . is an example—and Lewis’ reformulated account does not in fact help with the difficulty identified by Peter Menzies (Lewis (b), pp. –; Menzies (a), pp. –). For the discussion that follows, the most important feature of Lewis’ theory is his subsequent remarks concerning how an event has ‘different chances at different times before it occurs’ (Lewis (b), pp. –). In assessing whether an event e₁ is a cause of e₂, Lewis suggests that we take the chance of e₂ – p(e₂)—to be that which it had immediately after e₁ occurs or fails to occur (Lewis (b), p. ). Counterfactuals with probabilities in their consequents are, then, to be assessed in roughly the following manner (the details are given in Chapter , for summary see .). Go to the closest world in which e₁ occurs (or fails to occur), as laid down in Chapter , and evaluate the chance of e₂ just after e₁ occurs (or fails to occur). Lewis’ account captures the intuitive verdict that the bombardment by the subatomic particle is a cause of the decay in the case discussed in ... The bombardment made the chance of an atom of the element decaying very much greater than the chance would have been had no bombardment taken place. Unfortunately, it faces counterexamples in the form of cases of early pre-emption (Menzies (a), pp. –). Consider Figure .. The lettered circles are neurones that either fire (the filled-in circles) or don’t fire (the broken circles). The connections stimulate (forwards arrow) a neurone to fire or inhibit (small circle) a neurone from firing. A neurone that is both stimulated and inhibited does not fire. It should not be assumed that an arrow from one neurone to another, say b to f, implies that b’s firing causes f ’s firing in isolation. There may be other events in the causal circumstances of b’s firing that, together with b’s firing, cause f ’s firing. Similarly, unless otherwise said, it should not be assumed that b’s firing is an immediate cause of f ’s firing. There may be unrepresented mediating neurones firing. The neurone diagram just enables us to focus on a certain kind of structure of case. In Figure ., the process leading from b to e is unreliable. The inhibitory axon between b and c and the process leading from a to e are more reliable—the a–e



     a

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Figure .

process is very much more reliable left to itself. The problem is that Lewis’ account would imply that e’s firing probabilistically depends upon a’s firing in spite of the fact that c and d don’t fire. Just after a fires, it is still possible that b’s firing won’t inhibit c from firing and hence that the much more reliable a-chain runs to completion. So, at the point in time just after a fires, the chance of e firing later is very much greater than the chance would have been at that point in time if a had not fired (Menzies (a), pp. , ). Lewis’ analysis doesn’t just have problems with causation in neurones. Neurone diagrams provide a convenient way of discussing cases of causation with a certain structure quite generally and I shall be using them for that purpose, with cautions when necessary, in much of what follows. The conditions Lewis identifies are not sufficient for causation. What else is needed? I want to discuss two proposals that won’t work as they stand but which suggest an account that I believe will. Both attempt to characterize the way in which the pre-empted process has not run to completion whereas the pre-empting process has. Menzies suggests that e₁ causes e₂ only if there is a chain of unbroken causal processes running from e₁ to e₂ (Menzies (a), p. , the formulation has been adjusted to fit my discussion). The idea is that for any finite sequence of times between the time of e₁ and e₂, there is a sequence of actual events occurring at these times where x₁ is probabilistically dependent upon e₁, x₂ probabilistically depends upon x₁ . . . xn probabilistically depends on xn–, e₂ is probabilistically dependent on xn. Call this an unbroken causal process. A finite sequence of events is a chain of unbroken causal processes if and only if there is an unbroken causal process running from a to b, an unbroken causal process running from b to c, and so on. Talk of chains of unbroken causal processes is necessary to deal with the fact that e₁ can be a cause of e₂ even if there are some sequences of events between e₁ and e₂ which may not pairwise probabilistically depend upon each other. One example would be the finite sequence of events that just includes b’s firing and e’s firing in the original diagram (Menzies (a), pp. –, (), pp. –). Menzies’ theory allows b’s firing to be a cause since unbroken causal processes can be patched together

   -



between b’s firing and e’s firing whereas no chain of unbroken causal processes can be patched together between a’s firing and e’s firing. Unfortunately, Menzies’ account is inadequate—as he later recognized. First, it rules out temporal action at a distance. It insists that there must be events at all the times between e₁ and e₂ for e₁ to cause e₂. Any theory that failed to rule this out a priori would have an advantage (Menzies (), p. ). Second, it cannot handle cases of either deterministic or probabilistic late pre-emption, that is, cases in which the process pre-empted is pre-empted by the occurrence of the effect. Menzies has acknowledged that this is so for the deterministic case (Menzies (), pp. –). I focus on the probabilistic case that he does not discuss. It raises an important issue for my subsequent discussion. Consider Figure .. As before, the a–e process is very reliable whereas the b–e process is unreliable. The crucial difference is that it is e’s firing which inhibits d from firing. If e’s firing had not occurred at the time it did as a result of the b–e process it would have occurred later— and hence after d firing—as a result of the a-chain. The case obviously rests upon the assumption that particular events don’t have their times of occurrence essentially but could occur later than they did (Lewis (b), pp. –, –). The role of essential properties in causation is discussed further in .. The assumption receives additional support by the discussion of hasteners and delayers below (see ..). The problem that the case presents is that it is hard to see how Menzies’ proposal could obtain the result that a’s firing is not a cause. Remember d’s firing occurs after e’s firing. So at all times up until the time of occurrence of e’s firing, there will be events in the a-chain upon which e’s firing probabilistically depends. So it satisfies Menzies’ condition. It is only if we consider times after e’s firing occurred—but before it would have occurred if e’s firing had not been brought about earlier by the b-process—that we find a missing event: d’s firing. What do these problems show about Menzies’ account? He was right to suppose that the difference between pre-empter and pre-empted should be captured in terms of whether the causal chain between putative cause and effect is complete or not. It is just that he had the wrong account of what makes a process complete. We don’t need a chain of unbroken causal processes involving events at every moment in time between putative cause and effect. We just need all the events that were actually

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Figure .

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

    

necessary for the causal chain to be present. Understanding completeness Menzies’ way resulted in ruling out action at a distance and the problem with the late preemption case. But his way is not mandatory as I shall try to demonstrate. A second idea that might capture the notion of a causal process being complete concerns the time at which the probability of the effect is assessed. The thought is that Lewis identified the wrong time at which p(e) ought to be assessed. He suggested that it ought to be just after the candidate cause, a’s firing, occurred. But it should be assessed just before the effect occurred. In the case of early pre-emption, just before e’s firing occurred, elements of the a–e process would have failed to occur, namely the firing of c and d, so the occurrence or non-occurrence of a’s firing would not be relevant to p(e fires). This would reveal the fact that the a-chain is incomplete. P(e fires) would not be that high just before e occurred, given that e’s occurrence is a result of the unreliable chain. Nevertheless it would display the appropriate probability fluctuation given the presence or absence of, say, g firing. Unfortunately, once again, this delivers the wrong result in cases of late preemption. The problem is that e’s firing occurs prior to the pre-empted event in the a-chain. So at the time just before e’s firing, everything is in place for a’s firing to raise the probability of e firing. It is only after the firing of e occurs that things begin to go wrong as it were. So changing the time at which we assess the chance of an effect by itself won’t deliver the right result in cases of late pre-emption.

. Completed Causal Processes .. Towards an alternative analysis of completeness My account of what makes a process complete is best understood by considering a closely related approach upon which it tries to improve. To deal with cases of late pre-emption, Lewis introduced a notion of quasi-dependence which may be formulated as follows. Event e₂ quasi-depends on a distinct event e₁ iff either (a) there are events x₁ . . . xn such that x₁ counterfactually depends upon e₁ . . . e₂ counterfactually depends on xn, or (b) the intrinsic character of the process involving e₁ and e₂ is just like that of processes in other regions in this or other worlds with the same laws and in the great majority of these regions—measured by variety—these processes satisfy (a) (Lewis (b), p. ). This proposal manages to deal with most cases of deterministic late pre-emption. Consider a deterministic version of the set-up in Figure .. b’s firing on the bottom row would not satisfy clause (a) of this account because there is no event between b firing and e firing upon which e’s firing counterfactually depends. Take the firing of g as an illustration. If g were not to fire, e would still fire brought about by the firing of d on the top row. However, b’s firing would be a cause of e’s firing if it satisfied clause (b) and there is every reason to think that it will. In the great majority of circumstances, chains with the same intrinsic character as the b-chain will occur without chains of the same type as the a-chain. In these circumstances, Lewis claims, there

  



will be a chain of counterfactual dependencies of the kind to satisfy clause (a). Lewis dismisses cases in which the two processes nomically co-occur as ‘very peculiar indeed’ and suggests that they are spoils to the victor (Lewis (b), p. ). There are two significant problems for this approach. One occurs in the case of indeterminism where we substitute probabilistic dependence for counterfactual dependence in clause (a). As we have already noted, e’s firing probabilistically depends upon a’s firing whether or not the b-chain is present. So a’s firing satisfies the first clause of Lewis’ definition of quasi-dependence and hence the firing of a is proclaimed a cause. A second reason for feeling unhappy about Lewis’ approach is that it rules out brute singular causation in cases of pre-emption (Ganeri et al. (), pp. –). We have a case of brute singular causation if e₁ causes e₂ without any backing law. If this is allowed generally, then there is no reason to disallow it in cases of late pre-emption. Suppose the b-chain is a case of brute singular causation. Then in the great majority of circumstances intrinsically similar—i.e. b-type—processes may not stand in a chain of counterfactual dependence at all. The b-chain was a one-off. So the firing of b wouldn’t be a cause by Lewis’ account. Of course, if there were no other way to capture the intuitions we have about what are causes and what are not in cases of late pre-emption, then we might have to adopt this strategy. However, there is an alternative. Hence, it is a legitimate criticism of Lewis’ approach that it appears to gratuitously rule out brute singular causation—something that Lewis himself has said he is loath to do (Lewis (b), p. ). The alternative focuses on what Lewis might have had in mind when he appealed to the intrinsic similarity of processes in distinguishing between the pre-empting and pre-empted processes (Ganeri et al. ()). Suppose that both the b-type-chains and the a-type-chains occur independently of the other in the great majority of circumstances. When they do, both processes involve chains of counterfactual dependence up to and including an event of the same type as the firing of e. What led Lewis to suppose that only the b-type processes were intrinsically similar? The answer seems to be that, when a-type processes occurred independently of b-type processes, the atype processes have an event that they did not actually have in the case of late preemption case: d’s firing (Ganeri et al. (), p. ). Different circumstances bring out the fact that an event is suppressed on the pre-empted chain and the existence of this event in these circumstances constitutes the intrinsic difference from the preempted chain. This suggests that, instead of appealing to the existence or otherwise of intrinsically similar processes to ground the asymmetry between pre-empting and preempted processes, we can distinguish between them by differences in the actual token process in counterfactual circumstances. In more detail, the idea is that: For any actual, distinct events e₁ and e₂, e₁ causes e₂ iff there is a (possibly empty) set of possible events Σ such that (I) e₂ is Σ-dependent on e₁, and, (II) every event upon which e₂ Σ-depends is an actual event. The key notion of Σ-dependence is defined as follows.



    

For any events e₁ and e₂, and any set of events Σ, e₂ Σ-depends on e₁ iff (i) if neither e₁ nor any of the events in Σ were to occur, then e₂ would not occur, and (ii) if e₁ were to occur without any of the events in Σ, then e₂ would occur (modified from Ganeri et al. ()). The Σ-set mechanism formalizes the idea that we should consider the nature of a putative token causal process in counterfactual circumstances, the ‘actual event’ clause—clause (II)—identifies the asymmetry which distinguishes pre-empted from pre-empting causal chain. The basic idea is that, while in counterfactual circumstances, pre-empted processes may run to fruition, they will include non-actual events upon which the effect depends. There is simple appeal to Σ-dependence rather than the ancestral of Σ-dependence because the motivation for taking the ancestral— successful treatment of deterministic early pre-emption cases—is removed. For instance, taking Figure . to describe a deterministic case, there is no need to appeal to the counterfactual dependence of e’s firing upon g’s firing, and g’s firing upon f ’s firing, arguing by that point it has been settled that the a-process has died, and chain these counterfactual dependencies together to explain why b is a cause of e. You can simply consider whether, if the a-process (along the top) weren’t present at all, e’s firing counterfactually depends upon b’s firing. Let me run through a few examples to illustrate the thinking behind the proposal. Suppose I shoot a man dead before the poison you gave him took effect. I try to claim that I didn’t really kill him because if I hadn’t shot him, he would have died anyway (from your poison). Your natural response would be But if you had shot him without my having poisoned him (putting this event in Σ), he would still have died (satisfying clause (ii) of Σ-dependence). So you did enough to kill him by yourself. If neither you had shot him nor I had poisoned him, then he would still be living (satisfying clause (i) of Σ-dependence). I admit the same could be said of my poisoning. That makes us both potential causes of his death (satisfying clause (I) of the definition of causation). What makes you the cause and me not is that the causal chain from the administration of the poison to death is incomplete. If the poison had been administered without your shooting him, then there would have been events in the chain up to the man’s death, as the poison took effect in his body, that did not occur in the actual circumstances (so failing clause (II) of the definition of causation). The same cannot be said of your shooting (so it passes clause (II) of the definition of causation). That’s why you killed the man and not me.

Of course, it is open to me to argue that I only shot him because your poison was going to give him an agonizing death that I sought to avoid. In effect, I would be explaining how you were linked to the death by another complete causal chain because you caused my actions. But that would not mean that I did not kill him, albeit blamelessly. It would just establish that you did too (if correct). As another illustration, consider the example given by Figure . reproduced here for ease of reference. This time, though, let us take it to show a deterministic case of late pre-emption rather than the indeterministic case I described earlier. If we put a’s firing in Σ, then e’s firing becomes Σ-dependent on b’s firing. Similarly, if we put b’s firing in Σ, then e’s firing becomes Σ-dependent on a’s firing. So both are candidate

   a

c



d

e

b

f

g

Figure .

causes. The difference is that in the first case—in which we are assessing whether b’s firing is a cause—e’s firing is only Σ-dependent on actual events. It is not Σdependent on the firing of d, for instance, because if neither d nor a had fired (a’s firing being the event in Σ), e would still have fired as a result of b’s firing. By contrast, when we turn to assess whether a’s firing is a cause, we find that with b’s firing in Σ, e’s firing is Σ-dependent on d’s firing. But d’s firing is not an actual event. Hence a’s firing is not a cause (it fails clause (II)). This account seems to work well for most deterministic cases. It has the advantage of failing to rule out brute singular causation. It also doesn’t rule out temporal action at a distance since it doesn’t require that there is an event at every moment in time on the chain between e₁ and e₂. All it relies upon is the existence of possible events that were actually suppressed due to pre-emption. It also has the advantage of not ruling out the possibility of discerning causal relations when the two competing processes are nomologically correlated. In supposing that one of the events on the other process is not present, we are envisaging circumstances in which the nomological correlation between the two processes is disrupted.

.. Problems with the ‘absent event’ account of incompleteness Nevertheless, the analysis is committed to an ‘absent event’ account of incompleteness and there are cases in which this diagnosis seems less plausible. In those of frustration, the pre-empting process does not stop an event in the pre-empted process from occurring but simply, by causing the effect earlier, stops an event in the pre-empted process from causing the effect itself. Consider Figure .. a fires at time , b fires at time . It takes two units of time for the signal to travel between nodes of the circuit. There is no event on the a–c chain that b’s firing stops from occurring. Rather, b’s firing just makes d’s firing occur earlier than it would have. The last event (if there is one) in the sequence from a’s firing to d’s firing just fails to cause d’s firing because it has already fired (Noordhof (a), pp. –). No doubt there are some worlds in which it is not possible for there to be a failure of causation without the non-occurrence of some event. Nevertheless, it is not obvious that this must be so for every possible world. In which case, the characterization of incompleteness is inadequate.



     c

2

a

2

d

2

b

Figure .

Another, perhaps more tractable, source of difficulty of the same kind is raised by cases of trumping where the laws of nature proclaim that a certain process is inefficacious when in the presence of another. Here’s the example outlined by Jonathan Schaffer. At noon, Merlin casts the first spell of the day: to turn the prince into a frog at midnight. Later on, at  p.m., Morgana also casts a spell to turn the prince into a frog at midnight. At midnight, the prince turns into a frog. It is a law of magic that, if s is the first spell of the day and its aim is to bring about a certain result at midnight, then only this spell will have influence upon what happens at midnight. Hence, only the first spell, the claim runs, is a cause (Schaffer (a), p. ). Yet, the only way in which the process beginning with Morgana casting a spell seems incomplete is by it being trumped by Merlin’s spell. Trumping cases seem more tractable because they appeal to laws to explain what trumping involves. It is plausible that laws partly determine the types of events there are. So while we are unlikely to consider that, in general, x being the first F is distinct from x being an F, in a world in which being the first something is nomically recognized, such a distinction is much more reasonable. In which case, there is a non-actual event upon which the prince turning into a frog depends when Merlin’s spell is absent: Morgana’s spell being the first spell of the day. Admittedly, Morgana might think, if only my spell had been the first, then it would have turned the prince into a frog. The thought seems to concern a token event efficacious in one set of circumstances, inefficacious in another. However, if Morgana reflected on the way in which the laws related to spells, she might be persuaded to rephrase her thought as follows. If only I had cast my spell first, then the resulting spell would have caused the prince to turn into a frog. This is compatible with the resulting spell being distinct from the actual spell she cast.¹ Finally, let me discuss one more recently developed case (Paul and Hall (), pp. –). Consider Figure .. Here we have two distinct processes which give rise to a certain type of event E, let it be a ringing of the bell. The bell ringing as a result of ¹ I was partly inspired to make my present defence against trumping through reading Barker’s paper (Barker (), pp. –). However, there is an important difference. If you appeal indiscriminately to events, states, conditions, or anything else non-actual, you will be able to fix up problematic dependencies to discredit genuine causes.

  



a b

e1

e2

d c

Figure .

the c-process occurs a little later than that as a result of the a-process. The bell rings twice when both processes are present. c was pre-empted from producing e₁, the first ring, so produced the second. In order to establish that, a, say is a cause of e₁, we have to assess the counterfactual ‘If a were not to occur, then e₁ would not occur’. In the circumstances in which a is absent, there is only one event of type E brought about, that by the c-process. Since we are considering counterfactual circumstances, it is an open question what, if anything, is event e₁. It’s not obvious that, in the counterfactual circumstances, what one might be tempted to call e₂ is ruled out from being e₁. But if the putative e₂ is e₁, the counterfactual dependence is lost. Consider now c. How can we capture the fact that c was pre-empted from producing e₁? If we consider the circumstances in which the a-chain is absent, then what we might be tempted to call e₂ is, the challenge goes, really e₁ and we have c giving rise to it via a complete causal process. The appeal to gaps in the pre-empted process to characterize how it is pre-empted doesn’t work. So c ends up a non-pre-empted cause of e₁ after all by the account (Paul and Hall (), p. ). Contrary to what Laurie Paul and Ned Hall argue, it is legitimate to claim that in the set-up envisaged, counterfactual e₁ and e₂ are distinct events. No claim that events have very fragile essences is required. Appeal to essence, as we shall see in ., is an overreaction to what is, in fact, a need to identify the appropriate events in close-by counterfactual circumstances. While it may be the case that in a more distant possible world, the putative e₂ is in fact e₁, we are focusing on what we should say in a close-by world to our world in which a were not the case and the process from c to the putative e₂ were present. The generation of this counterfactual situation from a world in which there were two processes giving rise to two distinct events is the basis for denying that the putative e₂ is, in fact, e₁. Indeed, outside of any commitment to a counterfactual theory of causation, this is what we would be inclined to say. ‘How would you get rid of e₁?’ you might ask. ‘Get rid of the causal chain events from a that caused it’ would be a very natural answer. Events aren’t so difficult to get rid of that they stick around, caused by other causal chains in situations very similar to our own. By the same token, c does not stand in a complete sequence of actual events to e₁ as opposed to e₂.



    

.. Indeterminism, chance-raising, and the ‘actual events’ account of completeness Whatever the merits of the analysis regarding these cases of deterministic causation, it will become quite obvious that it is no good when we try to extend it to cases of indeterministic late pre-emption. Before we get to that point though, it is helpful to see how the analysis should be extended to deal with other cases such as indeterministic early pre-emption. The natural first step would be to substitute a notion of probabilistic Σ-dependence—for Σ-dependence—defined as follows. For any events e₁ and e₂, and any set of events Σ, e₂ probabilistically Σ-depends on e₁ iff (i) if e₁ were to occur without any of the events in Σ, then p(e₂) would be at least x, (ii) if neither e₁ nor any of the events in Σ were to occur, then p(e₂) would be at most y, (iii) x >> y. A natural way to think of this account of probabilistic Σ-dependence is that it provides a characterization of the chance-raising contribution of an event e₁ as compared with circumstances in which e₁ is absent as are other competitor causes (in Σ). At the limit, with all competitor causes from other causal chains in Σ, we are comparing the probabilistic contribution of an event against the maximal—since we talk of ‘at most y’—background chance of an effect, e₂. But weakening Σ-dependence to probabilistic Σ-dependence causes problems. Consider first the case represented by Figure .. The suggestion was that b’s firing satisfies the definition of causation if a’s firing is put in Σ. But in the case of indeterminism, it is not so clear. The problem is that even if a’s firing did not occur, it is still possible that c and d’s firing might occur. Since these are still options just after b’s firing, there is no guarantee that b’s firing (as part of the unreliable chain) raises the probability of e’s firing sufficiently to count as a cause. However, this is partly a problem because we have not been sufficiently clear about the time at which p (e’s firing) should be assessed. The problem arises if we take the time of a

c

d

e

b

Figure .

f

g

  



assessment to be just after the firing of b. So instead, let us take the time of assessment of p (e’s firing) to be just before e fires. This is the option we considered at the end of .. By then, it will be clear that c and d have not fired. So the background probability of e firing will be low. The firing of b will be a cause by the definition because, against this background, it very much raises the chance of e firing. There remains a problem with the formulation just provided because of the possibility that f and g may spontaneously fire anyway. Given the similarity weighting I defended in Chapter , there is no reason to deny that some of the closest worlds in which b does not fire, f and g do fire spontaneously, albeit very few. Defining Σprobabilistic dependence in terms of, at the limit, the maximum background chance of e firing means that these worlds fix the value for y. In which case, x will not be very much greater than y (Ramachandran (), pp. –). We may call this the problem of lost late chance-raising. We could avoid this difficulty by going back to defining causation in terms of the ancestral of our basic notion of dependence; in this case, probabilistic Σ-dependence. Unfortunately, this would only work if any case of indeterministic causation could be constituted from cases of causation with no intermediaries. Otherwise, the same reasoning would apply. So retaining this definition of probabilistic Σ-dependence would involve us in a commitment I said would be better to avoid above. Perhaps some causation is mediated all the way down. My preferred alternative is to adjust the analysis of probabilistic Σ-dependence to e₂ probabilistically Σ-depends upon e₁ if and only if () If e₁ were to occur without any of the events in Σ, then it would be the case that, just before t, the mean value of p(e₂) is x, () If neither e₁ nor any of the events in Σ were to occur, then it would be the case that, just before t, the mean value of p(e₂) is y, () x >> y. Here ‘t’ is the time, at a first pass, just before e₂’s occurrence or, if it does not occur, just before the time it would have occurred if it had. Obviously, for the response to be fully satisfactory, more also needs to be said about what fixes the mean values of p(e₂). Nevertheless, there seems no objection in principle to such an approach. For probability counterfactuals with true antecedents, only the actual world will be considered. In which case, the mean value of p(e₂) will be the actual value of p(e₂) just before t. For probability counterfactuals with false antecedents, we will be considering the closest worlds in which the antecedents are true. These may involve some small changes in the laws that hold along with slight differences in background circumstances that do not have an impact on the similarity of worlds. The mean value of p(e₂) when e₁ does not occur is fixed by the factors just outlined. These factors explain how larger and larger random samples of equally close worlds in which the antecedent is true, would tend towards a mean probability for p(e₂). Let’s consider now the application of the ‘actual events’ clause in the analysis of causation provided, with the revision appealing probabilistic Σ-dependence. For ease of reference, here is the adjusted analysis.



    

For any actual, distinct events e₁ and e₂, e₁ causes e₂ iff there is a (possibly empty) set of possible events Σ such that (I) e₂ is probabilistically Σ-dependent on e₁, and, (II)

every event upon which e₂ probabilistically Σ-depends is an actual event.

We are focusing once again on the case of indeterministic early pre-emption in Figure .. The firing of e will be probabilistically Σ-dependent on the firing of d whatever one puts into (or leaves out of) the Σ-set. This is not so in a deterministic version of this case since if the firing of g is not put in Σ (which it won’t be if we are testing to see whether b’s firing is a cause), d’s firing can’t raise the chance of e’s firing. P(e fires) would already be at . If the firing of e is probabilistically Σ-dependent on the firing of d, then this would seem to rule out the firing of b being a cause since it would fail the ‘actual events’ clause—due to the probabilistic Σ-dependence on firing of d—even though, intuitively, this event has nothing to do with b’s firing causing e’s firing. This is not a result we want. However, in fact there is no problem. All we have to do is put the firing of d as part of the Σ-set for demonstrating that the firing of b satisfies my definition. In that case, the firing of e would not probabilistically Σdepend upon the firing of d. The conditionals we would have to consider would be these. If d’s firing were to occur without the firing of d (or the rest of the Σ-set) occurring, it would be the case that, just before t, the mean chance of e firing at t would be at least x. If neither d’s firing nor d’s firing (nor the rest of the Σ-set) were to occur, it would be the case that the mean chance of e firing would be at most y. Since the antecedent of the first conditional is necessarily false, we could put any value for x including  and the conditional would be true. So the conditionals fail to proclaim (except trivially) that e’s firing is probabilistically Σ-dependent on d’s firing. We can rule out trivial satisfaction. So the firing of b does pass clause (II). This strategy will apply quite generally. The same trick won’t turn a’s firing into a cause of e’s firing because if you put one of the non-actual events in the chain (e.g. the firing of d) into Σ, e’s firing would not probabilistically Σ-depend on the firing of a. So even though the firing of a would pass clause (II) with this Σ-set, it would not pass clause (I). The analysis requires that there is a Σ-set such that the target cause and effect will pass both clauses. It is not available for a’s firing.

.. Refinement of the ‘actual events’ clause A more substantial difficulty with this characterization of probabilistic Σ-dependence is revealed by the case in Figure . for which I am grateful to Sungho Choi. The problem is that the proposal would proclaim the firing of a to be a cause of e’s firing. Here’s why. On this occasion, we are to suppose that all the connections indicated are deterministic. Put d’s firing, f ’s firing, and k’s firing in Σ. We then have the following true conditionals If a were to fire without any of d’s firing, f ’s firing, and k’s firing, then the mean value of p(e₂) would be .

  



d g

a

b

c

h

e

f

k

l

Figure .

If neither a were to fire without any of d’s firing, f ’s firing, and k’s firing, then the mean value of p(e₂) would be . The firing of a would pass the probabilistic Σ-dependence clause. Moreover, because g’s firing and h’s firing overdetermine e’s firing, the latter does not probabilistically Σ-depend upon either. Hence the firing of a would pass the actual events clause too. Sungho Choi has suggested that we might get past this problem because it will still be true that the firing of e probabilistically Σ-depends upon a non-actual event, the most likely candidate being the disjunctive event of the firing of g or the firing of h. The problem with this response is that it assumes that putative disjunctive events are genuine events and can be members of Σ. This is not an assumption upon which I wish to depend, especially in the light of what I argue later (Choi (), p. ; Noordhof (), pp. –). A natural diagnosis of what’s gone wrong is that, in searching to find a Σ-set to reveal whether an effect is probabilistically Σ-dependent on a particular candidate cause, we are not concerned with whether the intermediate links in the chain are also revealed to be candidate causes. Obviously, if we have a causal chain, the effect can be shown to probabilistically Σ-depend upon the intermediate links too. But there is no reason to expect that a Σ-set for the candidate cause will also be sufficient for the intermediate links. So having arrived at a Σ-set which makes e₂ Σ-dependent on e₁, we should consider arbitrary additions to the Σ-set which do not undermine the connection between e₁ and e₂—for example, by including events in the chain connecting them—but which may reveal that e₂ is Σ-dependent on other events in the chain. If there is a genuine causal chain, we will be able to add to this Σ-set any number of events (to yield a superset, Σ*) so as to reveal how the effect is probabilistically Σ-dependent on each of the events yet none of these events be non-actual. The following clause captures the idea.



    

(II)’ For any superset of Σ, Σ*, (where Σ  Σ*), if e₂ probabilistically Σ*-depends upon e₁, then every event upon which e₂ probabilistically Σ*-depends is an actual event. For instance, in the case described in Figure ., all we would have to do is consider what would happen if we added g’s firing to the events in Σ to get Σ*. The firing of e would probabilistically Σ*-depend upon a’s firing. So the connection between a’s firing and e’s firing would not have been disturbed. But now e’s firing would probabilistically Σ*-depend upon h’s firing. So the firing of a is ruled out as a cause.

.. Late pre-emption and the ‘actual events’ clause This has rectified the immediate consequences of introducing probabilistic Σdependence for the formulation of clause (II). Now let’s consider the problematic case of indeterministic late pre-emption in Figure ., reproduced again here for reference. a’s firing can satisfy clause (I) of the account ‘the probabilistic Σ-dependence clause’ with no events in Σ given that it is the very reliable chain. The question is whether the ‘actual events’ clause can indicate what is wrong with counting a’s firing as a cause. There is reason to think not. What we need is for e’s firing to probabilistically Σ-depend upon d’s firing. Then, since d’s firing is a non-actual event, a’s firing would fail to be a cause. Unfortunately, while it is true that the mean chance of e firing is pretty high if d has fired, its chance also seems pretty high if d were not to fire. To see this, consider first what is the case if we assess p(e firing) in the way that Lewis recommends—i.e. just after d fires or fails to fire. Then, since d’s nonoccurrence is settled after e has fired (inhibiting d from firing), we will be assessing the probability of a past event. Generally, these are assumed to have a probability of . However, even if this assumption is challenged, it may still be argued that p(e firing) will be pretty high. Given that the a–d chain is very reliable, if d has not fired, this is more likely to be due to its firing being inhibited by e firing than it is due to the simple failure of the c–d connection. So p(e) will be the probability that c’s firing and g’s firing already gives it plus the additional contribution that d’s not firing makes. There

a

c

d

e

b

Figure .

f

g

  



is no reason to suppose that this will be very much lower than the probability that d’s firing gives e’s firing. Things are no better if we assess p(e firing) in the way I have recommended, namely just before e fires. The same reasoning seems to apply. We would have to assess p(e firing) just before e fires given that it is settled that d does not fire. That would once more suggest that e is likely to fire. If the reasoning does not apply, then that would surely be because just before e firing, the firing or otherwise of d is not settled. In which case, there will be no change in p(e fires) at that point due to d firing or failing to fire in the future. Either way, e’s firing is not probabilistically Σ-dependent upon d firing. It would be a mistake to look to the ‘any Σ*-set element’ of clause (II) to resolve the difficulty. Suppose we make Σ* = {b’s firing, f ’s firing, g’s firing}. So long as there is still a background chance of e firing at the time it did in the absence of the b-chain, then the chance of e firing when d does not fire will still have a high mean value. Perhaps it will be argued that if b, f, and g don’t fire, then e’s firing would be invariably after d. In which case, the problem would disappear. However, the objector would only have to adjust the case so that e’s firing occurred spontaneously before d, so inhibiting it. Then the mean chance of e firing when d does not fire remains high.

.. Hasteners, delayers, and probabilistic dependence We need a change of tack. Consider once more our troublesome case of late preemption. One reason for thinking that a’s firing is not a cause is that d’s firing does not occur. But another reason for thinking that a’s firing is not a cause is that, even though the firing of a raised the probability of e firing, it did not raise the chance of e firing at the time e fired—only later (as a result of d’s firing). This might suggest the following account of probabilistic Σ-dependence which I shall call ‘probabilistic Σ-time-dependence’. e₂ probabilistically Σ-time-depends upon e₁ if and only if () If e₁ were to occur without any of the events in Σ, then it would be the case that the mean value of p(e₂ at t) = x. () If neither e₁ nor any of the events in Σ were to occur, then it would be the case that the mean value of p(e₂ at t) = y, () ()

x >> y, e₂ occurs at t.

The proposal appears to get the right answer in the case of late pre-emption. a’s firing fails to be a cause because, although a’s firing may raise the chance of e firing at some time (later than it did), it does not raise the chance of e firing at the time it fired (as a result of b firing). By contrast, b’s firing is a cause of e firing because it did raise the chance of e firing when it did. Unfortunately, this proposal is no good. There are cases of pre-emption I will discuss in .. for which it delivers the wrong answer but we don’t need them to see the fundamental difficulty. Any theory that places probabilistic Σ-time dependence at its centre is liable to ignore causal differences between hastening and delaying. Hasteners and delayers are usefully divided into two sorts: simple switchers and



    

discouragers/encouragers. A paradigm simple switcher would be railway points which can be set to send a train down one of two routes, the slow route or the fast route, for arriving at a particular station. Switching to the slow route is a delayer, the fast route a hastener. The proposal we are considering would make switching either way a cause of the train’s arrival at the station (just put events on the other line in Σ) and I see no reason to contest this verdict given the ones we are inclined to make regarding other pre-emption cases. There is no general asymmetry between hasteners and delayers such as ‘Hasteners are usually causes of what they hasten; delayers are not usually causes of what they delay’ (Bennett (), p. ). Both delaying and hastening simple switchers prevent an event occurring at one time by causing it to occur at another time (which is not the same as causing it to occur). However, if hasteners are not simple switchers, then they are encouragers. Whereas, if delayers are not simple switchers, then they are generally discouragers. This distinction corresponds to a causal difference. Discouragers of e are not generally causes of e, encouragers of e are. The problem for the proposed analysis of causation is that it does not secure this result and its failure looks unmotivated. Here are a couple of familiar cases of delayers as discouragers. Suppose that a forest fire occurs in June as a result of electrical storms. These electrical storms had occurred for the previous two months but there was heavy rain in April and the vegetation had been too damp to alight until June. If the heavy rain had not occurred in April, the forest would have caught fire in May. It should be clear that, if we just appealed to the analysis of probabilistic Σ-time-dependence offered above in an analysis of causation, we would have to conclude that heavy rain in April was a cause of the forest fire and not just the forest fire occurring in June. It raised the chance of a forest fire in June by delaying it from May. If the fire had occurred in May, the forest would have burnt down and there would have been nothing to catch fire in June (Bennett (), pp. –). Equally, suppose that a doctor’s treatment delayed the onset of a particularly unpleasant phase of an illness but, because the treatment was not entirely effective, it occurred after all at the end of the second week of illness. Again an analysis of causation just based on the notion of probabilistic Σ-time-dependence would make the doctor’s treatment a cause of the unpleasant phase of the illness and not just a cause of its occurrence at the end of the second week. I think that in both these cases, this would be the wrong diagnosis. Placing obstacles in the way of an effect, by itself, is not a way of causing it. Let me give two examples of hasteners as encouragers (Mackie (), pp. –). An invitation to give a paper in November hastened its completion that would otherwise have been in December. In this case, it seems intuitive to say that the invitation caused the completion of the paper. Smith has heart disease and would have had a heart attack on Saturday (when she ran a marathon). However, she has a row with her employer on the Wednesday beforehand and has a heart attack then. It seems intuitive to say that the row caused the heart attack. A plausible way of capturing the difference is to say that hasteners as encouragers generally prevent events from occurring later by, earlier, causing them to occur. This is not simply to say that hasteners as encouragers cause events to occur at t (where t is an earlier time than times at which the events would otherwise have occurred). If that is all that hasteners as encouragers were, then we would not have identified a

  



substantial difference from delayers. The only difference would be whether the time is earlier or later. By contrast, delayers as discouragers cause events to occur at time t’ (where t’ is a later time than times at which the events would otherwise have occurred) by, earlier, causing them not to occur (Mackie (), pp. –). Discouragers do not cause events to occur (as opposed to causing them to occur at a time) and, indeed, cause them not to occur. Encouragers do cause events to occur. It’s by doing this that they prevent the events’ later occurrence. Appeal to probabilistic Σ-time dependence obscures this difference. If there is a link between causation and chance-raising in certain conditions (e.g. absent the events in Σ), then we need to be sensitive to the distinction between raising the chance of an event and raising the chance of an event occurring at a particular time. A preliminary diagnosis of what is wrong with both the April rains and the doctor’s treatment being causes in the situations envisaged is that, while they raise the chance of their alleged effects occurring at a particular time, they don’t make their effects more probable per se. Having initially been in favour, Bennett offers three considerations against accepting any kind of hastener/delayer asymmetry which I should consider before we proceed on the assumption that it exists (Bennett (), pp. –). First, he suggests that if something undergoes a sequence of type identical events as a result of a certain type of cause—his illustration is striking a tuning fork to cause it to vibrate at various points during the day—then there is just causation of an event of vibration at a particular time. One event of vibration could not have happened earlier or later. My response is that even in this case the token events might have happened earlier or later. It is just that the individuation conditions for these events are much more refined. Moreover, even if there are such cases, ideally we should have a theory of causation that covers all causally related events and not just those that could not occur at different times to the times at which they occurred. In . I shall discuss the individuation of events further. For our present purposes, the important point is to consider whether an analysis of causation can be provided that allows for the possibility that events can occur earlier or later. If it can, then a reason in favour of insisting otherwise is removed. Second, Bennett appeals to the transitivity of causation. If a doctor massages a patient’s heart during a heart attack, the patient survives and then dies later, there is causation because, according to Bennett, the massage is a cause of the earlier survival and the earlier survival is a cause of the later death. In Chapter , I shall explain how my analysis of causation justifies the rejection of its alleged transitivity. In any event, although the cited cases involve mediate causation, for which the question of transitivity is relevant, the issues raised by hasteners and delayers are independent of it. Suppose that c (without d) raises the chance of e occurring to  per cent, c with d raises the chance that e may occur to  per cent, and d without c neither raises nor lowers e’s chance of occurring. Finally suppose that the first three times at which e may occur are t₁, t₂, t₃ and, of course, if e occurs at t₁, say, then it does not occur at t₂ though there may be some other E type event that occurs then. Then if c were the case without d, chance of e at t₃ is (. x . x .) = .. If c were the case with d, chance of e at t₃ is (. x . x .) = .. By having an entirely negative effect on the chance-raising of c, d functions as a delayer of e. Nevertheless it raises



    

the chance of e at t₃. c’s causing e can be taken to be a case of immediate causation at either of the three times unless it is appropriate to take e’s failure to occur at t₁ say as a cause of it occurring at t₃. My later rejection of negative causes has, as a consequence, that it is not appropriate. Third, Bennett suggests that the counterfactual approach does not require us to decide on whether time of occurrence is essential to event identity. We only appeal to counterfactual dependence to characterize immediate causation between two spatiotemporally contiguous events. Transitivity settles whether or not there is mediate causation. Setting aside the issue of transitivity for a moment, such an approach fails to account for the fact that we are strongly inclined to deny that the doctor is a cause of the death of the patient (later). We still need an account of this putative artefact of our thought and talk. One line, to be discussed further in Chapter , is to give a pragmatic explanation of why we mistakenly make this denial, along with others. An alternative is to identify a feature that distinguishes between hasteners and delayers to account for why we deny that the doctor is a cause of the death. If we are in the business of providing the latter, then we might as well take this to be a distinguishing feature of causation rather than, in the first instance, accepting that the doctor is a cause of the death at a time and then, after that, accounting for our resistance to saying he is a cause of the death by citing this feature. We have the task of identifying the feature anyway. Given that we do, the motivation for appealing to more restrictive conditions on event identity to avoid the problem of dealing with the hastener/ delayer asymmetry seems weak. As a result, I suggest the following generalization of the idea of probabilistic Σ-time-dependence. e₂ probabilistically Σ-depends upon e₁ if and only if () If e₁ were to occur without any of the events in Σ, then for some time t, it would be the case that, just before t, the mean value of p(e₂ at t) = x. () If neither e₁ nor any of the events in Σ were to occur, then for any time t, it would be the case that, just before t, the mean value of p(e₂ at t) = y. () x >> y. The intuitive idea is that, relative to the events in Σ, the presence of a cause does not just make the probability of an event at a time very much greater than it would be if the cause were not present. It makes the probability of the event at that time greater than the probability of that event at any other time if the cause were not present. Consider the April rains. They make it more probable that the forest fire occurs in June. They don’t make the forest fire more probable per se. If we compare the p(forest fire in June) just before June (there having been April rains) with the p(forest fire in May), say, just before May (there having been no April rains) we find that it’s not the case that the mean p(forest fire in June) >> the mean p(forest fire in May). Nor are matters helped if we put events in Σ which would ensure that, even if the April rains did not occur, the forest fire would not occur before June—for instance, the nonactual events comprising the various ways in which the forest might have caught alight before June—so drastically lowering p(forest fire in May). If we did that, then

  



the April rains would not even raise the chance of the forest fire occurring in June. The absence of the other events would already have ensured that the forest would not have caught fire before. The April rain will not be needed to guarantee the forest is not burnt down and could catch light in June. Similar considerations explain why the doctor’s treatment is not a cause of the severe phase of illness. Consider now the cases of hasteners as encouragers. In the case of the invitation to give a paper, we would put in Σ the events that would have brought about the completion in December. So, in effect, what we would be comparing are the following two conditionals: (a) If I were to receive the invitation without any of the events in Σ occurring, it would be the case that the mean value of p(the paper is finished at t) = x (where the probability is assessed at the appropriate point in November just before t). (a) If neither I were to receive the invitation nor any of the events in Σ were to occur in December, it would be the case that the mean value of p(the paper is finished at t) = y (where the probability is assessed at the appropriate point in December just before t). It is clear that relative to the absence of these events in December (December being the most likely time y would be largest), the invitation would raise the chance of completion in November to any other time. Similarly, we would put in Σ the event of running the marathon (and doubtless many other events which may also give rise to that heart attack but let’s keep things simple). The row would then raise the chance of the heart attack on Wednesday to its chance at any other time. Here the two conditionals would be: (b) If she were to have a row with her employer and were not to run the marathon, it would be the case that the mean value of p(she has a heart attack at t) = x (where the probability is assessed at the appropriate point on Wednesday). (b) If she were neither to have a row with her employer nor to run the marathon, it would be the case that the mean value of p(she has a heart attack at t) = y (where the probability is assessed at the appropriate point on Sunday (say) just before t). Again x would be very much greater than y. Notice that this is not what we found in the case of the April rains. When we put possible events in Σ which ensured that the forest did not burn down in June, the April rains did not raise the probability of the fire at all. Let me draw your attention to some important features of this proposal. First, although I put certain events in Σ which occur after the actual time of the effect, I do not hold that this makes any difference to the chance of the effect at that time. Rather, the chance it influences is the chance of the effect at the times at which it would occur given the absence of the cause. Second, the chance that I am assessing is the chance of an event occurring at a certain time assessed just before that time. For instance, consider a time just before the woman runs the marathon. The chance of her having a heart attack some time after that time may be quite high (given that it is not settled that she is not running the marathon). However, the chance of her having a heart



    

attack at precisely that time before the marathon is run is low regardless of whether it is settled that she will run it. If the world is deterministic, then all the events that occur have chance . Moreover, it is settled that they should occur at a particular time. My informal presentation of the idea behind the proposed analysis of probabilistic Σ-dependence may seem to work only for cases of indeterminism. I said that, relative to the events in Σ, the presence of a cause makes the probability of its effect at that time greater than the probability of that event at any other time if the cause were not present. If a hastener were absent, the chance of the effect would still be  at a different time. This worry ignores the original italics for relative to the events in Σ. In the deterministic case, we would put in Σ events that would, by being taken to be absent, make the chance of the effect occurring at any of the other times . This is something that we can do in the case of hasteners as encouragers that we cannot do in the case of delayers as discouragers. The key point is that, intuitively, hasteners as encouragers bring with them a causal path to the effect. So you can disturb all the other paths to the effect at different times by putting relevant events in Σ. By contrast, delayers as discouragers don’t bring with them a causal path but rather put obstacles in the way of one or other already existing causal paths. Hence, if we disturb the causal paths leading up to the effect at the time at which the delayer operates, all that we do is undermine the ability of the delayer even to raise the chance of the effect at a time. The interest of the recommended analysis of probabilistic Σ-dependence lies in the fact that it provides a univocal expression of what is involved in causing, and not just causing at a time, for deterministic and indeterministic cases. I suggested that delayers as discouragers caused events at a time by, earlier, causing them not to occur. That suggests that there might be discouragers that are causes because, in addition to, earlier, causing an event not to occur, they also later cause the event to occur. Here is a familiar case that seems to be exactly that: the fatal antidote to a poison. The subject would have died if he or she had not taken the antidote to the poison just ingested. The subject dies anyway, later, from a reaction to the antidote. Intuitively, the antidote both delays and causes the death. My proposal gets that result. Put the ingestion of the poison in Σ. Then the antidote raises the chance of the death later over the chance of the death at any other time due to the adverse reaction (Mackie (), pp. , –). Are there hasteners that aren’t causes because, later, they cause an event not to occur thereby causing it to occur at an earlier time (rather than simply causing it to occur)? It might be thought that the following is an example (Mackie (), p. ). I receive a subpoena requiring my attendance at the Old Bailey in September—just when I was planning to have my holiday in Paris—so I rearrange my holiday for August. However, this clearly doesn’t display the right structure. Receiving a subpoena makes me believe that I cannot go on holiday in September. It is this that leads me to change my holiday plans. The fact, if it is a fact, that later the subpoena causes me not to go on holiday (in September) is causally irrelevant to the change in my plan a couple of months earlier. So it is not true that the later causing of something not to occur is a cause of it occurring at an earlier time. In fact, the case is one of simple switching. Receiving the subpoena is a cause of the earlier holiday in the same way that being switched to the fast railway line is a cause of arriving at the station.

  



The proposed analysis can capture this. Suppose one puts in Σ events necessary for the occurrence of the holiday in September. Then receiving the subpoena makes the chance of the holiday in August very much higher than it would be at any other time. It seems that, if we are to obtain cases of hasteners as discouragers, we need backward causation from a later causing not to occur to an earlier causing to occur at a time. For example, suppose that I precognize that Eyjafjallajökull will erupt at the start of September and all flights leaving the United Kingdom will be grounded. Here, I assume, that precognition involves an event in the future causing a mental state, of precognition, at an earlier time. As a result, I rearrange my holiday for August. My precognition may be a cause of my holiday but the eruption of the Icelandic volcano is not. My account obtains that result. There are no events that one could put in ∑ that would make the eruption of the volcano raise the chance of my going on holiday. So the encourager/discourager asymmetry seems to rest on the fact that causes usually precede their effects.

.. Completeness at the right time A further refinement is needed to the analysis of causation. Suppose that the firing of a neurone, a, satisfies the first clause of the account by raising the chance of another neurone, e, firing at t over any other time. To simplify matters, suppose that the a–e connection is direct. There are no intervening events. Finally, suppose that e has some background chance of firing anyway and does at time t + , a time at which the firing of a does nothing to make the firing of e more likely. Intuitively, the firing of a is not a cause of e firing but it seems that the firing of a would satisfy both clauses of my account. So we need one more clause (III) e₂ occurs at one of the times for which the mean value of p(e₂ at t) = x and x >> y. This ensures that e₂’s satisfaction of condition () of the analysis—the probabilistic Σ-dependence condition—relates to the actual occurrence of e₂. Let me run through the cases of indeterministic late pre-emption (Figure .) and frustration (Figure .) to explain how the full proposal works which, for ease of reference, I set out below. For any actual, distinct events e₁ and e₂, e₁ causes e₂ (if and) only if there is a (possibly empty) set of possible events Σ such that (I) e₂ is probabilistically Σ-dependent on e₁, and, (II)’ for any superset of Σ, Σ*, (where Σ  Σ*), if e₂ probabilistically Σ*-depends upon e₁, then every event upon which e₂ probabilistically Σ*-depends is an actual event, (III) e₂ occurs at one of times for which the mean value for p(e₂ at t) is x and x >>y. The case of late pre-emption, Figure ., is reproduced here. Consider, first, whether the firing of b comes out as a cause. Let Σ include the firing of d. Then the chance of e firing at the time it did given that b fired would be very much greater than any of the chances that e has of firing at a time if b did not fire. So



    

a

c

d

e

b

f

g

Figure . c

2

a

2

d

2

b

Figure .

the firing of b satisfies the probabilistic Σ-dependence clause. It also satisfies the second clause—the ‘actual events’ clause—because there are no non-actual events on the b-chain. Consider now the firing of a. Given that e has a background chance of firing anyway, it may still occur prior to d’s firing. If we consider the chance of e firing later—intuitively at the time it would have been brought about by the a–e process— then it is  whether or not a’s firing occurred. The very same event of e firing can’t occur at two times. So the chance of e firing later—assessed just before e would then have fired—would already take into account the fact that e had fired earlier. Hence e’s firing can’t probabilistically Σ-depend upon a’s firing. a’s firing fails clause (I) of my account. And if e does not have a background chance of firing anyway or may not occur prior to d’s firing? Well then the difference between the firing of a and the firing of b is revealed by their respective times t at which the mean value of p(e fires at t) is x and x >> y. In the case of the firing of b, one of the times is the time, to, at which e actually occurred. Whereas, in the case of the firing of a, this is not so. P(e fires at to) is not raised by the presence or absence of the firing of a. If e fired as a result of the a–e process, it would have been later. So the firing of b passes and the firing of a fails clause (III). The difference would also show up through e’s firing being probabilistically Σ-dependent upon the non-actual firing of d. Thus the firing of a would fail clause (II)’ too. See Figure . for the case of frustration. Here both a’s firing and b’s firing satisfies the probabilistic Σ-dependence condition and, as we have already noted, the actual

  



events condition does not discriminate between them. Nevertheless, clause (III) rules out a’s firing being a cause for the same reason it did in the case of late pre-emption. The time at which d fires is not one of the times at which a’s firing satisfies the probabilistic Σ-dependence condition. The three clauses of the account can now be understood to work as follows. Clause (I) explains what it is for e₁ to be a cause of e₂ and not just a cause of e₂’s occurrence at t. Clause (III) makes sure that e₁ in fact stands in the appropriate relationship to e₂ for the time at which e₂ occurred. Clause (II), together with the decision to assess p(e at t) just before t, specifies what would have to be the case at the time at which e₂ occurs for the causal chain between e₁ and e₂ to be complete.

.. Competing signs of incompleteness One challenge to the analysis would come from cases where there is some other sign of completeness than the truth of the actual events clause together with the presence of chance fluctuation assessed just before the actual time of the effect. Douglas Ehring’s case A is intended to fit the bill. Case A involves two qualitatively indistinguishable particles, α and β, colliding at t. The laws say that one and only one will be destroyed as a result of the collision and, for each particle, there is a  per cent chance of it being the one destroyed. The survivor jumps discontinuously to a spacetime point e, let us suppose  metre away. The particles’ travel is indeterministic rather than deterministic. Their occurrence at earlier spacetime points gives a high, but less than , chance of them being at later spacetime points. Figure . gives a sketch of the envisaged situation. Ehring claims that my approach cannot capture the fact that it is α’s journey to t that is a cause of the location of a particle at e (β having been destroyed at t) (Ehring (), pp. –, –). The problem for my proposal is meant to be that the particle at e will probabilistically Σ-depend upon both α and β (with the other in Σ) so I must rely upon there being a missing intermediary (to wheel in clause (II)). But, from the description of the case, there is no missing intermediary. It pays to be careful about the character of the event at e. If the event is the α particle being present at e, then this event probabilistically Σ-depends upon the α particle travelling to t and not the β particle travelling to t. Both particles, though, are supposed to be qualitatively indistinguishable. Let’s call them Q-particles. Then a α

t 1m β

Figure .

e



    

second way of characterizing the event at e is the presence of a Q-particle at e. This event probabilistically Σ-depends on the α particle travelling to t, with the β particle travelling to t in Σ, and vice versa. However, the β particle being present at t (or surviving t if presence is required for a collision in the first place) is a non-actual event. So the β particle’s journey fails the actual events clause. Either way, the case does not present a difficulty to the analysis. It might be argued that a proponent of Humean supervenience cannot distinguish between two events at e on the basis of their involvement of numerically distinct, although qualitatively identical, particles. However, given that the example is appealing to it being a fact that the α particle is present at e rather than the β particle, if Humean supervenience is true, it doesn’t get off the ground. If Humean supervenience is not true, then it is legitimate to appeal to facts about identity upon which to base the appropriate counterfactuals. This is one advantage of recognizing the merely contingent truth of Humean supervenience and separating the counterfactual theory of causation from this programme. Cases of overlapping involve two or more events with both differences and something in common in their potential effects. The differences are utilized to state which one was, in fact, efficacious. The charge is that no other factor—for instance, counterfactual chance-raising via a complete process—will serve to distinguish between the two or more putative causes with regard to the elements in common. Some examples that have been provided can be dealt with by denying the overlap by much the same manoeuvre as I used with regard to case A. For example, suppose that U and Ra are placed in a box at t₀ and they are in an overlapping superposition of locations. Each has a certain probability of spontaneous decay producing an alpha particle. At t₁, there is an atom of Th, an alpha particle, and Ra so indicating that U decayed. Yet, the claim runs, each element raises the chance of an alpha particle (Schaffer (b), pp. –). Here we may say that, even if this is the case, the presence of Ra doesn’t raise the chance of the token alpha particle indicative of the decay of U. Other, magical, cases of overlapping are not susceptible to this treatment. Suppose that Merlin casts a spell with . chance of turning the king and the prince into frogs and Morgana casts a spell with . chance of turning the queen and the prince into frogs. As it happens, the king and the prince are turned into frogs. Schaffer argues that we may take it that this is a case of immediate causation and that Morgana’s spell raised the chance of the prince turning into a frog but did not cause it (it was Merlin’s spell that was responsible) (Schaffer (b), pp. –, see also Tooley (), pp. –). I don’t deny that there was a point at which Morgana’s spell raised the chance of the prince turning into a frog. However, I claim that at a time after the spell is cast and just before the prince turns into a frog, it does not. By then, the spell has proven ineffective. The fact that the queen is not turned into a frog demonstrates that this is the case. To argue that Morgana’s spell raises the chance of the prince turning into a frog right up until the very time that the prince turns into a frog is to beg the question against the chance-raising proposal. It is not as if the description of the case requires that this claim be made. The intuitive plausibility of the chance-raising approach presents a reason for not supposing that this is so. Suppose that Merlin’s spell is put in the Σ-set. Will my proposal then have the verdict that Morgana’s spell causes the prince to turn into a frog? The difficulty arises

  



if, although Morgana’s spell was not in fact successful, generally it would be, in changed circumstances. However, in those circumstances, there is a non-actual event upon which the prince turning into a frog will probabilistically Σ-depend: the queen turning into a frog. The crucial feature of the case is that the prince and queen turning into a frog constitute a unit as opposed to joint effects of a common cause via independent processes. Although there is only a  per cent chance of them turning into frogs, it is not possible for one element of it to occur—the prince turning into a frog—without the other element of it occurring. Yet there would be if Morgana’s spell caused these frog-turnings by independent processes. In which case, if the queen turned into a frog, the chance of the prince turning into a frog, assessed just before the prince turns into a frog, would be . Whereas, if the queen failed to turn into a frog, the chance of the prince turning into a frog, assessed just before the prince turns into a frog, would be . Hence Morgana’s spell would fail clause (II) of my account.

.. Absence of probabilities or probability raising When I first introduced the idea of probability raising, I noted (following Lewis) that causes should proportionately raise the chance of the target effect. The actual probability they may give to the effect may be very low but the chance of the effect without the cause is proportionately very much lower. However, there are cases in which, it has been argued, causes don’t give effects any probability at all or, if they do, it can only be . John Norton has provided the following example that illustrates the two points effectively (Norton ()). Consider a point mass placed at rest at the vertex of a frictionless dome with gravity acting perpendicularly to the dome, towards its base. According to Newtonian mechanics, two types of consequence are possible. First, the point mass remains at rest at the vertex. Second, at some time, the point mass spontaneously travels down the frictionless dome. All directions down the dome are equally possible as, indeed, is departure at any time. Because Newtonian mechanics doesn’t attribute any probabilities (although this is an indeterministic part of the system for the frictionless case), Norton suggests that whatever happens does not have any probability of happening at all. In any event, on the assumption that either the time or the various possible paths down the dome are continuous, there are an infinite number of possible times and paths for the point masses journey to start and down which it will go. So the probability of any particular time (or path) is . The case suggests a general objection to the analysis of causation provided earlier when there are an infinite number of times at which an event could begin to occur. In that case, the mean value of the chance of the event at an instantaneous point in time t is  although its chance over the time period in which its occurrence is possible is positive. In the present case, as remarked, no particular probabilities are assigned and so, at best, we can conclude that failure to move and moving down any possible path at any time are equally probable. So here the only legitimate probability assignment is . One response to a case in which there is no assignment of probability, or only the assignment of , is to deny that it is a case of causation. It would then not need to be covered by the analysis. This might be done without surrendering the idea that causation is part of the fundamental structure of the universe. Causation does not



    

have to be the only structuring feature and it can be essential to the understanding of other features of the world (as we shall see below, for example, in understanding processes and laws in Chapters  and , respectively). The response may be fortified by pointing out that the world does not contain such cases and so, although theoretically possible, they show nothing about the actual structure of the world. Nevertheless, it is plausible that the presence of the point mass is a cause of either it staying there at a later time or travelling on one of the downward paths down the dome, rather than moving away from the vertex of the dome in a perpendicular direction. There are two ways of capturing this point within the present framework. Both involve the assignment of probabilities not explicitly mentioned in the law. However, we are used to assigning probabilities to events not explicitly mentioned in laws. The legitimacy of the assignment will depend upon the coherence of its development. The first is to appeal to infinitesimal probabilities and claim that the presence of the point mass at an earlier time gives an infinitesimal probability to each of these options when compared to a zero probability for moving away from the vertex in a negative direction. This may still be characterized as the probability being very much greater. Second, as Mellor has pointed out, without appeal to infinitesimals, we can note that the presence of the point mass raises the probability of the point mass staying there for a later time interval or, for example, travelling down one of the paths in a  degree angle (for example). We might further argue that if the chance that attaches to a certain path is  but it is one of the paths in angle for which there is a positive probability, and the paths are equi-probable within that angle, then the  probability does not imply that this path will not be travelled. Similarly, if a positive probability attaches to a certain time interval, and each instant of that time interval is equi-probable, then the  probability that attaches to a particular instant in that time interval does not imply that the event does not happen. We might then argue that either the causal relationships may be retrieved for events characterized by these intervals (and not for a specific instant of occurrence or path) or that if the causal relationship holds for the intervals, and a particular time (or path) lies in that interval in the way indicated, then the fact that the  probability does not imply that the event doesn’t happen is a significant difference from the  probability that implies that the event does not happen. This would be taken as a special case or ‘probability’ raising. I discuss a similar issue with regard to the converse kind of case involving infinities in . (infinite sequences of events in which each event has some positive probability of occurring). The fact that cases involving infinities require special treatment does not undermine the overall framework. If Mellor is right that the sciences are only concerned with quantities in interval values, then the manoeuvre of explaining how an event occurring at a particular instant, or involving a particular path, may be fitted within the framework is unnecessary (Mellor (), p. ). However I wanted to rely upon no such claims about the sciences here to defend the viability of the approach with regard to this kind of case.

.. Causing effects and causing effects in certain time periods Let me discuss a problem case that reveals something of the conception of a cause that lies behind the account. Suppose that there is a certain kind of compound X

  



which, when initially formed, is highly unstable. After a certain critical time period— five seconds say—it then becomes relatively stable and is only likely to break down under bombardment by subatomic Y-particles. Its chance of breaking down during a one second interval after it is bombarded outside the critical period is . whereas its chance of breaking down during a one second interval in the critical period—whether or not it is bombarded—is .. If X is bombarded during the critical period, the chance of its breakdown is still around . because, let us imagine, the bombardment interacts with what makes the compound more stable, which, during the critical period, is not present. Suppose that a bombardment takes place after the critical period. Intuitively, we might want to say that the bombardment caused the breakdown of the compound. However, it does not look as if my proposal can get that verdict. The probability of there being a breakdown if there is a bombardment is at least .. But the probability of there being a breakdown in the critical period in the absence of the bombardment is .. So the bombardment does not pass the ‘probabilistic Σ-dependence’ clause of my proposal. Although the candidate cause significantly raised the chance of a breakdown at the time it occurred, it did not relative to other times it might have occurred because of the initial critical period. On the assumption that the very same breakdown can occur both during the critical period due to instability and after the critical period due to bombardment, I claim that we should deny that the bombardment is a cause of the breakdown. Instead, we should say that it is a cause of the breakdown occurring during a certain time period— the period after the critical period. We might capture this notion as follows. For any actual, distinct events e₁ and e₂, e₁ causes e₂ during time period T iff there is a (possibly empty) set of possible events Σ such that (I)

e₂ is probabilistically Σ-T-dependent on e₁, and,

(II)’ for any superset of Σ, Σ*, (where Σ  Σ*), if e₂ probabilistically Σ*-Tdepends upon e₁, then every event upon which e₂ probabilistically Σ*-T-depends is an actual event (III)

e₂ occurs at one of the times for which p(e₂ at t) is x and x >> y.

where e₂ probabilistically Σ-T-depends upon e₁ if and only if () If e₁ were to occur without any of the events in Σ, then for some time t in T, it would be the case that, just before t, the mean value of p(e₂ at t) is x, () if neither e₁ nor any of the events in Σ were to occur, then for any time t in T, it would be case that, just before t, the mean value of p(e₂ at t) is y, ()

x >> y.

Here I have just limited the account to a certain time period—that represented by T. Causes of e₂ during a time period T make the chance of e₂ very much greater than the mean background chance of e₂ during that time period. Causes of e₂ per se make the chance of e₂ very much greater than its mean background chance at any time. A recommendation of this approach to what I take to be a borderline case is that it keeps the distinction between causing an event to occur and causing it to occur at a



    

time while not involving itself in an unmotivated stipulation. If we claim that e₁ may be a cause of e₂ because it raises its chance in the required way merely during a certain time period, then we need to settle how small the time period could be for us still to have a genuine case of causing e₂ as opposed to causing e₂ to occur at a time or during a certain time period. There seems no obvious resolution of this matter. By contrast, my proposal is that the cause of an event will make the chance of it occurring at one time very much greater than the chance it has of occurring at any other time (given the events in Σ don’t occur). No arbitrary resolution is required.

.. Actually completing in time: catalysts and anti-catalysts My analysis so far takes a process to be actually complete if, in possibly counterfactual circumstances in which the events in Σ are absent, it involves no non-actual events and appropriately raises the chance of the effect at the time it actually occurred. Thus, it works on the assumption that the events in Σ don’t affect the speed of the process in question. If it did, then my account might proclaim a process actually complete when, in fact, it was proceeding too slowly to complete. Figure . is an example of what I have in mind. The crucial feature is the inhibitory axon between d’s firing and f ’s firing. It does not stop f firing but makes it fire later (it acts as an anti-catalyst). As a result, e fires at t (say) because of the b-chain. f ’s firing fails to raise the chance of e’s firing at t although it would have done if f ’s firing had not been slowed down. If the b-chain had not caused e to fire at t, f ’s slowed firing would still have raised the chance of e firing later. My proposal does not have a problem with getting the verdict that b’s firing is a cause of e’s firing. Just let Σ contain the firing of a. The problem is with whether the firing of a is a cause. If we put either b’s or d’s firing in Σ, it would seem that the firing of a would satisfy clauses (I) to (III). The new feature introduced by this type of case is that the appeal to Σ-sets may change the time at which a certain process will bring about an effect e₂. What we need to do is make sure that not only is the causal chain between e₁ and e₂ complete (clause (I) and (II)) and that the right relationship holds between e₁ and e₂ at the time at which e₂ occurred (clauses (I) and (III)) but also that e₁ is related to e₂ occurring at the time it did in the actual circumstances and not merely in some possible circumstances. f

a

e

b

Figure .

d

  



A restriction needs to be placed upon which events can be put in Σ. We want to put in events that compete to cause a certain effect, e₂, but we shouldn’t put them in if they also affect the other competitor causal process in some way. That suggests that the following constraint is appropriate. No event ei can be put in Σ to show e₁ is a cause of e₂ or vice versa if both (a) If it is a member of Σ’, then would satisfy (I) to (III) with Σ’ in place of Σ. (b) If it is not a member of Σ’’ (which otherwise shares all members with Σ’ and no others) and we have, instead, of the probabilistic Σ-dependence condition, the following as condition ()’ of the analysis of causation (*) If e₁ and ei were to occur, with none of the events in Σ’’ occurring, nor ei satisfying any of (I) to (III) regarding e₂, then for some time t, it would be the case that, just before t, the mean value of p(e₂ at to) = x. (*) If ei were to occur with neither e₁ nor any of the events in Σ’’ occurring, nor ei satisfying any of (I) to (III) regarding e₂, then for any time t, it would be the case that, just before t, the mean value of p(e₂ at to) = y () x >> y. then does not satisfy (I)’ to (III). The condition is really meant to capture what would be the case if we put ei as a member of Σ or not. Since it is plausible that a set has its members essentially, I appeal to Σ’ and Σ’’—distinct sets from Σ—to capture the point. The aim is to separate out the impact of an event, ei, upon e, through ei satisfying any of (I) to (III) regarding e₂ (call this its causal shell with regard to e₂) with any other impact it may have which would affect the relationship between e₁ and e₂ through, for instance, being an anti-catalyst. So the constraint is simply a formalization of the idea: don’t put ei in Σ if the verdicts on whether e₁ is a cause of e₂ is a cause would differ if ei is present but loses its causal shell with regard to e₂. If ei does not satisfy clauses (I) to (III) in the actual world, little would have to change. If ei does satisfy these clauses, then the laws and/or particular circumstances would have to change just enough so that the clauses cease to hold of ei and e₂. Any further change in the relationship between e₁, e₂ will then be due to ei’s influence on the potential causal connection between them. The constraint upon Σ-membership allows us to proclaim that, in Figure ., b’s firing is a cause. The failure of f to fire or, simply, its failure to satisfy any of the clauses (I) to (III) with regard to e’s firing, makes no difference to the satisfaction by b’s firing and e’s firing of (I) to (III) and (I)’ to (III) in the way indicated. By contrast, d’s firing cannot be put in Σ to enable us to proclaim (falsely) that a’s firing is a cause of e’s firing. If d’s firing is absent, then a’s firing, e’s firing would satisfy conditions (I) to (III). However, if d’s firing is present but d’s firing simply fails to satisfy any of (I) to (III) with regard to e’s firing, then a’s firing, e’s firing fails to satisfy (I)’ to (III). The reason for this is that the condition-relative chance-raising of d’s firing would not raise the chance of e’s firing in the required way at the actual time that e’s firing occurred.



     f

a

e

b

d

Figure .

To examine further the application of the constraint upon Σ-membership, consider Figure .. Here d’s firing is a catalyst speeding up the a–e process. If d had not fired, then the top process would have been slower and failed to complete by the time that e’s firing occurred. As things are, it completed. For the same reasons as those above, we may conclude that b’s firing is a cause—for instance by letting f ’s firing be a member of Σ. If the b–e chain is indeterministic, then the firing of a may be a cause if the a–e chain raises the chance of e firing significantly over that it has as a result of the firing of b without anything in Σ. Suppose the a–e chain doesn’t raise the chance significantly. Then the proposal can’t establish that a’s firing is a cause. Letting Σ = {d firing} will do no good because, with the catalyst gone, the firing of a will fail clause (III) of my account. If the b–e chain is deterministic, then the firing of a will not be a cause of e firing since it can’t raise the chance of e firing. It seems to me that these verdicts are plausible. When the firing of b not only raises the chance of e but also acts as a catalyst for another process, the other process only has independent causal credentials if it very much raises the chance of e firing. Of course, this does not stop us claiming that the firing of a and b are a collective cause. However, for those who are convinced that a’s firing should be considered a cause of e’s firing even in the circumstances described in Figure ., an adjustment might be made to my account of probabilistic Σ-dependence. Let the causal shell of e₁ with regard to e₂ be e₁’s satisfaction of (I) to (III) of my analysis with regard to e₂. Let Σ# share all members with Σ except for those who, instead of supposing them to be absent, we suppose them to be present but no longer to satisfy their causal shells for e₂. Then the suggestion is that e₂ probabilistically Σ#-depends on e₁ if and only if () e₁ occurred and the events in Σ which are not in Σ# occurred without satisfying their causal shells, but none of the events in Σ# occurred, then for some time t, it would be the case that, just before t, the mean value of p(e₂ at t) = a () the events in Σ which are not in Σ# occurred without satisfying their causal shells, but neither e₁ nor any of the events in Σ# occurred, then for any time t, it would be the case that, just before t, the mean value of p(e₂ at t) = b. () a >> b. We would then adjust the analysis by replacing clause (I) with (I*): either e₂ probabilistically Σ-depends on e₁ or e₂ probabilistically Σ#-depends on e₁. We

∑-   - 



would retain the original analysis as a definition of causal shell. a’s firing would be counted as a cause by the new analysis because we could retain the catalysing function of d’s firing while removing its independent raising of the chance of e₂. In those circumstances, a’s firing does raise the chance of e’s firing in the required way. One concern with this adjustment is that if d’s firing were no longer to have its causal shell, then it would lose its catalysing role too since this is related to the top row’s raising of the chance of e firing at the time it did. This concern is a mistake. The suggested analysis only needs to apply when the top row fails to raise the chance of e firing significantly. When a’s firing does raise the chance of e’s firing significantly, then there is no reason to consider putting d’s firing in Σ. If the top row’s firing does not raise the chance of e’s firing significantly, then as things stand, the catalytic role of d’s firing is not part of the causal shell if d’s firing with respect to e’s firing. Is there something that one could put in Σ that could make it part of the causal shell? If there were some subsequent event between d’s firing and e’s firing, then one could put that in Σ and, it would seem that the catalysing role would be part of the causal shell of d’s firing with regard to e’s firing. However, in those circumstances, there would be no reason to put d’s firing in Σ to show that a’s firing was a cause of e’s firing. Instead, one could put that subsequent event to d’s firing and retain d’s catalysing role as required. Any other event put in Σ though, for example an event in the a-chain, could not be used to demonstrate that the catalysing role was part of the causal shell of d’s firing. Nevertheless, I note this adjustment to my analysis as a possibility. I don’t work with it in what follows because I am not convinced by the verdicts regarding Figure .. The proposed treatment of catalysts and anti-catalysts also provides us with another way of obtaining the right verdicts in Schaffer’s trumping cases. The issue is whether the condition upon Σ-membership serves to distinguish between Merlin’s spell—the genuine cause—and Morgana’s spell, the would-be cause. Merlin’s spell cannot be put in Σ. While Morgana’s spell would raise the chance of the prince turning into a frog in the appropriate fashion with Merlin’s spell in Σ, if Merlin’s spell was not in Σ but just lost its causal shell, Morgana’s spell would fail to raise the chance of the prince turning into a frog because it would not be the first spell of the day. By contrast, Morgan’s spell can be put in Σ to establish that Merlin’s spell is efficacious.

. ∑-Dependencies and the Context-Determined Contrastive Character of Causation The Σ-set apparatus has enabled me to pick out a particular kind of dependency between events that constitutes the causal relation. Philosophers have questioned whether there is such a relation. On the one side, they have argued that causation is not a relation at all. I shall consider this matter in Chapter . On the other, they have argued that, although there may be such a relation, it is not a binary one but holds between three or more events. The idea here is not that, in fact, collections of events may count as a cause of a particular effect (in addition, to each counting as a cause in the circumstances). The idea is rather that causation is contrastive. The correct form of causal statements is not c causes e but instead c causes e₁ rather than e₂ or c₁ rather than c₂ causes e₁ rather than e₂, where c, c₁, e, e₁ are the target events and c₂, e₂ their



    

contrasting foils. The context of inquiry settles the events that are taken to be the foils for the candidate causes and effects (e.g. Schaffer (a), pp. –). In the present section, I will explain why my analysis undermines a principal consideration in favour of this move. Other reasons, for example those deriving from emphasis, negative causation, and transitivity, will be discussed in Chapter , ., Chapter , and .. The principal consideration I have in mind for appealing to these contrasts is that, in some cases, simple dependencies between cause and effect seem to fail due to, perhaps contextual, differences over what is counted as an absence of the target event, or the conduciveness of circumstances to supply replacements (Hitchcock (a), pp. –; Schaffer (a), pp. –, –). Here are some examples that I illustrate by appealing to simple counterfactuals before we consider how my approach may apply. Suppose that Penelope has been a moderate smoker throughout her life and has now developed lung cancer. We are interested in the question of whether her moderate smoking (a complex event with many different portions throughout her life) is a cause of her lung cancer. We don’t have to go into the complexities of my account to see the initial problem. If this complex event of moderate smoking had not occurred, what would be the case? There are various alternatives. First, she might have been a heavy smoker. Second, she might have been a moderate smoker but smoked at significantly different times and in different ways so that this would count as a distinct event of moderate smoking. In which case, it would constitute the nonoccurrence of the initial moderate smoking event I described. Third, she might not have smoked at all. The truth of the counterfactual ()

If she had not been a moderate smoker, she would not have got lung cancer

depends upon which alternative would have been the case. The reading concerning moderate smoking events is not a natural contrast for this counterfactual but an antecedent such as ‘if she had not smoked moderately at the various times she did through her life’ would make such a contrast possible. Suppose that Boris has high blood pressure and, as a result of this, a fatal heart attack. Again, if he had not had high blood pressure, various alternatives would be possible, for instance, low blood pressure or no blood pressure. The truth of the counterfactual () If Boris had not had high blood pressure, he would not have died depends, again, upon which alternative would have been the case. Note that when we compare this case to the first, a simple general reply is untenable: complete removal. If absence of moderate smoking means no smoking and absence of high blood pressure means no blood pressure, then the first counterfactual is true and the second is false. That suggests that different contexts are at work if, as seems plausible, both counterfactuals are true. Finally, consider the set-up in Figure .. Here the patterned neurone is a vigorous firing of c. The vigorous firing of c is the result of being stimulated by both the firing of a and the firing of b. The firing of e would have occurred even if there had been a feeble firing of c. The question is whether the counterfactual theory can capture the intuitive result that both the firing of a and the firing of b are causes of the firing of e. Lewis obtains this result by claiming that the following is true.

∑-   - 



a

c e

b

Figure .

()

If the vigorous firing of c had not occurred, then c would not have fired at all.

However, by Lewis’ own similarity weighting with which, in this respect, mine would not demur, we could achieve more perfect match and minimization of miracles if we only had to get rid of one of a or b firing in order to stop the vigorous firing of c (Lewis (b), p. ). In which case, the counterfactual is false. The contrastive approach to causation takes the issues raised by each of these cases as a sign that the causal relation is contrastive. Penelope smoking moderately rather than not at all was a cause of her cancer. Boris having high blood pressure rather than low blood pressure was a cause of his death. c firing vigorously rather than not at all was a cause of e firing. The context sensitivity comes in because different contexts of inquiry determine the different truth conditions attributed to these sentences as a result of the contrasts involved. In the case of Penelope and the vigorous firing, the contrast is an absence, in the case of Boris the contrast is a presence of a lower blood pressure. In other contexts, the very same sentences may express a counterfactual dependence with a different foil event to the target event. The Σ-set mechanism deals with these cases by, in effect, ruling out contrasts rather than making them. It treats them as a subclass of cases of redundant causation—the standard cases being pre-emption and overdetermination—except that the potential replacement causes are possible events rather than actual ones. So rather than having to consider whether, if Penelope were not a moderate smoker, she would be a heavy one, we have a counterfactual which in this case would read () If it were neither the case that Penelope were a moderate smoker nor that she were a heavy smoker (the event in Σ), she would not have lung cancer. The approach does not require that we put the same kind of events in Σ. Thus we don’t have to consider the counterfactual () If it were neither the case that Boris had high blood pressure nor the case that he had any blood pressure, then he would not have died but rather, simply, on standard assumptions, the original counterfactual (). The similarity weighting applied to the original counterfactuals can generate the required



    

contrast by itself. The appeal to a Σ-set is a supplement to this. Of course, if it is the case that Boris could not have blood pressure without having high blood pressure, then we would be inclined to judge that the counterfactual is false. In those circumstances, though, we would probably be equally inclined to conclude that Boris having high blood pressure was not a cause of his death. Finally, with regard to the vigorous firing case, my analysis would conclude that each of a’s firing and b’s firing is a cause by putting the feeble firing of c in Σ. In that situation, e’s firing would not occur (Ramachandran (), for a similar move). Although my analysis of causation allows variation in what may be put in Σ, that does not mean that it is also a contextualist account of causation. The context in which a causal statement is produced does not yield differences in what is put in Σ. The analysis instead holds that, if a causal statement is true, then there will be a Σ that shows how the cause raises the chance of the effect relative to that assignment to Σ. By its lights, a causal statement is true if there is some way in which the putative cause may be absent as a result of which it raises the chance of the effect by an independent complete causal chain. It does not depend for its truth upon a particular contrast— any contrast that does not provide a replacement cause will do. My aim is not to deny that there are true contrastive causal statements. Without doubt, all the ones mentioned are plausibly true. It is rather to establish that, in addition to this, there are true non-contrastive context-insensitive causal statements. It is just true that Penelope’s moderate smoking caused her cancer, Boris having high blood pressure caused his death and each of a’s firing and b’s firing are causes of e’s firing. For example, suppose we are in a culture in which everybody smokes, some heavily, some moderately, our friend Penelope dies from cancer and we are considering what caused her cancer. It would be bizarre to conclude that the answer is nothing. The intellectual impetus towards a particular contrast that shows up a cause of her cancer is the draw of a non-contrastive understanding of cause. Likewise, we see, in the case of Boris, that the truth of the causal statement by my analysis does not depend upon ruling out the no blood pressure case. That falls out of the contextinsensitive similarity weighting for counterfactuals outside of backtracking contexts and these contexts are not invoked when causal claims are made for the relevant events mentioned as causes and effects.

. Concluding Remarks The theory at which we have arrived is as follows. For any actual, distinct events e₁ and e₂, e₁ causes e₂ (if and) only if there is a (possibly empty) set of possible events Σ such that (I) e₂ is probabilistically Σ-dependent on e₁, and, (II)’ for any superset of Σ, Σ*, (where Σ  Σ*), if e₂ probabilistically Σ*-depends upon e₁, then every event upon which e₂ probabilistically Σ*-depends is an actual event, (III) e₂ occurs at one of the times for which the mean value for p(e₂ at t) is x and x >>y.

 



The first clause enshrines our understanding of the particular type of Σ-conditionrelative chance-raising required for e₁ to cause e₂ (rather than to cause e₂ at a time). The second and third clauses, together with the constraints upon Σ-membership and the time at which the chance of an effect is assessed, constitute the analysis of what is required for there to be a complete causal process between e₁ and e₂. Together they provide an analysis of the nature of a cause that can be put as follows. A cause, e₁, is something which (independently of its competitors) both makes the chance of an effect, e₂, very much greater than its mean background chance in the circumstances (that is, the chance without any of the competitors) (clause (I)) and actually influences the probability of the effect in this way at the time at which the effect occurred (clauses (III)) via a complete causal chain (clause (II) and the way in which probabilities are assessed).

Although the proposal has been developed primarily by consideration of cases of preemption, one consequence is that it also classifies cases of overdetermination as involving two or more overdetermining causes. I think that this verdict derives plausibility from its successful treatment of pre-emption. It has also struck many as independently plausible (e.g. Lyon (), pp. –; Schaffer (a)). Counterfactual theories have had a bad press. Often the charge is that they are prey to versions of the conditional fallacy (Shope ()). Robert Shope identifies, in effect, two potential problems for counterfactual accounts: first, in considering what would happen if the events in the Σ-set were absent, I might be making a causal relationship present which wasn’t there before and, second, considering what would happen if the Σ-set events were absent, I may disturb a causal relationship which actually holds. My account is developed to guard precisely against these difficulties. By insisting that there should be no probabilistic Σ-dependence on non-actual events I deal with the point that, in envisaging the events in Σ to be absent, the causal chain may be filled in between the intuitively pre-empted cause and the effect. This guards against making a causal relationship present which, before, was absent. Similarly, by introducing the constraints upon what can figure in Σ, I guard against disturbances of causal relationships that were present. I mentioned at the outset that the proponent of a philosophical analysis does well to provide an account of the practical significance of the subject of analysis. What is the point of having a concept of cause according to my proposal? Many have alighted upon the idea that we are apt to think of causes as means by which agents can achieve certain ends. One way of capturing this notion is to suggest that causes must raise the chances of their effects. This is considered central by Mellor (e.g. Mellor (), pp. –). The theory developed in this chapter indicates that, although this is roughly right, particular circumstances may disguise the fact that a particular causal route does raise the chance of the effects. In effect by stripping away these circumstances, we see causation for what it is. That is precisely what my ‘subtraction’ approach—through appealing to Σ-sets removing elements of the causal circumstances—does. It may be asked why we should be interested in the concept of something that, in certain circumstances, does not involve chance-raising. Indeed, such a line of thought convinces Mellor that putative redundant causes are no such thing (Mellor (), pp. –). My response is that we are interested in picking out processes that are a



    

means to an effect without them necessarily being the best means in terms of reliability and so forth. Information about causes constitutes the proper input into our practical deliberations where one consequence of deliberation will be how reliably a certain cause will achieve a certain end. My claim is not that this exhausts the practical utility of our concept of causation but simply that the concept I have identified does have plausible utility and hence suffers no disadvantage upon this score. There is no need to question the intuitive verdicts that led to the formulation of the analysis. There are similarities between the subtraction approach I favour and that set out by Strevens in Depth (). He appeals to the idea that, from a causal model describing the circumstances under which an event e is produced, there will be a distilled version of that model that implies that e is produced, with competing/ redundant elements removed (Strevens (), pp. –). This is akin to how the Σ-set mechanism is meant to work first championed by Ganeri, Ramachandran, and myself (()()). There are some differences however. First, Strevens relies upon whether there is a true or false non-interference condition for the trajectory of pre-empting/pre-empted causes, respectively (Strevens (), p. ). Talk of noninterference implies that the account does not aspire to be reductive. This is underlined by cases of indeterministic late pre-emption. Does the fact that the pre-empted cause undermines the pre-empting causes’ chance-raising relationship with the effect constitute interference or not? If it does, then the non-interference condition fails for the pre-empting cause. If it does not, then it seems clear that the interference is explicitly causal. A second difference is that Strevens only requires that the target effect is entailed by the distilled model. He does not distinguish between causing an effect and causing it to occur at a particular time. This has implications for his discussion of hasteners and delayers, especially when we turn to indeterministic cases, as we saw above. Popular alternatives to the subtraction approach I favour are fixing accounts. Keep certain things fixed and chance-raising or counterfactual dependency will be revealed. Proponents of fixing accounts include Hitchcock, Pearl, and Stephen Yablo (Hitchcock (), (b), Pearl (), Yablo (), ()). Fixing accounts face problems. Some of them will be much clearer when we consider the non-transitivity of causation in Chapter . One that is worth bearing in mind now concerns the proper understanding of chance. In the late pre-emption case, I noted that chance-raising would not be revealed just before the actual time of the effect. A standard manoeuvre of a fixing account is to say that we should hold fixed the fact that certain events did not occur—for instance, in the late pre-emption characterized by Figure ., d’s firing. Holding fixed the fact that d’s firing did not occur would not affect the variation of the chance of e’s firing, due to whether or not b’s firing occurred, assessed just before e occurred. At that point, it is not settled that d’s firing did not occur and hence e’s firing would be high whether or not b fired due to the a process. They can avoid this problem by considering the chance of an effect at a certain time rather than just the chance of an effect. However, then they fail to respect the difference between these two cases. Proponents of fixing accounts have to understand chances of effects in a different way if they are to avoid this consequence. Such an understanding of chance remains to be spelt out.

 



In Chapter , I presented the semantics for the counterfactuals used in the present chapter. In this chapter, I have presented the complete analysis. There are still many issues that arise before we can properly assess it. I hope to cover the main ones in the chapters ahead, for instance, the proper characterization of causal relata, whether causal non-symmetry is based in counterfactual non-symmetry, whether all counterfactuals are indicative of causal relationships, and, if not, what differentiates those which are, the question of the transitivity of causation, the nature of chance at a time, and so on. Nevertheless, my hope is that the relatively good performance of my proposal in treating the cases discussed in this chapter, and the notion of causation behind it, already shows that it has much to recommend it.

 The Non-Transitivity of Causation Relations can be transitive, intransitive, or non-transitive (amongst other things). A relation R is transitive iff, for all a, b, c, if a bears R to b and b bears R to c, then a bears R to c (Quine (), p. ; Suppes (), p. ). A relation R is intransitive iff for all a, b, c, if a bears R to b and b bears R to c, then a does not bear R to c (Quine (), p. ; Suppes (), p. ). A relation is non-transitive iff it is neither transitive nor intransitive (Suppes (), p. ). That is, it doesn’t follow that a bears R to c or that a does not bear R to c if the antecedent conditions are met. It is generally agreed that counterfactual dependence is non-transitive. Certainly the similarity weighting outlined in Chapter  supports, and cases of pre-emption illustrate, that view. Many have argued that it is highly intuitive that causation is transitive and make it carry some theoretical weight. For instance, Lewis appealed to the transitivity of causation to explain how the pre-empting cause is a cause in a case of early pre-emption (Lewis (b), pp. –); Ehring bases his denial that particulars are efficacious in virtue of their properties on their resultant threat to the transitivity of causation (Ehring (), pp. –). Some have argued that causation is intransitive (e.g. McDermott (); Hitchcock (b)). In this chapter, I will argue that it is non-transitive. I accept the counterexamples to transitivity but don’t suppose that this rules out cases in which all of the following hold: e₁ causes e₃ and e₁ causes e₂ and e₂ causes e₃. The question of the transitivity or otherwise of causation has an impact upon theory construction. Suppose you think that causation is transitive. Then you might begin by analysing immediate causation. By definition, c is an immediate cause of e if and only if c causes e and there is no distinct d such that (i) c causes d and d causes e and (ii) if either c were not to cause d or d were not to cause e, then c would not cause e. The first condition is insufficient. Consider Figure .. c is an immediate cause of e even though there is a d such that the first condition is met. If c were not to cause d or d were not to cause e, though, c would still cause e. Thus there is no d that meets both conditions and c counts as an immediate cause of e as a result. c is also a mediate cause of e by meeting condition (i). Thus it does not follow that if c is a mediate cause of e, it is not an immediate cause of e, or vice versa. For a theory relying, for its construction, upon causation being transitive, the basic case would lay down conditions that must hold if c is an immediate cause of e. A Variety of Causes. Paul Noordhof, Oxford University Press (2020). © Paul Noordhof. DOI: 10.1093/oso/9780199251469.001.0001

  



e

c

d

Figure .

Mediate causation could be defined in terms of chains of events standing in the relation of immediate causation to each other. Of course, it is not excluded that you might seek to characterize causation in terms of immediate causation even if causation is not transitive. Chains of immediate causation meeting an additional requirement might then constitute mediate causation. Nevertheless, if causation is not transitive, there is much less reason to take this route. You can go straight to ‘Go’ and seek to define the causation relation as indeed I did in Chapter  (starting at ..). The approach has the advantage of not resting upon the assumption that there are cases of immediate causation. If nature is continuous so that, between any two events, there is a third, then this assumption may not be met. In the present chapter, I discuss the standard counterexamples to transitivity (.) and explain how my analysis obtains the correct verdicts P (.). During the course of this discussion, I identify a further constraint upon -set membership or, rather, make explicit a commitment for which I argue later, namely that negative events P don’t exist and hence are not candidates for being put in . I close by comparing my treatment with fixing accounts of causation (.., ..) and, also, consider the extent to which my approach satisfies constraints on any account of causation favoured by Carolina Sartorio, from which the non-transitivity of causation is meant to fall out (.). Before I defend my approach, though, there are two other responses to the counterexamples to transitivity I consider. The first is to reject them because they rest upon a mistaken view about the relata of causation. The second is to argue that, contrary to our initial intuitive response, we should reject the apparent counterexamples and accept that causation is transitive even in these cases. The second and third sections of the chapter explain why I think these approaches are mistaken (., .).

. The Problem Cases Various cases provide strong prima facie evidence that causation is not transitive. I enumerate some of the most famous in the literature below. The second is familiar from Chapter  although, there, we focused on the hastening/delaying aspect. Dog bite: Jo is about to trigger a bomb by pressing a button with his right forefinger but a dog bites it off. Hence Jo triggers the bomb by pressing a button with his left forefinger. The dog bite is a cause of Jo pressing a button with his left forefinger. Jo



 -  

pressing a button with his left forefinger is a cause of the bomb exploding. Yet, the dog bite is not a cause of the bomb exploding (McDermott ()). April Rains: The April rains ensure that the forest is damp in May and so doesn’t burn down. This means that it is available for burning as a result of the lightning strike during June storms. The April rains don’t cause the forest to burn down in spite of causing the conditions necessary for the forest to burn down when it did (Bennett (), pp. –). Bomb: Billy puts a bomb under Sally’s chair. Sally notices the bomb and runs away before it explodes. She survives to receive a glowing medical report from her doctor. Putting a bomb under her chair is not a cause of receiving a glowing medical report even though it is a cause of something that is a cause of the glowing medical report (Hall (), p. , who reports the case as due to Hartry Field). Assassination: The Captain yells ‘fire’ to his assistant on spotting the victim. The assistant fires. Since the victim overhears the order, she ducks and avoids assassination. Yet it seems implausible to say that the Captain causes the victim’s survival (Hitchcock (), pp. –, who reports the case as due to McDermott). Defoliant: A weed in a garden is sprayed with a defoliant. This decreases the chance it will survive from . to .. The plant is sick for six months but then recovers. There is a causal process from spraying defoliant on the leaves to the recovery. Yet, in spite of this, it seems clear that spraying defoliant on the leaves was not a cause of the plant’s health six months later (Cartwright (), p. , in part, a reprint of Cartwright ()). As I have already noted, there have been broadly three responses to these cases. Some claim that, when properly described, taking causation to be transitive is compatible with denying that the putatively counterintuitive causes are causes because there is no intermediate entity that is an effect of the putative cause and a cause of the target effect. Some argue that, even if it is counterintuitive, they are causes due to the transitivity of causation. They seek to undermine intuitions to the contrary. Finally, some argue that the cases are genuine counterexamples to the transitivity of causation that a correct theory of causation needs to respect. My own position is the last of these. I summarize the approaches in Figure ..

. The Distinct Property Instances Strategy Implementation of the first strategy rests upon the following thought. Whenever it is implausible to conclude that, from the transitivity of causation, e₁ causes e₄, one of the alleged intermediaries between e₁ and e₄ is not a genuine causal intermediary. According to one familiar story, e₁ causes a property instance P and a distinct property instance Q causes e₄. For instance, the dog bite causes an instance of Jo pressing the button with his left forefinger and an instance of Jo pressing the button is a cause of the explosion (Ehring (), pp. –; Paul (), pp. , –; Strevens (), p. ). If these two property instances are distinct then there is no intermediary to connect the dog biting with the explosion. Call this the distinct property instances strategy.

    



Is Causation Transitive?

Yes

No

Distinct Property Instances Strategy: Counterexamples don’t involve chain

Fixing Accounts

Contrastive Approach

Subtraction Accounts

Undermining Intuitions

Causes as DifferenceMakers

Figure .

An alternative, pressed by Schaffer, is that if causation is contrastive, then counterexamples to transitivity can be avoided. The dog bite causes the left finger pressing rather than the right finger pressing. However, the left finger pressing rather than the right finger pressing does not cause the explosion (Schaffer (a), pp. –). If the discussion in . is correct, then causation is not contrastive in the required way. Although it is true that whether an event is a cause, or not, depends upon the contrast between what is the case if the event is present, and what happens if there is some kind of excision of the event from the circumstances in question, the verdict does not depend upon contrasts which may vary across the chain. Moreover, it seems possible to fix up contrasts for which a commitment to transitivity would yield the result that the dog bite is a cause of the explosion. For instance, the dog bite is a cause of a pressing with the left hand rather than a bungled pressing with the (injured) right hand. The pressing with the left hand rather than the bungled pressing with the injured right hand is a cause of the explosion. Therefore, it seems that with this common contrastive we must conclude that the dog bite is a cause of the explosion. As a result, I shall set this alternative version of the first ‘no intermediate entity’ strategy aside.



 -  

The success of the distinct property instances strategy rests upon two things. First, that, in all the problem cases, there are distinct property instances. For example, the instance of Jo pressing the button with his left forefinger should be distinct from the instance of Jo pressing the button. Second, the efficacy of one should not have implications for the efficacy of the other. Neither is obvious.

.. Property instances The question of whether instances of two distinct properties are identical can be answered via external considerations and internal considerations. By ‘external considerations’, I mean considerations drawn from whether their identification or differentiation serves to resolve certain distinct metaphysical issues. By contrast, ‘internal conditions’ are those relating to the nature of the properties themselves. Saving the transitivity of causation would be an external consideration against taking instances of two intimately related, but distinct, properties—such as being a button pressing and being a button pressing with the right forefinger—to be identical. However, another external consideration is the question of how the efficacy, or causal relevance, of some properties relates to those of other properties. The most familiar example of this is the case of mental causation. But the structure of the problem is more general. Let ‘narrowly physical properties’ be those properties identified by current physics, or some suitable extension of current physics resembling our current physics, and ‘broadly physical properties’ be those which aren’t so identified but whose instantiations are, in some way, constituted from or determined by instantiations of narrowly physical properties. Candidates for broadly physical properties include being a chair, being an earthquake, being a rain shower, being a tiger, and, if physicalism is true, being a pain or an itch, or many other such mental properties. Physics purports to have complete coverage: whenever two things are causally related, there will be a characterization of them in terms of narrowly physical properties which fully captures why they stand in the causal relation they do. If citing instances of narrowly physical properties serves to characterize completely why two things stand in the causal relations they do, then broadly physical properties seem causally irrelevant or, at least, that is the charge. In Chapter , we will discuss this issue but within the context of it presenting a challenge to the counterfactual analysis of causation. The present relevance of the issue is that one response to the charge has been to hold that broadly physical properties are efficacious because their instances are identical to those of narrowly physical properties. The proposed property instance identification relies upon a coarse-grained approach to property instance identity that has some independent plausibility. Rather than adopt a fine-grained approach in which any two distinct properties, or even finer, two distinct predications, have distinct instances, the proponent of a coarse-grained approach insists that property instances can serve as instances of many distinct closely related properties. For example, many have assumed that if an object is scarlet (say), then the instance of scarlet, the instance of red, and the instance of colour displayed by the object are identical. Its intuitive plausibility is taken across and it is argued that instances of mental properties are identical to instances of

    



physical properties that we count as unproblematically efficacious (e.g. see Macdonald and Macdonald (), (); Robb ()). Appealing to a coarse-grained approach to property instance identity to resolve the issue of mental causation, or causation by broadly physical properties more generally, is misguided. As we shall see in ., even if two properties have an identical instance, it makes sense to consider whether the instance is efficacious in virtue of being an instance of one property or the other (for further discussion Noordhof (c)). This does not mean, though, that coarse-grained approaches to property instance identity are mistaken. It is just that this will turn on internal considerations instead. For our purposes, the discussion breaks down into two parts depending upon whether properties are taken to be universals or some construction out of particulars (that is, a nominalistic approach). Universals can be wholly present at more than one spatiotemporal location. Recognition of universals is, thus, straightforwardly the denial of nominalism. The existence of a universal U wholly present at two distinct spatiotemporal locations means that there is something shared between these two locations, namely U. Nominalism denies that there is anything that might be shared in this fashion. If property instances are instantiations of universals, then a fine-grained account of property instances may appear appropriate. Two putatively distinct universals— such as that of being coloured and being red—will have different instantiations and these would count as different property instances (Ehring (), p. , (), p. ; Gibb (), p. ). Such an approach would, then, appear to support the distinct property instances strategy. However, appearances are deceptive. First, rather than finding that we have distinct fine-grained property instantiations, an alternative is to deny that one of the putatively distinct property instantiations exists. The most plausible examples in which we have to go fine-grained concern instances of determinables and their determinates: shape/square, colour/red, and so on. Yet, the existence of determinables has proved contentious (Gillett and Rives (), pp. –; Armstrong (), II, pp. –). This is damaging to the distinct property instance strategy. Take the dog bite case. Jo’s property of pressing the button with a left forefinger is arguably a determinate of pressing the button with a forefinger. It satisfies the central features of the determinate/determinable relation. These include the following. (di) Necessarily, if an object has a determinate of a determinable, then it has the determinable. Necessarily, if Jo has the property of pressing the button with his left forefinger, then he has the property of pressing the button with his forefinger. (dii) Necessarily, if an object has a determinable, then it has one of its determinates. Necessarily, if Jo has the property of pressing the button with his forefinger, then he either pressed it with his left or his right forefinger.



 -  

(diii) Necessarily, if an object has one of the determinates of a determinable, it cannot have any of the other determinates. Necessarily, if Jo pressed the button with his left forefinger, then he didn’t press it with his right forefinger. Perhaps satisfaction of the third feature is uncertain. One might wonder whether, if Jo pressed with the left, couldn’t he also press with the right forefinger? On reflection, though, this question might be similar in force to ‘If an object is red, could it also not be black by being red and black striped?’ If it is added that red excludes other determinates of the same determinable if an object is red all over then presumably a similar addition should be made to pressing with the left forefinger to get the proper comparison: ‘pressing with the left forefinger as the sole finger movement’. If Jo pressing the button with his left forefinger was his sole finger movement, then he could not be pressing the button with his right forefinger as well. We seem to have lost the putative difference between them once more. Even if there is a difference between cases of determinable and determinates, and the case of Jo’s finger, it is questionable whether this would do any good. What convinces those who deny that determinables exist is that the determinates of these determinables are sufficient to ground the truth of statements concerning attributions of determinables. The same holds for statements attributing pressings with a forefinger. So, if determinables do not exist, then it is plausible that there is no property of pressing the button with a forefinger and hence that the distinct property instances strategy does not apply to this case. However, I would not want to rest my rejection of the distinct property instances strategy on this response. As I shall argue in ..–, there is good reason to allow for the existence of determinables as well as determinates. So I’m committed to allowing that there are distinct properties here. Nevertheless, from that it doesn’t follow that these distinct properties cannot share instantiations. It is open to a proponent of universals to argue that the necessary connections between instances of determinables and instances of determinates described above suggests that their instances may be identical: the necessities supplying what is required for unity of property instance. This would not infringe against the claim that (PI) Property instance p₁ is identical to property instance p₂ iff the property or properties instantiated in p₁ are identical with the property or properties instantiated in p₂. It is just that the properties that characterize the instances will be redness and colour (say) rather than simply instances of red and instances of colour. Properties, so understood, it might be argued, display their intimate connection in virtue of how they are instantiated, viz at least one may be only instantiated with the other. It is perhaps more natural to suppose that, if the fundamental items in our ontology include universals, then distinctness of universals must determine distinctness of the ways in which they are instantiated. But identity of instantiation can be taken to display a deep truth about the nature of the properties instantiated. So even if universals are fundamental, it doesn’t follow that their distinctness implies distinctness of property instantiations.

    



Let’s turn now to the idea that properties are constructions from particulars (that is, nominalistic approaches to properties). Perhaps contrary to expectations, it is here that we have the best argument for recognizing distinctness of property instance. Resemblance nominalism takes these particulars to be classes of resembling objects, trope metaphysics takes properties to be classes of exactly resembling property instances. Suppose that Jo has the property of being a boy. The resemblance nominalist will take Jo to be one of the particulars out of which they build their resemblance class of boys. The trope metaphysician will take Jo’s boyishness to be one of the particulars. Jo has properties other than his boyishness. These will be no part of the trope metaphysician’s particular but they will be part of the resemblance nominalist’s. The distinct property instances strategy is hard to implement within the resemblance nominalist framework. There won’t be distinct particulars to block the application of the putative transitivity of causation. The same particular—for example, Jo’s pressing of the button—will be a member of both resemblance classes. This would apply just as much for those who take universals to be natural classes of objects (e.g. Lewis (a)). The main difference between these two forms of nominalism concerns the theoretical role given to resemblance not the particulars that make up the classes. By contrast, a trope metaphysics may hope to supply the required distinct particulars. It all depends upon how the theory is developed. One important motivation for trope metaphysics is that it is meant to avoid the problem of imperfect community that afflicts resemblance nominalism (e.g. Campbell (), pp. –, –). Here is how the problem arises. As I noted above, resemblance nominalists appeal to resemblance classes of objects to play the role of properties. A preliminary characterization of them might run as follows. A class of objects is a resemblance class if and only if (i) each member of the class resembles every other member of the class to a certain degree (at least) and (ii) no non-member resembles every member to that degree (Wolterstorff (), p. ; Manley (), p. ; Rodriguez-Pereyra (), p. ). The second clause is needed to explain why orange things are not members of the class of red things. Orange things may be more similar than dark red things to orangey red things but orange things won’t be more similar to all red things. Suppose that there are three objects a, b, c such that the properties F, G, and H are distributed according to the following table and that there are no other things which have more than one of the these three properties. Table . F

G

H

a

No

Yes

Yes

b

Yes

No

Yes

c

Yes

Yes

No

The community of a, b, c is imperfect because there is no common property in virtue of which they resemble each other. Nevertheless, each of a, b, c resembles each of the others to the required degree. No other object resembles them to that degree. Thus we



 -  

have a resemblance class of particulars. So, it appears, we cannot replace appeal to common properties F, G, or H in the table above with classes of resembling particulars. There have been attempts to resolve this problem for resemblance nominalism (e.g. Rodriguez-Pereyra (), p. ; Hirsch (), p. ). They rely upon more technical notions of resemblance that have their own commitments. For our purposes, it does not matter whether these proposals are ultimately defensible. Instead, we may note two things. First, if a trope metaphysics allows that two or more distinct tropes may share an instance, then they satisfy a necessary condition for the problem of imperfect community to arise. Second, although it is open to such approaches to appeal to the same solutions to which resemblance nominalists do, this particular motivation for their theory collapses. A trope metaphysics that successfully avoids the problem of imperfect community on its own terms is one that takes properties to be classes of exactly resembling tropes and, hence, eschews the possibility that two properties may share an instance. For example, instead of supposing that the property of being red is a class of roughly resembling tropes differing amongst themselves because members of the class are different determinate reds, each of which making ‘– is red’ true of objects that instantiate them, there will be a class of exactly resembling tropes—instances of being red—and other classes of exactly resembling tropes corresponding to particular shades of red. So it seems that there are internal reasons for allowing that, on some understandings of the nature of property, identity of property instances allows for the kind of distinctions the proponent of the distinct property instances strategy requires. This brings us to the second question: if these instances are distinct, then does it follow that one may be efficacious without the other?

.. Efficacy implication Even if there are distinct property instances, as the distinct property instances strategy requires, it is implausible that efficacy of one will be distinct from the efficacy of the other. The full defence of my position occurs in .... However, I can make the following points now in summary. First, even if the property instances are distinct, one seems to be necessarily connected to the other. For example, in the dog bite case, metaphysically necessarily, if the property of being a left hand button pressing is instantiated, then the property of being a button pressing is instantiated. Whatever causal powers the latter possesses seem determined by the instantiation of the former. It is certainly not obvious how this is compatible with denying that the determining properties have the effects of the properties whose causal powers they determine. Second, while it seems that () It was Jo’s pressing the button with his left forefinger that was the cause of the explosion of the bomb is true, whereas () It was Jo’s pressing the button with his left forefinger that was the cause of the explosion of the bomb

  



seems false, the difference lies not in a claim about the efficacy of some instances over others but rather in the different property causes invoked. Property causation involves a certain kind of generality and explanatoriness by a property rather than simple causation by a particular (.). The distinct property instances strategy concerns particulars—albeit often property instances—and not properties. Evidence for this verdict is the status of () It was Jo’s pressing the button, and not pressing the button with his left forefinger, that was the cause of the explosion of the bomb. Although it seems to express something we are inclined to endorse, it only does so with charitable reinterpretation. After all, we don’t really think that Jo’s pressing of the button with his left forefinger wasn’t a cause of the explosion of the bomb. Rather, it is the contrast we are inclined to assert. We take () as pointing to the difference between () and (). The gap between the overstatement involved in () and the plausibly true statement contained in () shows that () does not concern a distinction between two different particulars causing a target effect. So, even if we do have distinct property instances of the required sort, we have no grounds for appealing to it to block the apparent counterexamples to transitivity. Moreover, as Hall points out, even if the strategy did work for some of the putative counterexamples, they can be rephrased to reintroduce the difficulty. For example, suppose that, in a variant of the dog bite case, instead of pressing the button with his left forefinger, Jo orders an underling to press the button for him. Here the dog bite is a cause of the order that is, in turn, a cause of the button being pressed (Hall (), pp. –). This kind of case cannot be dealt with by the distinct property instances strategy. Indeed, we might also fit the original dog bite case into the same structure. The dog bite is the cause of Jo’s intention to press the button with his left forefinger and this is a cause of his pressing the button. My discussion explains why it would not help proponents of the distinct instances strategy to quibble over whether there is an additional intention simply to press the button which—rather than the intention to press the button with one’s left forefinger—is the cause of the button pressing. Even if we allow that there are distinct property instances at the relevant place in the causal chain, there will be cases where one inherits its efficacy from the other and hence supply counterexamples to the transitivity of causation. The success of the points in this section removes the motivation for considering the kind of metaphysics of properties that might support the distinct property instances strategy. Those who resist these points, though, have considerable work to do. The distinct property instances strategy cannot be divorced from general questions about the metaphysics of properties and, as we have seen, only certain approaches to the metaphysics of properties are congenial to the strategy’s ends.

. Undermining the Intuitions Those who accept that the putative counterexamples are genuine cases of causation point to structural similarities between these cases and others where we have no



 -   a

b

d

c e

f

g

h

Figure .

problem in allowing that causation is present. Thus, they argue, causation is transitive after all in spite of our prima facie inclinations to resist it. One proponent of this strategy is Lewis ((a), pp. –). He holds that they all have the structure in Figure .. We are to imagine one individual Lewis calls Red in control of two potential chains initiated by a’s firing and f ’s firing. If b fires, and hence the a–e chain completes, then Red wins. Black seeks to inhibit the completion of the a–e chain by initiating the firing of c. Unfortunately for Black, b’s firing stopped the f–e chain from completing by inhibiting the firing of g and now that this inhibition is absent, the alternative chain moves to completion. In Lewis’ terminology, g’s firing is Red’s available countermove—a move that Red would not have made if Black hadn’t stopped the completion of the a–e chain. Thus Black is the cause of the way in which Red won and that, according to Lewis, means that Black is a cause of e’s firing. It is pretty clear how the alleged counterexamples to transitivity fit the pattern identified by Lewis. Let me run through the descriptions at the beginning inserting the appropriate neuron firing to indicate this. Dog bite: Jo is about to trigger a bomb by pressing a button with his right finger (a’s firing) but a dog bites it off (c’s firing inhibiting b’s firing). Hence Jo triggers the bomb by pressing a button with his left finger (g’s firing). The dog bite (c’s firing) is a cause of Jo pressing a button with his left finger (g’s firing). Jo pressing a button with his left finger (g’s firing) is a cause of the bomb exploding (e’s firing). April Rains: The April rains (c’s firing) ensure that the forest is damp in May (inhibiting b’s firing) and so doesn’t burn down (e’s firing). This means that it is available for burning as a result of the June storms (g’s firing). Bomb: Billy puts a bomb under Sally’s chair (c’s firing). Sally notices the bomb and runs away before it explodes (g’s firing) rather than remaining seated (b’s firing). She survives to receive a glowing medical report from her doctor (e’s firing).

  



Assassination: Captain yells ‘fire’ to his assistant on spotting their victim (c’s firing). Assistant fires. Since the victim overhears the order, she ducks and avoids assassination (g’s firing). Hence the victim survives (e’s firing). Defoliation: A weed in a garden is sprayed with a defoliant (c’s firing). This decreases the chance it will survive from . to .. The plant is sick for six months but then recovers (g’s firing, e’s firing). In each case, the intuitive claim is that the event that plays the role of c’s firing is not a cause of e’s firing. Lewis argues that this intuition should be revised. In fact, the events playing the c-firing role are causes. Lewis diagnoses three sources of resistance to taking these counterintuitive causes as causes. First, some of them prevent the effect from happening earlier though cause it later. We mistakenly reject an event’s causal claims when it is a preventer. Second, generally these counterintuitive causes are causes of the opposite of the effect happening. Third, it doesn’t matter whether or not the counterintuitive cause will happen, the effect will still occur. Lewis is right that all three putative sources are illegitimate considerations against something being counted as a cause. Regarding the first and third, the same is true in cases of pre-emption but we don’t take this to discredit the pre-empting cause. Regarding the second, questions about what generally is the case don’t touch on whether causation happens in a particular case. Failure to recognize this has vitiated some accounts of singular causation that have drawn on chance-raising between types of events, however, once stated, the point is straightforward. Lewis is less successful in convincing us that these are the sources of the intuition that the events that play the c-firing role are not causes. After all, the first and third considerations are present in cases of pre-emption but they don’t encourage us to conclude that the pre-empting cause is not a cause (and for more general concerns about the treatment of causation he offers in his later discussion, Noordhof ()). Another proponent of the intuition undermining strategy, Hall, identifies an additional structural element to the alleged counterexamples to transitivity that he argues serves to justify rejecting the intuitions. The key point for Hall is the distinction between cases of switching which interact with the causal process giving rise to the target event (hereafter switching by interaction) and cases involving switching without interaction. Hall calls the latter simple switching but I eschew this terminology given my earlier discussion of simple switching and encouragers/ discouragers. My characterization of simple switching was in terms of causing an event to occur at another time than it would otherwise have occurred without causing the event. This kind of switching may involve interaction with the process, for example, receiving the subpoena interacts with the causal process of going on holiday. An illustration of switching by interaction is the following case. Railway Tracks: An engineer at railway points sees the train approach and throws the switch so that the train travels down the right hand side track rather than the left hand side track. The tracks reconverge later on and the train runs over a hedgehog. The switch is a cause of the death of the hedgehog (Hall (), pp. – or Hall (), pp. –).



 -  

Amongst a number of considerations that Hall offers in support of the claim that throwing the switch is a cause, let me draw attention to two. First, the switching is part of the causal process that gives rise to the death of the hedgehog. We would have to mention it in any explanation. Second, if we suppose that the left hand track is broken and would give rise to derailment, then the switching would be judged to be a cause of the killing since, otherwise, the train would not get there at all. Whether or not something counts as a causal process should not turn, it may be argued, on what holds elsewhere so long as this does not get in the way of the causal process completing to get to the effect. So the switching cannot fail to be a cause when the left hand side track is present (Hall (), p.  or Hall (), pp. ). As Hall puts it, causation is intrinsic in this sense. Some might question whether this is the right verdict given that the hedgehog would die in any case. However, this consideration cannot have the force it might appear to have because the same could be said about pre-empting causes and yet our verdict upon them is secure. In this context, it is worth noting that most if not all other accounts that claim that causation is non-transitive, also conclude that the railway track switching case is a case of causation (e.g. McDermott (), pp. –). I defend this evaluation further in ... By contrast, Hall denies that cases of switching without interaction can be causes. Hall provides the following example. Drunken Bad Guys: Bad Guy Leader orders his team to go to blow up the left hand side railway tracks down which the train is scheduled to go. The team stop off in a pub and get drunk. Hence they don’t blow up the track and the train arrives safely at the destination. Hall claims that the Bad Guy Leader’s decision is not a cause of the train’s arriving safely in the drunken bad guys case because it is only a cause of something that prevents the prevention of the train arriving safely, namely the drunkenness in the pub. Consider the original characterization of the structure of the counterexamples to transitivity in Figure .. The Bad Guy Leader’s order (c firing) overall inhibited the blowing up of the rail track (b firing) because it caused the team to stop off at the pub and get drunk. This would be an intermediate event between c firing and b firing. So what we really have is Figure .. This does not touch the central point that the order’s relationship to the train arriving safely at the destination (e firing) is entirely mediated by the absence of an event (the blowing up of the railway track (b firing)). Of course, given the structure provided above, all the other counterexamples to transitivity involve an absence of an event (Jo’s pressing the button with his right forefinger, the forest burning down in May, Sally remaining seated, the victim remaining upright, the plant continuing to flourish). However, in each of these cases there is a positive event on the f-chain that c’s

c

Figure .

pub drunkeness

b

   a

b



d

c e

f

g

h

Figure .

firing causes. So Hall takes the structure of the standard counterexamples to transitivity to be rather of the form in Figure .. Lewis’s characterization of the structure of counterexamples to transitivity is only accurate for the drunken bad guys case in which the connection is simply that of double prevention. Since Hall views this as a distinct kind of causation involving mere counterfactual dependence, he retains the plausibility of the transitivity of causation for cases involving causal processes, including interactions with these processes. I agree with Hall’s verdict in the drunken bad guys case but deny that this is because cases of double prevention aren’t causes. In ., I argue that cases of double prevention are cases of causation. That is not to deny that there are differences between this kind of case and those that involve substantial causal processes. But these are just subcategories of a unified notion of causation offered by my analysis. Hall’s attempt to rest the intuition that causation is not transitive on the distinction between interactive and non-interactive switching is implausible. On the one side, there are cases in which causation appears not to be transitive and yet interaction takes place: for example, the dog bite case or any of the others I detailed above. On the other side, there seem to be cases of switching without interaction in which we intuitively judge the switch to be a cause. Suppose that Billy and Suzy are running a race and they are evenly matched until Suzy gets cramp. Bill crosses the finishing line first. Suzy’s cramp is a simple switcher. It does not interact with the process by which Billy broke the tape at the finishing line. Nevertheless, it seems plausible that Suzy’s cramp is a cause of Billy breaking the tape at the finishing line. So Hall’s goal of identifying an explanatory feature that explains our intuitive judgements about when causation is present without undermining the case for causation being transitive is not successful. I have no doubt that Hall would reject this type of case on the grounds that it doesn’t involve a substantial causal process between Suzy’s cramp and Billy’s breaking of the tape. In Chapter , I defend further my claim that it is still proper to take Suzy’s cramp to cause Billy’s breaking of the tape by questioning the emphasis on substantial causal processes. For the moment, it seems reasonable to conclude that it is by no means obvious that Hall has identified the origin of our intuition that causation is not transitive in certain cases. In ., I will consider four accounts of why causation is not transitive and outline the reasons for favouring my own.



 -  

. Non-Transitive Analyses The most successful response to those who seek to reject the counterexamples to the transitivity of causation is to provide an analysis of causation that explains why causation is not transitive. Part of the success of the response will depend upon whether the analysis captures what we also want to say in other cases. Chapter  is my case that my own analysis succeeds in this respect. In .., I shall explain how it justifies an intuitive treatment of the non-transitivity of causation. In .., I compare it with the approaches of Hitchcock and Yablo. My argument will be that my preferred analysis more effectively captures the non-transitivity of causation. In .., I discuss the success or otherwise that my theory has in meeting the constraints Sartorio proposed for any theory of causation.

.. Probabilistic

P -dependence

From the perspective of my analysis of causation, the key idea is that, in the counterexamples to transitivity, the putative causes are not causes because they do not actually make the effect more likely and, indeed, outside of determinism, they make it less likely, than its mean background chance. This is quite compatible with these putative causes interacting with the causal process that gives rise to the effect. By contrast, while pre-empting causes may lower the chance of an effect by inhibiting a more reliable process, nevertheless they still raise the chance of the target effect when compared with its mean background chance. This differentiates them from the counterexamples to transitivity we have discussed. The actual failure to raise the chance of an effect over its mean background chance can occur for a variety of reasons. One possibility is that the switching from one process to another would occur anyway if a competitor process failed. The dog bite case provides a good illustration of this. Another possibility is that, in removing the effect of other processes to reveal the possible chance-raising powers of a putative cause, we remove the conditions under which the putative cause raises the chance of the effect. We have already seen how this is the case in our discussion of the April rains. In order for April rains to have the possibility of raising the chance of the forest fire at a certain time over all other times, we had to remove the conditions which would have given rise to the forest fire in May if the April rains did not take place. But this then meant that the April rains no longer raised the chance of the forest fire at the later time since, if all the Pmeans by which the forest fire might have occurred earlier than June are put in then the rains don’t raise the probability of the fires occurring in June anyway (..). A third possibility is that the only way in which competitor processes can be removed successfully in order to make the putative cause raise the chance of the effectPwill introduce non-actual events upon which the target effect will probabilistically -depend and/or involve the removal of negative conditions. The bomb, the assassination, and defoliant cases provide good examples of this. It would not be surprising if the cases provided a mixture of all the factors for P different assignments to . Because of my discussion of the second factor in .., I shall just discuss the first and the third factors in this section. In the dog bite case, the key conditionals are:

- 



P (D) If the dog bite were to occur without any of the events in , then, for some time t, the mean value of the chance of the explosion at t would be x. P (D) If neither the dog bite nor any of the events in were to occur, then, for any time t, the mean value of the chance of the explosion at t would be y. P It seems clear that, if nothing is put in , x would not be very much greater than y and so the dog bite would fail to come P out as a cause. The obvious concern is that there is something we might put in where P this is not the case. This seems unlikely. For instance, consider an assignment to of the right hand pressing. We would then get (D) If the dog bite were to occur without the right hand pressing the button, then, for some t, the mean value of the chance of the explosion at t would be x. (D) If neither the dog bite were to occur nor the right hand pressing the button then, for any time t, the mean value of the chance of the explosion at t would be y. It seems obvious that x would still not be very much greater than y. On the assumption that Jo is trying to explode the bomb, if he had not pressed the button with his right hand, he would have with his left. Thus we are, in effect, testing dog bite/non-dog bite given he is pressing with his left. That means either, assuming indeterminism, the dog bite makes it less likely for the explosion to occur (since Jo is distracted by the pain from his right hand) or, assuming determinism, at least not more likely for the explosion to occur. Hence x would not be very much greater than y. In making this claim, I’m not endorsing a backtracking conditional. The claim is not that if Jo hadn’t pressed the button with his right hand, then he would not have intended to press the button with his right hand higher up the causal chain, instead intending to press it with his left. Rather, the claim is that, having intended to press the button with his right hand and noticing that he had failed to do so, Jo would then have intended to press the button with his left hand. The intention to press the button with the left would be a causal consequence of notice of the failure. It might be argued that this intention to press the button with the left hand may P also be put in . In which case, there are two options facing opponents of the application of my analysis to this case. Either they accept that the intention to press the button with the left hand is the same as that which occurs when the dog bite occurs, or they must P claim it is different. If they accept that P it is the same intention, then putting it in would get rid of the probabilistic -dependence between the dog bite and the explosion. Hence a necessary condition for the dog bite being a cause of the explosion would not be met. They would have failed to establish that the analysis must yield P the counterintuitive verdict that the dog bite is a cause with this assignment to . Alternatively, and most likely, they will claim that the intention to press the button with the left hand that occurs when there is not a dog bite is distinct from the one that occurs when there is one. In which case, three things need to be established. First, that there is an appropriate criterion of event identity that would back this judgement. I have already explained how our usual causal talk relies upon individuating events in ways that allows various changes in their nature in different possible worlds without



 -  

differences in their identity. In Chapter , I defend this picture further. Second, that there would not be other intentions to press with the left hand or press by other of Jo’s extremities to take the place of the absent intention to press by the left hand. In which case, the structure of my response would be the same but just appeal to these P other intentions. Third, if all of these other replacement intentions are also put in , that it would still be legitimate to suppose that Jo would have pressed the button with his left hand if his right had been bitten earlier. The original causal circumstances involving a dog bite and Jo changing his hands as a result would seem to rely upon Jo’s determination to ensure that the bomb explodes. If all the replacement intentions in close-by worlds are removed, it is no longer plausible to suppose that Jo would be determined in the requisite sense. Here I make implicit appeal to the sustaining conditions behind a certain causal relationship in supporting counterfactual verdicts that McDermott makes explicit in his own theory (McDermott (), pp. –). I don’t have to insist that the sustaining conditions would not be present but just that they may not be present and so it would not be the case that Jo presses the button after having been bitten by the dog. Here a limited amount P of backtracking seems defensible (for further discussion of the impact of the -set apparatus on causal non-symmetry and backtracking, see .). The schematic characterization we gave of counterexamples to the transitivity of causation was Figure .. The points above remind us of the fact that the arrow from c’s firing to e’s firing does not indicate c’sPfiring raises the chance of e’s firing. The P standard approach of putting events in from the a-chain to bring out the probability raising of c’s firing on e’s firing does not work (and rightly so) if the absence of those events would result in the presence of events in which the f-chain is triggered (for example, the intention to press the button with one’s left forefinger). Let me turn to the case of the bomb. Here the relevant counterfactuals are (B) If Billy were to put the bomb under the chair without any of the events in P , then, for some time t, the mean value of the chance of Sally’s good health at t would be x. P (B) If neither Billy puts the bomb under the chair nor any of the events in were to occur, then, for any time t, the mean value of the chance of Sally’s good health at t would be y. P Obviously, if nothing is put in , putting the bomb under the chair does not raise the chance of good health since Sally would have been in good health anyway without Pthe threat of the bomb. The issue is, asP before, whether we could put something in to make good health probabilistically -dependent upon Billy putting the bomb under P the chair. Suppose we put in the event of the room being free from nerve gas. Then it certainly seems that the bomb being under the chair—and hence noticeable— would raise the chance of good health since it would encourage Sally to leave the room before she succumbs to nerve gas. There are two related points to make about this suggestion. The first is that it P involves putting in a negative event, i.e. nerve P gas not being in the room. Negative events should be excluded from being put in . Although the preliminary way I characterized the event did not wear its negativity on its sleeve—a room being free

- 



from nerve gas seems a positive feature—we should not expect that this is the case. Positive descriptions can be given of negative events and the only way we can work out whether these descriptions are of negative events is considering what must hold for them to P occur. I shall return to this matter in Chapter . Excluding negative events from is not just a helpful stipulation to deal with a difficult possibility. In Chapter , I argue that negative events don’t exist. Since they don’t have any impact upon actual causal processes, their removal is just a surreptitious way of changing the causal circumstances by introducing specific events into counterfactual circumstances. The second point P is that, in the circumstances envisaged good health would probabilistically -depend upon a non-actual event, namely Sally being Pa certain distance away from the nerve gas. This is not something that can be put in as it can P in genuine cases because then we would lose the probabilistically -dependency between the placing of the bomb and Sally’s good health. In the case of the assassination, the relevant counterfactuals are (A) If the Captain were to yell to his assistant to fire without any of the events in P , then, for some time t, the mean value of the chance of the victim’s survival at t would be x. (A) If neither the Captain were to yell to his assistant to fire nor were any of the P events in to occur, then for any time t, the mean value of the chance of the victim’s survival at t would be y. P Again, without any events put in , it seems clear that it would not be the case that x is very much greater than y. The victim would survive if no assassination attempt P were made upon his or her life. Events which might be put in in order to get the Captain’s yell to raise the chance of the victim’s survival include the non-existence of another bullet hurtling towards the victim which would hit if he or she hadn’t ducked. In which case, the response I made to the bomb case would have immediate application to this one. In the defoliant case, the relevant conditionals are P (D) If the plant had been sprayed with defoliant without any of the events in , then for some time t, the mean value of the chance of there being a healthy plant would be x. (D) If P neither the plant had been sprayed with defoliant nor were any of the events in to occur, the mean value of the chance of there being a healthy plant would be y. P Once more, put nothing in and the chances of having a healthy plant are certainly not raised by spraying it with defoliant. If we put the event of there not being deadly P leaf disease in the vicinity in , then the situation changes. Being sprayed with defoliant in such circumstances would raise the chance of the plant’s survival. However, again, similar responses can be made. First, the event P in question is a negative event. Second, the plant’s survival will probabilistically -depend upon the distance between its reduced flourishing and the presence of deadly leaf disease (for instance in other plants). This is a non-actual event.



 -  

Finally, in the case of the drunken bad guys, my analysis holds that the Leader’s decision to send the team that ended up in the pub is not a cause of the safe arrival of the train. The counterfactuals to consider are (DBG) If the Bad Guy Leader were to order his team toPblow up the left hand side railway tracks without any of the other events in occurring, then for some time t, the mean value of the chance of the safe arrival of the train at t would be x. (DBG) If neither the Bad Guy Leader were to order his team P to blow up the left hand side railway tracks nor were any of the events in to occur, then for any time t, the mean value of the chance of the safe arrival of the train at t would be y. P If nothing is put in , then the chance of safe arrival of the train at t is certainly not raised by the Bad Guy Leader’s order. If chances are to be assessed, as I recommend, just before the time of the putative effect, then there would be no variation at all since by that P time the team are already drunk in the pub. It is unclear what event one could put in which would make the Bad Guy Leader’s order raise the chance of the train’s safe arrival at t. The relative success of my account to generate our intuitive verdicts in this area from relatively meagre materials—a certain understanding of chance-raising, the P ‘actual events clause’, and a constraint upon -membership—suggests that it has identified a further structural feature to those discussed above and below which constitutes the basis for our conviction that causation is non-transitive. It is a feature that is compatible with allowing that causal processes may be transitive simply in the sense that if there is a causal process between e₁ and e₂ and e₂ and e₃, then there is a causal process between e₁ and e₃. It explains why this does not imply that e₁ is a cause of e₃. In the next two sections, I consider alternatives to my proposal.

.. Fixing accounts ... Hitchcock’s approach A contrasting approach to the non-transitivity of causation may be drawn from the causal graphs approach I mentioned earlier in Chapter . As I have already noted, its proponents take the notion of a causal mechanism as primitive and represent it by causal graphs of the kind I produce below (e.g. Hitchcock (b); Pearl (); Woodward (), pp. –). Causation is defined in terms of a particular kind of covariation of values in a causal model representing the causal mechanisms involved. For instance, Hitchcock proposes that c is a cause of e iff there is an active causal route from X to Z in an appropriate causal model (where c, e are distinct events, X, Z are alterations of them, a causal model is a system of structural equations on variables). An active causal route is defined by the counterfactual dependence of values of Z on values of X holding some value of a variable on another route fixed at its actual value (Hitchcock (b), pp. –; Woodward (), pp. –, -). From the

- 



perspective of this chapter, it is the fixing element that is crucial. Because it appeals to fixing an event (value of a variable) on another causal route, it is not well suited to reductive analyses of causation. Therefore, if my approach is successful in capturing the non-transitivity of causation, its reductive character provides an additional consideration in its favour. Nevertheless, fixing accounts are worth examining on their own terms to see whether they capture important ingredients of causal relationships that my own approach misses. Thus I will consider its application to the problem cases discussed above. Hitchcock argues that if the dog bite case is graphed as D

P

E

Figure .a

then his proposal will yield the result that the dog bite is not a cause of the explosion (where D takes  or  for whether there is a dog bite, P takes , , or  for whether there is a left hand, right hand, or no button pressing and E takes  or – for whether there is an explosion). There is no variable to hold fixed outside the D-P-E chain and whether D takes a value of  or , P will still take a positive value of  or , that is, a button pressing will take place (Hitchcock (b), pp. –). An alternative is that the dog bite case should be graphed as PL

D

E

PR

Figure .b

(with PL, PR a button pressing with left or right forefinger, respectively). Then it might seem that the explosion would counterfactually depend upon the dog bite keeping it fixed that Jo did not press the button with his right hand (Hitchcock (b), p. ). Hitchcock’s response is to note that this counterfactual is false for much the same reason I identified earlier. Jo doesn’t need a dog bite to make it the case that, given that he hadn’t pressed the button with his right hand, he would have pressed the button with his left. Although the two different graphical representations of the dog bite case didn’t affect the outcome, this is not always the case. As a particularly dramatic illustration of the issue, Hitchcock considers a situation in which a boulder falls down (F) on a hiker who ducks (D) thus saving his or her life (S) (Hitchcock (b), pp. –). The question is whether the falling boulder is a cause of the hiker’s life being saved. Hitchcock argues not. As he notes, there are two ways in which the circumstances might be graphed. In the following



 -   D

F

S

Figure .a

there is no intermediary to hold fixed in the potential direct causal connection between the boulder falling and the hiker surviving. The route is not active since the hiker would have survived given he or she ducked whether or not the boulder fell. Since there is nothing to hold fixed in the direct F-S route, there is no obvious way in which we can discern a counterfactual dependency between the boulder falling and the hiker surviving down the F-D-S route. Hence, if matters are graphed this way, the falling of the boulder fails to be a cause down either route: the preferred verdict. On the other hand, graphing it as follows yields a different result. D

F

B

S

Figure .b

Here B is an occurrence of the boulder, on its actual flight path, just about to hit the hiker’s head (if the hiker hadn’t ducked). Holding this fixed, then it is more plausible that the boulder’s falling is a cause of the survival than otherwise since if the boulder is present close to the hiker’s head and it hadn’t fallen, then the hiker would not have seen it coming, would not have ducked, and hence been killed by the boulder. Hitchcock dismisses this possibility as too farfetched to take seriously. Woodward argues that, in the circumstances envisaged by holding fixed B, the causal structure would be very different because we would now have to allow that there was a different means by which the boulder would be just about to hit the hiker’s head (Woodward (), p. ). Both responses have their flaws. Woodward fails to identify a distinctive problem with the representation suggested above. Any holding fixed of a value that would otherwise vary changes the causal structure to some extent. It is hard to deny that Hitchcock is right that the possibility considered is farfetched but this can be overdone. We can easily imagine a rock being thrown by an enemy so that the hiker does not see it until too late because he or she is looking up rather than straight ahead. We don’t have to imagine, as Hitchcock does, that ‘the boulder was mysteriously and instantaneously transported to a position immediately in front of the hiker’s head’ (Hitchcock (b), p. ). It is not obvious that what we must imagine is any more far fetched than, in the early pre-emption case, supposing that it is fixed that certain events in the pre-empted chain do not occur even in the absence of pre-emption. Yet it is upon this that the fixing accounts must rely to secure the verdict that b’s firing in the pre-empting process is a cause of e. Similar worries plague the value-fixing approach’s treatment of the other cases. For instance, in the bomb case, one value to hold fixed is the explosion in the room. In

- 



that context, if the bomb had not been placed under the chair, in a relatively visible place that Sally noticed, she would have died. What stops placing the bomb under the chair being counted as a cause due to this fixing? We have already seen how my approach supplies a reasonably straightforward resolution of the bomb case and others. The case of the hiker doesn’t seem to involve additional difficulties. It is not P easy to see how one might demonstrate that the hiker’s survival was probabilistically -dependent upon the boulder falling. Consider the following conditionals. P (H) If the boulder had fallen without any of the events in , then at some time t, the mean value of the chance of survival at t would be x. P (H) If the boulder had not fallen nor any of the events in , then for any time t, the mean value of the chance of survival at t would be y. P If we put nothing in then x is approximately equal to y since, if the boulder P hadn’t fallen the subject would still have survived. If you put the ducking in , then the falling of Pthe boulder would not raise the chance of survival. On the other hand, if we put in (say) the non-actual event of a flying bullet avoiding the portion of the hiker’s body above waist height, then imagining this absent would make the survival dependent upon the falling boulder. It is noticing that the boulder was falling which led the hiker to duck and hence, inadvertently, avoid the bullet from an enraged antihiking P farmer. However, in these circumstances, the survival would be probabilistically -dependent on the non-actual event of the bulletPpassing over him or her. If P you put this event too in , then the probabilistic -dependence between the boulder falling and the ducking would no longer be present. In addition, as I have already indicated, negative events such as a flying bullet P avoiding the portion of the hiker’s body above waist height should not be put in . Both of the moves made here seem rather more precisely constrained than a simple appeal to what is farfetched, or involves a significant difference in causal structure. This suggests that my approach more effectively captures why causation is not transitive. ... Yablo’s approach Yablo’s basic idea is also that (De facto) c is a cause of e iff e de facto counterfactually depends upon c (Yablo (), p. , ()), where de facto dependence involves some aspect of the actual causal circumstances being kept fixed, namely G. However, as we have already seen, not just any G can be picked. A preliminary constraint that Yablo considers is (Y) Dependence modulo G does not make for causation if (i) G is a threat to e that, although (ii) countered by c, was also (iii) launched by c (Yablo (), p. ). It is relatively easy to see how this is supposed to work. As we saw in ..., if we fix the event of the bomb exploding, then Sally’s survival would depend upon the bomb being placed. However, the explosion is a threat that, although countered by the



 -   a

c

d

e

b

f

g

Figure .

bomb being placed under the chair (since Sally noticed it), is also launched by it. Hence (Y) proclaims that we cannot take the event of the bomb exploding as the G we fix (Yablo (), p. ). A difficulty with this approach is that it would also seem to exclude what Yablo needs to fix in the case of early pre-emption (Figure .). Yablo must hold fixed the fact that an event did not occur on the pre-empted chain (say the absence of c firing) in order to obtain the de facto dependency for events in the pre-empting chain (Yablo (), p. ). But the non-occurrence of an event on the pre-empted chain is a threat to the effect that, although countered by events in the pre-empting chain, was also launched by them. Yablo’s preferred constraint is (Y) One event de facto depends on another iff some G putting the first in need of the second is more natural than any H that makes the need artificial (Yablo (), p. ). The key idea is that certain needs that a target effect has, in order to occur, are artificial. For instance, the good health report’s need for the presence of the bomb is an artificial need given that there is a bomb explosion (this being G). Whereas genuine causes aren’t addressed to artificial needs. Yablo seeks to make this precise as follows. Let the fallback needs for the effect be its needs after the point of divergence, from the actual situation, so that the candidate cause, c, doesn’t occur (e.g. the placing of the bomb). Let the actual needs be those events upon which a target effect is counterfactually dependent with a given G being held fixed. If the fallback needs are identical to a proper subset of the actual needs, setting c aside, then c relative to G creates, additional, artificial needs. Suppose we let G be e occurs if and only if c occurs. The actual needs will be c, and those events upon which c counterfactually depends. By contrast, the fallback needs will be much more extensive, for example, the other events which, intuitively, make up the causal circumstances for e. Yablo’s preferred constraint avoids having to concede that, as far as I can see, any two actual events are causally related. The specified G condition fails to be more natural than any alternative candidate for G, H, that makes the need for the candidate cause artificial.

- 



Let’s see how this proposal is meant to apply to the bomb case. Keeping fixed the explosion of the bomb, Sally’s good health depends upon placing the bomb under the chair for her to notice it. However, placing the bomb created the need for Sally to run away to stay in good health (Yablo (), p. ). The other needs she has for the good health report—healthy functioning of her body, etc.—are identical whether or not the bomb is placed. Thus, the placing of the bomb creates artificial needs given the preferred choice of G: the explosion. Yablo’s approach can avoid that result. The case of early pre-emption remains problematic. In order to establish that b’s firing is a cause of e’s firing, c’s failing to fire or d’s failing to fire has to be held fixed. The question is whether the restrictions on what can play the G condition allow for this. The fallback need, given b’s firing is absent, is for, amongst other things, c’s firing or f ’s firing. The actual needs, with G being the absence of c’s firing, is, amongst other things, f ’s firing. Prima facie, the fallback needs are a subset of the actual needs because the disjunction remains a need of e’s firing it is just that one disjunct is ruled out by the assignment of G and so an additional, more specific, need for f ’s firing is introduced. Putting the point another way, we could say that, given b’s firing is absent, the fallback needs are neither that c’s firing nor that f ’s firing occur since either would do. But the actual needs, in addition, include a need for f firing. As things stand, then, the absence of c’s firing is not something that can be held fixed. However, Yablo emphasizes that needs are not to be individuated so finely. Instead, there is just the need for a firing at that moment in time, satisfied by either chain. In securing the right result in the case of early pre-emption, Yablo reopens the case of the bomber. Consider what we described as the need for Sally to run away. We might as easily have described it as the need for the healthy functioning of her body, something that would be compromised if she remained in close proximity to the bomb. With this adjustment, the fallback needs would not be identical to a proper subset of the actual needs and the explosion could be a G that is held fixed. The individuation of needs, in this context, is too imprecise to be a good basis for capturing the non-transitivity of causation. The apparent distinction between the two cases just described is an artefact of the similarities and differences between the competing chains of events. Suppose, instead, the case of early pre-emption envisaged was a death by a shooting pre-empting a stabbing. Then the appropriate characterization of the need required to obtain the verdict that the shooting was a cause would be something like a life-threatening event. This is no more specific than the ‘healthy functioning of her body’ description being used to cover her running away.

.. Sartorio’s constraints on causation Sartorio has identified two constraints upon causation that have the implication that causation is not transitive. Causing by Preventing: If, for every feature F that X causes an event E to have, there is another feature G such that X causes E to have F only by causing it not to have G, then X is not a cause of E. (Sartorio (a), p. ) Causes as Difference-Makers: If c caused e, then, had c not occurred, the absence of c wouldn’t have caused e. (Sartorio (), p. )



 -   a Train

b

Points

d

c

Victim run over

f

Figure .

The causing by preventing principle covers delayers, affecting the temporal features of an event by preventing the events from occurring earlier, and extends to other features too. For example, a Samaritan disables would-be assassin  of the victim so, as a result, would-be assassin  steps in to kill the victim in a slightly different way. The principle suggests that the Samaritan would not be a cause of the victim’s death as a result of causing assassin ’s hit. My approach was developed in Chapter  with the distinction between delayers and hasteners in mind and track the verdicts about cases captured by the principle. Things are a little different with the causes as difference-makers principle. The case that Sartorio uses to motivate the principle is a version of the Railway Tracks case described earlier (Figure .). A victim is tied to the track. A train is hurtling down the line. Earlier there is a set of points, which somebody seeking to save the victim changes so that the train is diverted. Unfortunately, the line down which the train is diverted converges with the main track again before that part of the track to which the victim is tied. As a result, the train runs over the victim anyway. Sartorio claims that the changing of the points is not a cause and the causes as difference-makers principle can capture that. The absence of the point changing would also cause the victim to die. If causation were transitive, then it would follow that the point changing is a cause of the victim being run over by the train because the point changing is a cause of the train at a, the train at a is a cause of the train at b, and so on. Although the causes as difference-makers principle requires the rejection of transitivity, the rejection of transitivity does not require acceptance of the principle. This is a good thing because the principle is independently problematic. First, it relies upon absences being causes. As we shall see later, we have reason to resist this (Chapter ). Second, it makes the question of whether something is a cause depend upon factors outside the completion of the relevant causal process. For example, suppose that the track is broken on the bottom line at position f. In that case, switching the points to take the train down the a-b-c line is a cause of the victim being run over. If the point switching makes a contribution in this case, it shouldn’t cease to make a contribution just because the bottom line is broken. Third, it is very natural to look at that situation and conclude that, whatever I do, I’m going to cause that person’s death. The backing for such a claim is that, taking each route in isolation, it is true that failing to switch the points in the appropriate way would

  a Train

b

Points

d

f



Victim A run over c

Victim B run over

Figure .

not be a cause of the victim being run over (setting aside the point about negative causes). So, in isolation, point switching is a cause. In which case, switching the points in the non-isolated case should also come out as a cause, given that causation is just a matter of contribution to the relevant process. Fourth, consider a variant of the case above in Figure .. It would seem to be a consequence of the causality as difference-maker principle that a person who switches the points would be a cause of one or other of the victim’s deaths but, if the aim is to retain the link between causation and responsibility, could not be counted as a cause of the death of someone. But causing the death of victim A seems a very natural way of causing the death of someone.

. Concluding Remarks We have seen that attempts to dismiss the counterexamples to transitivity fail. My own analysis of causation has an explanation of why causation is non-transitive. Causes raise the mean chance of an effect against their mean background chance. Some influences on a causal process don’t do that. Fixing accounts seek to identify a way causes raise the chance of an effect, given that certain things are fixed as they actually are (rather than the mean background chance). We found that this idea was difficult to spell out in an effective manner to give the right result and that attempts to do so often undermined the treatment of causation in other areas. Of course, there may be some further adjustment to fixing accounts that deal with the difficulty. I have just tried to make clear the problems such approaches face. It is by no means obvious what the next move is. During the course of discussion, we have arrived at a clearer idea of how to think about switching in the sequence of events leading up to a certain effect. The key distinction is not between cases of switching that interact with a causal process and those that do not. Not all cases of switching that interact with a causal process leading up to a target effect are causes of it (e.g. the dog bite case), nor do all cases of switching that fail to interact with the causal process fail to be causes (the race is one example, and we shall consider others in .). Instead it is between those switches that raise the mean chance of the effect over its mean background chance and those that do not.



 -  

One move in my defence of my own treatment of cases of non-transitive causation was the rejection of negative events. I will present arguments in favour of this rejection in Chapter . Nevertheless, it should be noted here that, even if these prove unsuccessful, the cases were still treatable by application of the ‘actual events’ clause. So, in this respect, the arguments of Chapter  assist but are not necessary. Much more important will be the treatment of the nature of causal relata in the next three chapters. They are a necessary theoretical component for a counterfactual analysis of causation to work.

 Causal Circumstances Counterfactual analyses of causation implicitly recognize that causes operate in circumstances that, if the circumstances were not to hold, the effect, or the chance of the effect, would not be raised in the indicated way. Call these the causal circumstances of a cause, others have called it a causal field (e.g. Mackie (), pp. –). Given this characterization of the causal circumstances, each component of the causal circumstances will satisfy my analysis of causation. The causal circumstances for these other components will include the cause for which they are the causal circumstances. Two issues arise for causal circumstances so understood. The first is whether the causal circumstances plus a cause, for which they are the causal circumstances, should be counted as the real or philosophical cause as J. S. Mill suggests (Mill (), p. ). This is sometimes called the total, following Mill’s characterization, or complete cause. In the first section of this chapter, I shall briefly explain why not. The second issue is whether all the components of causal circumstances are themselves causes. Sometimes a distinction is made between the cause, or causes, and the conditions of the cause, or causes, which are the rest of the causal circumstances. Egalitarianism denies that this distinction is of significance. All components of causal circumstances are themselves causes. I shall defend egalitarianism against attempts to argue otherwise. Figure . gives an overall sense of the range of positions that have been outlined on this second issue. Please note this debate is distinct from the debate about whether particular kinds of entity are causes—events, facts, etc.—that will be the subject matter of Chapter , although I will touch on the issue at one point to discuss Bradford Skow’s proposal (Skow (), pp. –).

. Causal Circumstances and the Status of Total Causes The Millian approach to the analysis of causation identifies as a total cause of the effect the minimal complete set of events, states, property instances, or the like, which (under determinism) are together sufficient for the effect and which (putting aside redundant cases of causation) individually are necessary. Included in this minimal complete set will be a negative condition specifying that there will be no intervention breaking the connection between the remaining conditions and the effect (Mill (), p. , Mackie (), p. ). For any target effect there are likely to be a number of different total causes at different times and, in cases of redundant

A Variety of Causes. Paul Noordhof, Oxford University Press (2020). © Paul Noordhof. DOI: 10.1093/oso/9780199251469.001.0001



  Cause

Egalitarianism Pragmatically Selected (Lewis, Mackie, Mill, Preferred Option)

Context Determined (Schaffer)

Producing/Dependence (Dowe, Moore, see Chapter 11)

Triggering/Enabling Background Conditions (Lombard, Skow)

Normative Theories

Responsibility Attributing

Contra-Normal Condition (Hitchcock and Knobe)

Figure .

causation, more than one total cause at the same time. Any member of any of the total causes will individually be necessary for the effect. However, there will be no total cause that is the combination of all the particular total causes at different times due to the requirement that a total cause be a minimal set. Intuitively, a total cause at one time, say t, of a target effect, e, is all that is necessary and sufficient for e at t. As we have already noted, Mill suggests that the total cause is what we should count as the cause of an effect (Mill (), p. ). The analysis of Chapter  does not support such a view. It does not deny the status of cause to the total cause, if you are inclined to recognize such disparate and, often unintegrated, entities. However, it also confers it upon elements of the causal circumstances. The semantics for counterfactuals outlined in Chapter  keeps the causal circumstances fixed as far as possible in the counterfactual situations envisaged. Under determinism, the analysis then provides a way of characterizing how the elements are necessary in the circumstances and sufficient given the circumstances. The counterfactual analysis differs from Mackie’s famous INUS definition of deterministic causes—causes are Insufficient Non-redundant parts of Unnecessary but Sufficient conditions—in rejecting an apparently unmotivated asymmetry. Causes are characterized by Mackie as insufficient because the rest of the causal circumstances are needed, and yet they are characterized as necessary in those circumstances (although the circumstances in toto may be unnecessary due to competing causal circumstances) (Mackie (), p. ). However, if we keep fixed the circumstances that hold, then deterministic causes are both necessary in those circumstances and, given those circumstances, sufficient for the effect. If we don’t keep the rest of the circumstances fixed, then causes are redundant because the effect may occur as a result of different circumstances. Thus it is better to think of deterministic causes as circumstance-dependent sufficient conditions. A counterfactual analysis of causation builds in, and thereby recognizes, their circumstancedependent nature. The point Mackie seems to have had in mind is better characterized in terms of the independence condition we shall discuss later (..).

        Match Striking Presence of Oxygen Presence of Methane

Match Striking

Explosion



Explosion

Presence of Oxygen Presence of Methane

Figure .

The counterfactual analysis suggests that the decision to talk in terms of causes or total causes is largely an uninteresting matter of fixing the use of our terms. Consider the simple case of the gas explosion that is the result of striking a match in the presence of both oxygen and methane. Does anything substantial rest on understanding the causal arrow in one of the two ways in Figure .? The circumstance-dependency of causes invites us to think of the total cause as prior to the individual causes, but this would be a mistake. Let R be the complex relational property an entity has in satisfying my analysis of causation with regard to a target effect e. Circumstance-dependent causes having R needn’t be asymmetrically dependent upon the total cause of which they are a part having R. The total cause may have R because the individual causes that make up the causal circumstance stand to each other in certain relations as a result of which e is caused. The total causes and the individual causes may have R as a result of the individual causes, and the relations in which they stand to each other, collectively constituting the causal circumstances. There may be a two-way dependency. The two-way dependency will not hold if the total cause has emergent causal powers. If the causal relation is due to a fundamental law governing the kind of causal circumstances in question, then the components will have R because the total cause does. Outside of the special case of emergent causal powers, there are no grounds for giving priority to the total cause. Components of the total cause, as well as the total cause, are just as properly called causes. The argument of the present section makes mutual dependence contingent upon the absence of emergence. Resistance to this conclusion may stem from a commitment to Donald Davidson’s understanding of causes. To go back to the matchstriking example, his suggestion is that the event of match striking is an event of match striking in the presence of methane and oxygen. This more thickly described event is in no need of causal circumstances for it to cause the explosion (e.g. Davidson (b), pp. –, (b), p. ). Davidson is right that it is a mistake to suppose that a relatively thin description of an event that is a cause of a target effect requires that we identify richer causal circumstances to compensate. The event identified may involve much more. However, to establish that talk of causal circumstances is unnecessary, Davidson has



 

to go further. Any putatively necessary components of causal circumstances become part of a richer specification of the event instead. This is harder to defend. To illustrate the problem, consider the following two events: first, the match striking in the presence of oxygen and methane; second, the leak of methane into a place with oxygen and a match striking. These are distinct events otherwise Davidson’s events aren’t an alternative to the causal circumstances picture but another way of talking about total causes. In which case, they are two distinct independent sufficient conditions for the explosion. We have a case of overdetermination by Davidson’s lights, which clearly isn’t one. The challenge for Davidson’s position is to explain why we don’t get overdetermination in such cases without having to concede that causes operate in causal circumstances. The most obvious answer is for Davidson to argue that there is only one event that will count as the cause of another event. Then the situation just described doesn’t arise. My defence of egalitarianism closes off this line of response. Even if my defence were unsuccessful, Davidson would still be left with a certain kind of non-causal overdetermination because those entities that fail to qualify as causes would still be sufficient for the effects in the absence of the entities identified as causes.

. Challenges to Egalitarianism Egalitarianism is a straightforward consequence of supposing that my analysis of causation requires no supplementation. One version of egalitarianism concerns the causal circumstances of a particular event e. A second version of egalitarianism concerns the causal circumstances of a particular event e occurring at time t. Regarding the latter, delayers will naturally occur as part of the causal circumstances, and be pronounced causes according to the egalitarian. Regarding the former, delayers generally will not figure for the reasons I identified in ... This does not represent a limit to my egalitarianism since egalitarianism concerns what we should say about the components of causal circumstances. It does not insist a certain kind of entity—a delayer—should figure in causal circumstances, and be pronounced causes, come what may. Anybody who holds my position—and it is pretty much philosophical orthodoxy—does not deny that, depending upon context, it will be more natural to cite one element or another of the causal circumstances as the, or a, cause. The issue is whether this should be taken to reveal a substantial feature of causes or just the work of various pragmatic factors. I shall consider some candidate features of components of causal circumstances and explain why none of them should be taken as an additional essential feature of causes, although they do characterize features that some causes have. However, before I do so, I should sketch in more detail what talk of pragmatic factors is meant to convey. Consider the following candidate hard case for the egalitarian. A forest fire has been blazing and one forest ranger asks another: what was the cause of the fire? In fact, the forest fire had occurred after a lighting strike. The second ranger answers: () The presence of oxygen caused the forest fire. The immediate inclination is to judge that this is false. Yet, egalitarians are committed to it being true.

  



The first thing to note is that the question was ‘What was the cause of the fire?’. Egalitarians aren’t committed to any of the causal circumstances counting as the cause. Indeed, most of those who lack egalitarian sympathies would accept that talk of the cause goes further than anything that falls out from an analysis of causation alone. If there is something that is the cause, then context has singled it out from a narrower range than everything that is a cause of the target effect. The context may well have singled out the lightning strike rather than the presence of oxygen as the cause. We should not let this context—relating to ‘the cause’—make us mistakenly hear () as false when () doesn’t say that the presence of oxygen is the cause of the forest fire (cf. Schaffer (a), pp. –; Hart and Honoré (), p. ). It makes a causal claim about the presence of oxygen that can stand for many other entities as well, for example, the lightning strike. Pragmatic factors are envisaged to add, to the content expressed by a sentence, an implication that is the result of the speaker’s or writer’s intention in producing the sentence. In the present case, these factors take a true causal statement and imply something false. One conversational maxim that a speaker or writer should be taken to follow is Maxim of Quantity (i) Make your contribution as informative as is required (for the current purposes of the exchange); (ii) Do not make your contribution more informative than is required (Grice (), p. ). If a speaker or writer is following the maxim of quantity then the implication of () is that the presence of oxygen is the most appropriately informative piece of causal information that the forest ranger could be told. This implication is false given that the forest ranger might be expected to know that oxygen is present but may not have heard about the lightning strike. We hear ‘the presence of oxygen caused the forest fire’ as false as a result. The appeal to context of communication need not indicate pragmatic factors are at work. An alternative is that causal statements are semantically context sensitive. In .., I will consider this suggestion further. It draws upon the connection between causation and explanation.

.. Cause as context-sensitive explanatory factor In ., I rejected the claim that causal talk was context sensitive, favouring instead a particular, univocal reading of the contrast between the presence and absence of a target cause to determine its status as a cause. If causation had been taken to be context sensitive, then we would have a ready-made non-pragmatic explanation of the apparent context sensitivity of causal talk. As we saw, according to the contrastive approach causal statements are taken to have the following structure c₁ rather than c₂ causes e₁ rather than e₂. The context of inquiry would set the relevant contrasts—that is, what c₂ and e₂ we should have in mind—but the notion of causes would be univocal. The content of a causal statement overall, then, would vary depending upon context and, hence, have different truth values. Causal verdicts would closely ally with the particular



 

explanatory context in play as revealed in the selection of the appropriate contrasting foils to c₁ and e₁: c₂ and e₂. My basic objection is that there is an available common content to causal statements and there is no evidence of there being a context-determined element to our concept of causation on analogy with indexical concepts, for example. This is compatible with allowing, of course, that there are explicitly contrastive true causal statements. A pragmatic explanation denies that the content varies but claims that the apparent context sensitivity of causal statements is rather sensitivity to what would count as an appropriate contribution to successful communication. The contrast identified above as the content of the causal statement might, instead, characterize the current state of knowledge of the conversational parties, or their interests. Let me go through a few cases that, it has been alleged, give the pragmatic approach difficulties. First, the case with which we began: ()

The presence of oxygen caused the forest fire.

Schaffer invites us to consider different interlocutors. Venusians coming from an oxygen-poor environment in which there are lots of lightning strikes. For them, he argues, () would be true (concerning the forest fire on earth). Thus, causal statements have a context-sensitive content. The pragmatic explanation of the apparent difference in truth value is that, for the Venusians, the most appropriately informative piece of causal information is the presence of oxygen. Schaffer suggests that this kind of pragmatic explanation fails to capture the distinctive feel of such statements. They strike us as false not inappropriately uninformative or irrelevant (Schaffer (a), p. ). This doesn’t seem correct although I guess this may be a function of quirks in my humour or different experiences we have had. At school and amongst my social group, () seems both true and potentially funny in its inappropriateness, the amusement partly deriving from the fact that, strictly speaking, it is correct but utterly unhelpful. Consider now the following pair: () The points getting set to local rather than broken track caused the passengers to arrive at the station. () The points getting set to local rather than express track caused the passengers to arrive at the station. Schaffer argues that, unless we individuate events finely, ‘The points getting set to local rather than broken track’ and ‘The points getting set to local rather than express track’ pick out the same event of setting the points to local. Hence () and () would have to have the same truth value according to the pragmatic approach. Yet, we are inclined to deny () while accepting () (Schaffer (a), p. ). A pragmatic defence of my analysis of causation would not be committed to () and () having the same truth value. The sentences in question alter the default contrast of the points not being set to local for two distinct ways of this being so. The first involves the train going down the express track. The second involves the train going down the broken track. The chance of the passengers arriving at the station

  



would only be raised if the relevant contrast was with the train going down the broken track. The difference in truth value of these two sentences falls directly out of their explicitly contrastive nature. Again, on the assumption that we don’t individuate events finely, the following case is argued to be problematic: ()

McEnroe’s tension caused him to serve.

It seems intuitively false but if, as a coarse individuation of events would suggest, his, serving was his serving awkwardly, then the proponent of the pragmatic account is committed to the statement being true. The fuller sentence ()

McEnroe’s tension caused him to serve awkwardly,

by comparison seems true. The contrastive approach would capture this by noting that () concerns whether McEnroe serves rather than not serves whereas () concerns whether McEnroe serves awkwardly rather than not awkwardly. A number of factors seem at work here. The first is that the kind of event causation () describes seems more appropriately described as events-having-properties causation (for more detail see .., and Chapter ). Caused x to F is, thus, not a straightforward case of event causation. To bring this out, compare () with ()

McEnroe’s tension caused that serve.

Considering the serve in its entirety, which may include its awkward character, () seems much less problematic. Second, in the absence of a context in which the highlighted feature of the serve was its awkward character, speaking of McEnroe’s tension as causing him to serve infringes the conversational maxim described earlier. The remark is both too informative and underinformative. It is too informative in that explaining the occurrence of the serve may not need something as detailed as an insight into McEnroe’s mental state. It is underinformative in that, for example, something as central as McEnroe’s desire to go on with the match is not mentioned. It also infringes the maxim of be relevant and cooperative in one’s communication. Nevertheless, these peculiarities of the remark don’t mean that it is false that the tension was one of the causes of the serve by being responsible for the serve’s awkwardness. Finally, though, it should be noted that it is not at all clear that the correct account of coarsely individuated events will take McEnroe’s tension as a legitimate part of the nature of an event that is a cause of the serve. Even P if McEnroe’s serve is his serving awkwardly, if McEnroe were not tense, then the -probability of the serve would not alter. The serve would still occur, without being awkward. So although a pragmatic explanation of why ‘McEnroe’s tension caused him to serve’ seems false is available, it is by no means certain it is required. In rejecting the pragmatic approach, Schaffer makes two further claims. The first is that auditors aren’t tempted just to question the appropriateness of the candidate sentences but to deny them. I accept this is the case for the last two examples. But a pragmatic explanation is not required for them. With regard to the case of oxygen, as we have already seen, it is much less clear that we are inclined to deny it. A more natural conversation about these issues would go like this.



 

A: The presence of oxygen didn’t cause the fire. B: If the oxygen hadn’t been present, then the explosion would not have happened. A: Oxygen is a cause but it is not the main one. It doesn’t explain why the explosion happened now. B: Do you think there’s a distinction between causes and preconditions? A:

Yes, OK then I was right the first time, oxygen is not the cause.

The first sentence looks to be a denial, but of what? The speaker may simply be rejecting the conversational implication that the relevant, and most informative, thing to say about why the forest fire occurred is that there was oxygen present. In particular, that might be because the shared context, in which they are operating, is concerned with what is the trigger. B addresses this by emphasizing a more general mark of causation: counterfactual dependence. The most natural response, which A manifests, is to acknowledge the legitimacy of this extended sense of cause and then indicate what they were particularly looking for. This explains why they were inclined to deny a causal role to the presence of oxygen in the first place. When B brings up the issue of the existence of a distinction between causes and preconditions, then A goes back to the denial with which they began revealing that this was what motivated their thoughts in the first place. This pattern shows that we don’t have a solid phenomenon of denial. What we have is an expression of a certain kind of conversational expectation that can be moderated by theoretical considerations of the type I offer below. It is hard to model the fluctuation in terms of shifts in the contrast between the target cause and another event. I don’t deny that contrasts may change due to context. It is just that it is not a natural explanation of the kind of fluctuations just described. Schaffer’s second claim is that cancellation does not help. To recall, one mark of the pragmatic is that you should be able to cancel the implication quite explicitly whereas if the implications of what we say did not arise from conversational context but rather the content of what we say, then cancellation would just involve contradicting ourselves. Consider the cases in which I have offered a pragmatic explanation and seek to cancel the implication. We get () The presence of oxygen caused the forest fire but by that I don’t mean to imply that the lightning strike had no role in triggering it or that the presence of oxygen was the most significant feature. () McEnroe’s tension caused that serve but by that I don’t mean to imply that his desire to continue the match had no role to play nor that the tension was the most significant feature in the causation of the serve. The result seems more appropriate than the original. It encourages us to hear ‘caused the F’ as not implying uniqueness or significance, and we accept that the presence of oxygen was ‘a cause of the F’ and that the tension was a cause of the particular service McEnroe did. The phenomena that purportedly provided support for taking causation to be a context-sensitive matter are more effectively accounted for by the pragmatic view. This completes my defence against the counterattack that the workings of context to

  



which the pragmatic view appealed in fact rest upon something semantic that favours the context-sensitive approach to causation. We will now consider two particular ways in which it has been argued causes differ from their causal circumstances: causes as triggers and causes as contra-normal conditions. They represent two of the most significant candidates for supposing causes to have special features. A third, the distinction between producing causes and mere dependency conditions, will be the subject of detailed discussion in Chapter . In brief, my argument there will be that there are no grounds for limiting causes to producing causes. If, contrary to my arguments, egalitarianism about causes is false, that is not particularly damaging for my position so long as my position serves to characterize a necessary condition upon causes. It will just be incomplete without supplementation. Although I argue that neither of the features identified below invariably characterize causes, that does not mean that they need not be present for every causal circumstance. The first contrast—between triggering and enabling conditions—is a plausible example of features that must be present.

.. Triggering versus enabling or pre-disposing conditions Some take causes to be triggers rather than enabling or predisposing conditions. To give the well-worn example, they might say that striking the match in a room filled with the appropriate mix of methane and oxygen is a cause of the explosion and that the presence of oxygen is not. The mix of methane and oxygen enabled the explosion to take place. They are a cause of the presence of a capacity to explode that is activated by the striking of the match. If they hadn’t been present, the striking of the match would not have caused the explosion or, as Skow would put it, they are the reason why a particular cause caused an effect (Skow (), p. ). Nevertheless, they might have been present for some time without any explosion taking place. The trigger of the explosion, and hence the cause, is the striking of the match (Lombard (), pp. –). Lawrence Brian Lombard describes causes as producers rather than, as I have here, triggers. I have renamed them to distinguish the issue of this section from the distinct idea of a producing cause, involved in causal production, described in ... In brief, a triggering cause of e occurring at t is not only a cause of e but also causes e to occur at the time it did rather than another time. Two points throw into question the emphasis Lombard places on the distinction between triggering causes and enabling conditions. First, we don’t always favour triggers as causes. In a familiar development of the example above, the mixture of methane and oxygen occurred in a kitchen—a place where we would expect many match strikings to take place. It is very natural to say that, in those circumstances, the cause of the explosion was the gas leak and not the match striking. I give more illustrations in ... Second, triggering is often just the result of temporal order (Mackie (), p. ). Suppose somebody struck a match and, very slightly later, the deadly mix of methane and oxygen was present due to a hole in the gas pipe, as a result of which there was an explosion. Here the lighted match was not the trigger but the methane and oxygen mix. To answer the second point, Lombard argues that some triggers occur prior to their enabling conditions. Suppose that there is a row of dominos with the ninth missing. Quickly replacing it after the first has been toppled enables the sequence of falling



 

dominos to complete (Lombard (), pp. –). Lombard’s example illustrates why it is important to keep the issue of producing and triggering causes separate. The toppling of the ninth domino in the sequence is a producing cause in the sense to be defined later because it is a part of a genuine causal process. Replacing that domino is a producing cause as well because the movement of the domino into position is also part of a genuine causal process. Yet, the combination of these two producing causes is, for Lombard, an enabling condition for the sequence of dominos to complete. Almost any case of mediate causation will provide an illustration of what Lombard has in mind because the enabling conditions of the intermediate stages will occur after the initial triggering event unless backward causation is taking place. However, this very way of putting the point reveals the difficulty with Lombard’s counterexample. Enabling conditions should be understood to be those conditions that enable one link in the causal chain to produce a subsequent link without supplanting the candidate cause. They are not just any intermediate link in a chain of events between cause and effect that, thereby, enables the cause to bring about the effect. Relativized to the circumstances of a cause that enables it to produce a subsequent link, Lombard fails to provide a case in which triggering conditions precede enabling conditions. The suggestion that the distinction between triggering and enabling is often simply a temporal difference is not a denial of the distinction. Rather it is supposed to moderate its significance. If temporal precedence distinguishes between enabling conditions and triggers, then there need not be a deep ontological divide between them. They may be of the same ontological category with just the trigger occurring last. This leaves open the possibility that other salient features of the entities dubbed ‘enabling conditions’ may justify their identification as causes. It is not that they are entities of the wrong kind. For this reason as well, accounts which suggest we cite one thing or another as a cause simply as a result of pragmatic factors gain in plausibility. If what remains to be understood in a certain context is why the effect occurred when it did, then citing pre-existing causal circumstances rather than the trigger will seem inappropriate. The claim that enabling conditions or, as Skow calls them, background conditions are entities of the same kind as causes is rejected by Skow. For him, the key difference is that background conditions are states that are a reason why a token cause, c, caused a token effect, e (Skow (), p. ). To support this, he has a particular notion of state. States are objects instantiating properties whereas events involve objects being engaged in acts. According to Skow, engaging in an act is not to be understood as instantiating a property (Skow (), pp. , ). There are significant problems with Skow’s development of his position. First, he takes the example of match striking/presence of oxygen as a paradigm case of the distinction between cause and background condition (Skow (), p. ). This fits his distinction between event and state but we could recharacterize the case in a way that reintroduces the issue. Consider which is the cause, the match striking or oxygen permeating the match-striking area. Oxygen permeating would come out as an event according to Skow’s approach. But the issues over whether one is a cause and the other a background condition remain open. Second, Skow argues that the idea of a background condition is a ternary relation whereas cause is a binary relation. He contrasts

  



Striking the match caused the lighting of the match. The presence of oxygen was a background condition to striking the match causing the lighting of the match (Skow (), p. ).

However, notice the occurrence of ‘causing’ in the phrase ‘striking the match causing the lighting of the match’. What this indicates is that the background condition is a binary relation as well, relating the presence of oxygen to an event of one event causing another. Something isn’t a ternary relation because one relata has two constituents standing in a relation to each other. Third, a key feature of Skow’s position is that we name properties in the following way: being red, being present, and so on. This claim about naming explains why oxygen being present is a state but striking a match is not. It is an event involving the engagement of an object. There is no property of being striking (Skow (), pp. –). I’ll set aside the question of whether it is possible to name properties in Skow’s preferred way. One problem with Skow’s claim is that it obscures the distinction between sortal and non-sortal properties. Examples of sortal properties are being a tiger, being a mountain, being a father, and, with regard to a particular kind of movement, being a striking. In all of these cases, we plausibly name the properties by talking of the property of being a F. In which case, while there might be no property of being striking, there is a property of being a striking and the failure of the former to make sense is just the result of the fact that the property attributed is a sortal property. A second problem is that, in order to classify an object freezing or moving as events rather than states, Skow rejects the following candidate names for properties: the property of freezing and the property of moving (Skow (), p. ). There is a property of being freezing—and thus a state of being freezing (i.e. really cold)—but this is not picked out to be the property of freezing because when we say that an object is freezing, we are talking about a process and freezing characterizes an event. But it is questionable why we should prefer Skow’s way of naming properties involving being without an indefinite article, a, over the property of redness, happiness, etc. Once we allow them in, there is nothing particularly striking about allowing the property of freezing as naming a property of a process. Fourth, Skow suggests that background conditions operate at a different explanatory level to causes (Skow (), p. ). Background conditions are reasons for causal relationships to hold rather than being a reason for the effect to occur (which he counts a cause to be). However, it is plausible that causes operate at the explanatory level of background conditions. Suppose that c caused e is a case of mediate causation and that there is an intermediate cause in the causal chain from c to e. Then the intermediate cause is a reason why c caused e. Equally, suppose that there are at least two causes for a particular effect. My holding the nail steady is a cause, along with the hammer strike, of the nail going in. Each cause is a reason why the other cause is a cause of the effect. If the only difference between causes and background conditions is that the latter are not supposed to operate as reasons for the effect, then this way of characterizing the difference seems to presuppose the distinction between causes and background conditions rather than providing a basis for it (Skow (), pp. –).



 

Finally, if states are never causes in Skow’s sense, it is mysterious how we can perceive states. A natural requirement on perception is that what is perceived stands in a causal relationship to some, at least, necessary condition of a perceptual experience, for example, an internal brain event (e.g. Child (), pp. –). Even those who reject causal theories of perception, taking perception to be a relational matter involving, say, an object perceived as a constituent, are often prepared to endorse the requirement (e.g. Snowdon (), p. ). Contrary to Skow, then, the distinction between event and state does not naturally coincide with what we are inclined to designate cause and background condition respectively and the ontological significance of how Skow draws the distinction is questionable. I discuss other ways of drawing the distinction briefly in ... As we will see in Chapter , only a certain type of entity can play the role of a triggering cause: events. However, given the observation about temporal order in standard (non-backward) cases of causation, appeal to the type of entity alone cannot provide a full account of the distinction between triggering causes and enabling conditions. Some events will be enabling conditions rather than triggering causes. The example of oxygen permeating the striking area was just one example. The fact that the distinction between triggering causes and enabling conditions fails to correspond to a distinction between the ontological categories of the entities involved is a second consideration in favour of the pragmatic view. The final resolution of this issue will depend upon the discussion in . on process analyses of causation, since this is one of the main grounds for the distinction between causes and other conditions. The discussion of process analyses of causation must await the further material on causal relata, and negative causation in particular. However, the conclusion of that discussion can be summarized as follows. The differences to which process analyses of causation appeal do not constitute a difference between causation and something else, for example mere counterfactual dependence, upon which the distinction between causes and enabling conditions can be based.

.. Causes as contra-normal conditions Probably the most plausible, and significant, characterization of what serves to discriminate causes from the rest of the causal circumstances, is that they are in some way abnormal to, or intrusive into, a normal practice of some kind, or the default activity of a causal network (e.g. Hart and Honoré (), p. ; Hitchcock (b), pp. –). This cuts across the putative distinction between causes and enabling conditions discussed in ... For instance, we say that the severing of the artery, rather than the heart pumping the blood, is a cause of the blood loss. Nevertheless, it is the predisposing or enabling condition for the heart’s subsequent blood pumpings to result in blood loss. Similarly, we can allow that the poison in someone’s tea was a cause of their death, rather than their drinking of the tea, although the poison is an enabling condition and the drinking is the trigger. If only triggers were causes, we would have to deny that poisoning is a cause, as Lombard does (Lombard (), pp. , ). But, the presence of poison is what we alight on because it is not supposed to be in the tea. The approach also provides a plausible

  



diagnosis of why we consider the gas in the kitchen, rather than the match striking, to be a cause (Mackie (), p. ). The role of appeal to normal practices or, as some have characterized it, norms is even more obvious in the case of human activity. Hitchcock and Knobe describe a nice case where a supply of pens is available for administrative staff but faculty must supply their own. Professor A takes one of the two last pens, an administrator another, as a result of which there is no pen available to take an important message. Many have the intuition that the cause of these unhappy circumstances is Professor A, who did something he or she shouldn’t have done, and not the administrator. Subjects’ responses to vignettes such as this one under experimental conditions provide support for this (Hitchcock and Knobe (), pp. –). Moreover, it is not simply that Professor A has engaged in unusual behaviour in contrast to the administrator. Even if the behaviour of both faculty and administrators is typical— faculty are often taking those pens when they shouldn’t—subjects still judge Professor A the cause (Driver (a), pp. –, for the suggestion that it is the unusualness of the act, Knobe and Fraser (b), p. , for this response, Driver (b), notes that she had contra-norm behaviour in mind). In the discussion to follow, I will argue three things. First, the most plausible account of the inclination to single some items as causes over others is not the violation of norms but rather the desire to blame. Second, taking causes to be contranormal conditions is, contrary to what has been argued, not supported by appealing to the idea that we identify causes as means to make effective interventions. Third, we can give a pragmatic account of why we tend to identify contra-normative conditions as ‘the causes’. I deal with these in turn. The picture that Hitchcock and Knobe endorse envisages the sequence in Figure . involving causal judgements about agents. According to their NormViolation model, blame is one consequence of judging that an agent is a cause of a negative outcome but the most significant role for judgements of causation is to serve effective intervention in the world (Hitchcock and Knobe (), pp. –, ). Although blame is one means of modifying the behaviour of the individuals blamed it is not the only one (this role of blame is observed in, for example, Schlick (), pp. –). Mark Alicke, and co-workers, has put forward a contrasting approach (Alicke (); Alicke et al. ()). According to his Culpable Control model, attributions of causality occur as attempted justifications of the desire to blame. The alternative picture is roughly as in Figure . (Alicke et al. (), p. ).

Judgement of departure from norm (wrongful action with negative outcome)

Figure .

Judgement that agent is the cause of negative outcome

Blaming agent for causing negative outcome



 

Negative evaluative reaction to causal condition

Desire to blame agent for outcome due to: intentions, motives, actions, outcomes, race, gender, personality of agent or victim

Judgement that action is the cause of negative outcome.

Blame

Figure .

Alicke and co-workers describe experimental work in which subjects identify as the cause the agent they are most inclined to blame for a particular outcome. The following case illustrates the point. John is driving over the speed limit ( mph in a  mph zone). At an intersection, John is unable to stop as quickly as usual because of an oil spill. As a result, John goes into another car with substantial injury to the other driver. The case comes in two versions. In the first, John is hurrying home to hide an anniversary present for his parents he had left out in the open. In the second, John is hurrying home to hide cocaine he had left out in the open. Subjects almost invariably cited John as the cause of the accident if he were hiding cocaine but only around a third of them did so if he were hiding the anniversary present (Alicke (), pp. –). There are grounds to favour the culpable control model. Proponents of the norm violation model generate causal judgements as a response to norm violation. As Alicke et al. point out, while their culpable control model can take these into account—we want to blame people who violate norms—we also want to blame people for good or bad outcomes regardless of whether a norm has been violated (Alicke et al. (), pp. –). A case that favours their position involves a doctor deciding whether to authorize the use of an experimental medicine an intern wants to use, which is against hospital policy because of the risks. On one development of the story, the outcome is beneficial and the patient receiving the treatment responds to the medicine and recovers. On another development of the story, the patient dies. They found that when the doctor violated hospital policy and the outcome was bad, the doctor was pretty strongly felt to be a cause of the outcome, less so if the outcome was good. If the doctor obeyed hospital policy, he or she was judged to be more of a cause if the outcome was good than bad (though not as strongly as in the case in which the doctor violated hospital policy). It is hard to explain this interaction between norm violation and outcome on the norm violation model. It is what one would expect according to the culpable control model. Some debate over the relative success of these two models has centred on the connected phenomenon of what is known as the Knobe effect (named after Knobe who discovered it). In abstract, it is captured by the following asymmetry in people’s judgements about whether a subject intentionally does a certain action: If a subject A intentionally does O, knowing that O results in a side effect N (a negative outcome), then A intentionally does N (and is thus subject to blame).

  



If a subject A intentionally does O, knowing that O results in a side effect P (a positive outcome), then it is not the case that A intentionally does P (and is thus not subject to praise). An example is the chief executive officer of a company deciding upon a certain change in a manufacturing process that in one development of the story they are advised has a negative effect upon the environment and in the other a positive affect on the environment. In both developments, the chief executive officer expresses no concern about this outcome (Knobe ()). The line of thought seems to be that if normative considerations influence our judgements about whether a subject intentionally does the positive or negative side effect (P/N), then it will influence our judgements about causation. Both types of judgements are generally required to connect an agent with a certain outcome concerning which we hold them responsible, or not responsible. The significance of this connection for causation is questionable, however. Given that, at best, causation is a necessary but not sufficient condition of responsibility—and even this is questionable because we hold people responsible for omissions that do not seem to be causes—we might expect that the Knobe effect’s implications for causation would be commensurately weaker. It might influence what we take to be most salient as a cause but not whether or not something is a cause. Agents can escape blame while being causes so there is no reason to expect the correctness of our causal judgements to track whether or not we blame the agents in question. In any event, the competing position favoured by Alicke is that negative side effects of an action are the basis for blaming an agent for the action which are, consequently reflected in judgements about whether or not an action is intentional (Alicke (), p. ). To rule out this alternative, Knobe cites a study to show that our judgements of blame don’t antedate attributions of intention (Knobe (), p. ; Guglielmo and Malle ()). The idea seems to be that, if this is correct, judgements of blame don’t determine the attributions of intention although our concept of the latter is at the service of our practice of praise and blame. The Knobe effect shows something about the nature of intention: it is morally infused. In fact, the study likewise suggests that attributions of intention are prior to any normative assessment (Guglielmo and Malle (), pp. –). For example, give subjects the choice between: (A) The chief executive officer willingly harmed the environment. (B) The chief executive officer knowingly harmed the environment. (C) The chief executive officer intentionally harmed the environment. (D) The chief executive officer purposefully harmed the environment.  per cent chose (A),  per cent (B),  per cent (C), and  per cent (D). So there is no support from this study for the idea that norm violation is a key part of our understanding of whether somebody intentionally did something (Guglielmo and Malle (), pp. –). If that is so, there is even less support for the claim that norm violation is a key part of our understanding of causation. Although the culpable control model captured our attributions of causation somewhat better, there are two grounds for thinking that it does not reflect something



 

about the nature of causation. The first is that the determinants of the desire to blame somebody involve factors irrelevant by anybody’s lights to whether or not something is a cause. For example, somebody will be judged more of a cause of a negative outcome if subjects have a negative view of the person in general. Important debate over the causes of climate change will get enmired in the question of whether to exonerate or excoriate humans for their affect upon the changing natural environment. The identified determinants of the desire to blame demonstrate more how our attitudes may bias our causal judgements rather than that causation is the objectivization of inclinations to blame. Indeed the talk of rationalization of the desire to blame rather than, say, an essential role in the justification of blame suggests that the model is not taken by its proponents to provide further illumination about the nature of causation (e.g. Alicke ()). Second, subjects are asked to identify ‘the cause’ or, in other cases, evaluate the extent of an action’s influence down a causal chain, on a point scale of values. This is not addressed to the question of whether something counts as a cause but rather whether something is a particularly salient or striking case. We might ask subjects to assign values to how red various things are ( being most red,  being least red). The results would not tell us much about whether, say, things that are  are red. These points suggest that the experimental data that spoke in favour of taking norm violation as an essential element of something being a cause actually reveal something else that has nothing to do with the nature of causation. As we have seen, the main debate has centred over attributions of causation with respect to agents. While this was used to motivate and empirically ground the idea of causes as contranormal conditions we should not let its failure there determine the fate of the idea more generally. Indeed, Alicke et al. allowed that the idea of causes as contra-normal conditions ‘[is] almost certainly the primary determinants of causal citations for events that do not involve human agents’ ((), p. ). This brings me to the second point I want to make, that concerning whether causes are contra-normal conditions because these conditions enable us to make effective interventions (as Hitchcock and Knobe suggest). The connection is by no means obvious. The reasons for this vary depending upon how we understand the normal conditions against which causes are contra-normal. One understanding of normal conditions is statistical. Causes are the factors that don’t usually occur. To develop a general strategy to bring about a certain outcome O, we seek to identify the statistically abnormal and make it normal. If lots of match strikings are going to occur in a kitchen, then we had better make sure the gas supply doesn’t leak, as it is a statistically abnormal occurrence (Hitchcock and Knobe (), pp. –). Although this is a reasonable strategy, there are obvious exceptions. It may be statistically normal for houses to be built in a certain region, and statistically abnormal for there to be earthquakes, nevertheless we would not seek to manipulate the incidence of earthquakes while carrying on the building programme without safeguards. Intervening in the world can involve a trade-off between ease of manipulation and generality of strategy and, to weigh these effectively, we need to think of a whole range of factors as causes of a certain outcome, not simply the abnormal factors. On a second understanding of normal conditions, the behaviour judged to be a cause violates a moral norm. The example of the delinquent professor is a case in point.

  



As Hitchcock and Knobe recognize, by the criterion of effective intervention, there may be no difference between changing the behaviour of the faculty member and the administrator. Additional policy considerations about what is the best outcome decide things in favour of taking the delinquent professor to be a cause (Hitchcock and Knobe (), pp. –). However, this understates the issue. If the professor is particularly delinquent, it may be a much less effective strategy to seek to change his or her behaviour in spite of it being a better outcome if one could. This second understanding of normal conditions is in direct tension with the emphasis on effective intervention unless it is assumed that there is a legitimate expectation that human actors will tend to act as they ought to do. Even if such an assumption is legitimate, the existence of individuals who do not respond in this way suggests that, in order to be effective agents, we need to identify as causes things that are not contra-normal. On the third understanding of normal conditions, they are to be understood in terms of the proper functioning of mechanisms. So, if a machine or system breaks down, we will repair it by trying to identify the departure from how it was designed and restore it to its original designed state. Other ways of repairing a machine or system may work but one cannot be sure about the ramifications of moving stuff. So it is safer to stick with the design (Hitchcock and Knobe (), pp. –). Once more, the wisdom of this strategy is undeniable because, one might assume, the designers have thought more systematically and longer about how things might be organized. So it is natural to identify a contra-normal item as a cause of the breakdown. Nevertheless, we must be open to the thought that other aspects of the set-up that might count as normal are causes too. The whole design is misconceived. So it would be a mistake to suppose that, in identifying something as a cause first, we are ruling out that the other elements of the causal circumstances are not causes. If effective intervention requires leaving open normal conditions as causes, then the observations above actually seem helpful in developing a pragmatic treatment of the cases. This brings me to the third point I wanted to make. Between two interlocutors, there is a shared understanding of, and where relevant commitment to, the normal conditions, and what they should result in. The expectation is that the other person is going to identify how things have departed from the normal conditions and, hence, how things may be brought back to normal. Somebody who cites one of the normal conditions as a cause is infringing with regard to informativeness, and relevance to their conversational goals. Our response is not to deny that a normal condition is a cause—if an interlocutor makes the mistake of mentioning it—but to suggest that this was not what we are looking for in the context. Knobe has argued that the pragmatic analysis of this phenomenon has a problem explaining the behaviour of Asperger’s/high-functioning autistic subjects (Knobe (), p. ). They have difficulties in social cognition, in part the social cognition plausibly at work in the application of conversational maxims, and yet they display roughly the same pattern of attributing causation to subjects that have infringed norms. However, the experimental work he cites doesn’t seem to have the implications he claims for it (Zalla et al. (forthcoming)). Tiziana Zalla, Edouard Machery, and Marion Leboyer note that subjects with Asperger’s or high-functioning autism deal with their difficulties in sophisticated attributions of intentions—specifically that



 

a subject intends to do something they negatively value as a means to do something they overall value more—by adopting the simple rule that if an action infringes a norm, then it is intentional. For the sake of argument, let me concede that such subjects will correspondingly judge causes to be contra-normal events. The adoption of the simple rule in this case too does not show what is at work in those who do not have difficulties in social cognition. The simple rule is adopted to enable those with such difficulties to approximate the behaviour of subjects without the difficulty. Thus, there is no reason to reject egalitarianism about causes to be drawn from the observation that we often cite as causes of contra-normal conditions. Our tendency do so either derives from certain biases at work relating to the desire to blame or can be given a pragmatic explanation. I shall, however, need to return to the issue of normal conditions once more when I turn to negative causation in Chapter .

. Concluding Remarks It is undeniable that it feels more natural to identify certain things as causes, in the causal circumstances for a certain effect, than others. The question is what we should make of this fact. Egalitarianism suggests that we should look for the answer elsewhere than in the nature of causation. For something to be a cause, it need only satisfy the analysis I have offered earlier. Some of the causal circumstances must be triggers for the effect but not all causes need to be triggers. Causes also don’t have to have the additional feature of being contra-normal conditions. Although something being a contra-normal condition is often the reason why we identify it as a cause to others, this is a pragmatic matter and does not imply that we rule out the other elements of the causal circumstances as causes. Indeed, it best fits our causal reasoning if we don’t. Although, when we try to make an effective intervention in the world, we might consider the contra-normal conditions as items of manipulation, our causal reasoning needs to be more open than that and egalitarianism about what counts as a cause best fits this need. The social distancing policies during the coronavirus outbreak illustrate the point. Social distancing is an intervention on a cause of coronavirus deaths - social contact - that is not abnormal. The presence of the virus is abnormal. However, social interaction is easier to manipulate. The introduction of norms of social distancing provide a means of breaking a causal relationship. However, they don’t make going for a coffee with a friend, rather than the allowed one shopping trip a week, the cause of further deaths. My defence of egalitarianism is incomplete. We also need to discuss the case of omissions and the alleged distinction between producing causes and simple dependencies. Successful discussion of these matters awaits the discussion of the ontology of causes in Chapter  and of negative causation in Chapter . Nevertheless, what we have seen so far is that causation should not be taken to be a contextual explanatory matter, focused on triggering conditions or, in some sense, involving contra-normal occurrences. This is not simply an observation about how we use the term cause. I have connected the argument with claims about the utility of our concept of cause.

 



Claims about the concept of causation is one thing, the nature of causation another. In ., I explained how my analysis was not meant to be an analysis of our concept of cause. It was an analysis of the nature of causation. The present chapter has canvassed a number of different views about causes. Our term ‘cause’ could have picked out any of them. Many are closely related to our practices—of explanation, intervention, and responsibility—and we could have situated ‘cause’ in this context. The recognition that subjects’ concepts of cause may not reflect all the dimensions of the role that conceiving something as a cause may play is assisted by the emphasis upon providing an analysis of causation rather than our concept of causation. It allows for the possibility that, as we reflect upon our practice, and develop it by analysis of the entities to which it appeals, we make discoveries about their nature. These discoveries develop our concept rather than are embedded in it. We see the point in why we have talk of entities with such and such a nature.

 The Ontological Categories of Causes Chapter  focused on the question of whether causal circumstances were usefully divided into entities that were causes and those which were background conditions. I defended egalitarianism. There is no defensible distinction here. The discussion remained pretty much neutral on the question of whether causes fell into a particular ontological category, for example, events. The present chapter turns to that issue. Causation apparently involves facts, property instances, events, or even objects. Thus we have () The assassination of the head of state caused the revolution (event causation). () The fact that he lost his grip caused his fall (fact causation of an event). () It was the heaviness of the load that caused the lorry’s axle to break (property instance causation of an event). () It was the loudness of his greeting that caused the sharpness of her response (property instance causation of a property instance). () Don’s fall causes his death because his bones are brittle (fact causation). () I caused her annoyance (object causation of a property instance). In the last case, the ‘I’ seems to refer to an object and the sentence seems to take that object to be a cause of annoyance. Nevertheless, we should distinguish between the types of entities to which reference is made in true causal statements—various illustrations of which I have given above—from the types of entities that are responsible for the truth of the causal statements in question. The default position is to take the truth of these various types of causal statements to indicate that each of the various types of entities they concern are properly conceived of as causal relata. To shift us from this position, we need argument. This can come in two forms. First, there are direct considerations from particular causal relationships, and our talk of them. If it turned out that certain kinds of causal relationships required certain kinds of entities, then the complete theory of causation would include mention of these kinds. I shall argue that two ontological categories meet this requirement: events and properties. I’ll give examples of the latter later on because they need a bit more setting up and there are no immediately uncontentious cases of what I have in mind. Recognition of these two types of entities are all that is required for complete coverage of the causal relationships that hold unless a certain metaphysics of agency is adopted in response to the issue of free will. With that

A Variety of Causes. Paul Noordhof, Oxford University Press (2020). © Paul Noordhof. DOI: 10.1093/oso/9780199251469.001.0001

    



qualification, any other causal relationships we recognize can be seen to depend upon event and property causation. Any statement involving reference to other kinds of entities may be restated in terms of events and properties, whereas the converse is not true. There can be different constraints on what is involved in restatement. I don’t deny that some causal relationships are easier to state in terms of facts than events. One illustration of this is iterated causation such as that recorded in (): Don’s fall causes his death because his bones are brittle. A reformulation in terms of event talk would be the unattractive: the brittleness of Don’s bones causes Don’s fall’s causing of his death. Equally, in a world of facts and events, even if every case of fact causation held in virtue of a case of event causation, we would still need statements of fact causation to capture the causal relations which held between facts. As a result, the minimum acceptable constraint on restatement is probably best characterized in terms of supervenience. The question is whether a minimal duplicate of a world in which causal relations hold between certain kinds of entities is a duplicate simpliciter in terms of all the causal relations that hold. Call the entities used to characterize the minimal duplicate the supervenience-base entities and any other entities the supervening entities. The conclusion of the discussion will be that events and properties constitute an appropriate supervenience base and that, as things are, facts do not. Facts fail to cut things as finely as we need to capture some causal statements. At the same time, they cut things more finely than we need for other causal statements. The second point would not rule them out over events if there were other reasons to believe in their existence, for instance, because they are required as truth-makers in general. I will argue that they are not needed to play this role because such a role is not required. This brings me to the second form of argument in this chapter. It concerns the categories of entities that we need to recognize in the world in general, perhaps independently of causation. For example, if we need to recognize that the world is a world of facts, then it would be surprising if facts were not involved in causal relations. Arguments against the need for postulating a certain kind of metaphysical category thus are another way of reducing the types of entities between which causal relations hold. Those who are committed to the so-called Eleatic principle that An entity (other than causation or laws) only exists if it either causes or is capable of causing some effect may be sceptical of the distinction between these two forms of argument. The principle is taken from Plato’s Sophist in which the Eleatic Stranger offers as a mark of being ‘that they are nothing but power’, it is cited by Armstrong and appears to have been dubbed by Graham Oddie the ‘Eleatic Principle’ (Oddie ()). Samuel Alexander endorses a similar principle that, after Jaegwon Kim, has been known as ‘Alexander’s Dictum’ (Alexander (), Volume , p. ; Kim (), p. ). Causation and laws themselves are excluded because, presumably, neither have to earn their keep by being capable of efficacy, given that they are required for others to earn their keep. The worry of proponents of this principle, regarding the distinction between the two forms of argument, would be that our reason for concluding that a certain type of entity exists is that instances of that type of entity are causes, or



    

are capable of being causes. In which case, there can be no external arguments for, or against, the existence of a certain type of entity independently of causation. Elevation of the principle to this status is a mistake. It is one thing to adopt the Eleatic principle as a constraint. If you find yourself postulating the existence of entities that you acknowledge are neither causes nor have the capacity to be causes, consider whether your grounds for postulating their existence are good. It is another to think that the only grounds that one might have for postulating the existence of a certain type of entity are causal. It might be that there are non-causal theoretical reasons for recognizing the existence of a certain kind of entity. In principle, inference to the best explanation, or Quine’s account of ontological commitment, may provide such a basis (Quine (); Lipton (), pp. –, ). Equally, we might have grounds for believing in the existence of certain entities that, although they boil down to a matter of causality, we don’t conceive of them that way. In which case, it is best to keep the two forms of argument I have identified separate for epistemological purposes as I do in what follows. Probably the most significant problem in organizing one’s thoughts concerning the relata of causation is that while there is considerable disagreement over whether the relata are events, facts, states of affairs, objects, or property instances— to name the most obvious candidates—the differences can appear magnified, and/or harder to specify, because of differences of opinion about the nature of these ontological categories. Different theories of events or facts give rise to differences in their suitability as the relata of causation when really, there is broad agreement about the features the relata must have. Sometimes there appear to be entirely verbal disagreements between philosophers who favour fact causation (say) over event causation, or vice versa, arising simply from their disagreement about the proper analysis of facts and events. They are agreed about the nature of the entities that should figure in causal relations. Illustrations of this problem occur in ... For that reason, I want to go feature first, as it were: mention the particular characteristics that seem salient to the discrimination between these categories of entity and consider their relationship to the nature of causation. Which ontological categories possess these features is of secondary concern. The relevant features seem to be these. First, whether the entities falling under a particular category are continuants, that is, entities that don’t have temporal extent but are wholly present throughout their existence. Some have claimed that at least one of objects, facts, states of affairs, and property instances are continuants but, for each case, others have provided an alternative account of their identity. Second, whether they are truthmakers. Facts, states of affairs, and property instances have all been pressed into service here. Third, how finely they are individuated, and how this relates to claims of causal relevance. Coarse-grained accounts of events have made them seem ill suited, in which case, property instances and properties have been proposed as relata. Finegrained accounts of events go some way to obviate this need. The first of these features will be dealt with in .. The latter two will be the focus of . and ., respectively. I arrive at my advertised conclusions about why coarse-grained events may figure in the supervenience base by first explaining why causes must include noncontinuants (we need, at least, some causes to be triggers); second, explaining why

    



causes needn’t be truth-makers (there is no need for truth-makers and no particular features of the causal relation that require such an entity); and, third, explaining how my analysis of causation removes the motivation for attributing to causes essential natures of a particular kind and, also, for individuating them in a particular way. Events are the ontological category that fall out as a consequence of such observations. I begin the case for recognizing that the only other entity we need are properties to account for questions of causal relevance, and emphasis, in ..–. The case will be completed in Chapter . The result is an ontology of causation that recognizes, as causal relata, events and properties. We can situate the result in the sketch of the terrain in this area in Figure .. The initial distinction between single and plural approaches relates to whether or not more than one kind of entity is required to capture token causation on the one hand, and what is often known as causal or explanatory relevance on the other. The approach for which I will be arguing is a plural rather than singular approach. Some argue that only one kind of entity—events, facts, or property instances—are token causal relata. One of two attitudes is adopted to the issues that come under the general heading of causal or explanatory relevance. The first is to take them to justify a ‘fine-grained’ account of the causal relata reflecting differences of causalexplanatory relevance. The second is to take them to be more of a conceptual or

Single or Plural

Plural

Single

Relevance Merely Explanatory

Relevance Ontological

Events (Davidson, Lewis)

Facts (Mellor)

Events and Facts (Relevance) (Steward)

Fine-grained events (Kim, Goldman, Menzies) Trope Theory (Macdonalds, Robb)

Figure .

Events and Properties (favoured position) Continuants and Manners of Acting (Lowe)



    

linguistic matter. They concern, principally, whether we think of causes in a more or less illuminating way by appeal to an explanatory framework of, for example, laws. The alternative, which I favour, is to recognize that the proper characterization of token causal relata does not involve sensitivity to causal or explanatory relevance but take the latter to justify a second kind of causal relata. The latter part of this chapter and Chapter  defend the claim that this is properties. Once the second kind of relata is recognized, there is no motivation for adopting a more fine-grained approach to the first kind of causal relata. Of course, if a fine-grained approach had been able to provide a satisfactory treatment of causal or explanatory relevance, then the interest of the observation would be limited. I shall argue that this is not the case. At the beginning of this chapter I started talking about the ontology of causation and then moved to talk in terms of the relata of causation. Considerations mainly drawn from the case of negative causation show these to be distinct issues. You can have a certain view about the ontology of causation while denying that causation is always, or ever, a relation. I have set aside this point for now for ease of discussion. In Chapter , I will discuss this line of thought and defend the view that causation always involves a relation between a cause and effect. Negative causation is also often cited in support of the view that causation fundamentally concerns facts. So the conclusion of the discussion will be conditional upon what I say in Chapter  in this respect too. Before we get there, let’s see how a case for events, and a preliminary case for properties, can be built.

. Continuants as Triggers? Although not all causes are triggers, it is quite clear that some are. It is also plausible that, for any causal circumstances, there has got to be at least one element that explains why the effect occurs when it does, although this explanation may be moderated by the influence of a delayer. The need to explain the time of occurrence, when we can, provides us with one possible constraint upon what we must recognize as causal relata. If continuants are wholly present for each moment of their existence, then it is hard to see how they could play the triggering role. Suppose that a particular continuant exists from t₁ to tn and is a cause of an effect, which occurs at t₄. Then it is hard to see how the continuant could be a cause of the effect occurring then unless we recognize another entity, for example the continuant having a property just before t₄. Here I don’t mean to imply that causation must be temporally contiguous. The point is simply that there must be something about the continuant that causes the effect to occur at the time it did rather than at another time, under determinism. In the case of indeterminism, there must be something that raises the mean chance of the effect during a certain time period, over the mean background chance of the effect occurring anyway. This introduces the need for an additional category of entity. A familiar move, to fix ideas, would be to say that continuants only cause by being part of events. Not everybody would accept this line of reasoning. The most sophisticated discussion of the issue occurs within the context of an assessment of agent causation. Agent causation is not simply meant to be causation by an agent where, as it might be, the agent is a cause by figuring as a constitutive part of an event, for instance, the

  ?



event of an agent intending to do A (Taylor (), p. ). Instead, agent causation is taken to be a sui generis kind of causation not reducible to any other type. Philosophers have appealed to the idea to explain what makes something an action rather than a mere happening and how the putative freedom of our actions would not be threatened by the fact (assuming it to be one) that the world is governed by laws of nature alone. Regarding the second point, the thought is that if an agent’s actions are events which are the consequence of events involving the agent, which are in turn the consequence of other events, then the agent is just being acted upon as a passive instrument. Agents merely have a place in the sequences of events that make up the world (Reid (), p. ). For the same reason, proponents of agent causation resist the idea that an agent’s motives are causes of his or her action. They recognize that an agent’s motives may be caused by features of the world around him or her. Faced with the range of ice creams on offer in the bar in the cathedral square of Siracusa, the ice cream lover’s desire for an ice cream is an inevitable upshot. If this motive in turn was a cause, the ice cream lover would be a passive instrument acted upon by the all too obvious delights of Sicilian ice cream. Proponents of agent causation swap the causal picture for an advisory one. The agent may listen or fail to listen to the advice supplied by his or her desires (Reid (), p. ). Not every philosopher classified as a proponent of agent causation rejects the idea that the agent may be caused to act, but those who don’t deny that agent causation is a solution to the problem of free will (e.g. Taylor (), pp. –). A substantial line of concern about the coherence of agent causation centres upon whether we can make sense of a continuant—the agent—as a triggering cause. Taking agents to be continuants is mandatory to this picture because, if, instead, we supposed them to be made up of temporal stages—plausibly thought of as a sequence of events—then we could identify a particular temporal stage as responsible for an action and hence action would once more just be something slotted into the world of events governed by law (Broad (), pp. –). So proponents of agent causation have to tackle head on the line of objection to continuants being triggers with which I began this section. Proponents of agent causation differ in their response to this concern. Some accept that an explanation is needed. Randolph Clarke suggests that an agent’s perceptions and reasons settle the timing of an agent’s action but are not causes of the agent causing the action (Clarke (), pp. , , (), pp. –). Such folk are not opponents to the point I’m making here since these are non-continuants if they are to work as a response. However, others deny that an explanation of the timing of an action is even necessary (e.g. O’Connor (), p. ). To assuage worries over this, Timothy O’Connor compares the situation to one that occurs in quantum mechanics. A photon is fired at a screen with two slits. If it is detected at slit A, it will cause a green light to go on, and if it is detected at B, it will cause a red light to go on. It is indeterministic which light will go on. In fact, the red does. O’Connor suggests, and my analysis of causation agrees, that the firing of the photon is a cause of the red light going on but not an explanation of why it was the red light rather than the equiprobable green light which went on (O’Connor (), p. ). He suggests that the situation is no different with regard to whether an agent causes an action to occur at one time rather than another.



    

As a defence of agent causation, O’Connor’s response appears weak. Proponents of agent causation hold that agents deterministically cause an action to occur at a particular time and not that they are indeterministic causes of an event that may occur at some time or another (Clarke (), pp. –, O’Connor (), p. ). Indeterminism is taken to be a sign of absence of control (e.g. O’Connor (), p. ). Even if the connection is indeterministic, indeterministic causes still have a temporal element by raising the mean chance of an effect over its mean background chance during a certain time period. This is what agent causation struggles to explain. Moreover, since actions are events, there will be other events that explain the time of occurrence of the action. If agents don’t cause an action to occur at a particular time, then this is something that escapes their control with the consequent costs of the action’s time of occurrence being unfree or passive. So the question is how can something—a continuant—that is present prior to the action cause it to occur at a particular time without this being due to some property that the continuant acquires, for instance, at the time in question? Yet, this is precisely what is ruled out by these proponents of agent causation since, as we shall see, it is plausible that, if an object acquires a property, there is an event which is a cause of the action. Even if O’Connor’s defence of agent causation somehow worked, its implications for the point I am making would be minimal. It would establish that there are some causal circumstances that don’t require a triggering cause for the target effect. It would not establish that there is no need for triggering causes in most causal circumstances as a result of which non-continuant metaphysical entities need to be recognized as relata of causation. In which case, it is a qualification to the claim that only events and properties need figure in the supervenience base required to capture all the causal relations that hold in a world but does not vitiate the status of noncontinuants (ultimately events) for which I am arguing. There is another potential threat to my approach from agent causation. Proponents of agent causation have also argued that it constitutes a counterexample to counterfactual theories of causation (e.g. O’Connor (), pp. , –). Let s be a human subject, m be a mental event or a movement of his or her body, and a be an acting (for some, this is primarily a coming to have an intention, for others something to be characterized in terms of activities of the agent’s body). Then the problem is supposed to be that agent causation has the following structure: a(s, m). The token acting is an active relation between the subject and the outcome mental event or movement. A successful characterization of agent causation, then, needs to characterize the relationship between s and a. The difficulty is that a is a manifestation of the agency of a continuant, s, and there is nothing more to say about the relation between this manifestation and s than there is to say about the relationship between any other manifestation and s. Part of the problem for the successful characterization of the causal relation in this case stems from the very difficulty discussed about how a continuant can be a triggering cause. However, I have allowed that there can be non-triggering causes in ... So, in principle, there is nothing to rule out agent causation having this character. In which case, we can characterize the causal relationship, at its most general, by appealing to counterfactuals with the following antecedents: ‘if s were present’ and ‘if s were not present’. This is not an attempt to fit agent causation into

  ?



an event or fact model. There is no immediate conclusion to be drawn about the basis for the truth of counterfactuals from the fact that they have sentences embedded in the antecedent and consequent. Language is one thing, the entities in the world it seeks to characterize are another. Suppose an agent picked up a cup. Then the appropriate, albeit simplified, characterization of the causal circumstances are if the cup had not been there, the agent had not been present, and the agent had not noticed the cup, then the agent would not have picked it up. The second element may appear redundant on the assumption that, if the agent notices the cup, then the agent is present and if they don’t notice the cup, it doesn’t matter if the agent is absent. However, this is a mistake. Of course it is true that if one of the other elements of the causal circumstances is absent, then it doesn’t matter whether the rest are present because the target effect still won’t occur. That does not mean it is redundant. Equally, just because the agent notices the cup, it doesn’t follow that they will pick it up. What else is required? Well, according to the proponent of agent causation, the answer is simply the subject responding to what they notice. But, and this is the crucial point, there is no further characterization of the agent. They simply manifest a (in the example, a would be a picking up of the cup, if you limit the case to mental events, then it might be coming to intend to a, where a is a specific action). In which case, the presence of the agent is an essential element, and will be a counterfactual chance-raising element like any other. Of course, the counterfactual chance-raising element it provides will be the same for all manifestations of his or her agency. But that’s just the nature of the position. There’s the noticing, and there is the agent, and nothing else to be described causally. You can’t, on the one hand, be a proponent of agent causation, and deny there is any further characterization, and on the other prosecute the counterfactual theorist for mentioning in the antecedents of their counterfactuals the only elements they are allowed to mention. A residual feeling that the presence of the agent must be redundant, given that the agent noticing the cup is part of the causal circumstances, is very possibly as much of an objection to the agent causation picture. Nevertheless, some defence of it can be made against this concern. The first point is that just because the agent noticed the cup, it doesn’t follow that they continued to be present in order to act. Their existence might have ended just with the noticing. So mentioning the agent’s continuing presence is necessary, given it is not appropriate to mention an event of the agent deciding to pick up the cup (say). Second, as we will see later, the proper account of events does not have the objects that they involve as constituents. With this picture in place, the absence of redundancy will be much clearer. The remaining issue is whether the various elements of the causal circumstances are suitably distinct from the effects for which they are the circumstances, which they will be if parts of their minimal supervenience-bases are distinct (.,). I have argued that it is difficult to see how continuants can be triggering causes. The safe conclusion is that some causes are non-continuants. More boldly, there are reasons to think that some causes must be events, or facts with the same temporal structure. If continuants cannot play this role, it appears to follow that continuants cannot be fundamental causes of this type. The position is resisted by Jonathan Lowe who suggests that, in fact, continuants are fundamental because something like the following is true.



    

Event c caused event e iff there was some agent, A, and some manner of acting, X, such that c consisted in A’s X-ing and A, by X-ing, caused e (Lowe (), p. ). Lowe remarks that events do not possess causal powers, it is the continuants that do (Lowe (), p. ). It is in manifesting their causal powers that continuants display their efficacy. As we shall see in ., events should not be understood as consisting in A’s X-ing. Nevertheless, I shall set this issue aside for now. Lowe’s observation rightly draws attention to the fact that event causation may depend upon continuants manifesting their causal powers, and so recognizing that events are causes is not in tension with allowing that continuants are causes. However, this is not sufficient to show that event causation is fundamentally continuant causation. As the formulation suggests, it is not that A causes e, it is rather that A, by X-ing, causes e. The continuant’s manifestation of a power is an event and it is this manifestation—the event—that does the causing. Continuants, by possessing the power that is manifested, are a legitimate part of the causal circumstances. But events (or facts with the same temporal structure) are the vehicle for their role and bring to causal circumstances an essential element that the following sections are an attempt to characterize. The argument against continuants being triggering causes also extends to entities with temporal extent but no temporal parts even if the ontology of continuants— entities wholly present throughout the temporal extent—is eschewed (e.g. Parsons ()). The crucial feature both ontologies share is entities that cannot explain why a target effect occurred at a time given their presence at times which did not give rise to the effect. What changed? Of course any entities with temporal duration only part of which is relevant to why the target effect occurred face the same question. But entities whose duration is made up of their temporal parts (i.e. those which perdure) have a specific entity—the temporal part and its properties—that can provide an answer. This is the key difference that favours non-continuant, temporal part possessing entities. Nothing I have argued rules out the possibility of entities without this feature numbering among the causes, especially if there is agent causation. However, we have grounds for believing that there must, at least, be some causes that are triggering and these cannot be continuants or have temporal duration without temporal parts. The question is whether we need to recognize causes with other types of features, for example, truth-making or certain essential properties. It is to this that we now turn.

. Truth-Makers and Non-Truth-Makers In . I identified a particular causal role that must be played in the causal circumstances for an effect, whatever else is the case about them: a triggering cause. Continuants are ill suited to play this role but other entities may be. Debate over the various candidates for being causal relata is in part a debate over which category of entity is most plausibly thought of as supplying this role. The main disagreement has been over whether events, facts, or property instances are best thought of as causes in general, and triggering causes in particular. As I have already noted, differing accounts of the nature of each of these entities has obscured the discussion

-  --



so that the range of options is much narrower than may appear. Given the argument of the previous section, if property instances are continuants, they cannot be triggering causes. In .., we shall see that there are some grounds for supposing that property instances are continuants. If fact talk can take the place of both event talk and state talk, then it is plausible that some facts may be continuants and some not for the reason given below mentioned in the brief discussion of Helen Steward’s work. In .., I shall argue that a way to distinguish more sharply between events, property instances, and facts is to consider their role in truth-making. When we do so, part of the motivation for postulating facts falls away because, I shall argue, there is no truth-making role that needs to be played. The other motivations for recognizing facts relates to the need for disjunctive causal relata, causal relevance, and negative causation. We shall see later that they are inadequate to play the role of causal relevance and there are no negative entities—that facts may claim to best provide—required for true statements of negative causation. The end of this part of the chapter will explain why they are not needed for disjunctive causal relata either.

.. Facts, events, and property instances: narrowing down the options We can set aside, at the outset, certain accounts of facts that make them inappropriate to be causes. Once we get these out of the way, the significance of the issue of truth-making will be clearer. On one understanding, facts are simply what true sentences state. The following principle pretty much exhausts what we can say about their character. ‘P’ is true iff it is a fact that p (Mellor (), pp. –, (), p. ). It is compatible with this principle that facts are true propositions. On some understandings of propositions, this might make them constituents of the spatiotemporal world, but not all. If at least some, perhaps all, causes have spatiotemporal location, this notion of fact cannot capture what we have in mind by our causal talk unless it is developed in ways that will make it rather more similar to the substantial account of facts detailed below, for example, by drawing upon the particular notion of proposition I just mentioned. On another understanding, facts are ordered triples that obtain. Roughly, the thought seems to be that obtains iff x exemplifies the property of F at t (Taylor (), pp. –). If F, x, t exist, then the ordered triple exists regardless of whether x exemplifies the property of F at t. Suppose that we are at a time t – Δ and assume that future times exist. Suppose further that, at t, x exemplifies F at t. Then is an obtaining fact at t – Δ. It is not a condition on obtaining ordered triples that they only obtain at the time at which the relevant object exemplifies the mentioned property. Barry Taylor is mistaken when he says an ordered triple is located in a room in roughly the way that Jones’ buttering of toast in the kitchen is located in the kitchen (Taylor (), p. ). Either has no spatiotemporal location or it has a highly disparate one that includes wherever F and x are at times prior and posterior to t (Menzies (b), p. ). Neither option makes them a plausible entity to stand in causal relations. Of course, if the thought is really that obtaining ordered



    

triples are exemplifications of properties by objects at times, then this brings it much closer to a theory of events to be detailed below. Once these two implausible theories of facts have been set aside or developed further, the difference between events and facts becomes much less marked. Proponents of facts or, as some call them, states of affairs, emphasize the truthmaking role of causal relata. Proponents of events don’t. Let’s think about events first to get the contrast with truth-making in sharper focus. Events are typically thought of as changes, states as unchanges. Skow rejects this characterization arguing that there is an event of my standing stock still that involves me in engaging in an act. I argued against his view in .. so I will set it aside here. Even so, many philosophers have followed Kim and use the term ‘event’ more generally to cover changes and unchanges such as continuing to be blue (Kim (), pp. –). The stipulation has a further recommendation. Steward has recently argued that states differ from events in being continuants. For instance, the belief that p, or the state of being dilapidated, are wholly present for each moment of their existence and persist through time (Steward (), pp. –). By allowing events to cover changes and unchanges—as indeed Steward does too—we can talk of a kind of entity with temporal parts involving properties that change and those that do not. No questions need to be begged about the proper analysis of states using our vocabulary in this way. While it is true that the extension of our talk of events to unchanges goes against Lombard’s theory that events involve changes in properties possessed by objects over time, I don’t think any harm is done if we think of Lombard’s theory as an account of a potential subcategory of our notion of event (Lombard (), pp. –). Events are particulars but are not continuants. Instead, their existence has a temporal dimension and, just as they have spatial parts, so they have temporal parts. A general term N stands for an event if (i) we can speak of an N, the N, Ns, adjective Ns, and so on; (ii) it makes sense to say that N occurred; (iii) N is derived from verbs such as explosion (from explode), marriage (from marry); and so forth (Bennett (), pp. –). Perfect nominals are plausibly taken to refer to events. To take Bennett’s example, Quisling’s betrayal of Norway, and my retrieval of the golf ball, both pick out events. One temporal part of my retrieval might be the section when I climb the fence, another temporal part would be when I push the thistles aside. Bennett differs with Menzies over whether imperfect nominals—such as Quisling’s betraying of Norway—refer to events. Bennett takes them to refer to states of affairs or facts, Menzies takes them to refer to events broadly conceived (Bennett (), pp. –; Menzies (b), pp. –). Criteria (i) to (iii) don’t provide an obvious reason to suppose that imperfect nominals pick out events but we should be wary of supposing that they refer to facts. Language can be stretched—perhaps by too much philosophy—to allowing a sense to (i) to (iii) with regard to imperfect nominals. Equally, there seem to be cases where there is an event but no perfect nominal to describe it. For example, we talk about the harvesting of crops in

-  --



September but what is the corresponding perfect nominal? If it is suggested that, in this case, the harvesting is the perfect nominal because some of (i) to (iii) apply to it, then the case for rejecting betraying (say) weakens. Finally, as I have already noted, facts are understood in terms of truth-making and, if it turns out that there is no need for such entities, we won’t conclude that sentences containing imperfect nominals are false or truth-valueless. For instance, ‘His getting pneumonia was due in large part to the fact he swam the Channel’ does not lack truth value if there are no facts for ‘his getting pneumonia’ to name but there is an event of the onset of pneumonia. Skirmishing over which phrases pick out events will only take us so far. We should consider the nature of the entities we need to recognize. In the light of our extended talk of events, the following accounts have been suggested. First, events are the exemplification of properties by objects at times (Kim (), pp. –). Second, events are properties of spatiotemporal regions (Lewis (a)). Third, events are property instances (Bennett ()). Each of these allows that events aren’t just those things picked out by perfect nominals. The redness of a particular pillar box is not a perfect nominal but picks out an unchanging event according to any of these theories. This last comment plus the range of theories of events just given makes it only too clear how matters can get bogged down in discussion of particular theories of events, facts, and property instances since, according to some, Kim’s events are not events but facts and, as Bennett acknowledges, Bennett’s events are property instances (e.g. Wilson (), pp. –; Bennett (), pp. –). Both facts and property instances have been taken to be truth-makers. However, as I shall now argue, both Kim’s events and property instances fail to satisfy one of the distinctive requirements on truth-making and this failure is instructive. It shows us how ontology can be distorted by truth-making when, in fact, there is no need for this to happen. Truth-makers are not required.

.. Truth-maker necessitation The standard account of truth-making is given by the truth-maker necessitation principle. (T) T is a truth-maker for the proposition that p iff, metaphysically necessarily, if T exists, then p is true (e.g. Bigelow (), p. , he later adopts something weaker but not so as to touch the point below, p. ; Fox (), p. ; Armstrong (), pp. –). The definition may well need some revision but there is wide agreement that this is roughly right. Certainly, the three standard accounts of truth-makers seek to abide by it: facts or states of affairs; tropes, and Lewis’ particulars qua F. Formulation in terms of metaphysical necessity avoids concern about formulations that appeal to the idea of entailment bearing in mind the entity mentioned in the antecedent is not a proposition. Suppose that you are a modal realist who holds all possible individuals and properties exist. It doesn’t follow that every proposition is true about what is actually the case (Restall (), p. ). Hence (T) should be read, necessarily, if T exists in w, then p is true in w. Suppose that you take propositions to be sets of possible worlds, intuitively, those in which a sentence which expresses the proposition is true. Then (T) should be read as saying that, metaphysically necessarily, if



    

T exists in w, then w is a member of the set of possible worlds in which a sentence that expresses the proposition is true. Not everybody accepts that (T) is true but that is usually because they think that it needs strengthening. Thus, Gonzalo Rodriguez-Pereyra claims that T must be an entity in virtue of which p is true and Greg Restall claims that the connection between T and p must be an entailment of relevance logic (Rodriguez-Pereyra (), p. ; Restall (), p. ). Nevertheless, both would accept, I think, that truth-maker necessitation is a necessary condition upon truth-making. Others reject truth-maker necessitation for negative and general truths but implicitly retain it for other truths because, presumably, it is needed to motivate their talk of facts in the first place (e.g. Pendlebury (); Cameron (), pp. –). Why take the atomic fact O has F rather than O as truth-maker for the proposition that O has F if it is not for the concern that O might not have F in which case the proposition would be false? Truthmaker necessitation as a necessary condition on truth-making is all I need for the argument below. Commitment to the truth-maker necessitation principle has informed theorizing about the nature of truth-makers. Let me give a couple of instances. Proponents of facts or states of affairs as truth-makers take one form of truth-maker to be Fa at t, that is an object, a, having a property F, at time t. In order for this to serve as a truthmaker for the proposition that a is F at t, it is not possible for this fact to fail to involve a, F, and t. Fa at t does not necessitate the truth of the proposition that a is F at t unless, in all worlds in which this fact is present, the proposition is true. If the fact could involve different particulars, properties, or times, this would not follow. Thus Mellor notes that it must have its temporal location essentially in order to serve as a truth-maker for this proposition (Mellor (), p. ). Presumably he would say the same about a and F, as Armstrong does (Armstrong (), pp. –). The same commitment reveals itself in the proponent of a rather different kind of truth-maker. Lewis talks of a particular, a, qua F to pick out a particular counterpart relation, one in which the counterparts to the particular in question always have F. No doubt the same would go for t (Lewis (), pp. –, ). So long as truth-maker theorists are committed to (T) as an account of truthmaking, Kim’s events are not facts because they are not truth-makers. For the basic case, his theory of events is made up of two principal claims. Existence: time t.

Event [x, P, t] exists just in case the substance x has the property P at

Identity: [x, P, t] = [y, Q, t’] iff x = y, P = Q, t = t’ (Kim (a), pp. –; Kim (), pp. –). He contrasts [x, P, t] with taking events to be ordered triples such as since, as we have noted earlier, the ordered triple may exist without x having P at t (e.g. Kim (), p. , also Martin (), p. ). Another proponent of Kim-style events— dubbed by him situations—is Menzies (Menzies (b), pp. –). The crucial point is that Kim does not take the identity claim to imply that events have their objects, properties, or times essentially. He notes that theories of physical object identity do not suppose that the particular spatiotemporal relations that

-  --



distinguish one object from others are essential to it (Kim (), pp. –). Nor should the existence claim be taken to have the implication that the objects, properties, and times of events are essential to them. Instead, the claim is just that, in this world, the event [x, P, t] exists just in case x has P at t. The token event [x, P, t] in other worlds may have different constitutive objects, properties, and times and would, in those worlds, be picked out by [y, Q, t’] (say). As a result, it won’t be true that necessarily, if the event which, actually, is x exemplifying P at t, occurs, the proposition that x has P at t is true. There will be possible worlds in which the same event occurred at a different time or had a different constituent property or a different constituent object. A similar point can apply to the idea that events are property instances. If the identity of property instances is not determined by their objects, then they, and hence events so understood, cannot serve as the truth-makers of propositions such as that expressed by ‘a is F’. I discuss such a view further in ... It is, of course, not the only view of property instances one might adopt. Husserl’s moments are particularized properties ontologically dependent upon the objects of which they are properties (and, presumably, the times at which they are instantiated) (Mulligan et al. (), pp. –). It is on the basis of this understanding of property instances that Kevin Mulligan, Peter Simons, and Barry Smith take them to be truth-makers. The failure to be truth-makers identifies a way in which Kim’s events and property instances (on one understanding) are different from facts. If we must recognize truthmakers though, then this may be a consideration against events or property instances as the proper relata of causation. If we must recognize other entities as truth-makers, why should we, in addition, postulate such entities as events or property instances understood in a way that does not allow them to be truth-makers? However, I shall now argue, as indicated earlier, that there is no need for truth-makers or, more circumspectly, no need based upon the main argument for their existence so far. The standard argument in favour of truth-making runs as follows. ()

p is true in w₁ and false in w₂ (assumption).

() If (), then there is something, call it T, which exists in w₁ and which does not exist in w₂. () It is not the case that, metaphysically necessarily, if T exists in w then p is true in w (assumption). () In w₃, T exists and p is false (assumption). () If (), then there is something, call it C, which exists in w₁ and which does not exist in w₃. () There is a T* (= T + C + whatever other conditions hold in w₁ and fail to hold in other worlds in which p is false) such that, metaphysically necessarily if T* exists, then p is true. Therefore, () Whenever something is true, there must be something in the world that makes it true (in the sense specified by (T)) (Bigelow (), pp. –; Armstrong (), p. ).



    

To see what’s wrong with the argument, it is helpful to consider why Kim-style events fail to be truth-makers. Suppose that p is the proposition that Fido (a particular dog) ran across the yard at time t and that, in w₁, there is a Kim-style event of Fido exemplifying the property of running across the yard at time t. Given that the event is not essentially involving Fido or running across the yard or occurring at time t, then there is a world, w, in which this event takes place and yet the proposition is not true. To fix ideas, suppose that this is because Fido is walking across the yard instead. What is C in this case? It is hard to say. The difference between the worlds is that Fido is running in the first world and walking in the second. But that’s just the difference between the presence of the Kim-style event as it actually occurred and as it counterfactually occurred. There is, at least, one more instance of walking in w₃ and one less running, other things being equal, but this is already covered by the event being a running in one world and a walking in the other. So we have nothing, in addition, to add to w₁ to explain why the proposition that Fido ran across the yard at time t is true. Of course, we could add that there is something in the actual world that is essentially a running of Fido—e.g. a fact about Fido—but this would be questionbegging. We were looking for an argument to justify the claim that there is something that necessitates the truth of the proposition. We have not found it. To be clear why it would be question-begging to appeal to the fact that Fido is running it helps to keep in mind what the argument is meant to do. It is meant to provide a justification for truth-makers, and that means the truth-maker necessitation principle, which is the negation of (). The line of thought is that we must recognize the existence of entities for which truth-maker necessitation is true because there is going to be a difference C, to distinguish between w₁ in which p is true and w₃ in which p is false, in addition to T. This difference, the argument goes, will necessitate the truth of p. Notice the difference between the worlds as a result of which p is true in one and false in another is not one which assumes at this stage that p can only be true in w₁ if something necessitates that it is true in w₁. However, what the point about Kim’s events reveals is that we don’t need there to be something in addition to the event which is Fido’s running in w₁ for the proposition that Fido is running to be true. The world in which Fido is running is false can contain just this very same event, although in that world, the event will be Fido walking. To insist that the entity in w₁ must be an entity which necessitates the truth of the proposition is to take as a premise what was meant to be the conclusion of the argument. An objection already noted against truth-maker necessitation is that it fails to capture the explanatory relationship between the putative truth-maker and what is made true. For instance, if T is truth-maker for P, then by truth-maker necessitation, T and C is (Rodriguez-Pereyra (), pp. –, –). Nevertheless, it is assumed that a necessary condition for this explanatory relationship is that truth-maker necessitation is true. It is argued that the truth-maker for a proposition is the entity in virtue of which the proposition is true and this entity, although it stands in a more intimate relationship to the truth of the proposition than simply necessitation, does, at least, necessitate its truth. The example of Kim’s events shows this to be a mistake. Fido running across the yard at time t is true in virtue of Fido exemplifying the property of running across the yard at time t. We are not being given a much more extensive particular

-  --



like the whole world, or Fido with all his properties, or the like, as that in virtue of which the proposition is true. Nevertheless, the Kim-style event does not necessitate the truth of the proposition. One response to this line of argument is to say that I have not shown that there is no need for truth-makers. All that has been established is that truth-maker necessitation is false. Instead, a non-necessitating ‘in virtue of ’ relation is the truth-making relation. We need not quibble about names. The relevant points are these. First, for this weaker relation, there is no need to postulate the existence of entities with the modal properties of facts. Second, appeal to necessitation was thought to be required to explain how a certain item of reality made a proposition true. Kim-style events don’t make a proposition true, rather the truth of the proposition is based on the occurrence of Kim-style events given their particular character in our world. Sider’s metaphysical truth conditions are another example of truth-bases (Sider (), pp. –). In a slogan, there is no truth-making only truth-basing. The slogan may suggest a revitalized version of this first response. Consider the claim that Fido is running across the yard. If there is only a truth-base and no truthmaker, then doesn’t it follow that, however the world is, the claim might still be false? Truth does not supervene upon being. This would be a mistake. The claim that truth supervenes upon being is weaker than the claim that there are truth-makers for propositions such as Fido is running across the yard. The claim that truth supervenes upon being is Two possible worlds exactly alike in terms of the objects which exist, and properties and relations that hold between them are exactly alike in terms of the propositions that hold and fail to hold (e.g. Merricks (), p. ). This claim does not entail that, for particular propositions, there are entities with the essential properties required for truth-maker necessitation to hold (Merricks (), p. ). It has also been observed that such a doctrine is inadequate as a formulation of truth’s dependency on being (e.g. Merricks (), pp. –). For our present purposes, though, this is fine. The concern was that recognition of only truth-bases undermined the claim that truth supervenes upon being, which, if we endorsed it, would reintroduce truth-makers. We have seen that this is not so. If we want to add the idea that truth is dependent on being, then we can claim that propositions hold in virtue of worldly entities in the way I indicated above. This does not get us to truth-maker necessitation. Facts have been described as partly linguistic—items fixed up to play a certain linguistic role: truth-making (e.g. Strawson (), pp. –). We can now see that this charge is accurate. We don’t have to suppose that this involves taking facts to have a structure or constituents that mirror the structure of sentences or the propositions they express. Some proponents of facts do not go that far (Pendlebury (), pp. –). Facts, nevertheless, are entities postulated to have essential properties that enable them to necessitate the truth of propositions expressed by language. There is no need to postulate such entities in order to capture the idea that the truth of what we express is based in reality. This brings me to a second line of response to this argument. It might be said that the argument is only as strong as the case for believing in the existence of Kim-style events with the modal properties they have. However, talk of Kim-style events



    

was only to fix ideas. The important point is this. It is undeniable that there are objects, whether or not they may be reduced to something else, possessing properties at times. These are sufficient to play the truth-basing role and there is no need for, in addition, truth-makers, entities with the modal properties that make truth-maker necessitation true. So there is no reason to suppose that we must start with an ontology that takes truth-making as fundamental and, hence, start with a prima facie case for supposing that causation is a relation between truth-makers. Instead, I shall develop, in . a theory of events—as candidate triggering causes—and then consider whether causation can be properly thought to hold between them. Before that, there is one more argument to consider that purports to favour facts as the relata of causation.

.. Disjunctive causes: the return of facts? Sartorio has argued that we must recognize disjunctive causes and that, since the idea of disjunctive events is of doubtful coherence, we must recognize that causation involves disjunctive facts, and therefore facts. If the argument were successful, we would have an internal argument in favour of the recognition of facts, and fact causation. She invites us to consider the following case, one again involving philosophers’ favourite means of travel: trains. Suppose a Flipper switches a train down a branch track that reconnects with the main track running over a victim tied up on the rails. The main track between the switch and the rejoining point is disconnected. However, somebody, the Reconnector, connects up the main track so that, had the train gone down the track, it would have arrived to run over the victim. Sartorio’s argument then proceeds as follows. () The Flipper’s action is not a cause of the death (because the main track was reconnected). () The Reconnecter’s action is not a cause of the death (because the train didn’t go down that track). () The Flipper and Reconnecter together caused the victim’s death (because if neither had done what they did, then the train would have stayed on the main track and been derailed). () If the Flipper and Reconnecter together caused the death (but their individual actions did not) then either the conjunction of their two actions was the cause or the disjunction of their two actions was the cause. () The conjunction of their two actions was not the cause of the victim’s death. Therefore, () The disjunction of their actions was a cause of the victim’s death. () There are no disjunctive events. Therefore, () Disjunctive facts are causes (Sartorio (b), pp. , ).

    



Sartorio’s reasons for taking the cause to be disjunctive rather than conjunctive are, first, that the death of the victim is counterfactually dependent upon the disjunction of the actions and not the conjunction and, second, that it is implausible to suppose that a cause is conjunctive if the conjuncts fail to be causes. Although these reasons aren’t conclusive, they make the case for disjunctive causes over conjunctive causes plausible. The argument has the following problems, however. First, the claim that the Flipper’s action is not a cause of the death relies upon the causes as differencemakers principle that we found reason to reject in .. (Sartorio (b), pp. –). Our analysis would have the result that the Flipper’s P action is a cause of death (putting the reconnection of the main line track into . The verdict is plausible given that the case has the structure of a case of pre-emption and the train being switched down the branch line was part of the causal process leading to the victim’s death. Second, while there may be disjunctive facts in the sense of disjunctive true propositions, in the metaphysically loaded sense of fact with which we are working in this chapter, the existence of disjunctive facts is no more plausible than the existence of disjunctive events. Hence, even if Sartorio were right that we had to recognize disjunctive causes, there would be no reason to suppose that these disjunctive causes should be facts.

. Towards a Theory of Events Kim’s view of events is derived from the natural observation that when an event occurs, it is very often the case that it involves an object, or objects, having certain properties at certain times. Whether this is invariably the case depends on how liberal one is about objects, for example, does the atmospheric conditions in which lightning arises count as an object, and so forth (for other examples, Brand (), p. ). However, I want to set that issue aside for a range of concerns that arise from thinking about the duration of events. They arise when we focus on Kim’s move from the natural observation to the claim that events have constituent objects, properties, and times. I’ll return to the question of whether events need always involve objects at the end and show how the theory developed might respond to this possibility. The first point to notice is that it would be a mistake to build the time of instantiation into the constitutive property of an event. An object has the property of burning-at-t throughout its existence. This is not what we would say about the event (Bennett (), p. ). We would say it occurred for the duration of the burning and ceased when the fire was put out. By having the time as a separate constituent, Kim’s account of events avoids this difficulty. However, talk of constitutive objects is also problematic. In the case of the dog running, the dog persists for longer than it runs. If the dog is a constituent object of the event of the dog running, then this seems to give the event a longer temporal extent than it is supposed to have. In the case of those objects that are physical continuants, their spatial extent is determined by their spatial parts. Thus the spatial extent of my body is determined,



    

in part, by the fact it includes my hand as a spatial part. By contrast, although such objects have temporal extents—the duration of their existence—their temporal extent is not determined by their temporal parts because they have no temporal parts. If they had temporal parts, then an object could not be wholly present at a time. Instead, the temporal extent of such an object is determined by the period of time for which the object is wholly present. Suppose my hand survives the destruction of the rest of my body, for a while. Its continued existence does not add to the extent of the temporal existence of my body. Events are different from objects in having temporal parts. They are not wholly present at a time if their temporal extent is greater than that time. Only part of them is present. Their temporal duration is like the spatial extent of objects. The time they occupy is fixed by the existence of, at least one of, their parts. Kim’s existence condition for events is apt to obscure recognition of this point. It states that Event [x, P, t] exists just in case the object x has the property P at time t. This gives the conditions that must hold for the event to exist in a world. However, it does not fix the temporal extent of their existence. If an object is a constituent of an event, then the extent of the object will settle the extent of the event. Since events have temporal parts, they will last as long as their constituents do, and that includes their constituent objects. However, this gets the extent of an event wrong. Suppose we consider events like an earthquake, a war, a subject playing with a yo-yo, and so on. We don’t think the earthquake persists long after the tremors, the war long after the battles with people going about their lives, or the subject playing with a yo-yo lasting while the subject is sleeping. We can, of course, stipulate that the temporal duration of an event’s happening is when all three constituents of an event are present, the object, property, and time, but this doesn’t deal with the point that the temporal extent of an event may exceed this period. Moreover, since events are supposed to be happenings, the need for such stipulation shows that Kim’s theory doesn’t get the constituents of events right. The matter is not resolved by supposing that the object is a temporary constituent of the event for the duration of its happening. That doesn’t make it cease to have the temporal extent of the life of the object. It just makes its possession of this greater temporal extent a temporary matter. The difficulty is not a reason to think of events as instantiations of properties at spatial regions either. It is plausible that regions in space persist through time as well. In which case, if a region of space is a constituent of the event, then the temporal duration of the event will be the spatial region after the event has ended. Bennett’s account avoids the difficulty in its stated form but has a difficulty of its own. For Bennett, there is no constituent object or spatial region. Instead, events are instantiations of properties that occur in objects or regions at times (Bennett (), pp. , , –). It has the recommendation of capturing the thought that events occur at places and times rather than having them as a constituent. The difficulty, though, is that, if property instances are continuants, we lose the idea that events can be triggering causes. It is not the property instance that triggers a particular effect but rather the occurrence of a property instance at a particular time and place. So, even if

    



we pursue Bennett’s line, we would still be left with an examination of the nature of triggering causes. It is better to retain the idea that events may be triggering causes and explain our tendency to talk of events as occurring by saying that we have in mind their constitutive properties. I should note that Bennett offers another reason for preferring his approach to events based upon their individuation. I discuss this in the next part of the chapter. So what’s the alternative? It is to deny that the object, x, but rather the entity x-at-t is a constituent of an event. x-at-t is a certain duration of an object: a slice of its history. The formulation is meant to be neutral over whether objects are continuants or made up of temporal parts or stages and their counterparts (Merricks (); Lewis (c), pp. –; Sider (); Hawley (), ch. ). If objects aren’t continuants, then x-at-t can be taken to be a temporal part of an object. If objects are continuants, then x-at-t is not a part of the object but nor is the object part of it. Instead, x-at-t is part of x’s persistence through time (or s’s persistence through time if a liberal understanding of objects is eschewed and events are taken to involve spatial regions instead to avoid the attendant problems). Let us call x-at-t a temporally limited particular. Then a neutral expression of my theory of events is that they are the exemplification of properties by temporally limited particulars. The fact that these temporally limited particulars may themselves be either events (if objects are not continuants but have temporal parts) or sui generis durations of continuants (if not) suggests that the prospects of reducing events to objects, properties, and times are slim. The proposal I have just made operates at a different level to Lewis’ theory of events as properties of spatiotemporal regions. Suppose that the particular event of the dog running may, in another possible world, be a dog walking instead. In other words, being a running is not essential to the event. For Lewis, properties are classes and, corresponding to each event, there is a class of spatiotemporal regions—one per world—in which that event is said to occur (Lewis (a), pp. –). In the dog case, this will include regions in which the dog is walking and regions in which it is running. So Lewis’ property of a spatiotemporal region will not be the property of being a running. Rather it will be a property that, in different worlds, allows these different regions to be members of it. As a result, Lewis’ events are cross-world entities. He allows that Kim-style events and, indeed, implicitly my own, may appropriately describe what is occurring in a particular spatiotemporal region which is a member of his event properties but eschews them in favour of something which better expresses events’ modal performance. There is thus no reason to reject or select Lewis’ view of events on the basis of what has been argued here. However, there will be a reason to reject Lewis’ position if events may have different intrinsic properties accidentally. This would make them prey to the problem of accidental intrinsics. Lewis argued that, if objects were cross-world entities, then we could only avoid attributing contradictory accidental intrinsic properties to these objects by, counterintuitively, making these intrinsic properties relations to worlds (Lewis (c), pp. –). If events are cross-world entities with different intrinsic properties in different worlds, the same reasoning would apply. Of course, some other treatment of the problem of accidental intrinsics may prove successful and, in that case, it would be open to us to take both objects and events to be cross-world



    

individuals. My argument is just for parity of treatment. As we shall see in the next part of the chapter, it is plausible that events are coarsely individuated. This makes it more plausible that some of an event’s intrinsic properties will be accidental. So, I suggest that, subject to the qualification just made, it is better to think of events as intra-world entities with counterparts in other worlds. However, before I come to the more general question of how events are individuated, .. will focus on whether, contrary to Kim, events have essential properties due to the role they play in causation. I shall argue otherwise.

.. Causation and the essential properties of events According to many, events need to have the right essential properties in order for a counterfactual theory of causation to work. Consider events with too rich an essence and you lose counterfactual dependence, consider events with too poor an essence and you do so too. Here is a familiar case. (F) (F)

If John had not greeted Fred, Fred would not have responded. If John had not greeted Fred loudly, Fred would not have responded.

The intuitive truth of (F) and falsity of (F) is taken to suggest that the events specified in the antecedent are distinct, the descriptions corresponding to distinct essential properties, because they seem to have different causal powers. The reasoning goes like this. If John’s loud greeting was essentially a loud greeting, then the closest possible world in which it is absent may be one in which John greeted Fred (although not loudly). In which case, Fred would still have responded. (F) is false. Whereas, if John hadn’t greeted Fred at all, in the closest possible world, Fred would not have responded. (F) is true. On the other hand, if Fred responding was not essentially a response, then the event that is Fred’s response might have occurred in the absence of John’s greeting. It is just that in those circumstances it would not have been a response. So either counterfactual would be false for a different reason. Hence we must not give the event of Fred responding too poor an essence. Counterfactual theories appealing to counterfactuals like the one just given must get the essences of events just right (see e.g. Lewis (a), pp. –). Regarding the first point, my analysis of causation allows that events may have as rich an essence as we please. Any event which is distinct from an event with a rich essence, and which would cause the event P mentioned in the consequent in counterfactual circumstances, can be put in . Thus, the counterfactual we would be considering is: if it is neither the case that John had greeted Fred loudly nor that he greeted him at all, then Fred would not have responded. There is no need to recognize a distinction between ‘John greeting Fred’ and ‘John greeting Fred loudly’. My analysis recognizes that the latter can be a cause even if it has redundant features, like being a loud greeting of Fred. Regarding the second point, requiring that the event mentioned in the consequent could not have certain features is overkill. We don’t need to suppose that Fred’s response could not have failed to be a response but just that it would not have failed to be a response. In the closest worlds in which John’s greeting did not occur at all, it is not the case that the event picked out in the consequent would still have been present, but not as a response. It would take a far more distant world for that to happen.

    



As a result, it is a mistake to appeal to essential properties to seek to capture the idea that causes must be required for their effects (e.g. Yablo (a), pp. –). Just as my analysis can accommodate redundant causation when there are actually two, or more, competitor causal chains—as in the case of overdetermination and pre-emption—so it can also accommodate cases in which, although there are no actual competitors, there will be counterfactual competitor causal chains. It was this that motivated attributing particular essential properties to an event and it is this motivation that my analysis vitiates. By showing that cases of counterfactual competition are a natural extension of our verdicts for actual competition, we have a line of resistance to those who insist that events like John greeting Fred loudly could not have caused Fred’s response. We may just observe that, even if, if John hadn’t greeted Fred loudly, he still might have greeted Fred, it doesn’t follow that this token loud greeting failed to be a cause of Fred’s response. According to Yablo, appeal to essential properties of events helps us to articulate another constraint on causes, namely that they must be adequate for the effect. Suppose we consider the following two events: the bolts of a bridge snapping and the bolts of a bridge snapping suddenly. In the actual world, both events have the property of the snapping being sudden. The difference is that the suddenness is an essential property of the second event whereas it is not of the first. This is said to correspond to the intuition that it is the second event which is a cause of the bridge’s collapse and not the first since, if the collapse had not been sudden, support pillars could have been brought in to stop the bridge from collapsing. Thus Yablo concludes that the causally relevant properties of an event must be essential to it in order for it to be a cause (Yablo (a), pp. –). Yablo’s articulation of what we have in mind, in distinguishing between the bolts of a bridge snapping, and them snapping suddenly, as a cause of the bridge’s collapse, is questionable. For one thing, the bolts of the bridge snapping is adequate in circumstances in which no support pillars are added. Whether you adopt a subtraction or fixing treatment of the redundancy of causation, you will obtain this verdict. In the case of the fixing account, which Yablo endorses, you will just keep fixed there being P no support pillars brought in. My preferred analysis will allow that you can put in support pillars being brought in and the causal chain between the snapping and the bridge collapsing will be complete. Second, by anybody’s lights, causes are only adequate in the circumstances. This raises two issues. First, the suddenness of the bolts snapping is a second-order property of the bolts snapping. It is unclear why this second-order property should not count as part of the circumstances in which the bolts snap. In which case, the bolt snapping is a cause. Second, suppose it is argued that the proper way to think of the situation is not to suppose that the bolt snapping has a second-order property of being sudden but rather there is the instantiation of the determinate property of being a sudden bolt snapping of which a bolt snapping is a determinable. As we shall see in Chapter , and Yablo agrees, determinable properties inherit the efficacy of their determinates (e.g. Yablo (b)). Without a defence of the claim that the sudden snapping can neither be thought of as part of the causal circumstances nor the determinate of the determinable of bolt snapping, there is no basis for appeal to distinguishing essential properties to explain why sudden bolt snappings are causes



    

and bolt snappings are not. Indeed, even Yablo concedes that the latter have causal influence (Yablo (b), p. ). Of course, the rejection of certain properties as essential to events may meet with resistance. For instance, it might just be denied that the event that is a running of a dog across the yard is (has a counterpart which is) a walking in other worlds. My position does not depend upon fighting intuitions of this kind. Recognition that events may have some essential properties does not undermine the following two points. First, whether or not events do have essential properties, they don’t need to have them in order to play their appropriate role in causal statements. The analysis of causation will do that. Second, even if events do have essential properties, there is no reason to suppose that there will be enough events with the full range of essential properties to justify calling them truth-makers and, hence, under some analyses such as a version of Kim’s, facts.

.. An intermediate approach to event individuation I have argued that events are exemplifications of properties by temporally limited particulars. This leaves open a wide variety of different approaches to their individuation or identity conditions (I do not distinguish). To fix ideas, let me just note two things at the outset. First, as I remarked earlier, the identity conditions of a certain kind of entity need not cite the essential properties of individuals that fall under that kind. In the limiting case, they need not even be properties that all members of that kind must possess, for example, sets are individuated by their members but the null set has no members (Brand (), pp. –). Second, the identity of all entities is governed by Leibniz’s law: the indiscernibility of identicals. ðLLÞ ðxÞðyÞðFÞððx ¼ yÞ ⊃ Fx $ FyÞ: The attempt to provide identity conditions for entities focuses on the reverse direction: the circumstances under which the sharing of properties makes two entities identical. Of course, if two entities are identical if they share properties F, G, and H, then they will share all the other properties they have too. The primary purpose of providing a more specific account of the identity conditions of entities is to provide an insight into their nature by showing how their identity can be reduced to, by being captured in terms of, their possession of a more limited range of properties. It is that which I seek to provide below. Then in the section to follow that, I will discuss why the favoured approach has been rejected. The particular concern is that my approach fails to cut things finely enough to capture the distinct causal claims that we are inclined to make. My response to this is that the objectors have failed to distinguish between event causation and property causation, the latter involving a kind of generality I seek to make clear in Chapter . One suggestion, then, would be that two events are identical if they have the same temporally limited particular (Lemmon (), pp. –; Quine (); Davidson (), pp. – for what, in effect, are similar theories adjusted to my framework). This would be a particularly coarse way of individuating events because it would mean that they involve all the properties exemplified by a temporally limited particular. A familiar case shows why this seems implausible. Suppose that a metal

    



ball both rotates in a certain time period and, unrelatedly, becomes warmer. These distinct events have distinct causal consequences. Nevertheless they have the same spatiotemporal position (Davidson (b), pp. –). The counterexample led Donald Davidson to flirt with the idea that we should distinguish events by their causes and effects. The suggestion faces at least two difficulties. First, there seem to be counterexamples to it. For instance, suppose we have the following set-up. b

a

d

c

Figure . There are no intermediate events between a, b, c, d. There are no other causal relations in which these events stand either. In which case, b and c have the same causes and the same effects but are intuitively distinct events (Brand (), p. ). Second, for two events to stand in distinct causal relations, the entities with which they are causally related must be distinct. If these entities are also events and if none of them are distinguishable in any other way than by standing in distinct causal relations, then the account relies upon what it is meant to supply (Lowe (a), pp. –), (b), p.  for relevant discussion). An answer to this second objection might take the same form as the one later discussed for the powers network approach to properties (see ..). I discuss the general issues there. It would clearly be desirable to have an independent characterization of the nature of the events to correspond to the causal differences to which Davidson adverts. One possible development of my approach is to cut things as fine-grained as Kim. In which case, the identity conditions for my events would be x-at-t having P is identical with y-at-t’ having Q iff x-at-t = y-at-t’ and P = Q. This is to capture the fact that, say, we are apt to hear the first of (S) (S)

Socrates drinking hemlock caused his death, Socrates guzzling hemlock caused his death,

as true and the second false. Given that causal contexts are extensional and the phrases flanking the ‘caused’ meant to be referential, we only get distinct truth values for (S) and (S) if ‘Socrates drinking hemlock’ does not refer to the same event as ‘Socrates guzzling hemlock’. Yet Kim’s approach is faced with a problem that is reproduced for this version of my own proposal. The event of Socrates drinking hemlock has the property of being a guzzling and the event of Socrates guzzling hemlock has



    

the property of being a drinking. On what grounds should we say that one is, and one is not, a cause of the effect given that they share all the relevant properties? Kim’s answer was that while the events might have possessed these respective properties, they weren’t the constitutive properties of the event (Kim (), pp. –). Kim provided no further characterization of what ‘constitutive’ amounted to here and why, more importantly, it made a causal difference. He just noted that they weren’t to be taken to be the events’ essential properties. As we saw in .., Yablo departed from Kim at this point, but the departure was unmotivated. Call this the Possesses the Properties Anyway problem. In fact, it applies to any proposal that gives to an event more constituents than simply the property exemplified. Let’s go back to Davidson’s putative counterexample. If the event is the temporally limited particular involving the persistence of the ball, then this temporally limited particular will have the property of warming up as well. So, contrary to what we thought, the event of the ball moving does cause things that we would naturally attribute to the ball warming. In brief, fine-grained identifications of entities to stand in causal relations don’t work if you allow that the identified entities possess other properties to which the fine-grained identification does not advert. An entity is efficacious in virtue of any of the properties it possesses. This verdict is moderated if we see the appeal to property exemplified as placing a similar restricting role upon a particular that temporal limitation did. Events are temporally limited, property limited particulars. That does not mean that the more extensive entity I just identified involving no limitation of properties fails to be an event. These events are temporally limited particulars exemplifying all the properties of the temporally limited particulars. It is simply that we identify events that are more limited than that. These events don’t possess the properties that are not implied by the limitation any more than the events contain portions of a particular’s life outside of the temporal limitation. However, we can’t effect any limitation we please. For example, suppose I specify an event as ‘x being red’. It seems implausible to say that, just by such a specification, I have managed to pick out an event which is a being red but which does not have, as one of its properties, being coloured, or an object having a certain surface to be coloured. The events we identify must have a certain integration. They are not the fix-ups of our talk. The intermediate position I favour is that events are the exemplifications of all those properties required for the exemplification of maximally determinate properties. Suppose that we identify an event as the death or the explosion or the rotation of the ball. Then the event involves all the properties that were actually required for the event to be a death or an explosion or whatever. Moreover, it also involves all the properties which characterize that event more determinately, for instance, a death through heart attack, a chemical explosion, a rotation at such and such a turning speed. It might seem as if we could introduce even greater determinacy by appealing to conjunctions of properties with conjuncts specifying other properties also instantiated in the actual circumstances. Intuitively, though, the determinacy they offer regarding our target property—given by the initial description of the event as an exemplification of F—is spurious. One way to characterize this is to say that no conjunction of properties F and G is more determinate than F if it contains conjuncts that neither necessitate F nor were required for F to be instantiated (for a similar

    



related proposal, Ehring (), p. ). I shall discuss this kind of necessitation between properties and what is involved in the instantiation of one property requiring the instantiation of another in Chapters  and . My hope is that the discussion successfully articulates what are, independently, plausible features to which to appeal in this context. The crucial point is that these features are not to be understood in causal terms. The necessitation I have in mind is not causal necessitation. Although I shall spend some time articulating the framework in which we can understand this coarser notion of an event in Chapters  and , it is important to appreciate that it is not an essential part of my position regarding the proper analysis of causation. As I have remarked earlier, my account can accommodate a number of different views about the nature of causal relata merely serving to articulate what is involved in their efficacy if they are rightly thought of as causal relata. Instead, my reason for advancing the current proposal is that if I am right that we don’t need to fix up our event talk to make a theory of causation work, then it is worth considering what might have independent plausibility as an account of events that we naturally take ourselves to identify. My thought is that when we identify an event as Socrates drinking hemlock—say—we are providing a property specification that aids the auditor in thinking about an entity with two kinds of limitation. First, there is the temporal limitation determined by the period of time, partly determined by context, in which Socrates is drinking. Second, there is the property limitation. If the property specified is maximally determinate, then the properties are limited to the bundle of properties necessitated by the maximally determinate property. If the property specified is a determinable, then the properties are limited to the bundle of properties that, in the context, were required for the determinable to be instantiated. My two mentions of context here are simply to reflect the fact that, for example, it is too much to expect a little phrase like ‘Socrates drinking the wine’ in ‘Socrates drinking the wine caused him to be more loquacious’ to by itself pick out a particular event of Socrates drinking wine. It is plausible that the proposal can avoid Davidson’s original counterexample relating to the rotating and warming ball because these two characterizations pick out properties neither of which is required for the instantiation of the other. By contrast, a consequence of my proposal is that I must accept that ‘Socrates guzzling hemlock caused his death’ is true, on the assumption that guzzling is a more determinate property over which ‘Socrates is drinking’ is a determinable. As a statement about causation, this seems to me defensible. It is very natural to say that, although it didn’t matter whether Socrates guzzled hemlock rather than drank it, guzzling that poison did cause his death. Equally, to mention an earlier case, it seemed that John’s loud greeting caused Fred’s response although it did not particularly matter it was loud. The full defence of this point, and its relationship to a distinction between causation and explanation, will occur in Chapter . To give a preliminary justification, though, consider the following comparison. Suppose that either Emma or Will could perform a certain task that needs to be done. In fact, it is Emma who does it. Then it is natural to say that it doesn’t matter whether it was Emma rather than Will who did it. However, we would not deny that Emma’s activity caused the task to be



    

completed. Equally, a simple drinking rather than a guzzling would have sufficed for Socrates’ death. But, in fact, the guzzling was the cause. The points just made are recognized by Yablo when he distinguishes between world-driven and effect-driven causes. When causes are world-driven, we characterize them in terms of what actually went on. When they are effect-driven, we try to characterize what was essentially involved in a causal relationship, and what was redundant (Yablo (a), pp. –). The distinction is a good one but I question whether it should be played out in the characterization of events. Instead, they are better seen within the context of property causation and the identification of various explanatory virtues that might mark out a particular causal explanation. Let me illustrate the issue behind the last remark a little more fully. Consider the following: (S)

Socrates’ poor table manners caused his drinking of the hemlock.

The sentence seems straightforwardly false. As things were, how could one of the causes of Socrates’ drinking of the hemlock be his poor table manners? It is certainly not a triggering cause. But if you start thinking about the particular event that was his drinking of the hemlock—an event of guzzling some refreshment—then our verdict wavers. ‘That drinking of the hemlock’, one might say, ‘was certainly caused by his poor table manners’. We don’t really want to distinguish between the events and say there were two things going on there, a drinking and a guzzling, and Socrates’ poor table manners caused one rather than the other. Of course, we can be talked into it for the reasons identified above. But in doing so, we are arriving at something no more natural than endorsing (S) is natural. When asked to focus on the particular event, we are inclined to say ‘OK, it was a cause of it being a guzzling but not a cause of it being a drinking’. In making this manoeuvre, we have moved to the issue of property causation rather than event causation. The need to make a distinction of this kind has led others, for example Mellor, in a different direction: distinguishing between causing something to exist and affecting it (Mellor (), pp. –). He would say that being a drinking is an essential property of the effect whereas being a guzzling is not. Therefore, it cannot be poor table manners but rather Socrates’ acceptance of the laws of Athens that caused Socrates to drink the hemlock. Nevertheless, his poor table manners affected the particular event by causing a property of it, namely its guzzling. I don’t deny that there is this distinction to make if events have defensible essential properties. However, I do not take the distinction to be a fundamental one. We can reproduce the distinctions that we need anyway by talking of property causation in the sense I lay out in Chapter .

.. Emphasis and the relata of causation The phenomenon of emphasis has tempted philosophers to discriminate causes more finely than the account of the individuation of events I have provided. Indeed, it is cited by Kim in favour of his own particularly fine-grained analysis of events. Consider the following:

    



(S) Socrates drinking hemlock at dusk caused his death. (S) Socrates drinking hemlock at dusk caused his death. (S) Socrates drinking hemlock at dusk caused his death. The italics are taken to emphasize what is causally responsible for the death of Socrates. Thus, (S) seems true and (S) and (S) false. According to Kim, although it might superficially look as if all of these statements refer to the event of Socrates exemplifying the property of drinking hemlock at dusk, in fact three distinct events are being identified: Socrates drinking something at dusk, Socrates drinking hemlock, Socrates doing something at dusk (Kim (), pp. –; Menzies (b), pp. –). This is a puzzling position. One is apt to wonder what the rest of the unemphasized bits of ‘Socrates drinking hemlock at dusk’ are doing if they are not contributing to referring to a particular event, the one, as it were that the totally unemphasized phrase may be taken to pick out. This point prima facie favours those who take emphasis or stress to be explained by the fact that causation is a context-sensitive contrastive phenomenon (e.g. Hitchcock (a), (c), pp. –; Menzies (), pp. –). The case of Socrates’ unfortunate episode of drinking would be understood in the following fashion. (SC) Socrates drinking rather than taking hemlock at dusk in some other fashion caused his death. (SC)

Socrates drinking hemlock rather than something else caused his death.

(SC) Socrates drinking hemlock at dusk rather than at some other time caused his death. However, an adjustment to the railway tracks case we discussed earlier shows that the contrastive approach fails to undermine the case for individuating events finely to accommodate the phenomena of emphasis (as proposed by Menzies (), pp. –). In the original case, there were three tracks (local, express, and broken) and the train avoided disaster, and arrived safely at the station, by going down the local line at the points. Suppose that there are only two tracks: the express track is, in fact, the broken track. In that case, (R) The points getting set to local rather than broken track caused the passengers to arrive at the station, (R) The points getting set to local rather than express track caused the passengers to arrive at the station, would express exactly the same contrast on the assumption that events aren’t individuated finely. Yet people will still be inclined to find (R) true and (R) false. Of course, when they are reminded that the tracks are identical, then they may well say that both are true. But that kind of move will apply as much to cases used to motivate a finer individuation of events. So the contrastive approach can’t claim to respect the phenomenon and provide an alternative to adopting a finer individuation of events. Emphasis phenomena can also occur in explicitly contrastive causal statements. For example. Compare



    

(R) The train going down the local rather than the broken express track caused the passengers to arrive at the station. (R) The train going down the local rather than the broken express track caused the passengers to arrive at the station. We are inclined to hear (R) as true whereas (R) as false, or at least not obviously true, having in mind circumstances in which the speed of travel might have affected the derailment. It is quite unclear how this can be rephrased in an intelligible way using a further contrast. So there is no independent support for the contrastive approach to causation to be derived from emphasis. If the phenomena of emphasis does not favour a finer-grained individuation of events, or provide support for contrastive approaches, then it seems to favour the recognition of a second relata of causation. It is common ground amongst those who deny that the non-contrastive causal statements about Socrates pick out different events that they claim that different properties are efficacious or causally relevant. For instance, Fred Dretske claims that the statements pick out different event allomorphs, understood to be events possessing properties. He couples this with the claim that the events themselves are not causes. This would seem to have the implication that ordinary (unemphasized) statements of event causation are false (Dretske (b), pp. –). For instance, Dretske denies that S’s losing his wallet in the restaurant caused him to be suspicious. It was S losing his wallet at the time he did (just before the bill came) which caused him to be suspicious. However, this additional claim seems unnecessary. It is not that S losing the wallet failed to cause Dretske to be suspicious. It is rather that a particular feature of its loss caused him to be suspicious: the time. That suggests that the right thing to say is that the event is efficacious in virtue of its temporal property. Indeed, even this is an overstatement of the position. It is not simply the temporal property in virtue of which the event is efficacious. The event does have to be a wallet-losing in order for the temporal property to have the significance it does. Some argue that, strictly speaking, causal statements with emphasis are neutral over whether the events they seem to concern are efficacious. These causal statements just highlight efficacious properties (Sanford (a), pp. , –). However, there is no reason to deny that such causal statements still concern the entities that unemphasized causal statements do. If Socrates drinking hemlock at dusk describes an event, then so does Socrates drinking hemlock at dusk. Emphasis is used to make a claim about a particular feature of the event in addition to, rather than instead of, a claim about the efficacy of the event itself. The point is reinforced by the case of the lost wallet. The highlighted temporal property is only efficacious given that the event is a wallet losing. This brings the position being developed here very close to Cindy Stern’s position. Shorn of her technical presentation, her claim is that causal statements involving emphasis of F should be read as having the following form. c caused e and c’s having F is causally relevant to c’s causing e (Stern (), p. ). Stern says that c’s having F is a state of affairs or fact. This is a mistake for two reasons. First, highlighting or emphasis can apply as much to facts as to events. We

 



can say that it was the fact that Socrates drank hemlock at dusk rather than the fact that he drank hemlock at dusk that did for him. We are highlighting an aspect of a fact, and not a fact, in saying this and we need an account that is applicable to this as well. Second, there is no reason to suppose that c’s having F must involve having F essentially as we have seen facts are required to do to play their truth-making role. Instead, when we say that Socrates’ drinking hemlock at dusk was a cause of his death we are claiming that a particular event, Socrates drinking hemlock at dusk, was a cause of his death, the property of drinking hemlock was a cause of his death, that Socrates drinking hemlock at dusk possessed the property, and that the first causal relationship between the events held partly in virtue of the second causal relationship between a property and a death. Thus my favoured formulation, in brief, is c caused e partly in virtue of Fc causing e where Fc picks out a property possessed by c. An important feature of the proposal is the appeal to property causation. This is not merely to be contrasted with event or fact causation but also with property instance causation. Properties do not cause things simply if one of their instances do. Suppose mental properties supervene upon physical properties. In that case, aside from a successful development of trope metaphysics, it is plausible that instances of mental properties will be instances of physical properties (see ..). Some claim that, in spite of this, it would be false to say that, for instance, S’s fidgeting was caused by instances of physical properties in his or her brain, in virtue of those instances being instances of mental properties, for example, that of anxiety. Mental properties are thought to be inefficacious because, if physicalism is true, it is urged, physical properties do all the work. I do not endorse such a view myself but the issue is not whether or not it is true but rather whether somebody could adopt such a position if instances of mental properties are instances of physical properties. Understand causal statements with emphasis in terms of an appeal simply to property instance causation and the answer seems to be no. Yet, while the denial of efficacy to mental properties is mistaken, it is not incoherent. In Chapter , I will focus on what more is required for property causation and explain the significance of it for the phenomenon of emphasis. In brief, my conclusion will be that emphasis serves to pick out property causes that display at least one of two explanatory virtues: precision or location in a causal network.

. Concluding Remarks We have seen that continuants are ill-suited to play the role of a triggering cause. To explain why an effect occurred at the time it did, we need a temporally limited particular. Property limitation of the particular adds, to this picture, further specification of what was doing the causal work. These entities are events. Their general form is x-at-t having P. We set aside the question of how to describe events that failed to have an object involved, a candidate case being a flash of lightening. There are two alternatives. If we are liberal about the notion of objects, and the event in question is a spatiotemporal event as, plausibly, cases of causation will all involve, then x can be taken to be a spatial region limited to a particular time. No adjustment to the



    

formulation is required. Alternatively, if non-spatiotemporal efficacious events are allowed, then the temporal limitation will relate to the instantiation of the property. Thus, the form will be the instantiation-of-P-at-t. We argued that there are no grounds for endorsing facts to be drawn from truthmaking. Considerations internal to the understanding of causation—appealing to emphasis or the need for disjunctive causes—did not support recognizing fact causation either. As I noted at the outset, though, fact causation is compatible with my account. It is just that my account undermines the case for it. Opposition to events standardly utilizes facts to play their role. My rejection of the argument in favour of truth-making together with the observations about the lack of any need to attribute essential properties to events, and how individuation of facts differs from that of events, constitutes my defence of the category of events against sceptics, given that events are needed as triggers in causation (e.g. Horgan (); Melia ()). Aside from the case of agent causation, events may characterize any element in a causal circumstance involving causation by particulars. Their different constitutive properties will settle whether they are playing a triggering role or are a standing condition. Thus, while the argument in favour of triggering conditions provided the justification for appeal to events (given what I have later said about their character), their flexibility is the basis for the claim that one only needs to appeal to events as part of the supervenience base of causal relations between entities with one further qualification. The phenomenon of emphasis, and arguments in favour of a more fine-grained approach to the individuation of causal relata, did not undermine the case for events. Instead, it suggested that we needed to recognize a second kind of causal relata: properties. Chapter  develops this in some detail. Before we get to that, though, we need to consider whether causation is a relation at all, and a particularly troublesome type of causal claim: negative causation. In addition to throwing into question the relationality of causation, it is one final potential source of solace for proponents of facts. It will be the principal subject matter of Chapter .

 Negative Causation and the Relationality of Causation Up until this point, I have assumed that, in order to understand causation, it is reasonable to consider the conditions under which two events, c and e, are causally related to each other. This assumption may have engendered some anxiety. A number of philosophers take the view that causation is not, or not always, a relation (‘is not’, Mellor (), p. ; Martin (), p. ; ‘not always’ Lewis (b)). For those who deny it is a relation at all, demarcating two events and seeking to understand how they are related to each other, in order for the first to be a cause of the second, is a mistake. One source of resistance to causation being a relation depends upon a powers ontology, a second stems from negative causation. The two issues can interact in that a powers ontology suggests a particular view about negative causation (e.g. Martin ()). In the first section of this chapter, I discuss the idea that, in a powers ontology, causation is not a relation or, at least, not a relation other than that of identity. Causation involves the mutual manifestation of disposition partners. As we will see, this provides no grounds for denying that there is a distinction between cause and effect, and that causation is a relation between them. The nature of this relation may be different, in a powers ontology, to one envisaged in other ontologies. That is a separate matter. As later discussion about laws of nature will reveal, an ontology of powers concerns the realization of causation and not its nature. The third section of the chapter will be devoted to the issue of negative causation. Proponents of facts as the appropriate way to characterize causation, or an important element in causal explanation, often cite the case of negative causation as particularly supportive of their view (e.g. Mellor (), pp. –; Steward (), pp. –, for further discussion, Noordhof (b), pp. –). The view has some plausibility if we take facts to be what true propositions express. Statements of negative causation, such as Bill does not die because he does not get cancer, seem true and involve phrases expressing true negative propositions. However, when it is recalled that facts are supposed to be truth-makers, the apparent advantage over events vanishes. Negative facts as items of ontology are prima facie just as puzzling as negative events. I will explain how statements of negative causation are true without allowing for negative entities in virtue of which they are true. In Chapter , we developed a picture of the relationship between the truth of propositions, and the world they concerned, that was different from those who are fans of truth-making. Although negative causation will be discussed independently of

A Variety of Causes. Paul Noordhof, Oxford University Press (2020). © Paul Noordhof. DOI: 10.1093/oso/9780199251469.001.0001



      

this approach, it also provides the opportunity to highlight and develop features of it. Since negative causation only presents a challenge to the relationality of causation within certain approaches to truth-making, preliminary discussion of the nature of these approaches, and the favoured alternative, is a necessary preliminary to getting the issue into focus. That will be the subject matter of the second section of this chapter.

. Causation as Mutual Manifestation of Reciprocal Disposition Partners Proponents of a powers ontology suggest that causation involves the mutual manifestation of reciprocal disposition partners’ powers within a powers net (Martin (), pp. –). When we put sugar in water, sugar manifests its disposition to dissolve, water its power to dissolve. Likewise, two upright cards, whose bottom ends are resting on a table and top ends provide mutual support. In both cases, there is a continuous symmetrical interaction rather than a sequence of causes and effects. These observations are taken to conflict with assumptions I have made. First, that an analysis of causation can proceed by considering what has to hold between two events, e₁ and e₂, for one to be a cause of the other. Second, that e₁ can be a cause of e₂ without e₂ being a cause of e₁ (Martin (), pp. –). In fact, it is hard to see where the conflict lies. As I explain in ., causation is a non-symmetrical relation not an asymmetrical relation. This allows for the possibility that there will be cases in which there is mutual causation of the kind characterized above. However, mutual causation is also compatible with the presence of elements that are not mutual. For example, consider the connection between the two cards balanced at time t and being balanced at time t* (where, let us suppose, t* is later than t). The cards being balanced at an earlier time raises the chances of them being balanced at the later time, without disturbance, and there is no mutual interaction between being balanced at these two times. It is not the case that the cards being balanced at the later time assisted the cards at the earlier time to be balanced (or so we commonly suppose). Equally when you put the two cards together one stops the other from falling down which then, because it retains its position, causes the first to retain its position, and so forth. This to and fro of support is naturally characterized in terms, not of the existence of each card, but rather slices of this existence—temporally limited particulars with certain properties—which, first for one card, then for the other constitute the minutiae of mutual interaction between the cards. If you ask ‘Why do the two cards stay upright?’, then there will be no need to focus on this detail: you can just cite the fact they are resting against each other. However, if you ask the question, ‘What stopped card A from falling down at time t*?’, then talking of a continuous process, or the continuant card B, is not going to explain that. Each does as well for ‘What stopped A from falling down at t**?’ (where t** is not identical to t*), or any other time. To explain why the card didn’t fall down at t*, you need to give some details about what was the case at t* or a little earlier—that is, what was in place in time for an explanation of why the card didn’t fall at t*. So the analysis of causation in terms of

     



counterfactual chance-raising between events can be part of the story for why it is appropriate to talk of mutual manifestation of reciprocal disposition partners. To suggest that this story is not needed because, keeping questions at a certain level of generality, it doesn’t seem appropriate, is rather like denying that cell biology has any role in the explanation of the flourishing of a creature because one refuses to look through a microscope. C. B. Martin counsels against understanding the two pictures as compatible in the way that I have suggested. Here is the key passage that sets out his alternative. You should not think of disposition partners jointly causing the manifestation. Instead, the coming together of the dispositional partners is the mutual manifestation; the partnering and the manifestation are identical. This partnering-manifestation identity is seen most clearly with cases such as the following. You have two triangle-shaped slips of paper that, when placed together appropriately, form a square. It is not that the partnering of the triangles causes the manifestation of the square, but rather that the partnering is the manifestation. (Martin (), p. )

This is a very puzzling passage. Each disposition partner is a distinct thing from a particular manifestation and can exist independently of it. When they come together, there are conditions that must be met—for example, placing sugar in water—which have an independent characterization from the manifestation. Indeed, if they did not have an independent characterization, then there would be nothing which explained what coming together involved apart from the manifestation and, hence, no explanation for why a host of other ways in which the disposition partners may co-exist failed to result in a manifestation. So one might think that two disposition partners coming together is quite properly thought of as a cause and the manifestation an effect. Take the case of the two triangle-shaped slips of paper. Bringing them together involves putting the hypotenuse of each triangle flush with the other. This is distinct from the result. When the two triangles have come together, then this is identical to the manifestation. Two things having come together can be defined in terms of what counts as a successful manifestation of this coming together. Indeed, this will be inevitable if coming together is simply shorthand for mutual manifestation of the disposition partners. But that in no way discredits the causal picture with which I have been working. Much of my remarks have been focused on denying that the framework within which I have worked and the powers ontology are in tension. Indeed, as we shall see later, in .., I consider the powers ontology one possible truth-base for our causal talk. Nevertheless, they also have implications for any who might be tempted to deny that causation is a relation if the understanding of cause and effect offered by the powers ontology is adopted. The thought is that, rather than a distinct cause and effect, we have a coming together of disposition partners that is identical to the manifestation. There can’t be any relations—apart from the trivial case of identity— between entities that are identical. I hope it is clear why I think this line of thought is unsuccessful. It is, of course, quite true that, for a powers ontology, the relation between cause and effect is much more intimate. However, it is not so intimate that there is no possible relation that might hold between them.



      

. Truth-Making and Negative Existential Propositions: Options and Alternatives The differences between different approaches to truth-making, and between truthmaking approaches and my own, can be brought out by considering three ideas that are often mixed together, in the development of truth-maker theory. The first is that the truth of a proposition needs to be explained. The second is that an explanation of the truth of a proposition should be distinctively relevant by corresponding to the proposition’s distinctive subject matter. The third is that what propositions are true or false about worlds depends upon the way the worlds are, there is no independent variation. By the third, I mean just the supervenience of truth on being formulated in Chapter . Two possible worlds exactly alike in terms of the objects which exist, and properties and relations that hold between them are exactly alike in terms of the propositions that hold and fail to hold (e.g. Merricks (), p. ). Truth-maker theorists explain the truth of propositions by truth-makers that necessitate, or ground, their truth. They take these truth-makers to be distinctively relevant for the propositions whose truth they make and, thus, the truth of the propositions to depend on them. Propositions with negative ontological commitments present a particular problem for truth-maker theory. Negative existential propositions such as () There is no F, () There are no Fs, provide the most striking cases. Others include negative predications () ()

A is not F, A’s not being F,

and general propositions () All Fs are G, and propositions about entities that have come to be known as maximal bordersensitive entities are other examples. Consider the statement that all emperor penguins live in the Antarctic. Apparently there are about , emperor penguins who live there. These , penguins are not the truth-maker for the statement. The statement is false because there are one or two emperor penguins who have fetched up elsewhere, including a couple in San Diego Zoo. This demonstrates that, in addition, there must be no emperor penguins outside Antarctica. Even if they died out, given truth-maker necessitation, the , penguins would not necessitate the truth of the statement because there might have been penguins elsewhere. Indeed, the general statement is plausibly thought of as true unless there are penguins outside of Antarctica. This means it has, primarily, a negative ontological commitment. A proposition about a maximal border-sensitive entity is that Tibbles is a cat. A property is maximal if and only if, roughly, large parts of an F are not themselves

-    



Fs. A property F is border sensitive if and only if, again roughly, its possession depends upon what is going on outside of the possessing entity’s borders (Sider (a), pp. –). Maximal properties are particular types of border-sensitive properties. Shapes are border sensitive but not necessarily maximal. A floor mosaic can have triangles as part of a pattern where these triangles have triangles as parts. If we consider a cat, Tibbles, minus his left paw, the resulting entity, occupying all of the space of Tibbles except for the left paw, would not be a cat. Of course, if Tibbles lost his paw, he would still be a cat but that’s because he is not part of a cat. So, in saying that Tibbles is a cat, we rule out the possibility that he is the first kind of entity occupying the spatial extent of Tibbles except for the paw. Although maximal border-sensitive properties seem positive, their attribution comes with negative ontological commitments too. These examples underline a more general point. The ontological commitments of a statement, and specifically its negative ontological commitments, if any, aren’t immediately obvious from the statement. This is not just a matter of statements with apparently positive ontological commitments having negative ones but also the reverse. Consider the statement that Bill does not die. We might reject the idea that such a statement is committed to Bill possessing the property of not dying, and instead say it is committed to there being a collection of processes that constitute the workings of Bill’s living body. So while it may be the case that one of a has F and a does not have F has a negative ontological commitment, it may not be obvious which one. In the discussion to follow, I will sometimes make assumptions, for the sake of argument, about which has the negative and which the positive ontological commitments but these might be swapped over and the discussion proceed in the same way. My focus below will be primarily upon negative existential propositions but the theories identified would have application to these other cases. Negative existential propositions put the three ideas identified at the start of this section under pressure. Many treatments adulterate some of them. Only some of these treatments promise to threaten our understanding of causation. We can outline the territory as in Figure .. Truth-maker maximalism is the claim that every truth— even negative existential truths—has a truth-maker. Let us begin by focusing upon this idea, and the distinctively relevant truth-makers that such a view might seem to require. Accounts of negative facts or states of affairs come in two basic forms. They either recognize negative properties and relations or they recognize a negative instantiation relation that we might call uninstantiation (Hochberg (), pp. ; Brownstein (), pp. –, call it ‘negative exemplification’; Barker and Jago (), p. , call it ‘anti-instantiation’). I take the latter to include the idea that negative facts have constitutive properties or relations with  polarity (where their having polarity  is the corresponding positive fact) (Beall (), p. ; Priest (), pp. –). Although Randolph Clarke, and Barker and Mark Jago take polarity to be a third form of negative fact theory in which a positive or negative element together with the property stand in an instantiation relation to an object, there seems little evidence that the polarity account is explicitly put forward with the rejection of the second form in mind (Clarke (), p. ; Barker and Jago (), p. , the three options identified go back to Hochberg ()). Some proponents of an uninstantiation



       Truth-Maker Necessitation or Equivalent? Yes: Truth-Maker Theory Truth-Maker Maximalism?

No Truth Supervenes on Being

Yes Explanatory Relevance

Yes: Truth-Base Theory

No

No: Negative Existential Propositions Don’t Have Truth-Makers

Do Absences Exist?

Yes Are there distinctively relevant Truth-Makers?

Yes Negative Facts

No

Yes: Kusko

Totality Facts (Armstrong)

No: Eary Lewis

Worlds Having Essential Properties (Cameron)

Monism/ Fundamentality (Schaffer)

World qua Total (Lewis and Rosen)

Figure .

account take a does not instantiate F as identical to a instantiates not-F (Barker and Jago (), pp. –). In which case, they recognize no substantial difference between the theories. Others may want to deny the existence of negative properties or a relation of uninstantiation. Although there are these differences, they are united in taking negative truth-makers to be entities. If there are negative truth-makers distinctively relevant to the propositions they make true, then there is no challenge to the relationality of causation (Barker and Jago (), p. ). The challenge this position poses is rather to the claim that the relata of causation are events and properties rather than facts. My principal response to this position is three-fold: first, the argument I gave against truth-maker necessitation in ..; second, the argument from parsimony I note below against these kinds of distinctive subject matter truth-makers; third, the treatment I offer of negative causation in .. However, it is worth noting that, if this response is unsuccessful, the apparatus of negative properties or uninstantiation could be taken over to an events ontology. Negative truth-maker accounts are different from those which appeal to absences, rejecting the idea that absences should be taken as entities. Proponents of this position deny that every true proposition requires a truth-maker although, somewhat

-    



surprisingly, they think that the truth of negative existential propositions has implications about what exists in the world and not just what doesn’t (Kukso (), p. ). Absences are how a particular spatiotemporal region is (Martin (), p. , see also Kukso (), p. ). They are not an entity but the absence of an entity (Kukso (), p. ). The implications of such a position for the relationality of causation are unclear. Boris Kukso argues that an absence of an entity is not, itself, an entity and hence cannot be one of the relata of a causal relation (Kukso (), p. ). However, absences are said to exist. It is unclear why existence isn’t enough to be one of the relata. The position also seems seriously unstable. On the one hand, talk of spatiotemporal regions being a certain way makes them seem like negative events (and thus entities) (or negative facts or states of affairs, if you are committed to that kind of ontology, as Armstrong (), p.  notes). On the other, talk of existence without there being an entity makes it seem like the position is simply trying to respect the fact that there are true negative existential sentences. The latter option receives clearer articulation in a position set out by Lewis. The idea is that a negative existential proposition such as that there was no brake on the bike (hence explaining the crash) is primitively true unless there is something that falsifies it (Lewis (), p. ). If negative existential propositions are primitively true, they don’t imply that absences exist, just that there are true absence statements. The position does threaten the relationality of causation. But, by the same token, true propositions of negative causation provide grounds for the existence of absences, and for absences to be taken as entities. As we shall see in ., though, the truth of these propositions can be accounted for by other means. These means involve the recognition of causal relations between positive entities. So there is a prima facie dilemma between taking true statements of negative causation at face value in which case their truth provides grounds for believing in absences as entities, and not taking them at face value so removing the case for taking absences to exist at all. In addition, those who favour distinctively relevant negative truth-makers or absences face the charge, ironically enough, of displaying a particular kind of absence: lack of parsimony. They postulate lots of negative truth-makers—like my failure to have long brown ears with pink stripes and have to recognize an additional ‘that’s all folks’ truth-maker, for example, there are no more truth-makers than those. Without a truth-maker like this, we would have no truth-maker for no creature has long brown ears with pink stripes. By contrast, somebody who just recognized positive truth-makers plus a ‘that’s all folks’ negative truth-maker would have no need for the additional distinctively relevant negative truth-makers (Merricks (), pp. –). Why recognize them, if they do no work? There is a conflict, then, between the explanatory feature of truth-makers and distinct subject relevance. Although truth-makers that display the latter provide a particular explanation of the statements that concern them, considerations of parsimony show that we don’t need distinct subject-relevant truth-makers for every truth to have an explanation of every truth. Rejection of distinct subject-relevant negative truth-makers can come in three forms. First, negative truths may be true in virtue of a combination of positive facts plus a totality fact. Armstrong characterizes the totality fact as a type of



      

second-order property of totality, T, that an aggregate of Xs has to the property of being an X (Armstrong (), p. ). More specifically, it is the second-order property of an aggregate of facts or states of affairs (A(s₁, s₂, s₃ . . . )) that it is all the first-order facts or states of affairs there are, which we might represent T(A(s₁, s₂, s₃ . . . ), S), where ‘S’ is being a state of affairs (Armstrong (), p. , (), pp. –, ). For example, all the positive facts about the world plus the totality fact will necessitate the truth of ‘There are no penguins in the Sahara desert’. Armstrong suggests that if there are properties of the form T(A(x), P), then totality facts need not just hold for all first-order states of affairs in the way described but also for other properties e.g. (T(A(emperor penguin₁, emperor penguin₂, . . . ), Being an emperor penguin)) (Armstrong (), p. ). This allows for more minimal truthmakers than the whole world. The problem is that parsimony suggests that there are no grounds for recognizing these other totality properties, however, there are independent grounds for recognizing T(A(s₁, s₂, s₃ . . . ), S). The latter is required to secure the result that Armstrong’s envisaged property-specific totalities are all the totalities. The aggregate of facts having T to the property of being a fact is itself a fact, or state of affairs. A vicious regress is avoided because the third- and higher-order states of affairs or facts supervene upon all the first-order states of affairs or facts and the second-order totality fact (Kukso (), p. , for the objection, Armstrong (), p. , (), p. , for the response). A second approach, priority monism, accepts that truth-makers should explain the truth of propositions by appeal to necessitation or grounding. It also endorses the dependency of the truth of propositions on the world. However, it rejects the claim that the explanation should be distinctively relevant. The whole world is the truthmaker. In the case of negative truths, it is suggested that the standard argument in favour of dealing with them can be rebutted by taking worlds to be fundamental. When a duplicate of world w occurs as part of a larger world w* (D(w) + a unicorn), then w ceases to be fundamental. Fundamentality takes the place of the totality fact (Schaffer ()). The problem with this approach is that it cannot secure the desired result without an additional premise that vitiates the approach. w being fundamental is a truthmaker of there are no unicorns because, Schaffer’s thought runs, in the larger world w*, w is not fundamental. It is a part of the world with an additional unicorn (Schaffer (), p. ). The assumption is that D(w) rather than w* is the counterpart of w. This can easily be rejected. It seems plausible that w may have different inhabitants to the inhabitants it actually has. w* is such a world. In which case, the fact that w is fundamental cannot be a truth-maker for the negative proposition that there are no unicorns. There is one possible world, in which the counterpart of w is w*, in which there is a unicorn. Schaffer has been hoodwinked by labelling into thinking that w being fundamental provides a truth-maker. Of course, he could argue that w has its properties essentially (see below). In that case, though, it is the essentiality claim that is doing the work and not the fundamentality claim. A third approach takes worlds to have all the truths that hold at them essentially (Cameron (), pp. –). Consider two worlds, again, w and a duplicate of w, D(w), as part of a larger world w* (D(w) + a unicorn in addition). In w*, there is a

-    



unicorn is true, but in w, there is a unicorn is false. w* is therefore not a counterpart of w. If w* is not a counterpart of w, then w is sufficient to make the claim that there are no unicorns true. Apart from its success in providing a truth-maker for negative propositions amongst others, the proposal seems unmotivated. If particulars have counterparts, worlds are particulars, and there are other worlds, then worlds should have counterparts. One consequence of denying it would be that we would have to concede that our universe could not have been a different way to the way it is (Jago (), pp. –, for other difficulties). An objection to these approaches is that they are also unparsimonious. They are committed to facts of totality, worlds having essential properties or fundamentality because they put together the dependency claim with the explanation claim, while abandoning distinctive relevancy, and look for something that satisfies truth-maker necessitation. Instead, I suggest that we understand the dependency claim in the weak sense that truth supervenes upon being canvassed earlier. Thus Two possible worlds exactly alike in terms of the objects which exist, and properties and relations that hold between them are exactly alike in terms of the propositions that hold and fail to hold (e.g. Merricks (), p. ; Lewis (), pp. –). At first glance, the proposition that there are no penguins living in the Sahara desert is true in one world and not in another world because, in the other world, there are Saharan penguins. No negative facts are required for the truth of the no Saharan penguins proposition but just this difference between worlds. However, this does not completely side-step the problem. Consider the world w+ in which there are Saharan penguins. Why isn’t that world minus penguins itself a world that is exactly like the world in which there are no Saharan penguins? Yet this world is one in which ‘There are no Saharan penguins’ is false because it is part of a world, w+, in which there are Saharan penguins. Presumably the answer is that the world minus some entities is not a world. But that shows that built into the notion of a world is that there is nothing concrete existing outside it. Being a world is a maximal though border-sensitive property. Indeed, it is the most maximal concrete entity. The concern is whether we can make sense of worlds as the most maximal entities without negative entities. We can take worlds to be the most extensive entities without appeal to a negative entity just so long as we have some way of characterizing what makes it the case that something is part of a world along with the rest. For example, if standing in such and such spatiotemporal relations were the basis for worldly extension, then w+ minus the lone non-Antarctic-dwelling penguin would not be a world because there is an entity existing in spatiotemporal relation to other entities in the world that has been left out. Just so long as there is a positive account of the basis for worldly inclusion we don’t need a totality fact to say that’s all the entities there are. So it is a thesis about the extensiveness of worlds that is doing the work and not claims about them having all their properties essentially properties or being fundamental. The correct theory of extensiveness for worlds is obviously something whose development still needs to be done. If no account is available then we will have to fall back on a totality fact, but this would be justified on the grounds that no theory of worldly extensiveness is available.



      

In those circumstances, a fact of totality is required in any event to capture world boundaries. Either way, appeal to worlds is all that we need. This makes my position about worlds close to Gideon Rosen and Lewis’ claim that worlds are essentially total (Rosen and Lewis (), p. ). We have articulated a non-truth-making account of dependency. Even if worlds are the most extensive entities there are, they don’t have their inhabitants essentially and so a theory that appeals to them doesn’t satisfy truth-maker necessitation. The other two features of truth-making theory were distinctive relevance and explanation. The latter is understood in terms of necessitation. The truth-basing theory takes a different view. The truth-base of a proposition is explanatory of the truth of a proposition but, because it lacks the relevant essential features, does not necessitate it. The truth-bases of propositions explain the truth of a proposition in ways distinctively relevant to the propositions. In the case of negative propositions, the relevance of the subject matter will be looser, as we shall see when the discussion turns to negative causation in .. One challenge to the weaker notion of explanation to which I appeal is: in what way is it explanatory of the truth of the proposition? A provisional answer is to say that the proposition is true at least partly in virtue of the truth-base. This will not satisfy those who take the ‘in virtue of ’ relation to be at least as strong as necessitation. Consider a positive proposition of the form a is F. A particular a, which has the property F, is the truth-base of the proposition because, if the particular does have that property, then the proposition will be true. We don’t have to recognize the facts with their distinctive modal properties. We just have to talk in terms of particulars still having certain properties at different times or at different worlds. This seems to be Josh Parsons’ notion of truth-making although truth-maker theorists in the sense we have identified would not recognize it as such (Parsons (), p. ). They are committed to truth-maker necessitation. Lewis pointed out that particulars could satisfy truth-maker necessitation under a particular counterpart relation. For example, instead of talking in terms of the state of affairs a is F, we could talk of a qua F: a under the counterpart relation of it continuing to have F across possible worlds (Lewis (), pp. –). The favoured proposal resists the urge to identify an entity that satisfies truth-maker necessitation. Instead, it is a characterization of why an entity, which fails to meet truth-maker necessitation, is an explanation of the truth of a proposition. Perhaps the most substantial objection to non-distinct subject-relevant truthmakers, or for that matter my appeal to worlds in characterizing the dependency of negative statements upon being, is that it fails to account for how negative causal statements seem true. Totality facts, worlds, etc. don’t stand in local causal relations in the way that negative causal statements suggest (Kukso (), p. ). This provides a consideration in favour of the introduction of positive truth-bases to play the causal role. I explain how this works in .. Since my position differentiates dependency from explanation, and distinctive subject relevance, there is no argument from parsimony against positive truth-bases so understood. Once explanation has been divorced from truth-maker necessitation, we can recognize the role of positive entities in the truth of statements of negative causation. That is the line of thought behind ...

 



. Negative Causation The challenge presented by negative causation is more substantial. Consider the following: (N) (N) (N) (N)

Bill does not die because he does not get cancer. Kim has no children because she uses contraception. The deadly void caused the astronaut’s death in seconds. Brown’s failure to water the plants caused their death.

Their interest lies in the fact they combine negative elements with positive elements. The positive element is the causal relation, the negative elements are the entities which are numbered among the causes and effects. The non-relationality of negative causation follows from two claims. First, relations don’t hold without relata. Thus, if a causal relation holds, then there exist at least two entities, a cause and an effect, between which the relation holds. Second, either negative entities don’t exist or, to the extent that they do, they are not the kind of thing that can stand in causal relations (e.g. the totality fact lacks the distinctive relevance to subject matter that makes it an appropriate entity to stand in the envisaged causal relations). As we noted, negative causal statements also provide a consideration in favour of the existence of negative entities and, hence, the relationality of causation. Taking them at face value, they attribute causation to a negative entity. If something has effects, then it exists. So there are negative entities. In which case, those who argue in favour of the non-relationality of causation face a dilemma. In order to establish that causation is non-relational, they must argue that there are true negative causal statements. However, they must deny that the truth of negative causal statements indicates that there are negative entities of the appropriate kind. Their course of action must be to argue that negative causal statements are true in virtue of something different to what, prima facie, they seem to concern. My strategy of response is to argue that, if this is correct, then the truth-bases—given that I reject truthmakers—are positive entities standing in a relation of causation rather than the favoured non-relational case of causality. The two positions are united by the claim that it is by no means clear, from an immediate inspection of a piece of language, what its truth-bases are. They can’t just be read off. So, negative causal statements can be true because of causal relations between positive entities or something non-relational and positive (according to the competing position). There is a distinction between denying the existence of negative causation and, as Beebee does, denying the truth of negative causal statements (Beebee (b), pp. –). By the same token, any piece of language I use to specify a putatively positive entity may not, in fact, identify a wholly positive entity. We have already seen how this can be the case. If you allow for the existence of negative entities then ‘All penguins live in the Antarctic’ and ‘Tibbles is a cat’ both seem to have truth-bases that involve them. Consider the case of ‘Bill does not die’. On the assumption that there is no intermediate state to death and life, then it is plausible that ‘– does not die’ picks out something positive despite its negative character. So, although the development of my position will discuss particular cases, there should always be the background health warning: assuming that this



      

piece of language picks out a positive entity (and that is prima facie involving commitment to a negative one). I’ll give the resulting position in abstract terms that might be applied to any situation however these matters are resolved in the particular case. The theory I want to develop has two components. Suppose we have a negative causal statement of the form: ne₁ caused ne₂ (where ‘ne₁’ and ‘ne₂’ are, apparently, negative events). The position could as easily be developed in terms of facts but I will put it in terms of events so it is compatible with the rest of the theoretical development in the book. The negative causal statement depends for its truth on two sets of positive events. The first is the corresponding positive events to the specified negative events, that is e₁ and e₂. The second is positive surrogate events occurring in the actual situation to which the negative causal statement adverts. I will outline the role of each in turn. We can dub the combination of these elements the Two-Way Positive Dependency account.

.. Dependency on the corresponding positive events Phil Dowe put forward the following necessary and sufficient condition for negative causation. (PC) ne₁ caused ne₂ if and only if if e₁ had occurred, then e₁ would have caused e₂ (Dowe (), pp. –, Armstrong endorses it to avoid the argument from causation in favour of negative truth-makers, Armstrong (), pp. –, something like it is also present in Lewis (b), pp. –, absent mention of Lewis’ appeal to ‘biff ’). It has considerable plausibility. It captures the thought that the truth of a negative causal statement depends upon the presence of a causal potentiality that can take different triggers that will result in different outcomes. The following table may help to picture it. Table . Cause

Effect

C₁

E₁

C₂

E₂

C₃

E₃

Not (C₁ or C₂ or C₃)

E₀

Let E₀ be what would be the case if the causal potentiality were not triggered, if it is, then depending upon whether it is by an event of type C₁, C₂, C₃, we get the type of results detailed above. In the case of ‘Bill does not die because he does not get cancer’, getting cancer would be C₁, other forms of threats to life, C₂, C₃, etc. and not dying E₀. There exist potentialities in Bill’s body such that, if certain things happen, he will die. Failure to trigger these will mean he persists. That’s what (PC) captures. In the terms of my account, in the closest worlds in which he got cancer, there would be a complete causal chain to Bill dying. I shall assume for the sake of simplicity that Bill dying (as opposed to Bill’s death) is a positive event.

 



The rest of the examples could be fitted to this pattern. Let me just give one more illustration, namely the deadly void causing the astronaut’s death in seconds. Here we are to imagine that the presence of atmospheric pressure has certain beneficial inputs on the astronaut’s body, C₁, C₂, C₃. Examples of these are: pressure on the air in the astronaut’s lungs so it does not expand and disperse as it would if there were no pressure so ‘sucking the oxygen from the astronaut’s lungs’; resisting the vaporization pressure in the astronaut’s bloodstream so that the blood does not boil; providing warmth which replaces the dissipation of warmth from the astronaut’s body, something which would occur without check in the void (Lewis (b), p. ). So E₀, the astronaut’s death as a result of the air being sucked from his or her lungs, blood boiling, and warmth drained from his or her body is the result of the failure of these inputs which in daily life, outside the void, give rise to outcomes E₁, E₂, and E₃. Even on its own terms, the account needs revision. There are cases of negative causation in which, although the putative negative events aren’t pre-empted, the corresponding positive events are (Barker and Jago (), p. ). A variant of the plant-watering case makes the point. Smith, whose plants they are, has an enemy, Drake, who wants Smith’s plants to die. Drake is relaxed about this happening because she knows that Brown will be too lazy, or forget, to water the plants. However, if Brown does water the plants, then Drake will sneak into Smith’s office and poison them. In this case, Dowe’s condition is not met. It is not the case that Brown watering the plants would cause them to survive. This doesn’t undermine the intuition that Brown’s failing to water the plants was a cause because Drake was not active in those circumstances. Dowe should have the following: P (PC) ne₁ caused ne₂ if and such that if e₁ had occurred P only if there is some and none of the events in * occurred, then e₁ would have caused e₂. P Here the only events that may be put in * are non-actual events, intuitively those that might pre-empt e₁ in the changed circumstances in which it occurs. Even with this revision, there are, at least, two significant problems with taking the necessary condition to be a sufficient condition for causation. The first is that it denies that causation is essentially relational (a conclusion that Lewis accepts in (b)). Indeed, according to some, it has the implication that causation is not a relation at all. Thus Mellor writes ‘if there is such a relation [as the causal relation] then by definition what makes true all instances of “c causes e” is that it relates c and e’ (Mellor (), p. , lower case substituted for higher case to fit with the conventions adopted in my book). As a result, he embraces the conclusion that causation is not a relation. The reasoning appears to be as follows. ‘ne₁ caused ne₂’ is true without there being any entities ne₁ and ne₂. Thus we see, at the minimum, that it can be true that c caused e without there being any c and e but simply a truth-base for the attribution of causality. What are the conditions on the successful attribution of causality? Well there has just got to be a causal potentiality—but not a causal relation—which Cis can trigger. ‘c caused e’ is true for positive events c and e because the statement is committed to the existence of positive entities: c, e. However, as far as the causal element is concerned, all that is required is the presence of the causal potentiality and not a relation between c and e.



      

This is a rather puzzling line of reasoning. It seems reasonable to insist that the presence of c, e, and causal potentiality is not enough (the causal potentiality which is untriggered in the case of negative causation). In addition, we need it to be the case that c triggers the potentiality and hence stands in a relation to e. A causal potentiality untriggered would be a potential case of causation that is unrealized (Martin (), pp. –). But now we face the question of why this is required in the positive case but not the negative case. Isn’t the negative case better thought of as an absence of causation, which might have been present, rather than a case of causation in itself? In any event, those who want to retain the idea that causation is a relation face the problem of non-relationality. Second, there is the problem of profligacy. Once you allow that some negative causal statements are true it seems you must allow that lots are, even quite implausible ones. Suppose that Black lives at the other side of the city from Smith who has some office plants and from Jones who failed to close the fire doors as he was leaving the building, giving rise to an extensive fire. Black knows neither Smith nor Jones. Consider (N) Black’s failure to water the plants caused their death. (N) Black’s failure to close the fire doors caused the fire. It is certainly true that if Black had watered the plants, then he would have caused them to live. Similarly, if Black had closed the fire doors, then he would have caused there to be no fire. Yet, we would not want to say that Black’s failure in either respect was a cause of the events in question. The problem of profligacy also highlights a problem with recognizing negative entities as causal relata and, thus, attempting to deal with the problem of negative causation by this route. If negative entities exist, it is hard to deny that Black’s failure to water the plants is one of them. Given that this negative entity exists, it satisfies any analysis of causation that appeals to dependence, or something like it, with respect to the death of the plants. Moreover, there seem no constraints upon the negative entities that exist. Spencer failed to set off the sprinkler system in Smith’s office by telekinesis that would have watered them. An effective irrigation system was not present. The soil in Smith’s plant pots failed to have a higher moisture level, and so on. Without control over the introduction of negative entities, there is a huge proliferation of causation and a huge proliferation of entities in the world establishing their right to existence by being a cause. At every spacetime point at which property Q₁ is instantiated, corresponding to all the other properties that are not instantiated, there are also negative entities at that spacetime point. This is a point that is tacitly recognized by those who favour negative entities. Barker and Jago consider a version of the plant-watering case in which Bob, the plant owner, is kidnapped by Tralfamadorians for their zoo  million light years from Earth. His failure to water the plants, because in the zoo, is taken to be a cause (Barker and Jago (), p. ). Presumably not just Bob, the failure of anybody on the Tralfamadorian home world to travel to Earth to water Bob’s plants is a cause of Bob’s plant’s death. The problem of profligacy can make it look like we need to understand causation in terms of contra-normal conditions after all (McGrath (), pp. –). Suppose

 



that Brown had promised Smith to water his office plants. Then he would be blamed for their death and said to have caused it. Likewise, if he were fire safety officer in the case of the blaze resulting from failure to close the fire doors, his negligence would be said to have resulted in the fire. However, if I were to tell you where Smith’s office was, the plight of his plants, and explain how you might have access to his office (perhaps by breaking and entering), then although it is not at all obvious that there are normal conditions under which you count as the waterer of the plants, it still seems the case that if you fail to water them, you are a (minor) cause of their death. So it is, by no means, a completely clear-cut solution. More generally, while the problem of profligacy may tempt us to reopen the question of whether causation involves a contra-normal element, the considerations that we offered against this position have application here too. First, our causal verdicts are being biased by whether or not we want to blame the person. Brown failing to water Smith’s plants when he had promised seems culpable. Whereas we don’t feel that you should be blamed for failing to act upon something you had only just heard about, is relatively minor anyway (the death of a few plants—apologies to plant lovers), and involves breaking the law (if an office break-in is required). Second, effective intervention to secure a particular effect will also need to take into account failures to act that are not contra-normal. If I know you are a soft-hearted plant enthusiast who won’t let a bit of illegality stand in the way of saving the plants, then I should be cautious in telling you about the plants if I want to avoid Smith’s plants being saved or you doing something rash. The problem of profligacy is not to be resolved by an off-the-shelf attempt to reduce the apparent number of things we allow as causes that was seen to be ill-motivated in the case of positive causation. The revision of Dowe’s condition should, thus, not be taken as a necessary and sufficient condition. However, it is a necessary condition. Let me turn to the second component of the two-way positive dependency account before setting out the full account.

.. Dependency on positive causal surrogates We come now to the positive causal surrogates upon which the truth of negative causal statements depends. Consider the case of ‘Bill does not die because Bill does not get cancer’. If Bill gets cancer, then there is uncontrolled cell growth that eventually reaches the cells of one or more of his organs as a result of which he dies. Let p₁ be all the ways in which Bill’s body persists in normal cell growth. Then, I suggest, p₁ is positive surrogate for Bill not getting cancer. It has been positively characterized and, yet, given the laws of nature, it implies that Bill does not get cancer. The reason why p₁ is not equivalent to Bill does not get cancer is that, first, it does not entail it (independent of the laws of nature, outside of a powers ontology) and, second, there are other ways for Bill not to get cancer than by p₁ and some of these would have been other ways in which Bill might have died. For example, before the onset of cancer, he wasn’t paying attention as he crossed the road and got flattened by an articulated lorry. The first point explains why the proposal is not a version of the incompatibility approach in which positive entities are identified that are incompatible with the corresponding positive events to the negative event (e.g. Demos (), pp. – for the basic structure of the position). The second point also



      

explains why there is no type-type identification of negative events with positive events. The two points are compatible with taking the phrase Bill not getting cancer to pick out normal cell reproduction in his body that is token identical with a particular case of not getting cancer. Nevertheless, it would be a mistake to make this identification. This is so for two reasons. First, the identification would imply that distinctively relevant negative entities existed after all. Identifying not getting cancer with the normal cell reproduction, or failing to water the plants with, say, sitting on a sofa implies that that there are such things, they just have a surprising character. Second, such an identification would mean that the efficacy of omissions was just a matter of the efficacy of these positive entities. Suppose that the absence of c is taken to be identical with c*. Then, in the basic case, we would be comparing what happens when c* and not-c* rather than what happens when c* and c respectively. There is no guarantee that not-c* is properly considered to be c (for further discussion, Sartorio (), pp. –). To give an illustration, Wally is sitting around on the sofa watching television. His dad comes in and feels irritation at his son, not for the first time. Consider the statement (CG)

Wally’s failure to play computer games caused his dad to call him lazy.

The positive surrogate of his failure to play computer games is Wally sitting around on the sofa watching television. While it is true that Wally sitting around on the sofa watching television caused his Dad to call him lazy, I think it is a stretch to suggest that his failure to play computer games caused his dad to call him lazy. So we would not want to conclude from the efficacy of the positive surrogate to the efficacy of the target negative event. In Chapter , we will see how the efficacy of minimal supervenience bases has implications for the efficacy of the properties that supervene upon them. However, this presupposes a prior commitment to the existence of the supervening properties that is not to be assumed here and the connection between the supervenience base properties and the supervening properties is tighter. Although it is a mistake to think that true statements of negative causation are true in virtue of the efficacy of the positive surrogate alone, this is a necessary condition of their truth. Bill’s not dying because he did not get cancer is not just a matter of the fact that, had he got cancer, this would have caused his death. It is true because the cell growth in his body is under control, thus, his organs functioning normally, and so he is living. To see how the proposal works in a bit more detail, let’s now turn to the problem case of Black’s failure to water the plants. The key issue to settle is what would count as the positive surrogate of Black failing to water the plants. Suppose, as we noted earlier, Black is sitting on his sofa watching television. Then it is certainly true that, if Black watered the plants (rather than failed to water them), he would not have been sitting on his sofa watching television. This is one possible candidate for p₁. If this were the only possible candidate, then it would be easy to see why we are not prepared to conclude that Black is a cause of the plants dying. There is no causal chain from Black sitting on the sofa to the dryness of the conditions of the plants. Recall that Black did not know Smith and his plants. So, even if he had got up, he

 



would not have known where the plants were and, even if he had, would not have been able to enter the office, and so forth. All these break any putative causal chain between being on the sofa and the plants having watered soil. So p₁ does not raise the chance of the plants being watered. If p₁ were not to occur, there are lots of ways in which Black would be stopped from watering the plants, so the chance of the plants being watered is about as bad as it was from his remaining on the sofa. This assignment for p₁ fails my analysis for counting as a cause. There are other possible candidates for p₁, however. One would be a positive event taking place in the proximity of the plant which would not take place if Black’s body were there. If Black were in this location, he might be expected to see that the plants needed water and do it. The issue is why should this candidate p₁ be Black failing to water the plants rather than any other individual. If we don’t have an answer to this, then p₁ cannot count as a positive surrogate for Black failing to water the plants rather than somebody else, or something else entirely, and so cannot show why his failure to water the plants is a cause of their death. If that p₁ were not the case, there is no reason to suppose that the chance of the plants being watered is high and, even if it were, that this high chance is relating to Black now watering. Suppose there is a positive event around those plants that would only fail to occur if Black were present. Perhaps Black has a special scent or sheds skin with his genetic material. In which case the candidate positive surrogate would be those actual positive events that, if this occurred, would not be present. These are supposed to be what is picked out by the absence of Black watering the plants. We have, then, two possible positive surrogates to consider. The first, Black sitting on the sofa, would be absent if he just got up from the sofa. The other would only be absent if there were many changes to the actual world. Black would have to hear about the plants, get up, break into the office, and so on. The candidate positive surrogate we want is the one whose absence would occur in a world at least as close to our own as any other candidate positive surrogate’s absence. In considering whether a positive surrogate for a negative event is a cause, we don’t want to be considering worlds any more different from the actual world than we have to. Talk of positive surrogates should be understood in this way, hereafter. The discussion so far has traded upon the idea that Brown sitting on the sofa is a cause of the plants dying because, if he had not been sitting on the sofa, the chance of the plants dying would be significantly reduced. He would then be watering the plants. Black, on the other hand, would, if he were not sitting on the sofa, still not raise the chance of the plants surviving because, for example, he had no access to the office and no idea where they were. A variant of the plant-watering case makes things potentially more complex. Suppose that Jones promised Smith to water his plants but was sitting on his sofa and forgot. In those circumstances, one might suspect that sitting on the sofa was not a cause of the plant watering because, even if it had not occurred, the plants still would have died because Smith forgot about them. Yet, the objection would run, we would still say that Jones’ failure to water the plants is a cause of their death. In that case, we should say, it wasn’t Jones’ omission to water the plants that caused them to die. It was rather that he forgot. His forgetting caused him to sit on the sofa, but this positive surrogate was not a cause of the plants’ death. Even if he



      

were not seated, the plants would have died. Instead, his forgetting was a cause of the plants’ death. Of course, it feels very natural to say that Jones’ omission to water the plants caused their death too. To that extent, we might take the omission to have, as a positive surrogate, the forgetting. If we are being precise, though, it is better to say that the forgetting is a cause than that the omission is (given that the positive surrogate of the latter is sitting on the sofa). Putting the two components together, we get the following: P ‘ne₂ because ne₁’ is truePiff (A) if there is some such that if e₁ had occurred and none of the events in occurred, then e₁ would have caused e₂ and (B) there is some actual p₁, p₂, such that (i) if e₁ were to occur, p₁ would not occur and if e₂ were to occur, p₂ not to occur, (ii) if p₁ were not to occur, then e₁ would occur and if p₂ were not to occur, then e₂ would occur (iii) p₁ caused p₂. (A) is the necessary condition identified in .. and justified further at the opening of this section. (B) is an attempt to capture the relationship between the positive surrogates and the target negative events. The mutual two-way non-occurrence counterfactuals between the positive surrogate pi and the corresponding positive event ei to the target negative event capture how the relationship need not be one of straight incompatibility. The actual circumstances and laws of nature must be taken into account. To illustrate with Schaffer’s nice example: the positive surrogate of the absence of beer in the fridge may be that it is full of sausages because, in the circumstances, where somebody came back with a six pack and hoped to chill it, if the fridge had not been full of sausages, there would have been beer in the fridge (Schaffer (c), p. ). Initially, Schaffer tentatively rejects an account like mine, seemingly allowing for the existence of negative events with causal relations between them. These negative events are taken to have negative properties. But he later talks in terms of positive proxies of them. The resulting picture is unclear (Schaffer (c), p. ). In a later paper, Schaffer doesn’t talk of negative properties but negative descriptions, and the commitment to positive proxies is much more explicit (Schaffer (b), pp. –). By my lights, this is on the right lines but misses important developments in the overall picture. Sara Bernstein has also defended an account of omissions that has some similarities with the favoured account but there are significant differences. She suggests that omissions are three-part entities: there is an event involving the agent of the omission in the actual world, there is a non-actual possible event that is the omitted event (e.g. watering the plants), and there is a counterpart relation, determined by context, that the omitted event is a counterpart of the actual event (Bernstein (), pp. –). She takes omissions to be possibilities and, as a result, takes them to have no actual efficacy but only relevance (Bernstein (), p. ). Omissions are distinguished from other absences or negative events by involving the absence of events that occur in close-by worlds (Bernstein (), p. ). Other absences fail to have the absent event as a counterpart (Bernstein (), pp. –). It is presumably in this respect that her account avoids being a version of Dowe’s that we discussed earlier. Bernstein’s account has a number of puzzling features. The first is that it is unclear why an omission should be understood as identical to a possible occurrence of what

 



is omitted. There is no doubt of a relationship between an omission and the corresponding positive event—that I sought to characterize in terms of two-way counterfactual dependency—but to take the corresponding positive event as part of the omission is surprising. Second, the counterpart relation settles an entity’s modal features. A very liberal counterpart relation can allow that, for example, I’m a possible poached egg (Lewis (c), p. ). To suggest that a sitting on the sofa is a possible plant watering definitely lies at the liberal end. In the case of my being a possible poached egg, the apparent counterintuitiveness of allowing for this is given theoretical motivation and, it is suggested, concerns a far distant possible world very unlike our own. By contrast, Bernstein is arguing that Brown’s sofa sitting is a plant watering in a very close-by world much like our own. So the worry is that the only way it is plausible that this is a counterpart event is if the world is taken to be very different indeed, and with this difference, we have no reason to expect the causal consequences we would naturally attribute to watering the plants. They would die anyway in such a world (one might reasonably think). The final problem with the approach is that it takes natural concern about the very idea of the efficacy of omissions as captured by allowing that omissions only have causal relevance and not causation. The relevance is attributed to the actual event’s possession of the modal property of being a possible occurrence of the omitted event. One issue is why something being, for example, a non-actual possible plant watering is relevant to the plants dying. The relevant property of the event of sofa sitting is that it is not a plant watering, not that it is a possible (but not actual) plant watering. Bernstein’s omissions are tripartite entities so they involve something that is not a plant watering—sitting on the sofa—that plays the relevant causal role regardless of the counterpart relation. The point is reinforced when one remembers that precisely the same account can be given for absences that aren’t omissions, so the counterpart relation looks redundant. A second issue is that given that her tripartite entity has an actual component, the sofa sitting, that is a cause of the plants dying, it is unclear how she has captured the concern about the very idea of the efficacy of omissions. We don’t insist that all parts of an entity have causal consequences to attribute efficacy to that entity. So her account seems to have the straightforward consequence that omissions are efficacious whatever relevance they also have in virtue of the counterpart relation to the counterfactual event. By contrast, my approach suggests that negative causal statements have, as their truth-base, positive entities, but these entities aren’t the omissions. So no straightforward efficacy is attributed to omissions. If my analysis captures the truth conditions for statements of negative causation, then it should be clear that, while no relation is required between the (non-existent) negative entities, they do depend for their truth upon causal relations between positive entities or, at least, we have been provided no reason to reject this. To recall the line of reasoning I gave for the position that causation is non-relational, the case depended upon the truth of negative causal statements not requiring the existence of causal relations. We now see that this key premise is not satisfied. Negative causal statements do require the existence of causal relations but not between the putative negative entities that the negative causal statements are ostensibly about.



      

. Concluding Remarks The present chapter returned to two issues left open in the preceding chapters. The first was the rejection of truth-making and states of affairs or facts as causal relata. The second was the role of norms in the proper understanding of causation. We have seen that the proper treatment of negative causation does not require us to revise the conclusions at which we arrived earlier. Indeed, understanding negative causation better has helped us to develop the picture outlined in . on these matters. Separating the supervenience of truth on being from explanation and the distinctive relevance of truth-makers enables us to avoid arguments from parsimony against positive surrogates drawing upon the idea of truth-maker necessitation. If truthmaker necessitation were the proper characterization of how to explain the truth of all statements, and hence negative causal statements in particular, then a fact of totality, or the essentiality of properties of the world, would be the most parsimonious explanation of their truth albeit at the expense of identifying something that conveys their distinctive subject matter. By contrast, within my suggested framework, the existence of true negative causal statements provided motivation for recognizing the existence of positive causal surrogates as part of the explanation of their truth. The truth of negative causal statements thus, perhaps somewhat surprisingly, is the basis for an argument against the truth-making picture. The conclusions in the present chapter will also prove to be significant to the assessment of attempts to characterize causation in terms of substantial causal processes in Chapter . Before we get to that point, however, we need to understand the nature of causal relata a little better. Chapter  on property causation and Chapter  on their connection with counterfactual dependence will complete the job.

 Property Causation Even if coarsely individuated events are causal relata that does not exclude properties being causal relata too. Indeed, our causal talk can be committed to a causal role for properties in, at least, one of two ways: either for their instances or for the properties themselves. Property instance causation is a necessary condition for property causation. The latter involves a generality not present in the former. The principal aim of the present chapter is to formulate an account of property causation that both has independent plausibility and supports the claims made in Chapter  about causal relata. The chapter falls into four parts. In the first, I discuss property instance causation. More precisely, I will consider a particular challenge to taking it to be a matter of applying the analysis of causation offered so far to property instances. In Chapter , we will see how metaphysically necessary connections between events may support the counterfactuals distinctive of causation: for example, if I weren’t an animal, I would not be human; if I were not to have come from a certain zygote, I would not be Paul Noordhof, if I were not alive on  February , I would not be able to celebrate my fiftieth birthday, and so on. The focus will be on horizontal metaphysically necessary connections, that is, those between putative causes and effects. Vertical metaphysically necessary connections, unlike horizontal ones, run perpendicular to what is unproblematically agreed to be the direction of causation between wholly distinct events. The concern is whether they set up a spurious appearance of efficacy. Suppose that two property instances, b₁ and b₂, are causally related and, as a result, support the relevant counterfactuals. Let b₁ and b₂ metaphysically necessitate m₁ and m₂, respectively. It is plausible that, as a result, the corresponding counterfactuals hold of m₁ and m₂. The question is whether this is appropriately taken as indicating that m₁ is a cause of m₂. The question arises for all those properties that, intuitively, make up the layered picture of the world: between determinates and their determinables, micro-properties and the macro-properties whose instantiation they determine, and so forth. I discuss this issue before the horizontal case because it assists in my discussion of the latter. Discussion of this issue also enables me to flesh out the characterization of coarsely individuated events outlined in .. The notion of requirement to which I appealed in characterizing the relationship between properties that are part of the same event involves metaphysical necessitation. The details provided in . constitute my further contribution to this issue. The challenge to my analysis of causation from horizontal connections doesn’t arise in the case of coarsely individuated events because, if b₁ and b₂ metaphysically necessitate m₁ and m₂ respectively, then m₁ and b₁ are properties of the same event and, likewise, for b₂ and m₂. The problem arises A Variety of Causes. Paul Noordhof, Oxford University Press (2020). © Paul Noordhof. DOI: 10.1093/oso/9780199251469.001.0001



 

for property instances because, more plausibly, the instance of m₁ is not identical to the instance of b₁ (see .., .., and . for further discussion). There are broadly speaking two approaches to this challenge. The first appeals to more specific counterfactuals or more general patterns of counterfactual dependency. The appeal is usually situated within a contextualist approach to causation, involving appeal to context-determined contrasts. The second focuses on the character of the relationship between the M-properties and the B-properties. In the second part of the chapter, I evaluate the first approach and defend a version of the second. I argue that the first approach presents in name only, a solution to the problem outlined in .. Not everybody accepts the distinction between property instance causation and property causation. Some have sought to deny that there is anything more than property instance causation. In ., I argue that the reasons that speak in favour of recognizing causation by instances of properties, over and above causation by events, speak further in favour of distinguishing property causation from property instance causation. I then outline my account of the latter. The apparent truth of certain contrastive statements, and statements involving emphasis, is not simply a matter of whether or not the appropriate kind of property causation holds. This threatens the motivation for my analysis of property causation and promises a comeback for the approaches I criticized in .. It also reopens the question of whether I was right to conclude in Chapter  that coarsely individuated events may be the relata of causation. In the last part of the chapter I argue that, in fact, the relevant contrastive statements are false but they are taken to convey something true because of pragmatic implications they have concerning the explanatory virtues possessed by the properties identified as the causes: in particular, whether the properties occupy a distinctive causal role within an explanatory framework or whether they make the exact causal contribution required without redundancy. The reason why the statements are false is that, in conveying the explanatory virtues, they incorrectly deny causation to certain properties in the circumstances.

. Property Instance Causation Suppose that two properties, F and G, are not identical. A natural view is that their instances are not identical either. Nevertheless, there may be intimate connections between these instances. One such intimate connection that gives rise to the problem on which I will be focusing in . is that of metaphysical necessitation. This may well be a general characterization of a collection of more precise intimate relationships. That does not matter for the present purposes. Some will hold that if two property instances are this intimately related, then, in fact, they are the same instance. For example, this instance of colour is an instance of redness of a certain shade, this instance of shape is an instance of being an equilateral triangle, and so on. If that were generally correct, the problem would not arise in precisely this form (Macdonald and Macdonald (), (); Robb (), for further discussion Noordhof (c), (), some of the discussion below is taken from the latter paper although there are differences of emphasis and development). The challenge would be to justify the identification of instances given that the properties are not identical.

  



Causation may provide an answer. In which case, the discussion that follows may still be useful after all.

.. Minimal metaphysical necessitation relations between property instances According to the account of events defended in ., causation between events is causation between temporally and property limited particulars. The properties that constituted the limitation were said to stand in a certain intimate vertical relationship to each other. The most familiar examples involve determinate and determinable properties. A natural way to characterize a key feature of this relationship is that, for a particular determinable property D, its determinates D₁, D₂, D₃, . . . Dn metaphysically necessitate it: ☐m (x)(Dix ⊃ Dx) (‘☐m’ standing for metaphysical necessitation, as opposed to some more limited notion like nomological necessitation: ‘☐n’). While the determinable doesn’t metaphysically necessitate any particular determinate, it metaphysically necessitates one of the exhaustive potentially infinite disjunctions of determinates: ☐m (x)(Dx ⊃ (D₁x v D₂x v D₃x, . . . v Dnx)). Let an event be specified as having the property limitation F. Then it also has all the properties that are required for F (in the sense of metaphysically necessitated by F) and also it has some property from the disjunction, a disjunct of which is required for the instantiation of F (if F is a determinable) (I refer you back to (di), (dii), ..). Determinable properties are sometimes taken to be properties of their determinates. Thus an object is coloured because, say, it is red and red is a colour. The object’s redness and redness having the property of being a colour is taken to be the truth-base of the statement that the object is coloured. This seems ill-motivated independent of the question of whether determinable properties exist (see ..). It is often suggested as a way of understanding how there can be a metaphysically necessary relationship between determinates and determinables. However, a metaphysically necessary relationship between a property and a property of that property is no less puzzling than a metaphysically necessary relationship between two properties. It’s just that the mystery is disguised a little. If being a colour is a property of being red, then it might seem that the former will be instantiated in every possible world where the latter is. But the following questions arise. First, why couldn’t the property of being red be a colour in some possible worlds but not others? Second, what makes the property of being a colour the property of a property of being red? Answers may be available to these questions, which would no doubt appeal to the invariable nature of redness in this regard, but then the same kind of answers are available to those who seek to explain the metaphysically necessary relationship between two first-order properties: being red and being coloured (Noordhof (a), a discussion of Forrest ()). The thesis that determinable properties are properties of properties also appears committed to the existence of fully determinate properties. If, for any property, there is another property more determinate than it, it would follow that all properties would end up properties of other properties rather than properties of particulars. Determinables and determinates are not the only properties that stand in the kind of relationship I have in mind. Arguably, they are part of a more general category of



 

realized and realizing properties. One illustration of this may be mental properties. It is suggested that physicalism is a contingent truth (e.g. Lewis (), p. ). In some worlds, perhaps ours, mental properties may be realized by physical properties. In other possible worlds, different, non-physical, properties may realize mental ones. It is plausible—though may be resisted –that the non-physical and physical realizations of mental properties do not form a class of determinates. The properties, which are the realizers of mental properties, are a matter of the laws of nature that hold at a world. Thus some formulations of physicalism have only required that worlds nomologically like ours will have physical properties realizing mental properties by metaphysically necessitating them. If this is so, then the proper formulation of the second relationship identified above would be ☐m (x)(Rx ⊃ L₁(Ra₁x v Ra₂x v Ra₃x, . . . v Ranx) v L₂(Rb₁x v Rb₂x v Rb₃x, . . . v Rbnx) . . . v Ln(Rz₁x v Rz₂x v Rz₃x, . . . v Rznx)) where Li (where i is either  or , etc.) represented different bodies of relevant laws which held at worlds, R the realized property, and Rai, Rbi, etc. the various realizing properties in the world in question. The first relationship will stay the same because, given that certain properties are instantiated, related by certain laws, it follows of metaphysical necessity that the target realized property is instantiated. As an illustration of this second relationship, consider what many functionalists are inclined to say about mental properties. They may be realized by certain specific physical properties in a world in which physicalism is true and by ectoplasmic properties in a world in which dualism is true (e.g. Putnam (), p. ). The mental properties themselves are causal role properties. That is, they are instantiated if a certain causal role is instantiated. The occupants of this causal role are the realizing properties, for example, Ra₁x. However, Ra₁x only plays the role it does if certain laws relating Ra₁x to other realizing properties hold. Therefore, there is only a metaphysically necessary relationship between the property plus laws and the target realized property. This is not a version of dualism because the laws are not sui generis laws relating Ra₁x and R but rather relating Ra₁x with other realizing properties as a result of which R is instantiated. A third relationship that fits the characterization I have provided is the macro– micro-relation. Arrangements of micro-properties and relations, such as the properties and relations concerning fundamental particles, metaphysically necessitate macro-properties in the following sense: ☐m (x)(Aix ⊃ Mx) where Ai stands for a particular arrangement of micro-physical properties, including the relations which hold between them. It is Ai rather than the properties and relations by themselves that necessitate M. An event’s possession of properties and relations is not sufficient to ensure that the properties and relations in question are arranged in the right way for the instantiation of the macro-physical property. Equally, if a certain macrophysical property is instantiated, then one of a number of different arrangements of micro-physical properties should be: ☐m (x)(Mx ⊃ A₁x v A₂x v A₃x, . . . v Anx). Since the relationship between M and A seems similar to that between D and Di (determinables and their determinates), it may seem that the former can be assimilated to the latter. However, not every arrangement Ai need be a particular determinate instance of M. Instead, some will be and some will not be. For example, not every arrangement of dots and distances between them make up a square. So some As would not count as different ways of being the target determinable, which is an intuitive necessary condition for being a determinate (e.g. Funkhouser (), for

  



fleshing out of this idea). Thus, the two metaphysically necessary relationships are not sufficient for characterizing the nature of the determinable-determinate relation. Each of the relationships I have identified are not simply a metaphysically necessary relationship between the base properties—determinates, realizers, and arrangements of micro-properties—and the necessitated properties. Suppose that B is a base property. Then B and T will also metaphysically necessitate the relevant determinable, realized or macro-properties. Yet, T might not have anything to do with B in the sense of forming a more determinate property, an extension of the arrangement of micro-properties, and so forth. T could be anything. There may be more detailed requirements for each type of property relationship but a condition that they all seem to share is that B must, at least, be a minimal necessitation condition for the target properties. We might formulate this as follows. B is not the minimal necessitation condition of P if P is still instantiated if not B but B- (where B- is B without the instantiation of certain properties and no additional properties are instantiated except those which are metaphysically necessitated by the non-instantiation of these other properties) (Noordhof (c), p. ). The present concern is not with providing a full characterization of these various intimate vertical connections but rather to focus on an issue which arises for my analysis of causation when, at least, the identified metaphysical necessitation holds. Although the analysis was formulated in terms of events, it is intended to be applicable to causal relations between other particulars, for instance, between property instances, given that property instances are not events. Some argue that causal relations hold between events and that any properties of these events are not causes but rather causally relevant. I don’t mind if this different terminology is adopted. In that case, my analysis provides an account of the causal relevance of property instances. Thus the issue below arises one way or another.

.. The challenge from vertical necessitation relations Vertical necessitation relations come, according to many, in at least two strengths. I have focused on the stronger: metaphysical necessitation. Many would find space for a weaker—nomological necessitation—and argue that even these necessitation relations provide a challenge to the counterfactual theory of causation. Before I turn to what I consider the real challenge—the stronger challenge—I will explain why my analysis of causation can apply in a straightforward fashion to properties nomologically necessitated by base properties. I will address the position of those who take nomological necessitation to be as strong as metaphysical necessitation later in this chapter, and further in ..–. To simplify discussion, since greater complexity would not seem to touch on the concern, suppose the situation is as follows:

b0

Figure .

e1

e2

b1

b2



 

where the vertical and upward arrows represent nomological necessitation. Assume, for simplicity, that, for any two property instances or events, p₁ and p₂, if p₁ nomologically necessitates p₂, p₁ is a cause of p₂ and, hence, satisfies the terms of my analysis. The issue is whether, contrary to what I have drawn above, an implication of the analysis is that e₁ is a cause of e₂ and b₂ and, hence, my analysis of causation cannot allow for the possibility of instances of properties that are nomologically necessitated by instances of base properties but do not cause either the instances of base properties or each other: the kind of position advanced by epiphenomenal emergentists. The objection is that the following backtracking conditional must be true, ‘If e₁ were not to occur, then b₁ would not occur’. If that’s right, then b₂ would not occur and hence it looks as if e₁ is a cause of b₂. I shall address the objection in these terms. In order for us to accept the backtracking counterfactual, the usual perfect match considerations would have to be argued not to apply. It is hard to see why they do not. We can obtain a greater extent of perfect match if we envisage that the nomological relationship between b₁ and e₁ is disturbed than if we take b₁ to be off the scene too. In order for b₁ not to occur, there would have to have been some prior change in the causal circumstances leading up to it. That means that the extent of perfect match will end some way prior to b₁. By contrast, the failure of e₁ might arise from the causal circumstances of which b₁ is a part. Even if things were finely balanced, and we would not have a guaranteed extent of perfect match up to b₁, all we would have is the conclusion that it may be the case that b₁ does not occur which is not sufficient for the required counterfactual dependence to hold between e₁ and b₂. Moreover, since e₁ is putatively causally isolated, there is the possibility of perfect match after e₁ too, if we suppose that b₁ is still present. So there is no reason to suppose that a counterfactual analysis will be committed to denying the possibility of epiphenomenal emergentism (Noordhof (a)). In .., I consider whether my particular analysis of causation has features that vitiate the general considerations drawn from the semantics of counterfactuals I have outlined here and argue that it does not. In ., I discuss the different approaches to laws, some of which take nomological necessitation to be a variant of metaphysical necessitation. Further issues are raised at this point. With horizontal relations of nomological necessitation out of the way, let’s turn to metaphysical necessitation. The set-up we need to consider is very similar to the one detailed above. The thick arrows indicate metaphysical necessity.

b0

m1

m2

b1

b2

Figure . That is, b₁ and b₂ metaphysically necessitate m₁ and m₂ respectively and suppose that, by my analysis, b₁ is a cause of b₂. If b₁ is a competitor-absent chanceraiser of b₂, then if b₁ were absent, the chance of b₂ would be lower. The phrase ‘competitor-absent’ is to mark the fact that we are envisaging circumstances which

  



are free of overdetermination, pre-emption, or the like (setting aside what is the right thing to say about m₁ for the moment). If b₁ metaphysically necessitates m₁, there is no possible world in which m₁ is absent and b₁ present. Therefore, m₁ is a competitor-absent chance-raiser of b₂ too since, according to my analysis, competitorabsent chance-raisers are causes if the causal chain between them and the effect are complete and there is no reason to suppose that, in the case in hand, it must be incomplete, m₁ comes out a cause of b₂. The conclusion cannot be avoided by arguing that there might be a b₁* which occurs in place of b₁ to play the same role and so the chance of b₂ would not be lowered. My analysis does not claim that causes are chance-raisers of their effects. Rather they are competitor-absent chance-raisers. If a replacement, b₁*, occurs, then we don’t have circumstances in which competitors are absent. Call cases in which a replacement occurs in close-by possible worlds: close-world redundant causation. If actual-world redundant causation is legitimate, then close-by world redundant causation is too. My analysis secures that verdict. Put b₁*, and indeed any other possible replacement for b₁, in Σ. Then, without any of these events occurring, m₁ is a chance-raiser of b₂ and hence, on the assumption that the m₁–b₂ chain is complete, a cause of b₂. The question is whether this is a cost. The main argument against the verdict that m₁ is a cause is due to Kim (Kim (), pp. –, (), pp. –). Originally it was formulated as an argument against non-reductive physicalism. Indeed, it is to honour this—and hint that they are metaphysically necessitated—that I have dubbed the metaphysically necessitated properties m₁ and m₂ to suggest they might be mental though, of course, the argumentation is general. Kim presents the argument as follows. We assume, as our starting point, that b₁ is causally sufficient for, or fixes the probability of, b₂. My talk of probability fixing is to cover the case of indeterministic causation. It is not to deny that, if indeterminism is true, b₁ would be a cause of b₂. b₁ would be a cause by fixing b₂’s probability in the way required by the analysis. If m₁ is a cause of m₂, then m₁ either causes m₂ directly or indirectly by causing b₂ to occur. If m₁ causes m₂ directly, then it follows that either b₁ is not a sufficient cause of (or fixes the probability of) m₂ by causing b₂ or it is an overdetermining cause of m₂. If m₁ causes m₂ indirectly via b₂, then the same options arise but this time with respect to b₂. It seems that my analysis, and indeed any other counterfactual theory, is committed to supposing that in every case in which property instances metaphysically necessitate each other in the way described in the set-up, either b₁ cannot be a sufficient cause of (fix the probability of) m₂ in the circumstances or there is overdetermination. Prima facie, neither option is attractive. If b₁ is not a sufficient cause of (or probability fixer of) b₂, then it seems that, where the bs are those properties identified by physics, we’ve lost the claim that the physical world so understood is causally complete. It will not be true that, sufficient causes for the instantiation of all properties identified by physics will be instantiations of other properties identified by physics. Moreover, this is not because our current physics has failed to identify some property that a future physics might be developed to mention. Since it is plausible that non-reductive physicalism holds that all properties are metaphysically



 

necessitated by those properties identified by a correct physics which resembles our own, non-reductive physicalists would be committed to physics only being completable by mentioning all these other properties. This seems unacceptable. The alternative would be to accept that there is a massive amount of overdetermination. Indeed, the overdetermination is systematic. Any causation involving instances of properties that metaphysically necessitate other properties— determinables, realized properties, macro-properties—that is almost all causation involving instances of properties, will involve overdetermination. Again, if nonreductive physicalism is true, then all instances of properties are metaphysically necessitated by instances of narrowly physical properties, or arrangements thereof (where narrowly physical properties are those which are identified by some physics resembling our own). In which case, there would be systematic overdetermination in every case of property instance causation. If, as is further plausible, causation between events involves causation between property instances, viz some of those properties that were the property limitation elements of the respective events, then all causation, not just all causation by property instances, involves systematic overdetermination. It is simply that, in the case of event causation, since they are particulars limited by a bundle of properties in the way I have indicated, the overdetermining elements are part of the same event, so there is no overdetermination to be characterized in terms of events. Kim’s argument involves another simplification that might seem to mask a way out. There is usually not just one sufficient cause, or probability fixer, at a certain point in time for any effect. Instead, there are causal circumstances made up of many different property instances that are individually necessary and jointly sufficient to cause, or fix, the probability, given that the other property instances are instantiated. Thus it may seem that there is no problem with recognizing that the metaphysically necessitated property instances are sufficient causes, or probability fixers, too. That is incorrect. Suppose that the following five property instances are jointly sufficient for an effect e, or its probability, at a certain point in time: b₁, b₁₂, b₁₃, b₁₄, and b₁₅. Obviously, as the causal process develops over time, there will be a succession of sufficient causes, or probability fixers, making up the process—hence the limitation to a time. Kim’s argument putatively establishes that either b₁, b₁₂, b₁₃, b₁₄, and b₁₅ cannot be sufficient causes because all the properties which are metaphysically necessitated by b₁, b₁₂, b₁₃, b₁₄, and b₁₅ are also required or that there is overdetermination. The argument targets what we should say about a particular point in a causal chain with regard to the contribution of particular property instances. It is not making the mistake of assuming that there is only going to be one sufficient cause, probability fixer, at a time. The problem to which Kim’s argument draws attention obviously doesn’t arise if there are no plausible cases of property instances that are metaphysically necessitated by, but not identical with, other property instances. The difficulty lies in justifying this conclusion. When I provide examples both above and below, I don’t mean to rule out the possibility that with metaphysical necessitation comes identity. The point is rather to evaluate what we should say if it doesn’t seem obvious.

  - 



. Avoidance and Head-On Strategies Preliminary responses to Kim’s argument can be divided into avoidance and head-on strategies. Avoidance strategies claim that Kim’s reasoning does not apply to causation although it may apply to some other notion, that of determination for example. Thus they tend to deny that b₁ (the metaphysically necessitating property) is a sufficient cause (or probability fixer) of m₂ (the property metaphysically necessitated by b₂) even though b₁ is a sufficient cause (or probability fixer) of b₂. As my analysis has the result that both b₁ and m₁ are causes of m₂, the potential attractiveness of an avoidance strategy becomes a criticism of my analysis. In .., I explain how the avoidance strategy typically works and why it should not be pursued. A head-on response seeks to justify the verdict of counterfactual theories such as my own that, if b₁ is efficacious and b₁ vertically metaphysically necessitates m₁, then m₁ is efficacious (with some qualifications). In defending my theory, I will be offering a head-on response. This will involve two components: first, a defence of a certain view of property causation; second, a qualification to Kim’s appeal to overdetermination.

.. Avoidance strategies Avoidance strategies differ in detail but there are certain crucial elements in common to different versions of the strategy. One is some restriction upon interlevel causation. Either it can be denied altogether or there are contexts in which it is not appropriate to consider it (for the former Gibbons (), for the latter e.g. Menzies ()). If there isn’t a blanket denial of interlevel causation, then the standard recourse is to a contextualist element in causal statements. It will be part of their semantics that the context in which they are produced will rule out the impact of interlevel considerations in some way. Once more, the development of the contextualist element takes causal statements to be contrastive and allows context of utterance to determine (in part) the relevant contrast. A sophisticated development of this strategy, due to Menzies, holds that different levels are associated with different patterns of close-world redundancy. To take the basic case with which we are familiar, (PAm)

If m₁ were not to occur, then no necessitation base of m₁ would occur.

(PAb) If b₁(M₁) were not to occur, then some other necessitation base of M₁, b₂(M₁) may occur. If another necessitation base of M₁ may occur in the absence of b₁(M₁), it is not the case that there would be no instance of B₂, b₂. Whereas, this cannot be said if we consider what would be the case if m₁ were absent (List and Menzies (), pp. –, Menzies (), p. ). Appeal to different patterns of close-world dependency has a number of failings both of implementation and dialectically. On the implementation side, it makes the question of whether or not something is a cause turn on whether or not, if it were absent, a replacement would occur. It is natural to think that even if replacements would occur, this would not detract from the causal work the replaced is actually



 

doing. We would be alarmed at the prospect that we would receive no credit for things we did if somebody else would have done them if we hadn’t. As a brief contribution to domestic harmony, I suggest that it is ill-advised to argue that there is no need for you to do your fair share of the chores because, although they have been drudging away, in fact they shouldn’t be credited with anything because you would have done the chores, if they hadn’t. Moreover, and this is a related point, the reasoning in favour of rejecting the efficacy of the base properties in the circumstances envisaged—close-world redundancy—is not judged to be sound in the case of actual-world redundancy: i.e. cases of pre-emption and overdetermination. Without some differentiation between these two cases, appealing to close-world redundancy to capture the efficacy of the m-properties is unmotivated. The counterfactual reasoning with which I began this section has been taken to express another feature of causes which, thereby, provides a motivation for taking the previous points I’ve made to be inconclusive. Causes should be proportional to their effects, and not contain lots of redundant elements (Yablo a; Menzies ; List and Menzies , pp. –). This is alleged to be the difference between m₁ and any of its bases. As things stand, this last claim is susceptible to a deflationary response. The objector to the efficacy of m₁ can concede that talk of m₁ has a causal implication that talk of one of its bases does not: m₁’s absence ensures the absence of sufficient causes/chance-fixers, that is, any of the bases; talk of a particular base does not. Nevertheless, it can be argued, it is not that, by these means, m₁ is revealed to be the cause itself. m₁ is not, by anybody’s lights, a cause of any of its necessitation bases, rather its absence entails the absence of any of them. In brief, we have causal explanatory impact without causation. This response has to be dealt with head on. The avoidance strategy does not succeed in avoiding the issues relating to interlevel causation that were its motivation. The claim of proportionality is, plausibly, overstated in any case and, thus, doesn’t get past the difficulty raised by the exclusion argument. Considerations of proportionality entitle something to be counted a cause in the following sense. If c and c’ are putative competitor causes of e at the same point in the causal network, and c is more proportional than c’ for e, then if c’ is a cause, c is a cause. In brief, the reason for this is that more proportional causes are specified in terms of properties that enable us to capture a generality that less proportional causes miss. So if the latter is a cause, the former will be too. This will become clearer upon the development of my approach in ... The weaker claim does not support denying that the less proportional putative competitor cause is a cause. On the dialectical side, the worry is that even if causation is not simply a matter of determination, determination is a necessary condition. The fact that there might be different patterns of close-world redundancy for properties at different levels does not undermine the point that each property instance is properly taken as sufficient to determine the target effect property instance (or the probability of that effect under indeterminism). So there is still a competition of determination and Kim’s argument purports to show that, with regard to this competition, it is the lower-level property

  - 



that wins (Noordhof (b), p. –). Even if Kim concedes that we use the term ‘cause’ in the way that the proponent of the appeal to different patterns of close-world redundancy insists, what is, in effect, the same problem can be reformulated as a problem of competition of determiners rather than causes instead. Philosophical advance is rarely brought about by reclassification. The objections canvassed apply to any approach that seeks to appeal to different contrasts to provide distinct causal roles for properties in relations of vertical metaphysical necessitation. Thus, they will apply to non-contextualist contrastive approaches and approaches which take context to settle more than simply the contrast but also the causal circumstances which should be held fixed (Menzies (b), pp. –, (), pp. –). The objections do not presume that one type of property—for instance, narrowly physical properties—are causally fundamental. The charge is simply that both properties standing in a relation of vertical metaphysical necessitation should not be taken to be efficacious.

.. Head-on strategies The account of property causation that I wish to defend has two elements, a particularity condition and a generality condition. The full proposal runs as follows. F is a property cause of G if and only if Particularity: part of the (minimal) necessitation base for the instance of F causes part of the (minimal) necessitation base for the instance of G. Generality: (part of) each (minimal) necessitation base of F is such that all its instantiations would cause (or in the case of indeterminism, raise the - probability of) an instantiation of one of the (minimal) necessitation bases of G if they were in some causal circumstances C—where C may vary for each kind of necessitation base. The first component, the particularity condition, is part of the immediate answer to Kim’s argument. The second component is a response to a natural objection to the approach which goes beyond the considerations that Kim adduces and the response to this leads us to the second subject matter of the chapter, giving a proper account of the phenomena of emphasis and the like mentioned in ... Although generality is often taken to be indicative of an appeal to laws, the formulation of generality does not make the proposal a law-based account of property causation. For example, the claim is not that, in circumstances C, all Fs are followed by Gs. In circumstances C, Fs are not followed by Gs if F has the wrong minimal necessitation base for the circumstances in question. ... , ,   Let me comment on a few of the features necessary to understand the thought behind particularity. The appeal to minimal necessitation base is to be understood in terms of metaphysical necessity—just as with the characterization of the challenge from vertical necessitation. The intuitive idea, which I sought to analyse earlier in this chapter, is straightforward. Properties are efficacious in virtue of their instantiations. The minimal necessitation base for F is all that needs to be instantiated for a particular way of



 

instantiating F. At the level of properties, rather than their instances, it is hard to demarcate the relationship between F and the properties that are instantiated in its minimal necessitation base. For example, structural universals (if they exist) cannot be composed from other universals. The classic example to illustrate this is Lewis’ case of methane: CH₄ (Lewis (d)). It is not composed of four hydrogen universals and one carbon universal because there are not four hydrogen universals. If CH₄ involves four instances of hydrogen, then it is not a structural universal. It is a universal-instance hybrid that does not capture what is common to all instances of methane, for example, those instances that involve other instances of hydrogen than the ones that occur in the methane universal. A universal-instance hybrid cannot—as universals are taken to do—be wholly present in each instance. It will not be wholly present in any instance of a methane molecule because they will contain other instances of hydrogen not present in the structural universal (Lewis (d), p. ). We can’t understand structural properties in terms of property instance constitution either. Instances of methane may be composed from one instance of the property of carbon and four instances of the property of hydrogen but even this does not work for variably realized properties. A single universal cannot be constituted in various ways, even if its instances can be. So variably realized universals can’t be said to have other properties as constituents. Maybe there are ways of resolving these matters but we may sidestep the issue of how properties are related to the properties of their minimal necessitation base and focus on the property instances themselves. Given that the particularity condition is concerned with properties instantiated, its purposes are served by noting the relationship of minimal metaphysical necessitation between the instances. Of course, particular analyses of minimal necessitation base—and the background idea of property instance constitution—may fail. But since the idea is natural and, more importantly, does not implicitly draw on claims concerning the efficacy of the metaphysically necessitated properties, we could safely take it as a primitive without a concern that it vitiates the substance of the account of property causation. In the formulation, the appeal to ‘part of ’ is to allow for the possibility that something may count as efficacious only in virtue of an element of it being efficacious. The fire burned because of the presence of air in virtue of the fact that oxygen is part of air. I shall discuss this no further here but it is relevant to the issue of the efficacy of mental properties for which externalism is true (Segal and Sober (), Noordhof (c)). I return to it when we focus on explanatory virtues in . and when we turn to the discussion of the problem from horizontal necessitation in Chapter . Those who suppose that causation at the level of physics is fundamental can think of the particularity claim as a transmission of causality principle: a necessary condition for F to count as efficacious, and a necessary and sufficient condition for an instance of F to count as efficacious (which I distinguish from F being efficacious, as we shall see, from later discussion in .). My preference is to think of it as stating how causation between different levels of properties is in harmony. From this perspective, it is not an account of how M-properties are efficacious given that B-properties are efficacious in virtue of my analysis of causation. M-properties are efficacious in their own right by satisfying the analysis.

  - 



The defence of particularity has two components. The first is to show how it is a generalization from some intuitive cases in which properties so related are both efficacious. I explain why these cases should be taken at face value against some particular challenges that have been made to them. The cases I mention will be instances of the types of properties mentioned in ... In that section, I was concerned to explain how these properties give rise to the satisfaction of the analysis of causation. By now considering examples and noting that we find these examples very natural to count as efficacious, I undermine the claim that the verdict is a mistake. Those who insist that the verdict is a mistake are being radically revisionary. To such folk, I raise the second component of my defence of particularity: an accusation of asymmetry. Consider cases of macro-properties such as the properties of being an earthquake, a river, a glacier, a match lighting, having a surface with grooves, being a liquid, being methane, being sperm, and so forth. All have instances that seem intuitively efficacious. There seems absolutely nothing wrong with holding that an instance of the property of being an earthquake was a cause of an instance of the property of being the collapse of the buildings in the street. Admittedly the English is not very elegant but I put things in this manner just to make clear that we are not simply considering events (about whose efficacy everybody can agree) but also properties of these events. Yet, the instances of these properties are metaphysically necessitated by arrangements of narrowly physical properties. Determinable properties provide another illustration. If my  stone weight caused the chair to collapse, it seems a mistake to claim that an instance of the property of having weight in those circumstances was inefficacious. In this case, the former seems more adequate than the latter because my simply having weight is not enough to break the chair. Let’s suppose that if I were lighter, the chair would not have broken. Inadequacy is not enough to establish that the instance of the property of weight is inefficacious. Having weight is certainly necessary in the circumstances and it is sufficient if we count the way in which it is instantiated. Perhaps it will be argued that my talk of the way in which something is instantiated shows that the determinate rather than the determinable is efficacious. However, that is mistaken. We are inclined to say that something being a knife is a cause of the wounding in which it is used but, of course, we wouldn’t have a wounding if the knife were very blunt. It is because the knife is sharp that the wounding takes place. This doesn’t impugn the efficacy of the property instance of being a knife but explains how, in those circumstances, the property instance had that efficacy. The object being a knife was necessary in the circumstances for the wounding. If the sharp point had been at the top of a heavy flag-pole impossible to wield, no wounding would have taken place. Acknowledging how two property instances’ coinstantiation have a certain causal consequence does not undermine the case for the efficacy of each determinable instance. Otherwise, we’d need to explain why efficacy was undermined here and not in the case of causes working collectively part of causal circumstances to have a certain causal consequence. Moreover, determinate properties have a commensurate apparent flaw to inadequacy: superfluity. If the chair is incredibly fragile so that any weight applied to it is sufficient for it to break, my weight didn’t need to be  stone for the chair to break.



 

An instance of the property of being  stone has elements that are superfluous to requirements. Nevertheless, it seems plausible to say that, just because it is a weight property, it is legitimate to count it as a cause of the breaking. If there were general arguments in favour of either the uniform efficacy of the most determinate, or the uniform efficacy of the right level of the less determinate, then things would look different. The efficacy of determinable properties has certainly been questioned. The main charge is that determinate properties have all the causal powers attributed to determinable properties and, hence, there is no reason to take the latter to exist. It appeals to what has been called the ‘subset’ account of realization (e.g. Shoemaker (), pp. –; Wilson (), p. , (), p. , (), p. ). An object that has the determinate property of being a sphere of a certain size has all the causal powers that accrue to it as a result of that property. Obviously if the object is a sphere of a certain size, it is also simply a sphere. Yet, the reasoning goes, the latter property is not required by the object to confer the causal powers distinctive of being simply spherical. These causal powers are a subset of the causal powers of being a spherical object of a certain size. What confers no causal powers does not exist (Gillett and Rives (), pp. –). The reasoning is questionable in two respects. First, it seems to rule out the possibility that the instantiation of a determinate property has some of its causal powers because it involves the instantiation of a determinable property. In which case, the argument can hardly hope to establish in a non-question-begging fashion that determinables don’t exist. It appears to rely upon an antecedent commitment to the non-existence of determinables. If instantiations of determinate properties have the determinable’s subset of powers, by involving their instantiation, then there will be no double-counting of causal powers (a charge made by Gillett and Rives (), pp. –). Possessing the same subset of causal powers is a genuine form of resemblance between objects. Indeed, the subset view seems to provide a good reason to conclude that determinable properties exist. So, by their own lights, the arguments of those who deny the existence of determinable properties are unsound. Second, though, it is not clear that instances of determinable properties have causal powers that are simply a subset of an instance of the determinate property that realizes them. Suppose that there is a circular hole of  cm diameter. A sphere  cm or less can go through it, a cube would have to be around . cm or under to go through. The property of being a sphere has causal powers that the property of being a  cm sphere does not, namely passing through the hole for a range of sizes at or below  cm. By the same token, it has causal powers the property of being a cube does not, namely being able to pass through the whole with widths above . cm up until  cm, again powers the  cm sphere does not have. The point is reinforced when we consider cases which, while they are not naturally thought of as examples of the determinable–determinate relation, share with this relation the characterization of the second property being a way in which the first property is realized. For example, being a spherical rock is a way of being spherical. Suppose a spherical rock travels through a window at speed leaving a spherical hole in the glass (along with cracks spreading outwards). A spherical piece of cotton wool has no such effects. The property of being spherical has causal consequences the

  - 



property of being a spherical piece of cotton wool does not, namely that the former is a cause of the spherical character of the hole. Such cases only appear problematic if you assume that the powers of a determinable must be derived from a determinate rather than simply due to the determinables in their own right. A natural response is to say that, although a determinable property doesn’t have a subset of the causal powers of its determinate realizing property on a particular occasion, it can be thought of as having a disjunction of subsets of the causal powers, one subset for each of its determinates (Gillett and Rives (), p. , fn. ). That means that, for a particular instantiation, the determinable property does not have the causal powers it has when instantiated with another of its determinates. The response cannot constitute an argument against the existence of determinables and, in particular, not a causal argument against their existence. It presumes that there is no reality to a determinable other than its instantiation by a particular determinate of it. Standardly, an object or property has its causal powers regardless of whether it is in circumstances conducive to their manifestation. Applying this thought to the case in hand, the property of being spherical has the power to go through spherical holes for a certain range of sizes or make spherical holes in windows regardless of whether, on a particular occasion, it cannot because it has too great a size or is a characteristic of cotton wool. The claim can only be dismissed if it is thought that the existence of the determinable on a particular occasion is simply the determinate in which it is instantiated. Naturally enough, with this assumption, it will seem obvious that determinables have no distinctive powers free of their determinates and hence that determinables don’t exist. Of course, determinables require some determinate or other to be instantiated. This does not mean that, given all the determinates of a world, we have explained all the causal powers in that world. A world does not involve instantiations of all a determinable’s determinates. Even if it did, we would still lack an explanation of how, for a particular instantiation of a determinable, it has causal powers that outstrip those of its determinate. The fact that there are other determinates with different causal powers has no impact upon the causal powers of the particular determinable in question (for further discussion Noordhof (b), pp. –). I don’t pretend to have shown that determinables exist to the resolute sceptic about their existence. The argument of the last few paragraphs rests upon the assumption that they exist and shows that, on this assumption, there are resources to answer the sceptic about determinables. Arguments that they don’t exist rest upon claims there is no reason to believe if you’re not already convinced. Equally, though, if determinables don’t exist, we have one less problem case involving horizontal necessitation for my analysis of causation and one less type of counterexample to particularity. Efficacy doesn’t transmit to, or have to be harmonized with, entities that don’t exist (of course). My claim is simply that, if there is a metaphysically necessary relationship of the required type between instantiations of properties (each of which exist), then the necessitated will be efficacious if the necessitating are. It is sometimes argued that if you are committed to a sparse conception of properties—in which there are only properties corresponding to some predicates— you are committed to rejecting the efficacy, and thereby existence, of determinable properties, and the like (e.g. Crane (), p. –). This is a mistake. The efficacy of



 

instances of determinable properties is linked to the grounds we have for making causal inferences concerning patterns of causal activity. Suppose that only superdeterminates are efficacious, that is, those properties for which there is no further determinate. In observing a particular causal relation involving a superdeterminate, there is nothing in what we observe that could be the basis for inferring something about instances of any of the determinables under which the superdeterminate falls. If there is no commonality corresponding to the determinable predicate, then there is no common causal activity to be expected. Suppose the chair collapses under my  stone weight. Then we haven’t observed anything that is the proper basis for concluding that a similarly constructed chair would have collapsed if I had been  stone or that that particular chair would have collapsed if I had been  stone. Talk of proper basis for an inference is a bit vague, and deliberately so. It is a subject of debate whether these kinds of causal inferences can be justified. I shall touch upon the matter again in ... My current point is rather that the existence of certain kinds of generality in the world, related to the occurrence of causation, are a necessary condition for any such justification. Proper appreciation of the connection suggests that the putative dilemma of either sparse superdeterminacy or profligacy is a false one. Discussion of the truth-base (or truth-maker) of a causal statement invites focus on what is required to make the causal statement true so obscuring what may be required to provide a proper basis for the inferential relationships which we, intuitively, suppose that the causal relation may support: call this the inference base of the statement. Even if all that is required for the truth of ‘my  stone weight caused the chair to collapse’ is superdeterminates concerning the  stone weight and chair collapse, there is the further question of whether the causal relation supports a generalization, and if so which generalization. It is at this point that the significance of allowing the existence of some determinable, rather than others, makes itself manifest. These points don’t just apply to the determinable–determinate relation. They apply to any properties standing in the relationship of metaphysical necessitation in which one of them is more determinate than the other. Consider the case of pain and its realization in either, if physicalism is true and current theories of pain are correct, c-fibre and A-Δ fibre firing in humans and, let’s suppose, silicon state S₁ in silicon life. Suppose, for the sake of argument, such physical states are no more plausibly thought of as determinates of the determinable pain, than a spherical rock is a determinate of the determinable being a sphere. Nevertheless, the attribution of pain is a plausible basis for inferences across life forms about how they would behave. Commitment to properties as inference bases corresponding to their nomological role is at the root of the challenge of vertical necessitation to which the particularity claim is addressed. It should be noted that the appeal to inference base here involves no appeal to an idea of necessity. The claim is not that if we recognize determinables, then we grasp something that makes patterns of events conform to necessary connections between them. The point is simply that if we recognize no commonality, there is no basis, Humean or non-Humean, for an inference at all. The second component of my defence of particularity is the charge of unmotivated asymmetry. It concerns the different attitudes taken to, for instance, macro-causal

  - 



relations and other macro-properties. The challenge to the efficacy of vertically metaphysically necessitated properties allows that, for the sake of argument, the target properties exist but argues that there are no causal relations in which they stand. The absence of a causal role is then taken to impugn the existence of these properties. However, if you allow for the sake of argument that macro-properties exist, in virtue of the fact that their instances are constituted from instances of microproperties, say, then the same thing should be said of macro-causal relations. It is quite unmotivated to be concessive over the existence of macro-properties but then deny that it is legitimate to appeal to the existence of macro-causal relations to characterize the efficacy of these properties. The same point applies to the other cases, for example, determinable properties and determinable causal relations. Perhaps it will be argued that there is a distinction to be drawn between whether or not macro-causal relations exist and whether or not these causal relations hold between macro-properties. Macro-causal relations exist just so long as instances of micro-properties stand in the appropriate causal relations to each other to constitute them. The question of whether or not causal relations hold between macroproperties turns on whether instances of micro-properties (or arrangements thereof) determine that these macro-causal relations are present without it being necessary to concede that macro-properties have a further contribution to make. This line of response just reintroduces the asymmetry in treatment in the opposite direction. If macro-causal relations exist if instances of micro-properties stand in the appropriate causal relations to each other, then the putative macro-properties that are claimed to fail to stand in the appropriate causal relations are being understood as something more than instances of micro-properties appropriately related. Otherwise, instances of micro-properties standing in the appropriate causal relations would just be what a causal relation between macro-properties is on this understanding. Whatever view you take of macro-properties, treat macro-causation (one such macro-property) in the same way. Particularity does require qualification though. One reason stems from the need to deal with causal role occupant-committing properties, both higher order and first order. The former, at least, are intuitively inefficacious. If a property F has the property F* of occupying a certain causal role, then it seems that F, but not F*, is efficacious. Yet, F plus the laws that cover the relationship constitute a B-property that metaphysically necessitates the instantiation of F*. To illustrate, suppose that barbiturates, such as phenobarbital, occupy the causal role we may characterize as the sedative role. There is a metaphysically necessary relationship between phenobarbital (C₁₂H₁₂N₂O₃), the laws relating to these elements and their compounds, and the sedative role (in humans). But we would not take the sedative role, as opposed to C₁₂H₁₂N₂O₃, as the cause of sedation. The class of causal role occupant-committing properties is extensive. Functional properties, powers, and dispositions all fall under this category in one way or another, depending upon the theory adopted of their nature. It would be a mistake to try to exclude this kind of case by claiming that particularity only applies if the base properties are efficacious as a whole, where in the case just described, only part of the putative base property—the occupying property component—would be efficacious. As we shall see in ., it is plausible



 

that an efficacious base property implies an efficacious metaphysically necessitated property when only part of the base property is efficacious. Furthermore, F* would satisfy the conditions of my analysis of causation for some property instance whose occurrence is used to characterize F’s causal role, for example, an instance of sedation. The proper treatment of the issue thus cannot simply focus upon some immediate flaw in particularity. The problem also cannot be avoided by suggesting that particularity only applies if, at both the B-property level and the M-property level, the B-properties and the M-properties don’t metaphysically necessitate the instantiation of other members of their class, B and M respectively (i.e. are existence-independent of each other in the terminology of .). F* is not existence-dependent on property instances mentioned in its causal role, or vice versa. It can be instantiated without them. F* may metaphysically necessitate instances of properties used to characterize its causal role in certain specified circumstances, namely those in which the triggering conditions for these instances are met (i.e. are partial existence-dependent upon its characteristic causal role properties in the terminology of .). Nevertheless, it would be unwise to focus on this fact alone. If a powers ontology is true and the fundamental properties of the world have their nature essentially characterized in terms of their causal role alone—already mentioned in . (see .. for further discussion)—then such properties may metaphysically necessitate the property instances which characterize their causal role in triggering conditions and yet they are intuitively efficacious. Instead, we should insist that the important difference is whether our target property F* must include among its B-base properties an appeal to laws which is independent of any of the other properties that comprise its B-base. Laws that are independent of the nature of the properties that comprise the B-base should not be part of it. If we allow connections between properties independent of their nature to be part of the minimal necessitation base for a metaphysical necessitation relation, we trivialize the connection between the natures of the minimal necessitation base properties and those properties necessitated by them. In the case of the powers ontology, the nature of properties settles the truth of law statements. So there is no independent appeal to the character of the laws that hold in characterizing the B-base. With this restriction, we can deny that F*-properties stand in a metaphysically necessary relationship to the F-properties that occupy the causal role. At the same time, we should add to the restrictions upon the kind of entities which, when they satisfy the distinctive counterfactuals of our analysis, stand in a causal relationship. If a property, F*, necessitates a particular property instance, R, (mentioned in the causal role used to characterize it) in circumstances C and this is in virtue of the fact that F*’s instantiation can only be metaphysically necessitated by B-base properties which include a causal role occupying property and independent laws, then F*’s satisfaction of the counterfactuals is not indicative of F* standing in a causal relationship to that property instance, R. This restriction is not necessary in the case of events—the object of our discussion in Chapter —because events have the higher-order causal role properties in virtue of possessing the role-occupying properties. So events’ possession of the former does not impugn their efficacy.

  - 



In a powers ontology, it is plausible that the truth-base for the second-order description used to characterize F* is F–F, in this case, being a property which, itself, settles what laws hold. In these circumstances, F* would not fall foul of the restriction given above and rightly so, since it picks out the role-occupying property F which is efficacious. ...       If particularity in this form is defensible, then, to deal with Kim’s argument, we need to refine the characterization of overdetermination to which he appeals and, with it, refine our understanding of what is required for the causal closure of physics. The causal completeness of physics together with the claim that there is no systematic overdetermination is meant to yield the result that we have reason to believe that physics is causally closed. There are no non-physical entities that stand in causal relations to physical entities. The claim that physics is causally complete is best captured as follows. Completeness of Physics: At any time at which a physical event, holding of a physical fact or instantiation of a physical property, e, has a cause, then, without any non-physical causes at a time, physical events, facts, and properties either are sufficient causal circumstances of e or causal circumstances that fix the probability of e. The formulation deals with two problem cases that have plagued earlier formulations of the completeness of physics principles both due to Lowe. The first problem case has the following structure. Non-physical mental cause of b, m

b

n t0

t1

t2

Figure . At time to, there are sufficient physical causal circumstances, n, of a piece of behaviour, b. The physical causal circumstances of b causes b by causing some non-physical event at t₁. Appeals to the completeness of physics together with ruling out systematic overdetermination excludes this possibility because our preferred formulation requires sufficient or probability-fixing physical circumstances at each time at which b has a cause. The existence of the intermediary non-physical cause at t₁ is a time when this requirement is not met. Formulations that appeal to there being sufficient physical causal circumstances for any physical event without saying ‘at any time’ fail to rule out this kind of non-physical causation.



 

The second problem case has the following structure. m

n

b

Figure . In this case, n is the sufficient (or probability-fixing) physical causal circumstances for b but they are only sufficient or probability fixing in part because they cause a simultaneously occurring non-physical mental event, m, that is required to cause b. Focusing on the bottom arrow alone, n is not sufficient or probability fixing. It is because n causes b by two paths that the causal circumstances are sufficient or probability fixing. Our preferred formulation deals with this possibility by requiring that sufficient or probability-fixing causal circumstances have this character in the absence of any non-physical events, in the example, m. The requirement does not rule out the possibility that there are non-physical mental overdetermining causes. It only excludes the possibility that these non-physical mental causes contribute to the sufficiency of the physical causal circumstances. There are complications we can overlook. One is that, in the case of indeterministic causation, the existence of any non-physical cause of b will demonstrate that the physical causal circumstances do not fix the probability of b. In that case, the claim that there is no systematic overdetermination has no role to play. The important issue is that the non-physical cases need to be distinguished from the cases of causation in which particularity holds. This is what motivates a development of our understanding of overdetermination and causal closure. The relevant notion of overdetermination involves two causal chains leading to a certain effect each of which would result in that effect independently of the other. We could characterize this in terms of the analysis of causation offered earlier in which Σ must contain one or more entities from the competitor causal chain. If this is not possible, then the overdetermination is not independent, and does not present a problem. Systematic overdetermination involving independent causal chains is questionable, though not impossible, because if it is systematic, then the grounds for supposing that there are two such chains at work is undermined. For example, if there is always a chain of sufficient narrowly physical causation, which shadows any mental causation we are inclined to postulate, then it is reasonable to consider whether the grounds we have for recognizing mental causation really just point to the physical causation which shadows it. Such scepticism does not apply to the putative overdetermination that is not independent. Here patterns of causal relations between elements in that process are the causal process when taken together. A natural first characterization of the causal closure of physics is that Cause Condition: For every narrowly physical cause, there are only narrowly physical effects, and only narrowly physical effects are nomologically possible.

  - 



Effect Condition: For every narrowly physical effect, there are only narrowly physical causes, and only narrowly physical causes are nomologically possible. Talk of nomological possibility is required to capture the fact that we are not just interested in accidental closure. Suppose we have only narrowly physical causes and effects because the world is indeterministic, and the other potential causes and effects of narrowly physical items just failed to occur. This would not be causal closure in the required sense. Appeal to metaphysical possibility would be too strong because no set of laws could rule out the possibility that there occur an alien non-physical entity— that is, one not covered by them—that makes a one-off intervention. If particularity is correct, then there may be broadly physical causes and effects that are causally related to narrowly physical causes and effects. These are intuitively physical properties that are not recognized by a physics resembling our own but the other sciences, or indeed entirely unproblematic items of everyday life like being a chair or a table. Yet, intuitively, the existence of instances of such properties in causal relations with instances of narrowly physical properties need not be damaging to the view of physics that the preliminary characterization of causal closure seeks to articulate. According to the standard way of interpreting particularity, the causal relations identified by physics constitute the causal relations identified by the other sciences. So while it might seem as if non-narrowly physical entities causally intrude upon narrowly physical entities, and vice versa, the causal relations by means of which this is done are constituted from narrowly physical causal relations. This suggests the following: Cause Condition: For every narrowly physical cause, there are only narrowly physical effects, and broadly physical effects minimally metaphysically necessitated by them, and only narrowly physical effects, and broadly physical effects minimally metaphysically necessitated by them, are nomologically possible. Effect Condition: For every narrowly physical effect, there are only narrowly physical causes, and broadly physical causes minimally metaphysically necessitated by them, and only narrowly physical causes, and broadly physical effects minimally metaphysically necessitated by them, are nomologically possible. This characterization is compatible with the possibility that narrowly physical properties do not constitute a fundamental ontological/causal layer but rather represent one way of characterizing the causal relations that hold. In that case, broadly physical causation is not properly thought of as dependent upon narrowly physical causation but there is mutual constraint. Narrowly physical causation entails the metaphysically necessitated broadly physical causation, and broadly physical causation entails that there will be narrowly physical causation in one of the various ways in which the broadly physical causation is metaphysically necessitated. As I remarked earlier, if we take the verdicts of a counterfactual theory seriously with regard to what they say about the efficacy of broadly physical properties, then they qualify as causes themselves with no implication of depending upon the efficacy of narrowly physical properties. Particularity becomes a principle of harmony between different causal layers.



 

Harmony between the layers does not require that one of the layers depends upon the other. On the other hand, it requires more than would be present if non-physical emergent property dualism was true. The latter position requires a version of harmony too. The causal relations that hold between the non-physical emergent properties, and which hold between them and the narrowly physical properties, cannot be in conflict, on pain of such a world containing contradictions. Nevertheless, what ensures the harmony is independent laws relating narrowly physical properties with these non-physical emergent properties. The harmony does not simply result from the relations of minimal metaphysical necessitation between properties and causal relations. The contrast I have just drawn between two kinds of harmony may appear threatened if the powers ontology is true. It will be urged that one of the essential causal powers of a particular narrowly physical property, or arrangement of narrowly physical properties, is that it produces instantiations of non-physical emergent properties. In which case, there will be harmony backed by metaphysical necessitation even in a world in which non-physical emergent dualism is true. I have dealt with this objection elsewhere. In brief, my response is that a powers ontology is not committed to all the elements of a causal role being essential to it, specifically those relatively isolated outcomes which allegedly relate to mentality. Further, dualist pictures of the sort envisaged are not easily developed within a powers ontology (Noordhof (a), pp. –). If my characterization of the causal closure of the narrowly physical is compatible with a certain kind of harmony, two concerns may arise. First, it may be questioned whether the doctrine is strong enough to capture what we want. Don’t we want causation between instances of broadly physical, but not narrowly physical, properties to be dependent? Second, what needs to be added to harmony in order to get dependence? Regarding the first point, it cannot be denied that if we have causation in harmony rather than dependent causation, then, strictly speaking, we do not have causal closure. However, even dependent causation involves causation between narrowly physical and broadly physical entities and so isn’t causal closure of narrowly physical entities strictly speaking either. Talk of causal closure was meant to try to capture what is involved in the idea that physics provides complete coverage of causal activity. Physics does not need to take into account non-physical interventions. The causal closure claim does not have significant independent interest outside of that. Harmony of causes implies that, for any putative causal relation between types of entities, there will be a way of characterizing it in narrowly physical terms. Narrowly physical entities may not be causally closed but they do promise complete causal coverage in the sense just specified. It is the conviction that a proper causal explanation of narrowly physical instantiations of properties need not go outside instantiation of other narrowly physical properties that lies at the heart of the causal closure claim, and it is this that is preserved in the case of harmony. Regarding the second question, the difference between harmony and dependence, three approaches are possible. According to the first, there is no general grounding or dependence relation. Instead, there is a subset of relations of metaphysical necessitation that imply dependence. One would be macro–micro, another would be

  - 



membership of a set, for example, the set {Socrates} is grounded in the existence of Socrates. Dependent causation would be that which holds between entities of the dependent kind or which, as a causal relation, is of the dependent kind. According to a second approach to the distinction between harmony and dependence, there is no stronger notion than metaphysical necessitation. It is a mistake to suppose that one of the relata is grounded in, or depends upon, the other. Nevertheless, entities at one level can have more extensive explanatory credentials than entities at another level. For example, identifying concrete particular entities— like Socrates—is part of understanding the concrete world to which unit sets of these entities cannot be addressed. Nevertheless, once we have identified concrete particulars, then, given that they metaphysically necessitate their unit sets, we get the sets for free. Which is the ground, and which is the grounded, will depend upon a claim about the domain to which they seek to make an explanatory contribution first and foremost. Dependent causation will be no different from non-dependent causation. It just gets so classified because of the entities which it relates. According to a third approach, the distinction between harmony and dependence can be captured by the following claim. If causal relations between instantiations of properties are dependent upon causal relations between instances of properties that metaphysically necessitate them, then it is not metaphysically possible for there to be instantiations of these properties standing in the causal relations they do, without there being metaphysically necessitating properties of them that stand in the appropriate causal relations. If there is just harmonization, then this is possible. On the assumption that determinable properties and macro-properties must be metaphysically necessitated by determinates and arrangements of micro-properties, these will fall out as a case of dependent causation. Nevertheless, there may be properties that have both metaphysically necessitated instances and have instances which are not metaphysically necessitated. Consider the case of powers. As we shall see later, some philosophers take these to be fundamental. Others suppose that they are attributed to objects as a result of their categorical properties and laws. One option is to allow that both are possible. Powers don’t require such a metaphysical necessitation base however they may have it. In the latter case, the powers need not be identified with any particular metaphysical necessitation base because different categorical property/ law combinations may give rise to the same power. In these circumstances, it might be argued that the efficacy of the powers should be in harmony with their metaphysical necessitation bases, but is not dependent upon them because the powers in question might have been instantiated without such a metaphysical necessitation base. Of course, there is a tug to say that, when the powers are metaphysically necessitated by categorical properties and laws, then the causal relations are dependent upon the latter. But that is because we are inclined to read into the metaphysical necessitation, the view that the laws make the categorical properties efficacious by setting up relations between them. Once we take on board the idea that the powers need not be metaphysically necessitated at all, then the harmonization position becomes more plausible. Powers and categorical property/law combinations become different resolutions of detail of one causal reality.



 

With these revisions to the notion of overdetermination and the completeness of physics in place, we should say the following about Kim’s argument. First, and most straightforwardly, the claim that the systematic overdetermination involved is unattractive is mistaken. Overdetermination by dependent causal chains is unproblematic. So we can allow that both m₁ and b₁ are sufficient causes of b₂, say. Second, to the extent that the argument is motivated by the view that B-properties characterize some comprehensive level—such as are the properties identified by physics, are maximally determinate, or the like—then the absence of independent causation is all that is required for completeness.

. Property Causation Not Property Instance Causation Property instance causation is not property causation. The difference lies in the generality that is involved in the latter. We have causation by an instance, a particular, just if my proposed analysis is satisfied for that instance. If the instance is an instance of more than one property, then there is no reason to conclude—from the instance’s satisfaction of the analysis—that one or other of the properties is efficacious. Some rely upon this fact to provide an answer to one problem of mental causation, namely whether mental properties are efficacious if they are not identical to narrowly physical properties. They argue that an instance of a mental property is just an instance of a narrowly physical property and that if the latter is efficacious, then so is the mental property. For them, there is no further matter to be settled to establish a property is efficacious other than that an instance of it is efficacious. The position is often developed within a trope metaphysics that takes property instances to be ontologically fundamental, unstructured particulars. Their lack of structure is required to veto the question as to whether they are efficacious in virtue of one property or another property of which they are an instance. The fact that they are ontologically fundamental is meant to rule out the possibility that the challenge to the efficacy of the mental can arise in another way, with something more ontologically fine-grained. This is commonly known as the trope solution to property causation in general, and mental causation in particular. By contrast, those who appeal to identity of property instances outside of a trope framework now recognize that the problem of mental causation will recur as a problem of which property—understood as a universal—is causally relevant. So I set aside this position here (Macdonald and Macdonald (), pp. –). The trope solution to mental property causation faces significant difficulties. The first is that, as we saw in .., a trope metaphysics which allows for the possibility of shared property instances fails to deal successfully with the problem of imperfect community. So a trope metaphysical framework does not naturally lend itself to the development of a solution to property causation that trades upon the possibility that a trope is an instance of two or more properties. Moreover, the materials that trope metaphysicians would have to use to explain when two properties share an instance—for example, a certain kind of supervenience relation between the

     



application conditions for predicates of these properties—are ones to which alternative approaches to mental causation, such as that detailed in ., may also appeal. If the apparatus is available to both, then the straight cost to trope metaphysics in terms of loss of a solution to the problem of imperfect community is not worth paying. Setting aside the problem of imperfect community, the role of resemblance in a trope metaphysics threatens to raise the issue of property causation by other means. The standard picture is that tropes are fully determinate property instances; only tropes are efficacious; and these property instances are grouped together into types by resemblance. Determinable properties don’t exist. There are just weaker relations of resemblance between determinate property instances reflecting the fact that predicates putatively of determinable properties (hereafter, predicates of determinables) may be true of a range of different determinates (e.g. Heil (), pp. –). Only fully determinate property instances are typed by exact resemblance. The picture just sketched faces a dilemma. Either it faces a version of the inference-basing problem discussed earlier (...) or the resemblances corresponding to the application of predicates of determinables are substantial enough to raise the question of whether a particular trope has an effect in virtue of one resemblance or another. If it does, then it serves to reintroduce the issue of property causation. Suppose you observe that pain in particular subjects gives rise to withdrawal behaviour and you consider the question of whether this will take place in other, constitutionally different, subjects. A necessary condition for being entitled to conclude that it does is that there is, or you suppose there to be, a resemblance holding at the level of pain which supports that conclusion, given the, otherwise, diversity in these property instances from the different constitutions of difference subjects. However, given that this is meant to support a causal generalization, it seems that along with providing such support the following question is allowed. Is it the property instance’s resemblance with all other pain instances or, say, more specific resemblance to more determinate ways in which the pain is realized, or exact resemblance to the fully determinate way in which the pain is realized, which accounts for the causal relations holding? Presumably, the trope metaphysician would have to appeal to the less specific resemblance. If they resisted this, they would have no grounds for supporting the possibility of a causal generalization. The basic charge, then, is that those who only allow for the existence of fully determinate properties fail to capture the horizontal relations necessary to legitimate, amongst other things, our causal inferences. To see the need for horizontal legitimators, they needed to look in a different place from the question of what is required to make some particular statement true. A development of trope metaphysics can successfully defend itself from this charge by allowing that their structureless tropes have different resemblances to other tropes corresponding to the applications of predicates of determinables. It is not that each predicate just records the existence of some resemblance or other between the different determinates to which it applies. However, in so doing, they undermine the so-called trope solution to property causation that asserts the only issue of property causation is causation by property instances.



 

I have explained why the attempt to understand property causation in terms of property instance causation is problematic. Questions of causal relevance cut finer than intuitive ways of understanding the individuation of property instances. Equally, from ..– and .., we saw that the attempt to understand this as implying very fine-grained causal relata, or as a consequence of contrast classes set up by different specifications of properties, gave rise to counterintuitive results. They proclaimed certain properties inefficacious when they weren’t inefficacious. It was just that citing them picked out some further explanatory virtue. I shall focus on what these explanatory virtues are in .. These points, along with the plausibility of relating property causation to generality, constitute the defence of the second element of my account of property causation identified here: the first element being a property instance causation element. According to the Generality condition, (part of) each (minimal) necessitation base of F is such that all its instantiations would cause (or in the case of indeterminism, raise the -probability of) an instantiation of one of the (minimal) necessitation bases of G if they were in some causal circumstances C—where C may vary for each kind of necessitation base. If there were only one type of causal circumstances in which F were realized, and F were realized in only one way, then this condition would be equivalent to Every instance of F causes, or in the case of indeterminism raises the -probability of, there being an instance of G in C. Generality as I have specified it allows for the fact that different minimal necessitation bases require different causal circumstances for them to have an influence. The fact that an instance of F may fail to have a causal influence in some circumstances doesn’t impugn its efficacy as a property, and not just a property instance, in other circumstances. Generality also accommodates the fact that, under indeterminism, we should not expect that fi, an instance of F, will always cause an instance of G even when circumstances and realization don’t play a role in vitiating it. If a causal connection is indeterministic, it may just fail. So we cannot require causation in every case but simply that the property which is efficacious is a potential property cause in every circumstances of the right kind with the appropriate minimal necessitation base, that is, it raises the  probability of there being an instance of G. If generality holds, then an instance of F will not just be a cause of an instance of F but, in addition, it will be a property cause of F. Of course, I am not the first to recognize the implicit generality in property causation. Anybody who has offered an account of causal relevance in terms of law has also done so (e.g. Fodor (); Segal and Sober (), p. ). However, first, my proposal does not appeal to law because it is questionable whether there is a law if the pattern I have identified holds and, second, those who offered such an account often failed to appeal to the idea of minimal necessitation too. Yet an appeal to the latter is also required. Appeals to law by themselves struggle to explain whether correlation between broadly physical properties reveals that their instances are standing in a causal relationship. Broadly physical properties which are nomically, but not metaphysically,

     



necessitated by arrangements of narrowly physical properties will have a true general statement concerning their co-occurrence even if the broadly physical properties are intuitively inefficacious (Segal and Sober , pp. –). So something extra is needed. Either this can be part of the conditions under which the generality would count as a causal law, or it can be characterized independently. That these conditions are needed is not in dispute. Turning to the first point, my condition bears most resemblance to an account which appeals to a ceteris paribus law relating F and G to capture the generality involved in causal relevance. A preliminary analysis of ceteris paribus laws is that there is a ceteris paribus law relating F and G, if and only if, for all R, where R realizes F, there are some conditions C, such that, whenever R and C, then G and it is nomologically possible that R without C (Schiffer (), pp. –; Fodor (), pp. –). If the second condition were not met, then the law would be strict. The possibility of R without C provides conditions in which the correlation between F and G fails. An objection to this analysis is that ceteris paribus laws have what Fodor has dubbed ‘absolute exceptions’: realizations for F for which there are no circumstances C which, together with the realization, are sufficient for an instance of G. One way in which conditions may be unequal is if F is realized by a dud. Fodor accommodates this by allowing that F can figure in a ceteris paribus law if most of the time, it is not realized by duds for G, and for other properties, say H, with which it also stands in a ceteris paribus law, the dud realization does have circumstances in which it yields an instance of G (Fodor , pp. –). Others respond to this objection by denying the existence of ceteris paribus laws (Schiffer ()). Whichever way one goes, the characterization of my generality condition does not involve an appeal to laws. However, its motivation remains intact. If two properties are coinstantiated, then the effects of this instantiation may be due to one or the other of the properties. One famous illustration is the soprano’s singing of ‘my love’, at a certain pitch and loudness, causing the glass to crack. It is plausible that the soprano’s singing is an instance of that pitch, that loudness, and those words. Yet we would not conclude that the glass cracking occurred in virtue of those words. So how should we differentiate? According to the generality condition, the property of involving the words ‘my love’ does not serve to explain the pattern of causal relations concerning glass crackings, taking into account different ways in which the property of involving the words ‘my love’ may be realized. If the generality condition holds for a certain property for a target effect, then we have such an explanation. The causal relevance of a property, and not just one of its instances, is hard to deny if, for every type of minimal necessitation base of a property, there are circumstances in which an instance of that property always causes the target effect. Consider the property of being rickety. If something is rickety, it is likely to collapse. However, whether or not something will collapse depends upon the precise circumstances in which it is located and the precise way in which the property of being rickety is realized. If for every way of being rickety, there are circumstances in which collapse follows, then we can say that a collapse followed in virtue of being rickety. Otherwise, talk of ricketiness, at best, figures in a ceteris paribus law. If it does



 

not meet the generality condition, then, while various ways of being rickety may be causally relevant, being rickety is not. The generality condition is also related to, but importantly distinct from, a distinction drawn recently between sensitive and insensitive causation. A causal relation is relatively insensitive—between particulars, or types of things—if the counterfactual dependence between the causal relata holds in a variety of different background conditions. It is sensitive if this dependence is easily disrupted. List and Menzies extend this idea to include sensitivity, or otherwise, to the way in which the properties standing in the putative causal relation are realized. List and Menzies hold that both the way in which a property is realized, and the instance of the property, are to be counted as causes in such cases of sensitivity (List and Menzies , –, –). To illustrate, suppose that a certain kind of pain, Pa, has four necessitation bases N₁, N₂, N₃, and N₄ and let Bg be the utterance ‘That hurts!’. Suppose that, further, the following counterfactuals were true. If Pa were not instantiated in S, then S would not utter Bg. If N₁ were not instantiated in S, then S would not utter Bg. For the latter to be true, the closest worlds in which N₁ is not present are ones in which Bg wouldn’t occur even though there is a replacement, N₂, and Pa is, thus, present. In those circumstances, List and Menzies conclude that both Pa and N₁ are causes of Bg. I can see why it is plausible to suppose that N₁ is a property cause in that situation. It is far less clear why it is plausible to suppose that Pa is. Given what has previously been argued, we are allowed the question: Does N₁ cause Bg partly in virtue of necessitating Pa? Evidence that it is not in virtue of Pa is that, when a substitute realization, N₂, is present, Bg does not occur. List and Menzies suggest that the relationship between Pa and Bg is sensitive, depending upon the precise way in which Pa is realized. Instead, the sensitivity supplies evidence that it is N₁ rather than Pa that is the causally relevant property. If the sensitivity were just the result of a failure of the right causal circumstances for the realization in question, then the case List and Menzies cite would not be a problem. The verdicts of the two approaches would coincide. The difference stems from the decision to count as one source of sensitivity the way in which Pa is realized. It is here that I think their account yields counterintuitive verdicts. Sensitivity is not compatible with causal relevance. If property causation involves generality, then it is incompatible with brute singular causation. A consequence of this is that, while we can say that an instance of F caused an instance of G by being an instance of F, rather than F*, when there is generality, the approach does not allow that we can make this discrimination in cases of brute singular causation between properties. However, this does not seem to be an immediate problem. If there is no law, for example, covering F rather than F*, with regard to causing an instance of G, why should we suppose that G is caused by an instance of F rather than F*? The nearest one might get to a counterexample would have to appeal to modal considerations. Suppose that a certain shade of red—as a case of brute singular

    



causation—made a bull livid. Usually, he was not bothered by that shade of red at all and other shades of red had no impact upon him. Then one might claim that it was in virtue of a cape being a certain shade of red—say crimson—rather than red because, had the cape been another shade of red, then the bull would not have been livid. To accommodate this possibility, the generality condition would have to be extended to having a generalizing component across possible token instantiations. (part of) each (minimal) necessitation base in virtue of which that instance of F may be instantiated is such that all its instantiations would cause (or in the case of indeterminism, raise the -probability of) an instantiation of one of the (minimal) necessitation bases in virtue of which that instance of G were instantiated if they were in some causal circumstances C—where C may vary for each kind of necessitation base. F would count as a property cause if either disjunction of the generality condition were satisfied. I question whether brute singular causation might involve discriminations of this fashion. That would depend upon how we can make sense of brute singular causation. One might suppose that it cannot hold in virtue of this or that property if it is a one-off. Nevertheless, I provide this answer to show how the basic approach may be extended.

. Contrastive Causation and Explanatory Virtues The principal focus of the discussion so far has been on whether metaphysically necessitated properties are efficacious if the metaphysical necessitators are, for example, whether the efficacy of the more determinate undermines the claims for efficacy of the less determinate, which are necessitated by the more determinate. But there is an attack from the other direction that may seem to undermine the account of property causation put forward here: the charge of redundancy. To mention an example we discussed in .., is it correct to say that the guzzling of poison caused the death when just drinking the poison will do? The charge of redundancy also arises in another area, namely when we consider whether, at least partly, a relational property is a cause when its partially intrinsic necessitation base is a cause. For example, should being a hammer strike end up efficacious when, obviously, all that really matters is it being a strike by an object of a certain mass and resistance? The fact that the object in question was a tool—a partly relational fact—seems neither here nor there. The charge of redundancy seems raised by contrastive sentences concerning these cases. We are inclined to take to be true ()

It was the drinking rather than the guzzling of hemlock that caused the death.

Similarly, in the case of the hammer blow, we are inclined to take to be true () It was being struck by an object of a certain mass and resistance rather than being struck by a hammer that caused the nut to crack open. The challenge from redundancy poses a threat to the account of property causation detailed above because both the drinking and the guzzling, and the striking by a



 

hammer and by an object with a certain mass and resistance, come out as property causes by my analysis. So it seems that contrastive talk cottons on to something finer as one of the relata of causation. The puzzle is that it seems perfectly clear that outside of the contrastive context we are inclined to accept as true the claims that guzzling that poison caused his death and that the hammer blow caused the nut to crack open. We have also seen that two contrastive statements can seem to differ in truth value while concerning the same entities (e.g. the railway track case, ..). We can also hear contrastive statements as true that make the property of being a hammer a cause. For example, () It was being struck by a hammer rather than being struck by Jo’s favourite tool that caused the nut to crack open (where the hammer = Jo’s favourite tool). One of () or () must seem true when otherwise it is not. There is no reason to suppose that it is () that is the erroneous statement. We cannot explain the apparent truth of () and () by appealing to different contrasts. For this to be the case, failure to be struck by Jo’s favourite tool would have to be failure for the hammer to be Jo’s favourite tool in counterfactual circumstances rather than a failure of the nut to be struck by a hammer. But this is implausible. The closest world in which the nut is not struck by Jo’s favourite tool is one in which it is not struck by a hammer and not one in which Jo changes his tool preferences. So the implicit contrasts at work in the comparison contained in () are the same. Instead, the reason why we hear these contrastive claims to be true—when in fact they are false—is that, in seeking to understand why they might be asserted, we appeal to ways in which a causal explanation can turn out to be better or worse/more informative or less informative. Two virtues of causal explanations are that, first, they involve properties that play a distinct causal role and, second, they are the most precise characterization of what is necessary in the circumstances for a certain target effect (for further defence Noordhof (), pp. –). Both are extensions of the idea of property causation. The first focuses on the question of whether, in certain circumstances, the property identified will have a unique contribution. The second focuses on the question of whether there are redundant elements or whether the property in question is the most precise characterization of the causal contribution needed in the actual circumstances that held. It is this element to which J. S. Mill calls attention with his Method of Agreement (in which we should look at common elements to putatively distinct types of causes) to identify what he takes to be a cause (Mill (), pp. –, for more discussion Noordhof (c), pp. –). It also corresponds to Yablo’s idea that causes should be proportional to their effects (Yablo (a), pp. –). I don’t deny the importance of recognizing this feature but just the significance both wish to place on it— though, with Yablo, less so, when, for example, he notes that we often think of causes as just entities that have a place in the causal history of a target effect (Yablo (b), p. ). A unique contribution may fail to be present without redundancy if two properties could make exactly the same contribution in the same causal circumstances even though the precise contribution that one or the other makes is necessary. Redundancy is present with a unique contribution in those causal circumstances in

    



which the property in question has not a unique contribution to make, although some component of its minimal necessitation base does, but the property is still a cause. If a constraint on the existence of properties is that they should make a unique causal contribution in some circumstances—that is they have distinct causal roles— then the first of the two options I specified is not possible. We can’t have precision but non-uniqueness. However, it is clear that we should recognize the existence and causal contribution of properties that may, in certain circumstances, have redundant elements to the causal contribution that they make which display their significance in other circumstances. In so doing, we can tie together causal explanations as resulting from the instantiation of a single kind of property. All that is needed is this second point to recognize the two virtues of causal explanation identified. In the cases provided, the contrast is between a cause with greater redundancy and a cause with less. The falsity of the explicitly contrastive statements leads a charitable auditor to consider what the speaker might be trying to say which is true. It is very natural to hear them as making the claim that a causal explanation citing the less redundant cause has more virtue than one that cites the more redundant cause. In effect, the explanation makes the claim that it is such and such that should be focused on (from having more virtue) than that. They are pragmatically being taken to provide this additional information. Consider a parallel. Suppose both Aaron and Bob lend me money because otherwise I wouldn’t be able to pay my monthly rent. You remark how generous Bob was, you’re not so keen on Aaron and Bob gave much more. I reply, annoyed with your slighting of Aaron, () It was Aaron rather than Bob who was generous because what Aaron gave was half his week’s wages. Bob is much wealthier. The purpose of my claim is not to deny that Bob is generous but rather to suggest that there are features of Aaron’s circumstances that make it especially appropriate to single him out for being generous. In making the claim, I have overstated what I wanted to say. I, in fact, suggested that Bob was not generous by the use of ‘rather than’. It was as if, at that point, only one person could be singled out as the generous one for me. You know what I want to say and might find yourself agreeing with () even though, strictly speaking, it is false. This can be brought out by noting that () is made even more plausible by adding ‘really’ in front of generous in a piece of persuasive definition that subtly shifts the features to which an evaluative response is appropriate (Stevenson (), pp. –). Similarly, () can be made more plausible by adding words with a similar role () It was simply the drinking rather than the guzzling of hemlock that really caused the death. The virtues I have identified are not simply cognitive but have ontological import. It is not just that we find the explanations with the virtues easier to process or having a particular role in our cognitive mental lives. The properties with these virtues for our target effect have distinct features. We can advert to this by qualifying our use of the term cause. We can say that something is the minimal or non-redundant cause of a target. My suggestion in this section is that, when we do not qualify our use of the



 

term cause in this way, then we implicitly understand what someone is saying when they say ‘rather than’ or use emphasis in the ways indicated by adversion to these further standards that could be made explicit.

. Concluding Remarks The main focus of the first part of this chapter was a defence against a challenge to the counterfactual analysis of causation that derived from the possibility of vertical metaphysical necessitation. In order to answer the challenge, I developed an approach to property instance causation. However, property instance causation does not capture the only causal role for properties. The second part of the chapter developed a notion of property causation. This took up some of the remarks of Chapter  concerning the proper relata of causation, in which I defended a thick account of the nature of events. Causation between particulars is one thing, property causation another, and there are further features that items in the world may have which would make them even more useful in causal explanations. In full, my proposal was that F property causes G iff (a) part of the minimal necessitation base of F causes part of the minimum base of G and (b) each minimal necessitation base of F, Bi(F), is such that there is some causal circumstances Ci in which all of Bi(F)’s instantiations would raise the -chance of there being an instance of G. The additional features that property causes may have are precision or characterization of a certain unique contribution in a causal network: a proprietary causal role. I argued that causal contrastive claims of a certain type lead charitable auditors (or readers) to take speakers (or writers) to be highlighting one or other of these explanatory virtues when what they explicitly say is false, for example, it was being struck by an object of a certain mass and resistance rather than being struck by a hammer that caused the nut to crack open. It is false that the hammer failed to cause the nut to crack open. Of course, it is open to others to claim that causation involves some of these other features: for example, causes should not include redundant elements. But this would just be a terminological difference. So long as we agree on the different distinctions in the present chapter, it does not matter much which we say are the causes. The additional elements mentioned do not present a challenge to the counterfactual analysis but, at worst, a suggestion as to how it might be developed to capture what is included in our notion of causation. At best, the fact that we can recognize the distinctions, and that the different levels of refinement build up in a coherent fashion within my preferred framework, suggests that the framework has independent merit supporting the choice of terminology I have adopted.

 Non-Causal Counterfactual Dependence and Intrinsicality Counterfactual theories of causation generally hold that certain kinds of counterfactual dependence between two entities provide an analysis of causation if the entities in question are distinct in some sense (e.g. Lewis (b), p. ; Mackie (), p. ; Ganeri et al. (), p. ; Noordhof (a), p. ). The reason for this is that, if the entities mentioned in the antecedent and consequent of the relevant counterfactuals are not distinct, then the counterfactuals may be true for this reason rather than because of a causal relationship between them. It is true that if Tony Blair hadn’t given an interview on the radio this afternoon, an ex-prime minister would not have given an interview on the radio this afternoon. However, such a counterfactual does not hold in virtue of a causal relationship but rather because Tony Blair is an ex-prime minister and so is not distinct from the entity mentioned in the consequent of the counterfactual. There are broadly speaking two distinct, though related, approaches to this problem. The first focuses on the specific question of in what way should the entity mentioned in the antecedent of a counterfactual be distinct from the entity mentioned in its consequent in order for a causal relationship to be indicated. The second addresses the problem by providing a general analysis of intrinsic properties and, then, requiring that the relevant counterfactuals indicate a causal relationship only if the entities mentioned in the antecedent and the consequent are intrinsically characterized (Lewis (a), pp. –). The second approach cannot work alone because there is nothing to stop non-causal counterfactual dependencies holding between intrinsically characterized but overlapping events. However, it might be made to work in combination with some account of distinct existence. In what follows I will develop a version of the first approach but also outline an analysis of intrinsic properties that might be put to service in an approach of the second kind because it will be of particular relevance for the discussion in Chapters  and . In characterizing how the entities mentioned in antecedent and consequent of a counterfactual should be distinct, it would be natural to suppose that appeal can be made to the plural accounts of distinct existence outlined in .. However, this would be a mistake. For many of the candidate problem cases, things go according to plan. Consider the following If I hadn’t typed the letter r twice in succession, I would not have typed the word Larry (Swain (), p. ).

A Variety of Causes. Paul Noordhof, Oxford University Press (2020). © Paul Noordhof. DOI: 10.1093/oso/9780199251469.001.0001



-    

Here it seems that the event mentioned in the antecedent is not distinct from the event mentioned in the consequent by the spatial characterization of distinct existence (..). However, as we shall see in ., there are familiar problem cases that would plausibly be characterized as distinct by the relevant account of distinct existence. Instead, an appropriately weakened appeal to a modal characterization will seem more appropriate. As it turns out, appeal to distinct existence in the characterization of the counterfactual theory of causation has a different role to that which figures in the claim that there are no necessary connections between distinct existences. The problem with the modal understanding of distinct existence in the distinct existences principle is that any putative counterexample just demonstrates that the existences aren’t distinct. So we needed a modally independent characterization of distinct existence to avoid trivialization. However, in the present context, we are interested in the question of whether a particular counterfactual dependency is causal or reveals some other modal dependency. So a modal characterization takes central stage. It is a beneficial feature of the non-modal characterization of distinct existences that the possibility of modal dependencies between distinct existences is left open. That’s what we need to evaluate in order to determine the status of the distinct existences principle. By contrast, restricting the entities mentioned in the antecedent and consequent, of a counterfactual, to non-modal distinct existences is insufficient for the successful analysis of causation. Appeal to a modal characterization of distinct existence may tempt one to suppose that counterfactuals involving entities that fail it are true in virtue of this non-causal modal connection. There are two reasons to be dissatisfied with this. The first is that a non-causal modal connection between an event mentioned in the antecedent and an event mentioned in the consequent of a counterfactual is often insufficient to establish the truth of the counterfactual. In addition, the relevant similarity of circumstances needs to be taken into account. I will illustrate this in .. The second is that, as we shall see, the presence of non-causal modal connections does not imply there are no causal connections. Holding that the analysis of causation only applies to distinct existences leaves open the question how to capture the cases where there are non-causal modal connections as well. My answer to this will draw on the discussion of .... In brief, suppose there are two events between whose characterizing properties there is a non-causal modal connection. These two events will still be causally related if part of the properties’ minimal supervenience bases are causally related. In ., I go through some standard cases and explain how this works. A particular problem case is those causally characterized properties—powers, dispositions, and the like. I explain how they may be handled in .. All of the material in these parts of the chapter does not draw upon the notion of intrinsic properties. It appeals to the weaker idea that there are some properties that stand in modal connections to each other between the antecedent and consequent of the counterfactuals. Nevertheless, as I have already pointed out, an analysis of intrinsic properties is of independent value. The original characterization of Humean supervenience in ., and the discussion of the distinct existences principle and the principle of recombination in .., appeal to the notion of intrinsic properties. The idea also comes up in Chapter . Thus, I consider the proper

   - 



characterization of intrinsic properties in .. If causation is fundamentally a relation between distinct intrinsically characterized events, then this may be a world-relative notion depending upon the background ontology in play. This thought will be developed further in Chapters , , and .

. Distinct Existence and Non-Causal Counterfactual Dependence Consider the following apparently true counterfactuals () If Socrates had not died at t, Xantippe would not have become a widow at t (Kim (), pp. –). () If Xantippe had not been a widow at t, Socrates would not have died at t (Kim (), p. ). () If President Kennedy had been inaugurated for his second term, he would not have been assassinated. () If I had not turned the knob, I would not have opened the window (where one opens the window by turning the knob) (Kim (b), p. , (), pp. –). () If he had not exceeded the speed limit, the driver would not have broken the law (Mackie (), p. ). () If the penny hadn’t fallen tails down, it would not have fallen heads up (Mackie (), p. ). () If yesterday had not been Monday, today would not have been Tuesday (Kim (b), p. ). () If I grew four feet, I would be taller than Robert Pershing Wadlow ( ft . in), the tallest man in the world. Lewis’ original characterization of the distinct existence of events was that Two events are distinct if they have nothing in common: they are not identical, neither is a proper part of the other, nor do they have a common part (Lewis (b), p. ). He notes that this characterization is a constraint upon which counterfactual dependencies are indicative of causation rather than a requirement on causation because of the possibility of self-causation via intermediate steps in a causal loop. If e₁ is a cause of itself in this way, then cause and effect can’t be distinct existences. Time travel cases provide possible examples, as do worlds with circular time. His distinction relies upon causation being transitive which I deny. My proposal will have to capture the possibility of self-causation in another way to be discussed below (see ., p. ). Lewis’ characterization of the distinctness of events has questionable application to all cases. Consider the first. At least intuitively, Socrates’ dying and Xantippe becoming a widow involve different individuals with different properties. It might be argued



-    

that, in fact, they are the same event but, at least by Lewis’ understanding of events, they have a very different modal profile (for the point that they may be the same event in a kindred case, Owens (), p. ). Socrates’ death need not have involved a widowing—if he were unmarried—or a different widowing—if he were not married to Xantippe. Likewise, Xantippe’s widowing might have occurred in a different way, if she had been married to somebody other than Socrates. Our related analyses of distinct existence drawn from .. don’t fare better. The spatial characterization holds that A and B are distinct existences iff the spatiotemporal location of A is wholly distinct from the spatiotemporal location of B. This is problematic for two reasons. The first is that—returning to the case of Socrates and Xantippe—it is by no means clear that the entities mentioned in the antecedent and the consequent fail to be wholly distinct spatially. This will turn on the question of whether the relational property of becoming a widow instantiated by Xantippe should somehow be seen as spatiotemporally spreading to the death of Socrates. It is a reasonable position to hold that the property depends upon facts about properties of other distinct existences but is spatiotemporally located where Xantippe is. The second is that many of the cases mentioned in the antecedents and consequents above—indeed many cases of causation generally—are ones in which the entities so related aren’t wholly spatiotemporally distinct. Consider: running to the shops caused the blood to course round my body. This is an unproblematic case of causation but there is considerable spatiotemporal overlap between the running and the blood coursing. The second point indicates that the distinct arrangements characterization of distinct existences is more obviously applicable. It holds that A and B are distinct existences if and only if either (i) neither A nor any of its parts is a part of B nor B nor any of its parts is a part of A or (ii) although there is overlap of parts, the parts are differently arranged. However, we have already seen from the brief discussion of Lewis’ account of when two events are distinct above that this can’t cover all the cases. Indeed, consider what might be thought to be an easier case. President Kennedy is arguably a constituent of the entity mentioned in the antecedent and consequent of (). Both involve an object, President Kennedy, having a property. However, it is undeniably the case that the entities so mentioned are differently arranged. One possesses the property of being inaugurated, a necessary constituent of its instantiation is being alive. The other possesses the property of being assassinated, a necessary constituent of its instantiation is not being alive (afterwards). Instead, a necessary component of providing a proper account of the basis for the truth of the counterfactuals with which we began this section is to focus on certain relations of non-causal modal dependence (hereafter ‘modal dependence’). We don’t need to consider whether there exists a stronger notion of dependence, such as grounding, because the issue is whether there is another source—than a causal connection—for a certain kind of counterfactual dependence. Whether one or other entity standing in this relation of modal dependence is fundamental, or grounds the relation, is neither here nor there.

   - 



The first type of case we may call existential metaphysical dependence. It may be characterized as follows. An instance of F existentially depends upon an instance of G if and only if metaphysically necessarily, if F is instantiated, then there is some instance of G. The characterization is in terms of some G rather than a particular instance of G because we can’t assume that instances of F have the instances of G upon which they depend as an essential part of their instantiation. As we shall see in .., certain theories of causation rely upon the possibility that the objects in which properties are instantiated are not essential to these property instances. If that is the case, there is no reason to assume that property instances should depend upon some specific property instance as opposed to some or other instance of a certain property. Chapter  outlined many cases of existential metaphysical dependence of property instances. If a determinate property is instantiated—for example, a particular shade of red—then there is some instance of its determinables. The property of being coloured or the property of being red would both have instances, though which instances is left open. If a certain arrangement of micro-properties is instantiated—for example, instances of dots of colour standing in a certain spatial relationship, then there is some instance of the macro-property, in the envisaged case, the property of being striped. If an instance of a realizing property is instantiated—if physicalism were true, c-fibre firing or A-δ might be an example— then there is some instance of the realized property, in this case the familiar one of being in pain. There are other cases, though. Some relational properties are a case in point. If two entities, a and b, stand in a relation to each other, then each may be attributed certain relational properties. For example, if the property of being a widow is instantiated, then there is some instance of the property of being dead. If the property of being sunburnt is instantiated, then there is some instance of the property of being a sun, (assuming overuse of tanning beds burns your skin without being sunburn) and so on. If a relational property is instantiated in x, there does not have to be a y (which is not identical to x) in which some distinct property is instantiated. Entities can have relational properties just in virtue of their own structure. For example, I can have the property of being a vertebrate, which means I have a vertebral column in my body. This is one of my relational properties but its existence does not depend upon some other object, but rather a part of me (Francescotti (), p. ). Arguably, relational properties of this kind are all macro-properties but we don’t have to decide this issue here. The second type of relation of modal dependence we may call disjunctive existential metaphysical dependence. An instance of F disjunctively existentially depends upon some instance of either G₁, or G₂, or G₃ . . . if and only if metaphysically necessarily, if F is instantiated, then there is some instance of a G-disjunction property. Disjunctive existential dependence is the weaker kind of dependence displayed by determinable, macro-, and realizing properties with regard to their determinates, arrangements of micro-properties, or realizer properties. It is not that there should be



-    

some instance of a certain property. Instead, there is a disjunctive set made up of the minimal supervenience-base properties of these properties and there should be some instance of one member of this set. There is a third kind of relation of modal dependence we may dub partial existential metaphysical dependence. An instance of F is part of the minimal supervenience-base Bi for G and an instance of Bi existentially depends upon some instance of G. Many of Goldman’s cases of level generation provide good illustrations of this kind of metaphysical dependence. A relatively unproblematic illustration is a subject’s extending his arm out of a car window (F) being a conventional level generation of signalling to turn (G) (Goldman (), pp. –). The minimal supervenience-base of signalling to turn will include the extension of the arm and the highway conventions governing this (Bi). I don’t pretend the characterization of the second part of the minimal supervenience-base will be easy but this doesn’t affect the structure of the point. The extension of the arm has partial existential metaphysical dependence on the signalling (G). That is, although the extension of the arm does not metaphysically necessitate some instance or other of signalling, it is part of a minimal superveniencebase that does. As a result, if there is no signalling, then one or other part of the minimal supervenience-base must be absent. The relationship described in () If I had not turned the knob, I would not have opened the window (where one opens the window by turning the knob), is a case of causal level generation with seemingly the same structure (Goldman (), p. ). Turning the knob, in the context envisaged, is what opens the window. The action of opening the window is described in terms of a successful outcome. According to Kim and Goldman, the action of turning the knob is a cause of the outcome—the window being open—but not the act of opening the window. However, the action of turning the knob is part of the minimal supervenience-base of the act of opening the window and so has partial existential metaphysical dependence on the opening. To complete the categorization of modal dependence relations here, if there is partial existential metaphysical dependence, then correspondingly, one would expect there to be partial disjunctive existential metaphysical dependence. The opening of the window would stand in this relationship to the turning of the knob. There are sceptics regarding the existence of each of the types of properties that stand in these relations of existential dependence. For example, some deny the existence of determinable properties, others structural properties which would seem to imply a denial of macro-properties (e.g. Armstrong (), pp. –, –, though for a change of heart see Armstrong (); Gillett and Rives (); Lewis (d)). If the sceptics are right, the problems that face the counterfactual theorist of causation are reduced. The friends of the counterfactual theory can say that the counterfactual dependencies that hold between property instances that exist are always a sign of causation. Who cares if there are true counterfactuals we

-     



assert on the basis of ways of describing entities if these counterfactuals indicate nothing about reality?

. Non-Causal Counterfactuals and the Similarity Weighting When faced with the kind of examples in ., it is tempting to think that the truth of the counterfactuals depends upon the existential dependence relations. However, when we think about their character, it is pretty clear that this is not the case. I will begin by illustrating the point with Socrates and Xantippe. Then I will generalize the message. Consider once more () ()

If Socrates had not died at t, Xantippe would not have become a widow at t. If Xantippe had not been a widow at t, Socrates would not have died at t.

The temptation is to think that they are true simply because somebody cannot become a widow without somebody else (the person to whom they were married) dying. Xantippe’s widowing is existentially metaphysically dependent on there being an instance of death, indeed, death in the person to whom they are married. Socrates’ dying is partially existentially dependent upon there being an instance of widowing. Although there is clearly a connection between the events of Socrates dying and of Xantippe’s becoming a widow, this is not sufficient to make the counterfactuals true independently of the similarity weighting for possible worlds. There are worlds in which Socrates did not die before Xantippe but Xantippe became a widow because she was married to someone else. Hence, if we consider all worlds in which Socrates does not die before Xantippe, it is not true that Xantippe did not become a widow in all of them. We need to consider the closest worlds in which the antecedent is true. It is plausible from our similarity weighting that the closest worlds in which Socrates does not die before Xantippe are still ones which preserve similarity in particular matters of fact up until then, one particular matter of fact being that Socrates married Xantippe. What about ()? If we consider all the worlds in which Xantippe is not a widow, then it is not true that Socrates does not die before her. He might still have died before her while not being married to Xantippe. In order for Xantippe not to be a widow, she would have had to be married to someone else. This would involve a further reduction in the period of perfect match. Hence, in order to preserve perfect match for as long as possible, we retain the fact that Xantippe was married to Socrates. In which case, Socrates would not have died before Xantippe. The similarity weighting predicts that this type of backtracking conditional will be allowed. A distinction may seem tempting. If we take the counterfactuals to concern whatever may turn out to be Xantippe’s widowing in different possible worlds, then there will be worlds in which Xantippe is widowed through being married to someone else who dies. Nevertheless, it may be argued, if we think about the particular token event of Xantippe being widowed, it is not plausible that it could



-    

be a widowing as a result of the death of somebody else (Yagisawa (), pp. –). The charge is that the difficulty I have raised trades upon a failure to recognize this distinction. In ., I argued that there is no reason to suppose that events have rich essences of the envisaged kind. Even if the objector were right about this particular case, it is unlikely that this move will always be available to explain why the counterfactuals are true. So it seems that the counterfactuals expressed in () and () do not have a special form of evaluation but are evaluated just like any other counterfactual. The point made with regard to Socrates and Xantippe is entirely general. Unless there is a metaphysically necessary connection between property instances—rather than just between one instance of a property and some instance of another property—the corresponding counterfactuals concerning individuals with these properties will not be true in virtue of the connection alone in all possible worlds. The truth of these counterfactuals will rely upon a more restricted range of worlds with similarities in matters of fact. There is no distinct form of counterfactual evaluation but just the same form of counterfactual evaluation with input from the existential dependency relations between properties outlined above. The point is even more obvious with regard to the disjunctive cases since there, similarity of context is needed to settle which disjunct is in play. For instance, in the circumstances in which the following counterfactual is true If I hadn’t opened the window, I wouldn’t have turned the knob, there is no other relevant minimal supervenience base for opening the window. For example, suppose that the knob broke as I turned it, you are annoyed with me about this, I’m seeking to reduce your attempt to pile responsibility onto me, and you asked me to open the window. The truth of counterfactual would naturally figure as part of my fight back, perhaps with the addition of an ‘as you asked’.

. Non-Causal Counterfactual Dependence and Causation It would be simple if we could adopt the following restriction. Where the entities mentioned in the consequents are characterized in terms of properties that stand in a relation of existential dependence to properties that characterize entities that are mentioned in the antecedents, their truth could not count towards satisfaction of my analysis of causation. In these cases, the absence of an entity upon which there is some kind of existence dependence implies the absence of the entity that existence depends in this way. Unfortunately, the restriction is too strong. As we have already noted, there are true instances of these counterfactuals relating entities that stand in a causal relationship. So my suggestion is that this is the case when, as we saw in ..., part of the minimal supervenience bases of the properties, which stand in one of the relations of existential dependence, are causally related. In ... I noted that we count air as efficacious because part of its minimal supervenience base includes oxygen. An instance of the property of being a hammer flattens nuts even though the property of being a hammer is relational—involving

-    



being designed and made as a tool—and any object with the same mass, resistance, and wieldiness would do as well to flatten nuts. Instances of being a hammer or being air may not provide as good an explanation in the sense I discussed in ., but this does undermine their causal credentials. Here are some cases to illustrate how the idea works in the present context. Whatever properties of Socrates and Xantippe upon which dying and becoming a widow minimally supervene, it is clear that instances of them in Socrates at t are not going to stand in a causal relationship to instances of them in Xantippe at t. For one thing, since a widowing is the instantaneous result of a death, there would have to be superluminal causation. Even if, as we shall see in Chapter , there may be some cases of superluminal causation, there are no grounds for supposing that property instances can be identified to show that this is one of them. For another thing, it is hard to see what properties would be a plausible candidate even if somebody was only a widow after the person they married had been dead for ten minutes (say). The absence of instances of properties in the minimal supervenience base to satisfy the analysis of causation shows that the counterfactual dependency that is observed between Socrates dying and Xantippe being widowed stems from the existential dependency relations between the properties of dying and widowing alone. In the case of Kennedy failing to be inaugurated, we have a backtracking counterfactual dependency that, in conjunction with () If Kennedy hadn’t been inaugurated for his second term, he would have been assassinated, might be taken to establish the backward causation of the assassination of presidents by failures to inaugurate. The plausibility of the backtracking counterfactuals in this case rests on the fact that Kennedy’s inauguration is existentially dependent upon his being alive and, hence, on his not being assassinated. Part of the minimal supervenience base of Kennedy being inaugurated will include his body living at the time of the inauguration ceremony. The question is whether this satisfies the favoured counterfactual analysis of causation with regard to his not being assassinated. In this case, the problem does not arise with the connection between the living body at the time of the inauguration ceremony and the earlier (counterfactual) failure to be assassinated. The problem is rather that the failure of his body to be living at the time of the inauguration ceremony does not raise the chance of his assassination earlier. That event will, as we will see in our later discussion of causal non-symmetry, already have a very high probability because it is multiply overdetermined by events in the future. So () doesn’t become indicative of causation because of how the application of the approach recommended here applies to (). In ., I adopted Goldman and Kim’s discussion of the case of knob turning and wrote that my window opening was not caused by turning the knob, although the opening of the window was. In fact, Lewis’ treatment of the issue as a case of piecemeal causation seems more plausible. My window opening is a causal process starting with, some mental states, also involving a knob turning, and resulting in the window opening. The last element—the window opening—is caused by my knob turning. As a result, my knob turning is a cause of my action of opening the window by causing a part of it. Part of the minimal supervenience base of my knob



-    

turning—my fingers turning the knob let us say—is a cause of the opening of the window, which is part of the minimal supervenience base of my action of opening the window. So, although () has been cited as a cause of non-causal counterfactual dependence, that is a mistake. In the case of () If he had not exceeded the speed limit, the driver would not have broken the law (Mackie (), p. ), it is hard to identify part of the minimal supervenience base of exceeding the speed limit that is not existence-dependent upon part of the minimal supervenience base of breaking the law and yet which stands in a causal relationship. The most natural components would be the actual speed that the driver is travelling and the legal facts of what the speed limit is. There is no causal relationship here. A couple of temporal cases raise additional issues. () If yesterday had not been Monday, today would not have been Tuesday. () If George had not been born in , he would not have reached the age of twenty-one in . In each case, there is existential dependence. George being twenty-one in  requires an instantiation of being born, twenty-one years earlier, absent time travel. Today being Tuesday requires an instantiation of being Monday. In both cases, though, in addition, part of the minimal supervenience bases includes periods of time: present periods of time and earlier periods of time. If there is causation between time periods then () and () may also characterize a causal relationship. Another case that raises an interesting issue is () If the penny hadn’t fallen tails down, it would not have fallen heads up. This is cited as a case of non-causal counterfactual dependency but it is not clear that it is so. The argument in favour, I guess, is that the penny having the property of falling tails down existentially depends upon an instance of a property of being heads up. If that is correct, the treatment goes on as normal. However, the coin falling tails down not also being heads down or, at least, not heads up, seems the consequence of laws governing the structure of pennies. If a penny could fall like a slinky

Figure . then there is no existential dependence. In which case, () looks more like a case of a causation. We come to the last case of those I listed at the outset. () If I grew four feet, I would be taller than Robert Pershing Wadlow ( ft . in), the tallest man in the world. The minimal supervenience base of the property of being taller than Robert Pershing Wadlow includes my subsequent height and Robert Pershing Wadlow’s height. My

 



growth is a cause of my subsequent height. So it is a cause of the instantiation of the property of being taller than Wadlow and, also, given the heights of everybody else, a cause of the instantiation of being the tallest man in the world. So () comes out as a causal relationship. The illusion that it is not one stems from the thought that the counterfactual just reflects a definitive relationship between heights ( ft  in is taller than  ft . in) as opposed to a point about growth. Other candidate cases of non-causal counterfactual dependence, involving causal relations too, naturally fall under the subject matter of . on causal properties. So I shall discuss them in that context.

. Causal Properties Certain causally characterized properties (hereafter causal properties for short) present particular difficulties for the application of the proposal outlined in the previous part of the chapter and, indeed, the development of a counterfactual theory of causation. Others are less problematic. In the present section, I discuss the issues that arise. Some causal properties are attributed to an event, c, in virtue of it being a cause of an effect, e, for instance, being a fatal poisoning or being the victory blow. They involve forward commitment to the existence of an event, or other kind of entity, of which their possessors are taken to be a cause. Other causal properties are attributed to an event, e, in virtue of being an effect of c, for instance, being sunburnt (here c would be the sun’s rays), being an action (here c would be an intention), being a perception of c. They involve backward commitment. Some of the items on this list are contentious, for example, some philosophers of perception deny that c would be a cause rather than a constituent of its perception. I give them just to indicate the kind of property that may fall under it. These can be dealt with relatively unproblematically by the approach I have defended. For example, consider ()

If I hadn’t been struck by the sun’s rays, I wouldn’t have been sunburnt.

Although being sunburnt is existentially dependent upon the sun’s rays, there still seems to be a causal relationship the counterfactual captures. Part of the minimal supervenience base of being sunburnt is being burnt and the sun’s rays are a cause of that. Some may find this conclusion counterintuitive. They claim that the property of being sunburnt cannot be caused by the sun’s rays striking the body (e.g. Dardis (), p. ). However, as we have already seen, it is a mistake to suppose that, because a certain property instance is existentially dependent upon some instance of another property, there is no causal relationship also present. Some characterizations of the antecedent and the consequent can disguise the fact that there is an existential dependence. Consider () If I hadn’t been in the sun’s rays for four hours, I wouldn’t have been sunburnt.



-    

An instance of the property of being sunburnt doesn’t require that there is some instance of being in the sun for four hours. However, we have a case of disjunctive existential dependence. An instance of being in the sun’s rays for four hours is one of the determinate disjuncts for the determinable of being exposed to the sun. So, once again, the proposal described in . has immediate application. A third kind of causal property are those that involve commitment to the occupancy of a causal role without, necessarily, any commitment to in virtue of which property the role is played. Examples of causal roles, Rs, specified in schematic terms include: Single Track O has causal role R iff, in C, if T were to occur, O would cause M (where C, T, and M represent types of circumstances, triggers, and manifestations by O respectively). Multitrack O has causal role R iff, in circumstances C₁, if T₁ were to occur, O would cause M₁, in circumstances C₂, if T₂ were to occur, O would cause M₂, . . . in circumstances Cn, if Tn were to occur, O would cause Mn (where Ci, Ti, and Mi represent particular types of circumstances, triggers, and manifestations, n may be infinite). Causal roles may also differ depending upon whether the circumstances include internal states of O. By themselves, properties committed to the occupancy of a causal role are not necessarily existentially dependent properties. As we shall see, that turns on whether their proper characterization involves there being an instance of a property distinct from themselves to occupy the causal role. Falling under the category of properties involving commitment to the occupancy of causal roles are dispositions, powers, capacities, and functional properties (such as those attributed to mental states, the workings of machines, and biological organisms). Very often, philosophers do not discriminate between these properties because they raise the same issues. However, to the extent that they do, dispositions are taken to involve commitment to the occupancy of a certain causal role where the trigger causes a manifestation in the object that possesses the disposition. Powers, on the other hand, involve a commitment to the occupancy of a certain causal role, where the trigger causes the manifestation in a distinct object to that which has the power. More often than not, there will be an instantiation of some of the distinctive causal relations of the role since, de facto, isolated mental states or machine components are unlikely. Nevertheless, this is not required by the characterization of the properties. It is well known that the connection between the correct attribution of such properties and the truth of counterfactuals such as those described above is problematic (Martin (), pp. –). There are cases in which certain counterfactuals that are used to characterize a disposition are true but it is incorrect to attribute the disposition. Reverse electrofinks present one example. As a result of an electrical charge, they enliven dead wires so that they conduct electricity. So it’s true that, if the wires were to receive an electrical charge, then they would conduct electricity. Yet, intuitively, the wire did not have the disposition to conduct electricity prior to the stimulation. There are also cases in which the counterfactuals aren’t true. As a result of a stimulus, electrofinks deaden a wire so that it does not conduct electricity. Yet,

 



beforehand, the wire did have the disposition to conduct electricity. Other, masking cases, involve changes in the circumstances, rather than the putative possessors of the disposition, as a result of which the disposition’s manifestation does not take place (Bird ()). As things stand, these problems, relating to the putative link to counterfactuals, could be excluded if the specification of the circumstances, or the description of the trigger, were detailed enough to rule out the possibility of certain finks or masks. The threat is that, for any more detailed specification of these circumstances short of ‘whatever it takes’, it will always be possible for ascriptions of dispositions to be true when the relevant counterfactuals aren’t or vice versa. For some, these observations reveal that powers and dispositions incline but do not necessitate (or, if you prefer, necessitate in a different way to logical or metaphysical necessity). From this point of view, there are no circumstances C including the presence of a trigger T such that, if F is instantiated, then E (where F is a candidate power or disposition) (Schrenk (), p. ). Such properties present no problems for the account I am seeking to defend here since they do not support counterfactuals in virtue of non-causal metaphysically necessary connections. A more modest reaction to the problems raised by finks and the like is to admit that we can provide no non-trivial analysis of dispositions in terms of counterfactuals but argue that this does not break the link between dispositions and the kind of truths that counterfactuals state. The situation is analogous in this respect to the position of those who argue that consciousness is a physical property but doubt whether we are, or perhaps ever will be, in a position to specify its nature (e.g. McGinn (); Stoljar ()). Our inability is not taken to indicate the falsity of physicalism about consciousness but just suggests that it is not a property that we can, at least at present, grasp. In the case of causal role properties, the reason would be because of the complexity of all the possible interventions that would need to be grasped. Moreover, the problem cases work upon the assumption that a proper analysis of dispositions in terms of counterfactuals requires identification of one or more precisely specified counterfactuals that, if true, imply the truth of the ascription of the disposition. An alternative is that correct attributions of dispositions rely upon a context-determined range of counterfactual truths of a certain type holding. For instance, an object is fragile if there are a wide variety of different true counterfactuals concerning droppings, fallings, or strikings, in various circumstances, and the object breaking. The existence of finks and masks would not threaten such a proposal because they would be classified as just some instances where the counterfactuals may fail to be true amidst a plethora of other instances in which they hold (see Manley and Wasserman (), () from whom I have taken this idea). Either way, it is legitimate to discuss the problems that properties committed to the occupancy of causal roles present in terms of such counterfactuals. At best, such discussion will involve simplifications concerning the particular properties discussed rather than ignoring a dimension of the threat. Within this broad demarcation of the territory of causal role properties, there is an important distinction between taking the descriptions to pick out whatever property, in fact, occupies the causal role where this may vary between worlds and, on the other hand, taking these descriptions to characterize the nature of a property (Lewis (),



-    

(); Lewis () adopts the former position). Under the latter heading, there are then two options. According to the first, the properties so characterized are higher-order properties possessed by instances of properties that, in fact, are occupants of the causal role, or by the entity that possesses those instances (Prior et al. ()). According to the second option, the properties characterized are not properties of role occupants but rather characterize properties an important part of whose nature is this causal role. Under this second option there is a final distinction between those who take the characterization to exhaust the nature of the properties and those who think there is an additional qualitative characterization (the former: Shoemaker (), Swoyer (); Bird (a); the latter: Martin (), (); Shoemaker (); Ellis (), p. ; Heil (), pp. –). We shall discuss these matters further in ... Thus, our territory may provisionally be mapped as in Figure .. The first position on causal role properties drops out of our discussion. Since causal role specifications are just a way of picking out the distinct properties that occupy such a role, they are not committed to a distinctive kind of property. The

Causal/Functional Role Characteriztion

Description Picking Out Occupant Property (Lewis)

Characterization of Nature of Property

Property of Property Which Is Occupant (Prior, Pargetter, and Jackson)

Occupant Property Characterization

Additional Qualitative Nature (Martin, Heil, Late Shoemaker, Ellis)

Characterization Exhausts Nature (Early Shoemaker, Swoyer, Bird)

Figure .

 



application of my analysis of causation to this case will vary depending upon the property that is, in fact, picked out but normally it will be straightforward and independent of the apparatus of this chapter. The second type of position, and its subcategories, is of more particular interest. The concern that the first of these raises—where the causal role specification captures a higher-order property—is that, although instances of the property are taken to be inefficacious, my account will be committed to them being efficacious. Here is how the argument might run in the simple case. At first glance, the higherorder property satisfies my analysis of causation because its instantiation is settled by whether or not another property, which occupies the causal role, is present. For example, consider sulphuric acid’s power of being corrosive of iron. Adding water (T) to iron in concentrated sulphuric acid, H₂SO₄ (O) yields FeSO₄ (M) and hydrogen ions that bond into H₂. If the power is a higher-order property, then it is possessed in virtue of the acid’s chemical structure. The concern is that the higherorder property becomes efficacious because the chemical structure is by my account. But this is counterintuitive. The discussion of ... explained why the higher-order property cannot be counted as efficacious. It has, as part of its minimal supervenience base, an independent appeal to law. The event characterized by the higher-order property (so understood) will be efficacious in virtue of the lower-order property, e.g. H₂SO₄. So no additional problem is presented by the case. Part of the higher-order property’s minimal supervenience base does not include an independent appeal to law if the higher-order property is attributed within a powers ontology: an ontology that takes the fundamental properties of a world to be powers. But then there is no reason to presume that the property of having a property that occupies a certain causal role R is distinct from the property of occupying R. The property that occupies the role is both the cause of the manifestation and is responsible for the truth of the higher-order predication concerning its occupancy of the role. The issue then becomes what we should say about such causal role properties in a powers ontology. Properties in a powers ontology present two distinct challenges. The first is that instances of causal role properties should be classified as causes and, thus, the apparatus of the present chapter should not rule this out. Events involving the instantiation of these properties should have their efficacy in virtue of these properties with regard to the instantiations of properties that characterize their downstream causal role. The second is that the manifestations of causal role properties should not be classified as causes of the causal role properties of which they are the manifestation. The events involving their instantiation should reflect this fact. There are two ways we can deal with this issue. First, as we noted earlier, the metaphysically necessary connection between a causal role property R, its trigger T, the circumstances in which it is instantiated C, and its manifestation M only holds if there is, in addition (or as part of the characterization of C) a ‘no interference condition’. My observation earlier that there might be a limited number of ways in which interference can occur with regard to a particular causal role, but we are ignorant of what they are, still means that a ‘no interference’ condition (however limited) is required. Such a condition should not be part of the minimal



-    

supervenience base for M. The various ways in which I identified how one property is existentially dependent on another property was not intended to capture the kind of necessity—a kind of necessity distinctive of causation—that involves a ‘no interference’ condition. Consider standard cases of supervenience, for example, the property of being striped supervening upon a determinate arrangement of colour. No no interference condition is needed. Any candidate interference would, in fact, mean that the minimal supervenience base was not instantiated. Moreover, as I have already argued, there are no negative entities required to make propositions true. In which case, there are no negative entities to capture a no interference condition. Of course, in a world W, there may, in fact, be no interference between the instantiation of R, with T and C holding, and M. However, given that W doesn’t have its nature essentially, it wouldn’t be the case that metaphysically necessarily, if R, T, C, and W, then M. So R neither existentially depends upon M nor is part of a minimal supervenience base that existentially depends upon M. If that’s the case, then the apparatus doesn’t throw into question the satisfaction of my analysis of causation by events with these properties. The second way of dealing with the issue is not to appeal to the observations about ‘no interference’ but rather the fact that the instantiation of causal role properties so understood fix the laws that hold. This will be explained in more detail in ... We could take these to be an exception to the apparatus of the present chapter for this reason with regard to the instantiation of those properties that characterize the causal role of these properties. We now need to focus on M. There are two types of cases to consider. First, suppose the manifestation properties, M, are characterized either entirely in terms of the causal consequences to which they tend to give rise, or their characterization is partly in terms of the instantiations of properties from which they typically arise. In either of these cases of the first type of case, M properties are not existence-dependent in any of the ways we identified on TRC. So long as M may be instantiated uncaused, even if it isn’t actually instantiated that way, the conditions are not met. In that case, then T, R, or C’s satisfaction of the analysis of causation with respect to M is sufficient to establish that they are causes. Moreover, there is no reason to suppose that M satisfies the analysis of causation with respect to any of T, R, or C, with M in cause position. The second type of case understands M as requiring a certain kind of aetiology. Thus M is disjunctive existence dependent upon TRC. In those circumstances, we focus on part of the minimal supervenience base of M, M-, which is the causal consequence role of M without the required causal antecedents. There is no reason to reject the claim that powers with the complex causal role indicated have, as a minimal supervenience base, subcomponents of their role together making it up. M- is not part of a minimal supervenience base for R since M- might be caused without R, or be instantiated uncaused. It would not be part of a minimal supervenience base for R that includes the property of being caused by R because then it would be redundant. M- does not satisfy the analysis of causation with respect to any of T, R, or C, with M- in cause position. So the apparatus correctly captures the thought that M is not a cause. The former type of case is far more familiar. Most causal role properties have typical causal antecedents but don’t require these antecedents. Nevertheless, I mention the second to cover all eventualities.





. Intrinsicality An advantage of the proposal I defended in . and . is that it does not require identification of certain properties as intrinsic properties for a defence of a counterfactual analysis of causation. Indeed, as we saw, there can be counterfactual dependencies partly as a result of existential dependencies that hold of intuitively intrinsic properties so an appeal to an additional idea of distinct existence is needed in any event. Nevertheless, an account of intrinsicality has independent interest both for the discussion of the intrinsicality of causation in ... and recombination in ... Although the nature of intrinsicality seems straightforward, it is plausible that it is a mixture of a number of distinct intrinsic-making features. Different accounts of intrinsicality have emphasized different ones. My inclination is to take the intrinsic properties in a world, w, as the best satisfiers of three intrinsic-making features. They draw on some of the recent discussion of intrinsic properties. I shall discuss the relationship between these intrinsic-making features as a way of clarifying the precise nature of their envisaged contribution. The first feature we may call External Independence. In order to understand this notion, we need a bit of introductory material. Properties have conditions of instantiation. Unlike the properties themselves, these may involve more than one instance of another property and will specify how these instances should be existence. For example, in the case of putative structural properties such as methane CH₄, the conditions of instantiation may be something like this. x instantiates methane if and only if x has proper parts y₁, y₂, y₃, y₄, y₅ (where y₁ ≠ y₂ ≠ y₃ ≠ y₄ ≠ y₅), y₁ instantiates hydrogen, y₂ instantiates hydrogen, y₃ instantiates hydrogen, y₄ instantiates hydrogen, y₅ instantiates carbon, and Bmethane (y₁, y₂, y₃, y₄, y₅). The instantiation conditions for x’s instantiation of methane make clear how distinct proper parts of x must instantiate distinct elements and that these proper parts will be bonded in a certain way (the arrangement of the methane molecule). To take another example, the property of being accompanied by a circle has the instantiation condition: x instantiates the property of being accompanied by a circle if and only if there is a wholly distinct entity, y, such that y is a circle. The instantiation conditions of a property will be highly detailed and it is important to appreciate that something that might not look as if it requires the existence of wholly distinct entities at one level of detail will require it at another if the properties of x’s parts require, for their instantiation, wholly distinct entities from x to have certain properties. Maximal border-sensitive properties are an interesting case. The property of being a cat, for example, requires that an object that possesses this property is not embedded in like material of the same, or similar, kind. A cat is still a cat if it is embedded in granite though, on standard assumptions, we might expect that it is a dead cat. On the other hand, an object that is Tibbles the cat minus one paw is not a cat because the paw is material of the same kind integrated with the object. We might



-    

formulate this negative condition in the following way, drawing on the discussion of negative truths earlier. x instantiates the property of being a cat if and only if x has the property of being cat* and w (where w is a world that does not include x being embedded in a cat). Here the property of being a cat* is instantiated by x if and only if, if x were not embedded in a cat, then x would instantiate the property of being a cat. This is not meant to be an analysis of the property of being a cat*. It just provides a way of identifying the entities, properties, and relations that must be instantiated if the property of being a cat* is instantiated. Reference to w is overkill in most cases. The important issue is just how things are at the border of x. It does no harm to simplify and always talk of the completely inclusive w. Properties may have different conditions of instantiation. Disjunctive properties are a natural example of this. The property of being red or square has the instantiation conditions of the property of being red and the instantiation conditions of the property of being square. For the purposes of the discussion of instantiation properties, we do not assume that properties only correspond to some of the predicates, disjunctive or otherwise, we can formulate. Sparse conceptions of properties would make the discussion a lot easier. The external dependence or independence of an instance of a property is a consequence of the instantiation conditions of the property and the entity to which the property is attributed. Thus, the primary question is whether a particular property has an internal or external instantiation. If x’s instantiation of a property by x requires some wholly distinct object y or the world w to be a certain way apart from x, then the instantiation is external. Otherwise, it has an internal instantiation. If it is possible for a property to have an internal instantiation, then there may be lonely and accompanied instances of the property, and absences of the property. Externally independent properties have only internal instantiations (Francescotti (), pp. –, contains roughly this as an account of intrinsic properties). Appeal to conditions of instantiation steers a middle path between two other features to which appeal has been made to characterize intrinsic properties. On the one side, there is whether having or lacking the target property is independent of accompaniment or loneliness (Langton and Lewis (), pp. –). Any basic intrinsic property must have the following options: its possession and nonpossession must be possible for an object that is the sole existent and one that is accompanied by others. Many extrinsic properties can have some subset of these without being able to have all of them. The table below illustrates this. Table . Property

Lonely

Accompanied

Possessed

Being lonely Being fattest man

Being fattest man Being ignored by others

Lacked

Being ignored by others

Being lonely Being fattest man Being ignored by others





The property of being lonely—a property that has good claims to starting modern discussion—is not accompaniment independent (Kim (a); Lewis (b)). An object can be lonely without anything else existing in the world but it cannot be accompanied. You can be the fattest man by being the only man but you can’t lack it while being the only one. You can lack the property of being ignored by others if there is nobody else around. You can have or lack it when accompanied. But you can’t have it when you are lonely. Accompaniment independence can capture much of what is involved with external independence but it relies upon an appeal to various possibilities. It thus comes unstuck with necessary objects and properties. The property of being self-identical is not accompaniment independent since nothing can fail to be self-identical either by itself or accompanied by others. Yet, it is plausibly an intrinsic property. If the number  is a necessary object, then it is not possible for any object to have any property unaccompanied. In which case all putative intrinsic properties fail the loneliness condition. We can’t adjust our understanding of accompaniment independence for necessary properties so that, if an object can’t lack a property, then there don’t have to be accompanied and lonely cases of the property being lacked. There would be no way to distinguish between the property of being self-identical that is plausibly intrinsic and the property of being accompanied by the number  which is more plausibly extrinsic. We also can’t, as Langton and Lewis do, restrict the analysis so that loneliness or accompaniment only concerns contingent objects. If I exist, there is a singleton set {Paul Noordhof}. The set is a contingent existent but always accompanies me (Francescotti (), pp. –; Cameron ()). Accompaniment independence is an attempt to capture the idea of external independence in austere modal form. We can take the modal properties of intrinsic properties to be a result of their nature or an articulation of their nature. The problems we have just identified tilt the balance towards the former. The modal properties are a result of the nature of properties and cannot capture all that is required in the idea of external independence. But is the idea of instantiation conditions capable of doing the heavy lifting or in danger of being an empty appeal? As I noted, appeal to instantiation conditions steers a middle path. The other side is accounts of intrinsic properties that draw upon the ‘in virtue of ’ relation. One natural development of this idea appeals to facts about the essences of properties. For example, it has been said that my singleton does not make all my properties extrinsic because it is not part of their essences that the objects to which they are attributed have a singleton (Cameron ()). Properties may have instantiation conditions as part of their essences but the appeal to instantiation conditions does not make that assumption. It makes the more minimal assumption that it is metaphysically necessary that properties have such and such instantiation conditions. A consequence of adopting this more minimal assumption is that it may appear a property can have a number of different instantiation conditions since there seem no particular constraints upon their formulation. For example, in a world with more than one entity, the property of being a square might be thought to have, as part of its conditions of instantiation, the property of being accompanied by a square. In such a world, an object could not be square without other objects having the property of



-    

being accompanied by a square. There would be no similar pressure to take the property of being accompanied by a square to be part of the essence of a square. The property of being red might have as the condition of instantiation for its instantiation in an entity x: x’s possession of the property of being red and w contains no other objects or x’s possession of the property of being red and x being accompanied by other objects each of which possess the property of being accompanied by red objects. The condition adverts to the way the world is independently of how the target object x is. It could easily be denied that these worldly conditions are part of the essence of the property of being red. How can we resist the claim that they are part of the instantiation conditions for the property of being red? We seem to require more than just appeal to instantiation conditions to characterize external independence. In fact, without appeal to the essence of properties, there are some constraints upon what may count as the instantiation condition of a property. These constraints follow from modal claims about particular instantiations of properties. Suppose that an object is red in an accompanied world. Might the instantiation of red in that object have been present, or remain present, if the object were the only object in the world? The answer would be no if one disjunct of an instantiation condition for redness was red and accompanied. But it is not. Suppose that an object is red in a world with no other entities. Might the instantiation of red have been present, or remain present, if the object were in a world with other entities? The answer would be no if one disjunct of an instantiation condition for redness was red and lonely. But it is not. The property of being red does not come in two forms, an accompanied instantiation and a lonely instantiation. Each instantiation of redness in an object may remain despite other changes in the world that do not have a causal impact upon the object in question. The appeal I have just made draws on an element of Peter Vallentyne’s analysis of intrinsic properties as those properties an object retains through contractions of the world and of Yablo’s preliminary analysis of intrinsic properties as those an object retains through expansions of the world (Vallentyne (), p. ; Yablo (), pp. –). However, the point is not to give an account of intrinsic properties in terms of contraction and expansion but rather to note something about the instantiation conditions. So the appeal is not committed to claiming, for example, that the property of being Paul Noordhof is an intrinsic property of mine even if it depends upon my essentially relational property of coming from a particular zygote (Yablo (), pp. –, by contrast Marshall (), pp. –, claims it is). The commitment is avoided if the property is of a kind—for example, an origin property—that may be lost by some object in a contracting world, this would be an object for which origin is not an essential property, but, since my appeal concerns the conditions for instantiation in a particular object rather than a direct analysis of intrinsicality, this is a detail we do not need to consider here (Vallentyne (), p. ). In sum, then, the idea is that these features assist to refine our understanding of instantiation conditions so we can then use external independence as a feature of intrinsic properties. The modal properties of instantiation explain why we should not take the instantiation condition of the property of being red in x as x having the property of being red and lonely or having the property of being red and accompanied.





The modal properties do not make the instantiation conditions of necessarily coextensive properties the same. For example, the property of being red and accompanied by the number  may have a distinct instantiation condition from the property of being red. This will turn on the question of whether the number  is a distinct object from that which possesses the property of redness. If necessary properties—like the property of being accompanied by the number —are necessary because their conditions of instantiation are just the existence of any object, then the property is intrinsic. Otherwise, the property comes out as extrinsic. The fact that the matter is not resolved until we understand more about the metaphysics of mathematical objects is an advantage of the proposal. Some analyses are committed to resolving the matter one way rather than another (Langton and Lewis (), same instantiation conditions because properties necessarily coextensive, p. ; Francescotti (), p. , distinct instantiation conditions). This is a mistake. A lot will depend upon the correct understanding of sentences concerning putatively necessary objects. Another example of necessarily coextensive properties helps us to appreciate another point about the appeal to instantiation conditions. Ralf Bader has suggested that two properties of the following structures F and F v (F & G) should not be taken to be the same property in spite of being necessarily coextensive. An object having a counterpart according to counterpart theory would be a case in point. An object, x, is its own counterpart in the actual world. In other possible worlds, x has distinct objects as counterparts. There is no object that fails to have a counterpart simply in virtue of its own existence. However, it also has a counterpart in virtue of these other objects. Let F be the property of having a counterpart that is its possessor and G be the property of having a counterpart that is distinct from its possessor. F v (F & G) is the property of having a counterpart. But this is necessarily coextensive with F. A similar point can be made about the property of having a duplicate, if an object counts, trivially, as a duplicate of itself. In each case, one is intrinsic and one is, plausibly, extrinsic because it has partly extrinsic instances (Bader (), pp. –). So we have another case in which necessary coextension does not imply that both are intrinsic. The properties of having a counterpart that is its possessor and having a counterpart have different instantiation conditions. This might be thought to have an unacceptable consequence. Consider the property of being red (R) and the property of being red and lonely (R & L) or red and accompanied (R & A). If F and F v (F & G) are distinct properties, there seems no reason why R and (R & L) v (R & A) fail to be distinct properties. Yet, we might want to differentiate between the two cases. F and F v (F & G) seem genuine properties whereas (R & L) v (R & A) just seems to be redness. We cannot differentiate these pairs of properties by straight appeal to the modal properties of instantiation conditions, except by brute force. The modal properties of R’s instantiation conditions do not change the instantiation of R whether the object that possesses R is lonely or accompanied. However, there are no grounds for holding the same for the property of (R & L) v (R & A). Once it is accepted that necessarily coextensive properties may be distinct, the instantiation conditions of (R & L) v (R & A) may be different from the instantiation conditions of R. In which case, there is no reason to deny that (R) is a distinct property from (R & L) v (R & A) given (F) is



-    

a distinct property from F v (F & G). To claim that the instantiation conditions in the case of (R) and (R & L) v (R & A) are the same where (F) and F v (F & G) are different is just to proclaim a modal difference by brute force. Instead, we should distinguish between the two cases by recognizing a second feature of intrinsic properties: their role in the characterization of duplicates. We may dub this second feature: Duplicate Characterization. It is often said that duplicates share all and only their intrinsic properties. As Lewis observes, we are familiar with the notion of duplication from photocopying and so on (Lewis (a), p. ). Nevertheless, he takes appeal to duplication alone to be disappointing because the relevant sense of duplicate is of objects that share intrinsic properties (Lewis (a), pp. –, (b), p. ). Thus, he appeals to perfectly natural properties as a way to break into a tight circle of interdefinables, as he puts it. He holds that Two things are duplicates iff they have exactly the same perfectly natural properties, and their parts can be put into correspondence in such a way that the corresponding parts have the same perfectly natural properties, and stand in the same perfectly natural relations (Lewis (c), p. , (a), p. ). Lewis doesn’t seek to characterize the naturalness of a property or, for that matter, a perfectly natural property. The naturalness of a property is taken as a primitive. He does suppose that perfectly natural properties are identified by physics (Lewis (c), p. ). Although this provides no further insight into the character of perfectly natural properties, it does give us an indication of the properties that will, in fact, fall under this category. Perfectly natural properties are not to be understood as properties that figure in the fundamental laws of nature. If this was taken to be a distinctive feature, then Lewis would have no way of avoiding the objection to his best system analysis of laws we discuss later. The simplest and strongest system of laws is that which involves a massive predicate, F, that correctly characterizes all that is the case in the world. In such a world, everything is F would hold (Lewis (a), p. ). This formulation is ruled out because perfectly natural properties must pick out genuine resemblances independent of their place in laws (Lewis (a), pp. –, , –). The leading idea of this second feature is that there are certain genuine resemblances that are the basis of duplication. Two objects may share extrinsic properties too. These extrinsic properties may be genuine resemblances. However, these genuine resemblances don’t make the objects duplicates but rather the environment in which they are located appropriately similar. The genuine resemblances that are localized on objects, and determine whether or not they are duplicates, are the objects’ intrinsic properties. If duplication characterization were the only feature of the intrinsic, we might have reason to hold that we could as easily have taken intrinsic properties as the basis for an understanding of duplication. Instead, the proposal is that each feature is an intrinsic-making feature. Possession of either is sufficient for meeting a minimal standard of intrinsicality but possession of both by a property makes it more intrinsic as a result. Moreover, one of the principal reasons to recognize the existence of a property is that it corresponds to a genuine resemblance in the world. That is why we





take the property of being a square to exist and the property of being a square or a circle not to. Consider the case of (R & L) v (R & A). Because Langton and Lewis take necessarily coextensive properties to be identical, they are faced with explaining why, although there are references to external conditions, this is, in fact, the intrinsic property of redness. To achieve this, they rely upon genuine disjunctive properties having more natural properties as disjuncts, disjunctive formulations of non-disjunctive properties having less. The proposal I’m advancing doesn’t have this explanatory burden. Instead, the feeling that (R & L) v (R & A) does not express a genuine property, unless it expresses redness, derives from another source. While it is true that duplicates either share or lack this property, the reference to the circumstances in which the objects characterized are located shows that a more effective characterization of the fact that they are duplicates is provided by R. There is no ground for recognizing (R & L) v (R & A) if R is recognized. The combination of necessary coextension plus an instantiation condition that reflects the genuine resemblances of the objects to which both are attributed gives R a status that (R & L) v (R & A) does not. Thus, we are mistakenly inclined to take (R & L) v (R & A) to be redness if it expressed any property at all. By contrast, the grounds for differentiating between (F) and F v (F & G) stem from counterpart theory. Although it is true that these properties are necessarily coextensive, the latter property is the basis of other modal properties of the object to which it is attributed. For example, if an object is cubic but has a counterpart that is round, then it is possibly round. Duplication characterization provides a reason for recognizing the existence of one property rather than another necessarily coextensive with it unless the other property has another explanatory role to play. Let’s consider a couple more cases to see how the favoured approach applies. The property of being either cubical and lonely or non-cubical and accompanied may be accompaniment independent but it is not external independent. It also fails to characterize duplicates. Suppose two objects are duplicates. Specifically, they are both cubical (amongst other things). Nevertheless, one of the duplicates is in a world all by itself, the other is accompanied. Only one of these duplicates has the disjunctive property just characterized, the lonely cube. We have an explanation of why this property is extrinsic without relying upon an appeal to the idea that the disjuncts are more natural than the disjunctive property. It is true that we are relying more upon the idea of duplication than Langton and Lewis’ proposal but we are not taking this as primitive either. It is based upon resemblances between objects. The change of emphasis is helpful when we consider a problematic case for Langton and Lewis’ approach. The property of being such that there is a cube is possessed by an object if either it is a cube or it is accompanied by a cube (Marshall and Parsons (), p. ). Langton and Lewis’ treatment of the property depends upon the following claim: being accompanied by a cube is a more natural property than being such that there is a cube (given it is conceded that being a cube is more natural than being such that there is a cube). If the claim is false, the property of being such that there is a cube is not counted as a disjunctive property. If it is not a disjunctive property then, since its possession is accompaniment independent, it is classified by their account as a basic intrinsic property. Yet possession of this property



-    

would not be part of the characterization of why two objects are duplicates. One could have it in virtue of being a cube, another could have it in virtue of another object being a cube. Langton and Lewis struggle to establish that the property of being accompanied by a cube is more natural than the property of being such that there is a cube. Their focus seems to slip onto a different question, namely whether being a cube is more natural than being such that there is a cube (Langton and Lewis (), p. ). Nobody has denied that. It is very hard to see, though, why the set of the worlds with cubes in them fails to count as, at least as natural, as the set of worlds in which objects are accompanied by cubes. The property of being such that there is a cube has a complex instantiation condition because it is a property that can be instantiated either by objects in a world, or by a world. We might characterize this as follows. x instantiates the property of being such that there is a cube iff either if x is a world w and there is at least one object y that is a proper part of w, and y is a cube or x (either w or a proper part of w) is a cube or there is a wholly distinct object y, y is a member of the same world w as x, and y is a cube. This has one instantiation condition that fails to satisfy external independence. In addition, the property fails to characterize duplicates. Two non-cuboid duplicates may differ in their possession of this property because one is accompanied by a cube and another is not. We can concede that the property of being such that there is a cube is at least as natural as the property of being accompanied by a cube while still identifying why the property fails to be an intrinsic property for the two reasons just given. It highlights the problem with appealing to the naturalness of properties as a way into the proper understanding of duplication. Resemblances that might be picked out by laws of nature needn’t rely upon being clear about the instantiation conditions for the property in question. That the world is such that there is a cube may be what is important. By contrast, the role in characterizing duplicates does require clarity concerning the objects in which the properties are instantiated, that are duplicates as a result. The discussion so far supports an analysis of intrinsic properties in terms of external independence and an appeal to duplication as part of an explanation of why other cases aren’t a challenge to such an analysis. However, there is a second reason for taking duplicate characterization as a mark of intrinsic properties that changes the picture. According to priority monism, any property an object has—where the object is a proper part of a world—is had in virtue of a global property that the world possesses. Call it ‘D’. This would make all properties external dependent to some extent. However, this is compatible with a class of properties only being external dependent in one respect—their dependency upon D—and characterizing duplicate objects within the world. The problem is how to characterize this class of properties in a way that acknowledges that they fail along a dimension of intrinsicality but still count as intrinsic properties relative to the world being a world in which priority monism is true. It is hard to do this in a way that does not directly appeal to duplicate characterization. For example, in addressing this issue, Kelly Trogdon seeks to appeal to two different kinds of ‘in virtue of ’ relation instead: inter-virtue of and intra-virtue of.





x having P holds inter-virtue of y having Q if y is of a different ontological level to x—either by y being a proper part of x, or being of the same ontological category of proper parts of x, or x being a proper part of y, y being w for example. x having P holds intra-virtue of y having Q if y is on the same ontological level as x (for example, by y being x). He then claims that x has P in an intrinsic fashion only if, for any individual y and property Q, if x has P intra-virtue of y’s having Q, then Q is either fundamental or independent of accompaniment (Trogdon (), p. ). The rest of the analysis appeals to Langton and Lewis’ notion of accompaniment independence, and is a development of the analysis put forward by D. Gene Witmer, William Butchard, and Trogdon (Witmer et al. ()). We don’t need to focus on those details here to pick the central point. Trogdon’s proposal is unsuccessful. First, recall that if x has P intra-virtue of y having Q, it does not follow that Q is a fundamental property. Indeed, the whole point of the ‘intra-virtue of ’ relation is that it does not hold, in monist worlds, with respect to fundamental properties. In which case, consider a property related to D, being accompanied by Dx. Dx is a list of all the entities apart from x in a world, w, that instantiates D, at the ontological level of the entity x, and the properties and relations they have, and no more. That is, just like D, Dx has a negative condition: there’s nothing more at that ontological level except for x. If x is a mereological atom, then Dx is a complete and exhaustive specification of the world w except for x. Nevertheless, it is not a property instantiated by w and, given it also does not include x, is not D. If monism is true, then many, if not all, of x’s putative intrinsic properties, will hold intra-virtue of x being accompanied by Dx. The problem with Trogdon’s analysis does not turn on the question of whether being accompanied by Dx is an acceptable specification of a property although it is hard to see how this could be resisted. Consider an objection due to Alexander Skiles. Skiles argues that Trogdon’s analysis would not yield the result that the relational property of being a molecule such that there is an atom to which one is attending is extrinsic because it holds across ontological levels. Trogdon argues that the relational property of being a molecule such that there is an atom to which one is attending is sometimes instantiated intra-virtue of being a molecule such that there is a wholly distinct atom to which one is attending. The latter is not independent of accompaniment (Skiles (), pp. –; Trogdon (), p. ). Trogdon’s answer just takes Skiles’ objection as a challenge about whether there is an accompaniment-dependent instance in virtue of which the attention to an atom holds. The property of being a molecule such that there is a wholly distinct atom to which one is attending appears to be a plausible candidate. However, it does not address the point that this is an interlevel relation and thus does not hold intra-virtue but only intervirtue of the atom. The only way Trogdon can deal with the case of interlevel attention is by insisting that the ontological level of a relational property is settled by the entity that possesses it, in this case, the molecule, and not any other relata in virtue of which the relational property is specified: the atom. In which case, by the same token, all the putatively intrinsic properties of an entity x are possessed intra-virtue of x being accompanied by D. The fact that D is a property of worlds is no



-    

longer relevant to the ontological level. So there is no reason to formulate the argument in terms of being accompanied by Dx as I did above. All intrinsic properties, therefore, come out as extrinsic if monism is true. The general point is that there is no way to appeal to an ‘in virtue of ’ relation that may hold between target intrinsic properties and non-fundamental properties that won’t, as a consequence, allow that putative intrinsic properties hold in virtue of other properties than D. It is better to recognize duplicate characterization as a second feature that comes into its own in worlds in which priority monism is true. On the other hand, duplicate characterization is not appropriate as the only feature of intrinsic properties. First, external dependence identifies the way in which properties in a monist world fail to be intrinsic. Second, those who deny that identity depends upon origin will be inclined to consider identities intrinsic. Yet two duplicates will be distinguished by the identities that hold true of them respectively. Such intrinsic properties don’t have the second characteristic (Eddon (), pp. –). M. Eddon has argued that the intrinsicality of identity properties show that duplicate characterization is no part of the notion of intrinsic properties. Instead, we just have the class of intrinsic properties understood in other terms of which two subclasses are qualitative properties (that characterize duplicates) and nonqualitative identity properties (Eddon (), pp. –). This misstates the situation. First, as we noted, we need to appeal to the idea of duplication to explain why we don’t have to recognize (R & L) v (R & A) in addition to (R). Second, if priority monism is true, then there is a sense in which properties aren’t intrinsic in that they fail external independence. Nevertheless, we still need a distinction between intrinsic and extrinsic properties to characterize duplication. Although external independence and duplicate characterization are the central characterizations of intrinsicality, a third feature contributes towards a property being intrinsic, that of Recombination Maximization. This picks up on the role that intrinsicality is meant to play in principles of recombination used to specify what is possible. It is obviously related to external independence but is a distinct feature from this. One way of seeking to characterize it is as follows. Properties that are either external independent or characterize duplicates count as more intrinsic to the extent that any recombination of these properties constitutes a possibility. Constraints on recombination are ways in which the properties are less intrinsic. Consider causal role properties in a powers ontology. These powers will characterize duplicates. So they will satisfy this feature of intrinsic properties. The characterization of many of them will not involve any object distinct from their possessors having properties. So they will satisfy a form of external independence. Nevertheless, combinations of powers, triggers for powers, plus the powers themselves will have instantiation conditions that will identify further objects that must have properties. While powers themselves may be capable of lonely instantiation, combinations of powers may not be capable of being so combined in isolation. This makes it legitimate to extend our characterization of intrinsicality to recognize this further way in which there may be conditions on instantiation. Rather than bundle this into external independence, we have a separate feature of recombination maximization. If a powers ontology is true of a world, then the intrinsic properties of that world will be causal role properties that perform well by the first two markers and, relative

 



to that world, maximize the possibilities of recombination. Nevertheless, in other possible worlds there may be non-causal role properties that perform better regarding the third marker. In sum, then, the position defended here is that the intrinsic properties of w are those that best satisfy the three features of intrinsic properties identified in w. A certain kind of purist might insist that external independence is the key notion of intrinsicality but given the role intrinsicality plays in a number of key discussions, the world-relative notion seems to fit the issues better.

. Concluding Remarks In the first part of this chapter we saw how there may be true counterfactuals, and thus satisfaction of the analysis of causation, without causation. We found a way round that without appealing to the notion of distinct existence or intrinsicality. The key idea was that, if there was a non-causal modal connection between the characterizing properties of events mentioned in the antecedent and consequent of the appropriate counterfactuals in an analysis of causation, then the events will still be causally related if part of the properties’ minimal supervenience bases are causally related. A particularly significant feature was that the approach allowed a standard appeal to the counterfactual analysis to characterize causation if a powers ontology was true. This rested upon two observations. First, the key difference between the non-causal modal connections that illegitimately suggest a causal relationship and the, potentially metaphysically, necessary connections of a powers ontology is that the latter will involve a no interference condition. Straight appeal can be made to this feature to indicate when satisfaction of my analysis indicates a causal connection. However, if I am right about negative properties, then there will be no way of formulating any of the metaphysical existential dependence relationships I mentioned that would throw the verdict of my analysis into doubt. In which case, no separate appeal to the ‘no interference’ condition will be needed. Second, the relevant properties in a powers ontology fix the laws that hold in a world. We can appeal to this feature to distinguish between non-causal and causal connections. There is no problem with this appeal given that any counterfactual analysis will draw upon the laws that hold in the similarity weighting. Hence there is no competition between this ontology and the development of the analysis of causation developed in this book. I shall develop this point further in ..– and .. My account of intrinsic properties developed in . recognized three markers of intrinsicality: external independence, duplicate characterization, and maximizing recombination. The intrinsic properties of a world w are the properties that perform best with regard to these markers. This provides for a third way of explaining how a powers ontology can draw upon the analysis of causation provided in earlier chapters. There are causal relations between events in a world w if their instantiation of intrinsic properties in w satisfies the analysis. In ..., I will argue that the sense in which causation is intrinsic is not the notion developed in . but something less which just requires that the claims of a



-    

process to be causal are not undermined by competitor processes. The issue of intrinsicality will come up again with regard to the principle of recombination (..). There I argue that, contrary to what is standardly thought, the principle of recombination is not a good basis for settling all the possible worlds there are and it does not rely upon the fundamental entities recombined being intrinsic in way that places no constraints upon recombination.

 Processes and Prevention Counterfactual theories of causation take a liberal approach to causal processes and don’t treat them as fundamental to the proper characterization of causation. They characterize causation simply in terms of a counterfactual dependency of some kind and, more or less, suppose that a characterization of causal processes will drop out of the analysis. Many find such an approach counterintuitive because it abstracts away from the reality of causal processes involving, as it might be, transfer of energy, transmission of a mark, genuine independently circumscribed natural necessity, or the like. From the point of view of the theory defended in this book, such anxieties mistake what may be the truth-base for some causally important counterfactual truths with the reality of causation. My plan in the present chapter is as follows. I will begin, in ., by reviewing the attractions of, and problems facing, theories of causation that place the emphasis on identifying features of causal processes over and above relations of counterfactual dependency. I dub these process theories. I will argue that they need to appeal to counterfactuals at crucial points—so they are no substitute—and they have unfortunate commitments we would do better to avoid. A key difference between their approach and my own reveals itself in the classification of prevention, double prevention, overdetermined prevention, and causation by omission. This is the subject matter of .. Process theories deny that these are genuine cases of causation whereas counterfactual theories allow that some of them are. Process theorists claim their own treatment is more plausible in three respects. First, it better captures the intuition that such cases are distinctively different from cases of causation involving substantial causal processes. Second, it lends itself to the proper characterization of what is involved in action at a distance. Third, it explains how causation is intrinsic. The first respect tends to be motivated by cases involving agents, and what they are responsible for, the latter two respects, while sometimes illustrated by cases involving agency for dramatic appeal, don’t rely upon this for the considerations supplied. In response, I shall explain how two theses undermine these considerations in favour of process theories. The first is that causation comes in different varieties, and what process theories assert should hold of all causation only holds of one variety. The second is that, drawing upon my discussion of Chapter , the truth-base of causal statements may not involve the relata that these statements specify. When we put these criticisms alongside the difficulties that process theories face in themselves, together with the prima facie counterintuitive denials they make regarding certain standard attributions of causation, we have sufficient reason to reject the process

A Variety of Causes. Paul Noordhof, Oxford University Press (2020). © Paul Noordhof. DOI: 10.1093/oso/9780199251469.001.0001



  

theories’ approach to prevention, double prevention, overdetermined prevention, and causation by omission. An empirical test case for my own approach to the characterization of causation and action at a distance will be its treatment of quantum mechanical entanglement. The worry is that a counterfactual approach rules out certain ways of characterizing this entanglement when really we require more specific theoretical considerations to arrive at such conclusions. In response in ., I deny that the range of options is reduced in any substantial way by my approach although there may be some differences over their characterization. In any event, process theories also suffer from a kindred objection. They rule out the possibility of superluminal causation where my own position allows it (see e.g. Aronson (), pp. –). So, at worst, the objection is not one that can be cited against counterfactual theories and in favour of process theories.

. Process Theories .. Types and motivation The details of process theories vary. Perhaps the earliest, due to Hans Reichenbach and developed further by Wesley Salmon, appeals to the idea that only causal processes transmit marks (Reichenbach (), p. ; Salmon (), p. ). For instance, if I shine a torch in the direction of the wall and introduce a piece of red perspex into its beam, the light on the wall will be red. The mark—in this case, the colour of the perspex—has been transmitted from the point of introduction to the wall. Later theories have talked about the transfer of energy or the conservation of a quantity (such as energy or momentum) throughout the process or the persistence of a trope (transference: Aronson (), pp. –; Fair (); Skyrms (), p. ; conservation: Dowe () and later Salmon (); persistence of a trope: Ehring ()) (Figure .). All of the theories are reductive. They seek to provide an account of the nature of causation in terms of something else that does not involve explicit appeal to causality. They don’t claim that causal processes are sui generis. Thus their disagreement with counterfactual theorists isn’t over whether a reductive account of causation is possible but rather over whether counterfactuals and chance are sufficient to provide it. This is not to say that they go so far as to accept the doctrine of Humean supervenience. As we shall see, some rely upon identity through time failing to supervene upon arrangements of qualities. The point is rather that Humean supervenience does not fail due to the character of causation. Process theorists often insist that they are only providing an account of causation in this world (e.g. Aronson (), p. ; Salmon (), p. ; Dowe ()). They do not claim that causation is a natural kind and, hence, that what they identify here will count as causation in every possible world. A relatively unexplored position is that such process theories serve to characterize the essence of causation so that, in all possible worlds, causation will have the character they describe. Strictly speaking, without a commitment to their characterization of causation holding in all possible worlds, these

 



Process Theories

Contingent

Transfer of a Quality or Quantity

Necessary

Conservation of Quantity

Mark Transmission (Early Salmon, Reichenbach)

Conservation of Quantity with Appeal to Genuine Objects (Dowe)

Conserved Quantity (Aronson) Energy (Fair)

Conservation of Quanity with Appeal to Transmission (Later Salmon)

Persistence of a Trope (Ehring)

Constancy of Quality or Structure (Russell)

Figure .

process theories are not competitors to the counterfactual theory. Nevertheless, they are adopted often as a result of criticisms of the counterfactual theory. So they challenge the theory while not entering the same competition (as it were). Some cite as the principal reason in favour of process theories the difficulties that counterfactual theories have with pre-emption (Ehring (), pp. –). I take it that my discussion in Chapter  has put this concern to rest. My counterfactual analysis was specifically developed to deal with the variety of difficulties pre-emption throws up. During the course of that chapter, I discussed all of the cases to which process theorists have appealed, for example, Ehring’s Case A. Others emphasize that process theories can distinguish between mere regularities and causal processes (Aronson (), p. ; (), pp.–). Obviously this is not something unique to them. A counterfactual theory can do so as well. A third reason for finding process theories attractive is that they explain how there can still be causation when a putative cause lowers the chance of the effect. Initially, this may seem counterintuitive. If causes make things happen, then it might seem obvious that they should make those things more probable. Nevertheless, there are cases where it is plausible to suppose that something is a cause and yet lowers the chance of an effect. One famous example involves a golfer slicing his or her drive towards a tree (away from a hole) only for it to bounce off and hole in one. It seems that slicing the drive lowered the chance of getting a hole in one and yet caused



  

it (Rosen (), pp. –). To give another, a woman might take the pill to avoid thrombosis, which is more likely after pregnancy. Nevertheless, taking the pill can also be a cause of thrombosis even though thrombosis is less likely to occur than if the woman were pregnant (Hesslow (), p. ). Some do not agree with these verdicts. They prefer to keep the straightforward connection between causation and chance-raising. Thus they will say that the golfer holed in one despite slicing his or her drive rather than because of it. They distinguish the slicing from the driving and hold that it was the fact that the golfer drove the ball that caused the hole in one (Mellor (), p. ). Put aside the question of the nature and individuation of causal relata for the moment (discussed in Chapter ). This manoeuvre doesn’t capture the intuition that in order to get the hole in one that way a slicing was needed. If retention of the straightforward link between chance-raising and causation were required to capture the fact that causes are means to ends or to avoid having to count the dog-bite case as a case of causation, then the validity of the intuition that slicing the ball did cause the hole in one may be questioned (Beebee ()). The balance of considerations would favour the retention of the link. If the argument of Chapters  and  is correct, then that is not the situation. My analysis distinguishes between condition-relative chance-raising—where a cause raises the chance of an effect down a particular path relative to the background chance—and cases of hindrance (e.g. the dog bite), in which an event fails to raise the chance of an effect down any causal path relative to background chance. Hence dog bites can be distinguished from slicings. In the case of slicing the drive, just put in Σ one of the events on the path that the golf ball would have taken if the golf ball had not been sliced. In the absence of that path, slicing the drive does raise the chance of the golf ball going in the hole in one. Furthermore, because the analysis requires chance-raising down a causal path relative to background chance, it is plausible that we capture an intuitive idea of what makes something a means to something else. My causes may not be the best means in the circumstances, nevertheless they are certainly a means. I suggest that this is the most appropriate notion to show the pragmatic worth of our concept of causation. They are a natural input to the process of practical deliberation. We need a notion of a means—rather than best means—as an input to our practical deliberations in order to work out what is the best thing to do. Process theories are not only unnecessary to achieve the correct verdicts in the range of chance-lowering cases, they cannot even argue that they avoid having to appeal to the kind of apparatus I have recommended. Since there is a continuous causal process between the dog bite and the explosion, they are in danger of pronouncing that the dog bite is a cause of the explosion. Those process theorists who have addressed this issue appeal to a similar notion of condition-relative chanceraising to the one that I have characterized (e.g. Dowe (), pp. –). The question is whether, once they do, there is any further need for the rich notion of processes to which they appeal. So I come to the fourth and final consideration in favour of process theories, which will be the centrepiece of the second part of this chapter. Process theories capture an important distinction between mere dependencies and substantial causal processes ignored by counterfactual theories (Dowe ()). Included amongst these mere

 



dependencies will be some between enabling conditions and the effects of enabled causes. So it is no surprise that others have emphasized that process theories allow us to draw a distinction between causes and enabling conditions which counterfactual theories do not (Aronson (), pp. –). I have already discussed this matter to some extent in ... The comments there together with the discussion in . constitute my complete treatment of the general issue. It is hard to deny that there is an important distinction of some kind between mere dependencies and the substantial causal processes favoured by process theorists. Suppose that a bus runs over a pedestrian. I could have shouted a warning that would have alerted the pedestrian to the oncoming bus, but I failed to do so. There is a physical process of bus movement, impact, and death that is lacking between my omission to warn the pedestrian and the pedestrian’s death, even though the pedestrian’s death also depends upon my omission. The question is whether we should characterize this difference in terms of the presence or absence of causation. In the remainder of this part of the chapter, I will show how process theories fail to capture what is involved in causation without appeal to counterfactuals. If the truth of certain counterfactuals is required to transform non-causal processes into causal processes, then their truth in other cases is prima facie grounds for counting them as causation too. We seem to face a situation in which we have different varieties of causation rather than causation versus no causation. This verdict will be strengthened if the intuition of difference is shown to be inadequately captured by the difference between substantial causal processes and mere dependencies.

.. Mark transmission theory The success of Salmon’s Mark Transmission Theory rests upon identifying conditions, in which a mark is transmitted, that do not appeal to causality. No illumination is provided if transmission of a mark is characterized in terms of an event, e₁, having a certain feature M (a mark) which causes another event, e₂, also to have M. Appeal to counterfactuals at this point would also be damaging. Counterfactual theorists can argue that mark transmission theory just provides a characterization of a particular kind of causation—mark transmission—in terms of counterfactuals. So Salmon looks at processes that simply involve the presence of a mark throughout the process—no requirement for counterfactual dependence or causation here—and then seeks to identify conditions that, if they fail to hold, show that the process in question is a genuine process. Consider a rotating beacon casting a light beam onto a wall. The process involving the light travelling from beacon to wall is genuine because, as we saw before, if we put a piece of red perspex in the way of the light travelling from the beacon to the wall, the light beam subsequent to the perspex changes colour. By contrast, if we put the perspex at some point on the wall, the light beam travelling along the wall up to the perspex does not change colour after hitting it in its journey further along the wall. Salmon’s preliminary characterization of mark transmission is as follows. (MT) A mark that has been introduced into a process by means of a single intervention at point A is transmitted to point B if and only if it occurs at B and at all stages of the process between A and B without additional interventions (Salmon (), p. ).



  

So far, there is no appeal to counterfactuals. Suppose now that just as the red piece of perspex is placed at a certain point on the wall, a red lens is placed in front of the light. Thus we have the apparent continuation of a mark—the redness of the light—after the introduction of the perspex. There isn’t any further intervention in the light travelling across the wall but now it seems that this must be counted as a causal process. In response, Salmon goes counterfactual. He starts by identifying a particular type of process in which mark transmission occurs. Let P be a process that, in the absence of interactions with other processes would remain uniform with respect to a characteristic Q, which it would manifest consistently over an interval that includes both of the space-time points A and B (where A 6¼ B) (Salmon (), p. ). There is a transmission of a mark if the process mentioned in (MT) is P and the mark is changing Q to Q*. The light travelling across the wall would not have remained uniform because the lens was going in anyway (Salmon credits the objection that led to going counterfactual to Cartwright, personal communication) (Salmon (), pp. –). Unfortunately, a minor modification of the case reintroduces the same problem. Just suppose that if the red perspex were not placed by the wall, the red lens would not be introduced in front of the beacon and conditions are otherwise the same. Then the white light would remain white travelling across the wall in the absence of the putative point of interaction with the other process envisaged: the placing of the red perspex. Perhaps it might be thought that Salmon’s characterization of causal interaction gets past the problem. CI: Let P₁ and P₂ be two processes that intersect with one another at space-time point S, which belongs to the histories of both. Let Q be a characteristic that process P₁ would exhibit throughout an interval (which includes subintervals on both sides of S in the history of P₁) if the intersection with P₂ did not occur; let R be a characteristic that process P₂ would exhibit throughout an interval (which includes subintervals on both sides of S in the history of P₂) if the intersection with P₁ did not occur. Then, the intersection of P₁ and P₂ at S constitutes a causal interaction if () P₁ exhibits the characteristic Q before S, but it exhibits a modified characteristic Q’ throughout an interval immediately following S; and () P₂ exhibits the characteristic R before S, but it exhibits a modified characteristic R’ throughout the interval immediately following S (Salmon (), p. ). Consider the point on the wall immediately after the red perspex that is red due to the light passing through the red lens. Do we have a further interaction at this point so that the mark is not transmitted ‘without further interventions’? We have fixed it so that the light passing along the wall is a process because of the counterfactual dependence of the introduction of the lens on the placing of the perspex on the wall. However, this putative process would not alter, in any way, the red beam of light running through the lens. In which case, condition () of the

 



account of causal interaction would not be met. So we have no grounds for supposing that the light hitting the wall after the perspex is a further intervention. Questioning the details of Salmon’s account, of course, does not mean that no account of this type will work. Indeed, the theories discussed in the next two sections are plausibly thought of as developments of Salmon’s ideas. Even at this point, though, we can see the basic structure of the problem. Salmon seeks to capture the notion of causation in terms of the idea of a genuine process. The question is whether this can be done without appeal to either a causally loaded notion or the truth of counterfactuals that, if they could be relied upon, would provide an independent account of causation. Subsequent sections will draw attention to the first difficulty, here let me underline in a little more detail the second. The counterfactual dependence I introduced between the placing of the perspex and the introduction of the lens dramatizes how other dependencies can be responsible for the pseudo-process’s satisfaction of candidate marks of a genuine process short of appeal to counterfactual dependence between its stages. However, if appeal is made to the latter—or some sophistication of it given the discussion of Chapters  and —then prior success of the counterfactual theory has been conceded. Perhaps such considerations eventually convinced Salmon of the need to abandon the mark transmission theory—with its appeal to counterfactuals—for the conserved quantity theory outlined below (Salmon (), pp. –). The pressing question is whether the basic structure of the problem reproduces itself. Will appeals to counterfactuals that are naturally taken to provide an independent analysis of causation be required to distinguish causal processes from other processes that, without appeal to counterfactuals, process theories are committed to being causal but which shouldn’t be so counted? Is the only way to avoid this, to appeal to a causally loaded notion that betrays the demands of analysis?

.. Transference theories Transference theories appeal to persistence rather than counterfactuals to remedy the failings of the mark transmission approach. Causation is taken to be a kind of persistence. Suppose that a motorcycle collides with a brick wall and knocks it over. There is energy in the movement of the motorcycle and there is energy in the wall toppling over. Suppose, as won’t quite be the case because energy is dissipated, the quantity of energy in the motorcycle’s movement up to the wall is identical with the sum of the energy in the motorbike subsequent to impact and the wall toppling over. Identity in quantity by itself does not seem sufficient for causation. We could just have a case of annihilation together with unrelated and coincidental creation of energy. So transference theorists take the idea that the energy in the bike’s movement is transferred to the wall literally. The same instance of a property or trope—the particular quantity of energy—is present in the wall as was present in the movement of the motorbike (Aronson (), pp. –, (), p. ; Ehring (), pp. –). Because, as already noted, energy may dissipate, sometimes there will only be partial identity of property instance or trope (Fair (); Ehring (), pp. –). One objection to transfer theories is that they involve an asymmetric notion—that of transfer—that is causal. Stripped of such talk, all we would have is the identity of a property in the motorbike and the wall at different times. No causation is, as yet,



  

implied. So recent transfer theories simply appeal to the persistence of a particular property or quantity and look elsewhere to capture the asymmetry. We shall look at accounts of asymmetry, or as I shall argue there non-symmetry, in Chapter , some of which were developed in the context of transference theory, for example, the independence condition discussed in ... I shall discuss the matter no further here. Some transference theories are offered simply as accounts of what causation is in our world focusing on conserved quantities such as energy (already mentioned) and momentum (e.g. Fair (), p. ). Douglas Ehring elevates the approach into an account of what causation is in any possible world and, probably as a result, does not limit his appeal to energy and momentum. In his view, causation simply involves the persistence of tropes (Ehring ()). I shall focus on the latter to indicate general difficulties with the approach. The fundamental problem is that it is not obvious that identity is the proper basis for causation. Indeed, it rather seems that causation should be part of an analysis of what is involved in identity over time. Transference theorists are committed to providing an entirely non-causal story of property instance or trope identity over time (Ehring (), pp. –, –; Kistler (), pp. –). Since they take tropes or property instances to be transferred between objects, they cannot individuate them by the objects that possess them. Spatiotemporal individuation is no help either (Schaffer (), pp. –, gives such an account). When a trope transfers from one object to another, they change their spatiotemporal position. The issue is what makes the tropes at these distinct spatiotemporal positions numerically the same trope. Trope or property instance identity ends up a primitive with these entities understood as continuants. However, if it does end up a primitive to which we can appeal, then it is not needed for an analysis of causation as my discussion of Ehring’s case A involving two qualitatively indistinguishable particles revealed earlier (..). Indeed, not relying upon a primitive account of trope identity in the analysis of causation enables us to recognize a further distinction that would otherwise be obscured. Let me deal with these claims in turn. Ehring has argued that primitive identity without causality is required for the proper account of motion, in particular, to characterize the indeterministic rotation of a homogenous disk in a simple world containing nothing else in it to help to differentiate segments of the disk (Ehring (), pp. –, (), pp. –). To summarize a complex debate, the standard move of those who look to qualitative differences to analyse motion is to claim that the possibility of rotating homogenous disks in such simple worlds reveals that there are directing qualities: qualities with a built-in vector indicating direction of travel (e.g. Lewis (), pp. –). The indeterministic case is problematic because, if the direction of travel is indeterministic, only the presence of a particular property instance at a location settles whether motion has, in fact, taken place. If the chance of a segment rotating to another position is less than , then, the argument runs, the only way to settle whether rotation has taken place is whether or not the segment in question is in the other position. In a move corresponding to the move I made in the discussion of case A, the presence or absence of rotation would show up in whether, say, a segment, x₁, of the disc at a spatial position s₁ at time t₁ would, just before t₂, raise the mean chance of x₁ at s₂ at t₂ together with the presence of x₁ at s₂ at t₂. If yes, then there is rotation, if no, then there is not.

 



Primitive identity provides the resources for my favoured counterfactual analysis to deal with this case and, thus, to capture the causal relationship between the segment’s presence at different positions at different times. While it is true that appeal to primitive identity alone may seem to deal with the case, to develop a theory on this basis is misguided. My approach can deal with the case using the same materials and, at the same time, cover worlds in which there is rotation but no primitive identity. This leaves it open to the sceptic about primitive identities to press for a reduction of identity in terms of causation. In any event, if primitive trope identity is allowed, then appeal to it alone obscures a distinction. Consider the following possibility. A token trope, q₁, is destroyed at space-time point p₁ and fortuitously recreated at p₂, given its destruction. By fortuitously, I mean that the presence of q₁ at p₁ does not raise the chance of q₁ at p₂. Indeed, while it is at p₁ the chance of it being at p₂ at the same time is . When it is destroyed, it has a minute non-zero chance of being at any later space-time point (an infinitesimal chance if there is an infinite number of such points). Ehring’s theory is committed to the following. First, that what has been described is a distinct possibility from one in which there is just a fortuitous creation of another Q, q₂, at p₂. Second, the presence of q₁ at p₁ is a cause of q₁ at p₂. The position I favour holds that it is coherent to deny that these are two distinct possibilities (if primitive identities are rejected), however, if primitive identities are accepted, then there are two cases to distinguish. One in which there is fortuitous non-causal recreation. The other in which q₁ at p₁ is a cause of q₁ at p₂ (because the relevant chance-raising counterfactuals hold). I think the combination of the challenge to coherence— because of the intuitive appeal of a causal account of identity—together with, if primitive identity is allowed, two distinct cases represents a clear consideration in favour of the preferred approach. You can’t, on the one hand, insist that identity is primitive and then, on the other, deny that there could be a fortuitous recreation of the very same trope.

.. Conserved quantity theories Conserved quantity theories involve the idea that (CI*) A causal interaction is an intersection of world lines which involves exchange of a conserved quantity. (CII) A causal process is a world line of an object which possesses a conserved quantity (Dowe (), p. , (), p. ). One of the main proponents of this type of theory is Phil Dowe. Salmon has also been convinced by such a theory in his later work with a difference to be highlighted below (Salmon ()). As I’ve already noted, they are non-committal about the nature of causation in other possible worlds than our own. Conserved quantity theories improve on transference theories in, at least, one of three respects (see Dowe (), pp. – for other potential advantages). First, they don’t appeal to the notion of transference that relies upon an implicit appeal to a causal asymmetry. Ehring is an honourable exception here because he is quite clear that an independent characterization of causal asymmetry is required (Ehring (),



  

pp. –). Second, they don’t have to claim that energy (which is the most popular and plausible quantity to be conserved) is transferred from cause to effect (Dowe (), p. ). This deals with a troublesome array of counterexamples. For instance, if we put ice in water, we are inclined to say that the ice caused the water to become colder. Those who claim that causation involves transfer of energy from cause to effect must deny this since the energy departed from the water to the ice. So, from their perspective, the water becoming colder was the non-causal result of the water melting the ice (Aronson (), pp. –). Again, Ehring’s more general theory of trope transference need not have this consequence although, if he takes tropes to be sparse, there may still be cases in which our intuitive causal judgements have to be revised. To illustrate the structure of the concern rather than making any claims about a particular case: if coldness were not a trope, but just the absence of a trope of heat, then the verdict that I indicated Ehring might avoid would be reinstated. Third, conserved quantity theorists don’t need to appeal to the idea of there being a trope or property instance of a certain amount of energy, momentum, or the like which is passed from one object to another. Conservation means conservation in the amount of energy or momentum there is. Exchange of a conserved quantity is taken to be a change in value for that quantity from one object to another (Dowe (a), pp. –; Dowe (), pp. –). Given the problems described in the previous section this is welcome. Nevertheless, conserved quantity theories’ rejection of the idea of transmission has costs nicely illustrated by a case with which we are familiar. Salmon notes that the beam of light travelling along a wall irradiates it with energy and as the spot moves the radiant energy of the wall shifts with it (Salmon (), p. , for another example, Hitchcock (), p. ). It would seem that Dowe’s theory has the mistaken verdict that the light moving across the wall is a causal process. Salmon takes this to suggest that we need the idea of transmission after all and appeals to his original characterization of causal processes to characterize it (Salmon (), p. ). We have seen that this doesn’t resolve the problem. Dowe deals with the case by claiming that causal processes only take place within genuine non-gerrymandered objects, that is, any object found within the ontology of science or common sense (Dowe (), p. ). Gerrymandered objects are any objects you can splice together from parts of other objects by unrestricted mereological composition. The possession of energy by each part of a gerrymandered object is insufficient for there to be a causal process. The various segments of the wall across which the light travels is a gerrymandered object. Hence the irradiated sequence of wall parts, due to the light moving across the wall, is not a causal process (Dowe (b), pp. –). Dowe’s response has significant costs. First, to avoid circularity, Dowe must eschew causal continuity as even a necessary condition upon object identity. Yet, it is plausible that being the same object over time requires causal connections between its temporal stages to recognize the difference between the continuity of an object and a series of qualitatively identical replacements (Shoemaker (), pp. –). There are challenges to the claim that causation supplies us with a necessary condition for identity of objects that, if successful, would remove this cost. Suppose

 



that there are two machines: a table destroyer and a table creator. The table destroyer disperses the matter of a table. The table creator selects, by chance, matter from across the universe to create the table. As things turn out, the table creator selects the very same bits of matter and arranges them in the same way as was present in the table before the table destroyer was activated. Eli Hirsch urges that, in such circumstances, we would conclude that the table persisted in the absence of causal connection between the stages in its history prior and posterior to the activation of the machines (Hirsch (), pp. –). If the particles of matter from which the table is constituted after the operation of the machines were entirely independent of what came before, then I don’t think Hirsch’s conclusion that the table persists could be justified. Persistence of objects does not depend upon retaining the same matter. We allow replacement of parts. It is not obvious that simple resemblance, or occupancy of the same spatiotemporal position, are enough to establish an identity. The real problem with Hirsch’s case, though, is that it is not at all clear that there is no causal connection between the stage in the history of the table prior to the operation of the machines and a stage after the machines. If the first machine had not operated, the matter would not have distributed to the places it did. Although the second machine operated by chance, the places where it sought matter to assemble into the table would not have contained the relevant matter if the first machine had not dispersed the matter of the table to these places. The second machine, no doubt, would have secured matter from other areas. However, we are used to this type of reasoning. The fact that a different causal process would have taken place resulting in a certain effect does not mean the actual process starting with the actual distribution of table matter fails to be a cause. In circumstances in which all these, in effect, preempted beginnings are absent (in the terms of my theory, if we put all the obtainingmatter-at-other-places events in Σ), the chance of the table being created by the tablecreating activity would be very much lower than it would otherwise be. So there is a causal connection between a stage prior and posterior to the operation of the machines and we have no counterexample to causation being a necessary condition for persistence. The table persists precisely because there is a causal connection. It is also unclear how, at least by the criteria for persistence he canvases, Dowe can rule out the gerrymandered patches from constituting a single object. The first is simply that an object persists at time t + Δ from time t if it is wholly present at time t + Δ, having been wholly present at time t (Dowe (b), p. , (), pp. –). The identity of the object at the later time with the object at an earlier time is taken to be a primitive matter of self-identity for which no further analysis is, thus, required. Nevertheless, this does not exclude the question of whether the identity of an object over time requires certain relations between stages of its life history, for instance, causal connection. If we take self-identity as a primitive, we just change the import of the question. When are these primitively self-identical objects present and when not? Why aren’t gerrymandered objects primitively self-identical over time? The causal conditions, rather than being identity conditions, threaten to become existence conditions for objects, which would be just as damagingly circular (Kistler (), pp. –, for a related worry). Dowe seems to recognize the force of this type of concern when he notes the worry that there shouldn’t be ‘empirically



  

inaccessible’ elements in a theory and denies identity should be taken as a primitive in a deep sense as opposed to just a placeholder for something more substantial (Dowe (), pp. , –). Without appeal to causation, Dowe has nothing to say to the person who claims that the successive irradiated wall segments is a non-gerrymandered object. This is particularly troublesome bearing in mind that the other criterion of persistence Dowe considers are relations of resemblance (Dowe (), pp. –). It is hard to see how these rule out the allegedly gerrymandered object involving the travelling patch of light counting as a genuine object since the patches of light at spatiotemporally successive places across the wall strongly resemble each other in many respects, indeed, as many as one might expect a travelling object to resemble itself at earlier stages in its history. So I conclude that Dowe’s theory needs to appeal to causal continuity at precisely the point where he seeks to distinguish genuine causal processes from merely apparent processes. An alternative analysis of causation, such as the one I have provided, serves to characterize the distinction Dowe needs. If that’s right, then Dowe’s attempt to provide an alternative approach to the analysis of causation is forlorn. The conditions outlined in my analysis also seem to be necessary to deal with a third problem that Dowe’s account faces: insufficient but complete causal processes. Suppose that two gunmen try to shoot a vase with subsonic ammunition. Gunman B’s bullet hits the vase first, Gunman A’s bullet passes through the empty space where the now shattered vase once was. We are inclined to say that Gunman B is the cause of the vase breaking. Nevertheless, there is a causal process involving the exchange of energy from Gunman A’s shot to the vase, namely the loud noise of the firing travelling through the air and vibrating the molecules of the vase. Due to the subsonic travel of the bullets this noise would strike the vase first. Why doesn’t this process make Gunman A’s shot a cause of the vase breaking, along with the loud noise from B’s gun and B’s bullet striking the vase? One attempted solution appeals to path-specific chance-raising. Dowe suggests that C would raise the chance of E were p the only process between C and E (Dowe (), p. ). Unfortunately, this seems to make Gunman A’s bullet a cause by other means. If p, the actual path of Gunman A’s bullet, were the only process between C and E, then the vase would not have been destroyed by Gunman B’s bullet. In this case, Gunman A’s firing would raise the chance of the vase being destroyed. So the condition does not rule out the verdict that Gunman A’s shot is a cause of the vase breaking. There are, at least, two causal processes between Gunman A firing (C) and the vase breaking (E). It is just that the one that involves actual exchange of energy is not the one that involves counterfactual path-specific chance-raising. Dowe acknowledges that such cases spell trouble for the approach and tries something different. He adds to his overall account of interaction involving conserved quantities, the following requirement for any exchange involving more than one conserved quantity, the changes in quantities are governed by a single law of nature.

 



Dowe suggests that we may understand the appeal to laws in terms of simple covariance (Dowe (), pp. –). This may be able to deal with some cases but it doesn’t explain why Gunman A is not a cause in the case presented above. The impact of the sound waves on the vase and the impact of the bullet both involve exchanges of energy. The loss of energy from Gunman A’s gun represented by the loud bang is matched by a gain in energy in the vase due to the sound’s wave front hitting it. So there is a single law of nature that covers the sound wave/vase interaction as that which covers the bullet-striking/vase-shattering interaction with regard to the exchange of a conserved quantity. Nevertheless, Gunman A’s firing is not a cause of the vase breaking. The sound wave from Gunman A’s gun causes something in the vase, for example, the vibration. It does not cause the breaking. The place of vibration does not differ from the place of breaking. So we can’t get past the problem by identifying distinct spatial locations where the exchanges of energy occur. The difficulty is how to connect up the distinct causes—travel of sound waves, travel of the bullet—to the appropriate effects: vibration and shattering of the vase. Dowe’s first attempt at a solution appealed to the type of counterfactual that I used to develop my analysis. The further difficulty I have identified is also familiar from the discussion in Chapter . I cited a version of it as motivation for the ‘actual events’ clause. The reason why Gunman A’s shot is ruled out as a cause is that, in circumstances where it does run to completion by including (say) the penetration of the structure of the vase, there will be non-actual events upon which the breaking of the vase Σ-depends. The presence or otherwise of a causal process involving the sound of the bullet hitting the vase is irrelevant to this assessment. To disqualify the latter from securing Gunman A’s firing being a cause of the death, Dowe needs the idea that the process that is actually complete—the sound travelling—is not one which, if it occurred alone without the bullet travelling from the gun, would not raise the chance of the vase shattering. These points underline once more that it is counterfactual considerations—specifically counterfactual considerations concerning chance-raising—that settle whether or not a genuine causal process is at work. The causal process itself has, at best, a minor role to play.

.. Moral Process theories promised to provide a substantial notion of causation and not just a weedy notion based upon counterfactual dependence. The discussion in this section has shown that they have significant difficulties making good on this claim. They can certainly point to features of causal processes. The problem is explaining how these features capture the efficacy involved in the processes. If process theories are just empirical theories trying to identify common features of actual causal processes, then talk of transmission or exchange of conserved quantities has significant intuitive appeal. It is plausible that the fundamental causal laws concern these quantities. However, the issue is whether, in noting this fact, we have identified what causation is—even in this world—as opposed to what causation involves. I take it that the limit of the ambition of process theorists is not simply to identify the fundamental efficacious properties of events, states, and objects. This



  

would not tell us what causation is but just what, fundamentally, it holds between. For instance, those who say that causation involves energy transfer would, on the more limited ambition, just be saying that two events are causally related in virtue of their properties involving energy. Who could deny that? But it was not what was advertised. When we look at the task of explaining the nature of causation even in this world, it seems that process theories have problems at precisely the point that you would expect if process theorists had only managed to identify, at best, the fundamental efficacious properties of events (rather than what causation is). At crucial points, they either appeal to counterfactuals to distinguish genuine causal processes from accidental associations involving their favoured features or put something in the place of counterfactuals which, in fact, either (i) failed to play the required role, (ii) required causation for its characterization, or (iii) involved unattractive redundant commitments (in the case of Ehring’s theory). Of course, since my discussion has focused on particular process theories, and their failings, there is always the prospect that some other theory might be developed which avoids the difficulties I have identified. All I can argue at this point is that the persistency of the problems makes the prospect look dim. With this preliminary conclusion in place, I shall turn to consider the remaining reason in favour of process theories of causation, namely that they capture an intuitive difference that the counterfactual approach struggles to acknowledge. If they prove not only problematic to develop but also mistaken in the intuition they seek to capture, then there is little further reason for persisting in seeking a viable form of process theory.

. The Intuitive Difference, Action at a Distance, and Intrinsicality I begin the discussion of this part of the chapter by giving examples that, according to some process theories, generate the intuition of difference. I then go on to consider the various options available for the successful characterization of this intuition and criticize the arguments of those who see the divide in terms of causation and its absence. I then consider how these arguments may be bolstered by questions concerning the intrinsic character of the causal process, action at a distance, and certain quantum phenomena. I explain how my own position, which recognizes that causation comes in varieties while at the same time identifying what is common to all cases, can deal with the matters raised.

.. The cases and the intuition of difference Consider the following cases. Positive prevention: A child runs into the road (a, c) but is grabbed by his father (f) attending to the child (b) from the path of an oncoming car (d) so preventing the accident (e).

  ,    

a

c

d



e

f

b

Figure .a Lack of prevention by omission: A child runs into the road (a, c, d) and, because the father is inattentive (b doesn’t fire), he fails to grab the child (f) and the child is hit by the (braking) car and injured (e).

a

c

b

d

e

f

Figure .b Positive prevention by omission: The mother didn’t distract the father (g doesn’t fire) so he noticed that the child was running into the road (b). He grabbed the child from the path of an oncoming car (f) so preventing the accident (e). a

c

b

f

d

e

g

Figure .c Double prevention: The mother shouted at the father (g) distracting him so he failed to grab the child (not-f) so allowing the child to run into the road (d), who is hit by the (braking) car and injured (e). or Suzy is piloting a bomber on a mission (a, c, d) to blow up an enemy target (e). Billy is piloting a fighter as her lone escort. An enemy fighter seeks to intercept the



  

bomber (b, f). Billy shoots it down so (g) preventing the enemy fighter from stopping the bombing (Hall (a), p. ). I note this for later. a

b

c

d

e

f

g

Figure .d The cases seem intuitively different from the kind of causation involved in (say) a billiard ball colliding with another billiard ball, a fire consuming a forest, or, for that matter, the car hitting the child. We can note that in the latter there is energy transmission or exchange between cause and effect whereas in the cases described above energy is not transmitted or exchanged from the prevention or omission to the effect (always designated e). As I have already indicated, some proponents of process theories argue that this intuition is best captured by denying that preventions and omissions are causes at all. Dowe suggests that what unites these cases is that they all involve a negative relata or intermediary and are better understood as counterfactual claims about genuine causal processes (Dowe (), p. ). We discussed this thesis in .. Others, not necessarily proponents of process theories, claim that, while they are cases of causation, they demonstrate that causation is not a unitary kind. Hall has argued that there are, at least, two kinds of causation: mere counterfactual dependency and production, the latter involving the kind of intrinsic nomically characterized processes which might, for instance, involve transmission or exchange of quantities and which, under determinism, would be sufficient for their effects in the absence of other events (Hall (a), pp. –). Hitchcock has suggested there are even more than two without seeking to characterize them in much detail (Hitchcock ()). My characterization of Hall’s position simplifies matters a little. Hall sometimes talks of two concepts of causation and other times of two kinds of causation (Hall (a), pp. – for the former, Hall (b), p. ). Hall’s reason for this is that he is not ‘sufficiently clear on what underlies this distinction between concepts and kinds’ (Hall (a), p. ). A mere difference of concepts allows for the possibility of no difference in kinds but just different ways of thinking about it. That doesn’t seem to be what Hall has in mind. Rather, the proper characterization of his position seems to be that there are two distinct kinds of causation with some overlap.

  ,    



Intrinsically nomically characterized processes need not involve counterfactual dependence if there are competitor processes. When there are not, then there will be overlap. However, there will be cases of counterfactual dependence without intrinsic nomically characterized processes. These will be the cases involving putative negative events described above. The third option, the one that I favour, holds that, setting property causation aside, causation comes in various forms and yet there is a common nature: counterfactual chance-raising as analysed in Chapter . The defence of this analysis in Chapter  and subsequent chapters constitutes my reason for adopting the third option rather than the second, favoured by Hall. So I will focus on the viability of the first option in what follows. I turn to the further considerations Hall offers for recognizing two distinct kinds of causation in the subsequent section. In brief, then, the territory looks as in Figure .. Our present focus is on the left hand side of the hierarchy and specifically the idea that taking causation to involve genuine processes captures an important difference we are inclined to say exists between double prevention, causation by omission and the rest, and those cases of causation involving a genuine process between cause and effect. Dowe recognizes that we are prepared to count some of the cases outlined above as cases of causation. Nevertheless, he argues that, on grounds of

Causation Common kind?

Yes Different Concepts?

Yes Hall ‘Two Concepts’

No Causation as Genuine Processes?

Yes Rejection of Double Prevention/Omissions

Process Theories

Figure .

No Processes/Dependencies?

Yes Hall ‘Two Kinds’

No Different Realizations?

Yes Favoured Position

No Causal Pluralism (Anscombe)



  

theoretical simplicity, we should do otherwise. As I have already noted, he points to two common features of the cases. First, they involve counterfactual claims about genuine processes, for example, what would happen if a certain prevention had been absent. Second, they involve negative relata or intermediaries. Both features are insufficiently discriminating. There is a significant difference between the cases mentioned above and the claim that Tony Blair’s failure to warn me about the protruding chair leg this morning is a cause of the stubbing of my toe. We are inclined to take the cases as true and the claim about Tony Blair as false (given Tony Blair does not know me from Adam, was not there, etc.). Not even his most ardent critic would also want to place this relatively trivial instance of pain far removed from his sphere of activities at his door. Nevertheless, it is true that, if Tony Blair had warned me, then I wouldn’t have stubbed my toe. This is a counterfactual claim about a particular causal process: the events leading up to the toe stubbing. So Dowe’s thesis would place the Tony Blair case on a par with the other cases. This seems to be a mistake and when I discussed so-called negative causation in . I explained what more was required. By itself, the mistake is not fatal since it is still open to Dowe to deny that my richer characterization of what is involved in negative causation actually properly characterizes causation as opposed to something rather less significant. The structure of his position would remain even if the characterization of what is common to omissions, preventions, etc. is not. It is when we turn to the details of negative causation that an alternative candidate explanation of the intuition of difference emerges. Dowe’s second common feature of cases that fail to be causation is that they either involve negative relata or a negative intermediary. We are in agreement that there are no cases of causation with negative relata because there aren’t any such things (Dowe (), p. ). In ., I explained how this is compatible with taking negative causal statements to be true whereas, I presume, Dowe would take negative causal statements to be false, strictly speaking. The entities they concern don’t exist and the relation they attribute doesn’t apply. By contrast, from my perspective, positive prevention, lack of prevention by omission, and positive prevention by omission, while expressed by true causal statements, fail to count as cases of causation between the entities they seem to concern because at least one of these entities doesn’t exist, rather than anything to do with the nature of the causation involved. The major difference between us concerns cases involving positive relata with negative intermediaries, that is, cases of double prevention. There is no reason to deny that the mother shouting at the father is a cause of the child being knocked over by a car. On the very plausible assumption that the mother’s shouting was not intended to have this tragic and perhaps unforeseen consequence, some may (mistakenly) be reluctant to say that she was a cause of her child’s death. So let me change the example. Suppose that I deliberately shoot the signalman (f) who is about to warn the express train driver that there is a broken-down train in the track ahead (d) in the hope of causing death and mayhem. As a result, the express ploughs into the brokendown train to considerable loss of life (e). In such circumstances, it seems to me that we should say that I am a cause of the crash. Similarly, Billy shooting down the

  ,    



Hammer

Trigger

Figure .

enemy fighter does seem one of the causes of the successful destruction of the enemy target. Give the mother a malicious intent towards her child in shouting at the father and we are only too easily inclined to claim that she was a cause of her child’s death. Perhaps, because the cases above wear their non-process character on their sleeves, it will seem possible to deny that these are cases of causation. The compelling thought that causation involves some kind of impact transmitted from cause to effect guiding, and modifying, intuitions about when we have a genuine case of causation. However, there are other cases which seem absolutely central cases of causation, better understanding of which reveal that they aren’t to be understood in terms of transmission of anything from cause to effect. Here are two in a bit more detail. Consider first how a single action pistol works (Figure .). When the sear is removed (shown by the arrow) by pulling the trigger, the hammer comes down, so firing the pistol, because the hammer is on a spring. The process runs from the hammer coming down to strike the firing pin, or percussion cap, to ignite the propellant of the bullet to the bullet’s travel. Pulling the trigger prevents the preventer of the hammer coming down: the sear’s position. It is not part of the process as opposed to an enabler of the process taking place, exactly in the same way we saw above. Yet, we would not want to claim that, if somebody fired such a gun and killed somebody, the bullet going through their heart, say, the gunman was not a cause of the victim’s death. Another case would be turning on a light (Figure .a). To turn on the light, we need to complete the circuit so that the current flows round and, thus, through the light filament. At the moment, the circuit is shown with the light off. Household light switches work on this principle. In the cross-section in Figure .b, the light switch is shown on. To turn the light off, we push the switch down and some move away the circuit connection marked by B from the contact point A. Thus, in turning on a light we are enabling a process to take place (preventing a preventer of the process), in turning off a light, we are stopping the process. Yet, by Dowe’s lights, our switching a light on or off does not cause the light to go on or off. To recall from ., one of the cases used by Siegel to illustrate the experience of causality is switching on and off a light. Woodward suggests that perception of causality depends upon the perception of some contact-mechanical relationship signalled by a specific spatiotemporal relationship (Woodward (), p. ). Although there is temporal proximity between turning on the light and the light going on, there is no spatial relationship or



  

SPST Knife Switch

Light Bulb

Battery Lamp Holder

Figure .a

Household Light Switch Wiring Wall

To Light

Cover Plate On

A B

Switch Handle

Off Switch

Electrical Box For Housing the Switch

Incoming Electricity

Figure .b

perception of a process. The existence of a process between cause and effect is no part of our everyday understanding of cause nor even is it essential to our perception of causation. Nor are these isolated cases. To give a final, gruesome, example, chopping somebody’s head off is naturally thought of as a cause of their death (as Dowe acknowledges, Dowe (), p. , the example is McDermott’s). However, it is because chopping off their head stops the flow of blood to the brain that death occurs. There

  ,    



is no process from the chopping to the death. Rather, chopping off the person’s head interrupts the process whereby their brain stays alive. My rejection of causation involving negative events as relata has no problem classifying all these as cases of causation. Since my theory does not rely upon pairwise counterfactual dependency in order to establish causation between spatiotemporally distinct events, the fact that there are negative intermediaries does not mean that I have to recognize some cases of causation involving negative relata. By contrast, Dowe must deny that these are cases of causation because they do not involve genuine causal processes, for instance, conservation of a quantity. It seems to me that my own account has a better claim to capture the intuitive difference between the cases identified at the beginning of this section. In my hands, all of the cases involve causation. Some between the entities referred to—for instance, cases of double prevention—and some between the entities in virtue of which the negative causal statements turn out to be true (the positive causal surrogates of Chapter ’s discussion). This last difference constitutes the real basis for the intuitive difference between the cases. Dowe seeks to explain away our intuition that certain cases of double prevention are genuine cases of causation by making two moves: epistemic blur and practical equivalence (Dowe (), pp. –). He notes quite correctly that we may be uncertain whether a particular causal process involves the prevention of an inhibiting event from occurring or the bringing about of a positive event and this results in our blurring the difference between genuine cases of causation and mere counterfactual dependency. Lewis provides a nice illustration of the point. In the application of train brakes by the emergency cord, a valve is removed from a reservoir that is part of the brake mechanism allowing access to the outside air. If the brakes are air brakes, then the air in the reservoir is above atmospheric pressure. The removal of the valve allows air to escape, this removes a force that prevents the brakes from applying, and so the brakes stop the train. If the brakes are vacuum brakes, the air in the reservoir is below atmospheric pressure, the air flows in, expanding the reservoir and providing a force for the application of the breaks. In this case, by Dowe’s lights, we have genuine causation (Lewis (b), p. ). I agree that we may be uncertain over whether we have a positive causal process or the prevention of a preventer. But it is hard to see how this could explain our certainty that there is causation in such cases. Rather we should be uncertain whether or not there is causation (if Dowe is correct). It is not as if we feel certain that there is causation because we assume that the process involved has no negative intermediary and this is borne out by the fact that our intuition that there is causation persists when we find out what is actually going on. This brings me to Dowe’s point about practical equivalence. Even if he is right that both causation and omission or prevention may play a similar practical role so we treat them all the same way, this does not explain why our intuitions persist when we know the actual causal circumstances. Moreover, appeal to practical equivalence is a two-edged sword. If all of these cases are genuinely practically equivalent, then we have reason to suppose that we might have developed a concept—causation—to pick out those things that do play the practical role in question.



  

Practical equivalence at one level, though, does not mean that there are no practical differences. A significant difference between Dowe’s genuine causal processes and the other cases is that, if we set off a genuine causal process, it can be a means to bring about an effect by itself whereas, in the other cases, the causes are means by which some other causal process can bring about an effect or be stopped from so doing. The causes just remove obstacles from these other causal processes or place obstacles in their way. Recognition of this difference can have an impact upon how one acts. However, it can provide no succour to Dowe’s position since, if there is this important practical difference, then Dowe has lost his explanation of the persistence of the intuition that, in all of these cases, we still have causation. By contrast, taking the cases to reveal the variety of causation, we can recognize both the common practical elements that might have been the basis for our introduction of the concept of causation and, within that, the practical variety just mentioned which leads to differences in the kinds of cause we recognize under this unitary concept. For those sceptical about the appeal to intuitions, and the explanation of intuitions at work in the discussion, it is worth remembering that we are evaluating Dowe’s appeal to intuition as a basis for his emphasis on genuine processes in developing an analysis of causation and his attempt to explain away evidence that he has mischaracterized the nature of this intuition. In this context, it is fair to appeal to similar materials to show that his approach is inadequate.

.. Causes as producers and the disjunctive account of responsibility In the introduction to Chapter , I noted that I would discuss in Chapter  the idea that causes are producers rather than just anything that satisfies the clauses of my analysis of causation. We have seen, in .., that it is by no means clear that the difference between causation as production and as something involving counterfactual dependence is significant enough to divide the causal from the non-causal. I relied, in part, on very natural ways in which we understand causation to suggest that the division arose elsewhere. It did not concern the nature of causation but rather the absence of relata. The analysis I gave of negative causation in . involved two components: the application of my analysis of causation to positive surrogates and a counterfactual application of my analysis to the corresponding positive events of any putative negative causes/effects. That makes the relationship between candidate negative causes and their effects more complex than straightforward cases of positive causation. By my lights, the key element is the fact that, since omissions don’t exist, agents are linked to the consequences for which they are responsible because they do something else that may, or may not, be linked in their mind to omitting to do something that would avoid the consequences. My verdict would be challenged if the identified difference—the involvement of negative elements—were traceable to a significant difference in a notion the understanding of which has a central role for causation. This is Michael Moore’s position. He argues that a disjunctive theory of responsibility is appropriate because of the substantial difference between our responsibility for our omissions and for what we

  ,    



cause, in the sense of produce. He identifies the following significant features, which I shall go through and explain how they favour, instead, my own position. First, statements about our omissions don’t talk about particular events as candidate causes. They just concern the absence of a certain type of cause. If I failed to throw Jones a rope, there is not a particular event of my failing to throw such a rope (Moore (), p. ). My analysis of negative causation explains how this is not quite the right thing to say since there are positive surrogates. Nevertheless, even if I concede this is the case, it is not so in the case of double preventions (for further detailed discussion of Moore’s work and some of the issues raised in this section, see Schaffer (b)). There are particular events of, say, my pulling the trigger of a single-action pistol and my victim being struck with the bullet. Moore urges that double preventions are still problematic because they involve negative intermediaries (Moore (), p. ). However, given that there is a dependency between some particular action of an agent and some outcome, the relevance of negative intermediaries is hard to see. It would take peculiar commitment to the consequence of a theory to claim that shooting somebody with a pistol involves a diminished responsibility because of this. Second, it is suggested that our omissions fail to stand in the same kind of relationship to the outcome as the case of production, or anything like it. It is not that we cause something. It is that we omit to stop something else causing something (Moore (), p. ). The case of double prevention once again is different. A positive act of ours makes a certain change to the causal circumstances of the process later on, which ensures that the process continues. This is not omitting to stop something that would work just fine without us. Acknowledging that we are inclined to take cases of double prevention as causation, especially when focusing on shootings and the like, Moore suggests that we vary in our attitudes depending upon how close the harm is to that which we effect by double prevention. In the case of shooting somebody, the connection between cellular death and putting a bullet through a subject’s heart is deemed close. By contrast, Moore argues, if we tie up the lifeguard deliberately so that he or she cannot rescue a drowning man who we have as our enemy, the responsibility is less (Moore (), pp. –). The contrast drawn is not at all obvious. First, compare shooting a person through the heart with stabbing them through the heart. Outside the details of muscular action which may also involve non-process causation—in which case all actions fall on that side making Moore’s distinction explanatorily useless for the purposes at hand—the stabbing is a productive cause whereas the use of the single-action gun is not (Schaffer (b), p. , on muscular action). Yet, there is no significance between these two cases at all in terms of responsibility. One wouldn’t suggest that knife crime was particularly heinous. Second, consider the contrast Moore drew between the shooting and the lifeguard. We are responsible for a person’s death both ways. However, to the extent that there is any variation in our attitudes of the kind to which Moore appealed, it is present in positive cases too. Supplying an alcoholic with alcohol because you are sufficiently frustrated with them that you want them to die seems less reprehensible than shooting them dead—or, at least, less reprehensible to the same degree as



  

the contrast between the lifeguard case and the shooting case. Variation is not something distinctive of non-causal cases. So, if Moore’s appeal to closeness worked, it provides a candidate alternative explanation to distinguishing between causation and dependency that can apply across the board to explain variations in our attitudes. Third, Moore observes that there is a large difference between what he calls our positive duties of beneficence and our negative duties not to do harm (Moore (), p. ). If I stab you, I receive significant penalties and moral disapprobation. If I fail to stop you stabbing somebody when, perhaps, so doing would not put me in danger, the penalties and disapprobation are much less. Once again, the case of double prevention is different, at the very least on the side of the moral disapprobation involved. If I deliberately distract somebody from warning of the oncoming train resulting in a number of deaths, then I will receive considerable moral disapprobation. Even more obvious cases are those mentioned earlier involving shooting or decapitation. To the extent that the large difference is justifiable, it more closely supports my suggestion that the distinction lies between omissions and the rest. The question is whether the agent’s responsibility is the result of a negative cause. The fourth consideration is drawn from cases of overdetermination by omission. A school bus mechanic fails to fix the bus brakes (f). The driver fails to apply the brakes to the bus (g) at the stop sign (which would have been useless due to the mechanic’s failure). The bus fails to brake (d). As a result, the bus fails to stop at the sign (b), goes into cross traffic, and lives are lost (e). The diagram is a

b

c

e

f d g

Figure . Moore claims that, in these circumstances, neither the repair nor applying the brakes were necessary. Both were sufficient for the bus not braking. By contrast with cases of positive overdetermination, where both are at fault, Moore claims that, in this case, neither can be blamed for the accident though both can be blamed for their omissions ‘unconnected to the harm’ (Moore (), p. ). As Moore notes, though, such a verdict is controversial. There are others who would be inclined to say that both are responsible to some degree—in whatever way those who are responsible by omission are. Overdetermination by omission is no different from overdetermination in positive cases, whatever the difference might be in responsibility due to the actions being omissions rather than positive actions. The latter verdict is reinforced, as Moore fairly points out, by a variant of the case in which the

  ,    



mechanic deliberately fails to fix the brakes and another individual deliberately fails to warn the bus driver of an unmarked danger on the road (g) (and for that reason the bus driver doesn’t attempt to brake (d)). One thing worth registering is that these two cases need some adjustment in order to be well characterized as cases of overdetermination by omission. Since the driver never attempts to use the brake, arguably an event is missing in the sequence of events leading from failure to repair to the bus crash. However, let’s for the sake of argument suppose that the case is of the kind envisaged in the diagram above. The controversial character of the verdict suggests that this is an unhappy basis for resting a substantial distinction between causation and something else. It is much more likely that the controversy arises from the absence of relata instead because both were omissions. Consider a corresponding case of overdetermined double prevention, a variant of fighter/bomber discussed earlier. a

b

c

d

f

g

h

e

i

Figure . a to e represents the flight path of the bomber to dropping the bombs (e). d, f, g is the envisaged flight path of the enemy interceptor. h is the message to the interceptor to abort the mission upon which the pilot doesn’t yet have the time to act, g is the shooting down of the interceptor by the escort fighter (i). Both the message to abort and the shooting down are sufficient to remove the preventer (the interceptor shooting down the bomber). Each prevention is completed. The message is received and the fighter about to stand down when the interceptor blows the fighter out of the sky. It seems clear that both are overdetermining causes of the bomber successfully dropping her bombs. Both the agent who sent the message to stand the fighter down and the interceptor who shot the fighter down are both responsible for the resulting destruction from the bomber getting Pthrough. My analysis would achieve this result by respectively putting h and i in . If that is correct, then whatever controversy attaches to the case of the bus accident arises from the role of omissions rather than the absence of a producing cause. As a result of this discussion, it seems clear that there is no basis for recognizing an intuitive difference between producing causation and mere counterfactual dependence, however sophisticated. What differences there are arise from cases where there are negative relata and not intermediaries. Equally, as a result, there is also no argument for taking causes to be the productive elements of a particular causal



  

circumstance. Nevertheless, there may be other features of productive causes versus non-productive causes that justify Dowe’s demarcation. I consider two in .., and argue otherwise.

.. Locality and intrinsicality I have recognized that there are a variety of different cases of causation, some of which involve the kind of causal processes analysed by process theorists. Hall has argued that these have two distinctive features that are not shared by cases of double prevention and the like. First, they don’t allow causal action at a distance on the cheap. Second, they are intrinsic (Hall (), (a)). I have my doubts whether these features are sufficiently discriminating to constitute part of a theory of a wholly distinct kind of causation. This does not rule out the possibility that they are distinctive features of one kind of realization of causation and, thus, constitute a subcategory of causation. ...  Let locality be the thesis that there is no action at a distance. This is not meant to be a necessary truth but rather one which may hold in some possible worlds and not others. The charge is that if the counterfactual analysis is true, then we would have lots of it in our world on the cheap. Double prevention cases are taken to be an illustration of this. Whereas, the question of whether or not there is action at a distance is a substantial matter. Intuitively, action at a distance occurs if there is a causal chain between c and e that has a spatiotemporal gap. We might characterize the absence of action at a distance for cause c upon e as follows. There is a spatiotemporal path between c and e where, at each spatiotemporal position on that path, there is an event which is caused by c and which causes e. Action at a distance occurs by c upon e if the condition specified does not hold. Suppose I have a gun that works by action at a distance. I fire the gun and the bullet dematerializes from the chamber and rematerializes in your heart. There will be no spatiotemporal path from the gun to your heart such that there is an event at each spatiotemporal position in it which is caused by the firing of the gun and which causes the bullet in your heart. Consider now Hall’s double prevention case of Billy shooting down an enemy fighter so enabling Suzy successfully to bomb and destroy an enemy target (and variants of it) (Hall (), (a), pp. –). There is a continuous causal chain leading up to Billy shooting down the enemy fighter. Then, the argument goes, there is nothing between the fighter going down and the bomber continuing on its path to dropping the bombs. You don’t have to postulate the existence of negative events to think that this claim is questionable. Consider all the events that actually hold on the possible flight path from the position of the enemy fighter to the bomber. Many of these events, involving air conditions in which the enemy fighter is not located, would not be present if the fighter had not been shot down. And these air conditions are a cause—because they

  ,    



involve no enemy fighter firing its weapons—of the continuing safe journey of the bomber. So, unlike the case of genuine action at a distance described above, we can put together something that does not involve action at a distance for the fighter and bomber case. Hall has, in effect, two lines of response to a retort of this kind. The first is that it will not be possible to identify a continuous path of such events because, had the interceptor attacked Suzy’s bomber, the bomber would have shifted position seeking to evade the attack (Hall (), pp. –). However, this response doesn’t work. It might be a consideration if we were thinking of a possible sequence of events leading up to, say, a missile penetrating the bomber’s side and its destruction. But our focus is on the sequence of events leading up to the continued safe flight of the bomber. The air conditions around the actual flight of the bomber, rather than the possible flight due to evasive action, would still be caused by the destruction of the fighter since, for example, they would be showing the effects of the actual flight path of the bomber and none of the consequences that might otherwise be the case if the bomber had shifted its position earlier with the fighter on the scene. These air P conditions would count as causes of the actual flight ofP the bomber—raising its -probability—and putting other possible flight paths in —the successful conclusion of the bombing mission. Hall argues, in addition, that this strategy will have an unfortunate consequence. Consider the variant case in which the interceptor receives the instructions not to shoot down the bomber without the time to act upon it before being shot down. Hall claims, and I agree, that the air conditions, etc. will be the same subsequent to the shooting down of the interceptor. So I must accept, given the nature of the strategy, that these are still causes of the bomber’s safe completion of the mission. Further, he notes, and I agree, that the fighter is a cause of the interceptor going down. So, he notes, by transitivity of causation, I must accept that shooting down the fighter is a cause of the bomber completing its mission successfully even though the fighter did not make that any more likely since the fighter had been instructed, by that time, not to shoot down the bomber in the first place (Hall (), pp. –,  fn. —the case described in () talks in terms of the omission of the instructions to shoot the bomber down but this raises additional considerations not relevant at this point). One problematic step in this argument, as must be guessed, is the appeal to the transitivity ofPcausation. If it is the case that shooting down the fighter does not increase the -probability of the bomber successfully completing the mission, then it is not a cause. The theory defended in Chapter  does not support Hall’s reasoning. In addition, Hall develops the case as a challenge to a straightforward counterfactual theory that is forced to deny that overdetermining events are causes. Instead, it takes their disjunction to be a cause. The preferred theory is not a straightforward counterfactual theory. We can recognize that the described case is one of overdetermined double prevention. Each—the instructions and the shooting down—is P a chance raiser of the bomber successfully completing with the other in . Moreover, the causal chain is complete. Both preventative measures occur and they share the causal chain subsequent to the shooting down.



  

Let me note, in passing, I’m leaving open the question of whether it is appropriate to recognize overdetermining and pre-empting omissions. If it is, it may be necessary P to allow negatively specified events as members of although very often, there will P be a positive event which we can put in to play the same role. For example, consider the variant of Hall’s case set aside above where the interceptor required omitted positive P instructions to shoot the bomber down. We would not have to put this omission in Pto explain how the shooting down of the interceptor was a cause. We could put in the order not to send the instructions that was a cause of the omission. Hall’s second line of response (that I mentioned above) invites us to consider a new case that will lay strategies like the one I have defended to rest ‘once and for all’ (Hall (), p. ). It draws on an old case put forward by Michael McDermott (McDermott (), p. ; Hall (a), p. ). I throw a ball at a window. In its path, someone, Suzy is traditional, catches it. Behind her, there is a huge brick wall impenetrable to the ball. For some, it seems obvious that the catcher doesn’t prevent the ball from hitting the window because the brick wall is in the way (Hall (a), p. ). For others, the catcher stopped the ball from hitting the window because the ball didn’t even reach the wall (McDermott (), p. ). Hall’s variant case has the bomber with an impenetrable shield. Hall takes it as obvious that the shooting down of the interceptor would not count as a cause in the case when the shield is always up. Suppose, instead, the shield was quickly put up when the bomber saw the fighter shot down. It is plausible that, in that case, the destruction of the fighter might also count as a cause of the bomber successfully completing its mission. If it is denied, though, that this is a case of action at a distance for the reasons canvassed above, Hall argues, then we would have to claim that the destruction of the fighter was a cause even if the shield had always been up because the same air conditions would hold around the bomber (Hall (), p. ). This second line of response isn’t successful. The more minor point is that someone could argue that the air conditions around the bomber would not be caused by the destruction of the fighter if the shield were always up. That would be a point of difference with the situation in which the shield was put up afterwards. The important point is that it is plausible both that the catcher stopped the ball from hitting the window and that the fighter stopped the interceptor from shooting down the bomber because the wall and the shield did not play a role. The ball neither hit the wall nor the missiles of the interceptor hit the shield. We have a case of pre-emptive double prevention. The favoured analysis would give that result. The crucial point is that the events needed for the wall, or the shield, to protect the window, or the bomber, respectively are missing. My resistance to double prevention cases being cases of action at a distance on the cheap has derived from the following consideration. There are spatiotemporal paths from preventers of preventers to their effects in which, at each point in the P path, there will be events that display the requisite kind of probabilistic -dependence on both the cause and the effect. Disturb these conditions sufficiently and the connection will break. This is not so for genuine action at a distance. There are no effect inhibitors that depend upon the absence of the cause. The connection

  ,    



can be broken so that the effect is inhibited. But this will always be independent of the cause. Nevertheless, it is worth bearing in mind that there is another empirically informed response. This would be to insist that the form of action at a distance involved in pre-emption cases is not the substantial kind involving—for instance— spatiotemporal breaks in energy transmission. As such, then, the question of whether or not something is a case of substantial action at a distance concerns the relata involved rather than the form of causation itself. ...  The other feature alleged to distinguish substantial causal processes from those given a straightforward counterfactual analysis is that substantial causal processes are intrinsic. The basic idea is that If c, d₁, d₂, d₃, and e is a sequence of the events ending with e and containing all the causes of e from the time of occurrence of c (call this the complete causal process from c to e) and another process c*, d₁*, d₂*, d₃*, and e* is intrinsically identical to it in terms of the events which constitute it, and their spatiotemporal relations to each other, then, given that the same laws hold, the causal process from c* to e* is complete with c* being a cause of e* (Hall (b), p. , slightly adjusted to fit with my terminology). The qualification ‘given that the same laws hold’ is required to set to one side the question of whether the intrinsic character of the causal process settles which laws hold. As we shall see in Chapter , some accounts of laws depend upon the patterns of events which hold in a world. The intrinsicality or extrinsicality of a causal process in the required sense doesn’t turn on the nature of laws. We can illustrate the intuitive force, as well as the potential contrast with cases of double prevention, by considering the following diagram already produced earlier. a

b

c

d

f

g

h

e

i

Figure .d Focus first on the top chain of events a to e. It is tempting to think that this sequence of events will be a causal process resulting in e no matter what context you put it in. For example, we could put that top row in the following diagram and it would still be a causal process, indeed a classic example of early pre-emption.



   a

c

d

e

Figure . Consider now the claims of g to be a cause of e in the first diagram. The most immediate chain g, f not occurring, d occurring, and e occurring would not count as the full causal process. If there had been no possibility of f occurring, then g would not count as a cause. For example, if the so-called interceptor had no interest in shooting down the bomber, then the fighter shooting down the interceptor would not be a cause. b needs to occur (that is, the interceptor must be flying to intercept the bomber). So, the charge runs, cases of double prevention are not causal processes in the same sense because whether or not they count as a causal process will depend upon the context in which they are instantiated. One problem with this line of reasoning can be brought out by focusing back on the top rows of the diagrams. It must be remembered—neurone diagrams are selective representations of causal structure—that, in fact, the causal process depends upon various other causal conditions which, together with the occurrence of the events represented, c say, are required for the occurrence of e. These other conditions can fail to be present. So there is a context in which the causal process represented by a, c, d, to e is not a causal process leading up to e’s occurrence. The following might happen. a

c

d

e

g

Figure . There might be a disturbing condition g that breaks the connection between d and e. There is no intrinsic difference between the process in this case and in the preceding case. A natural response is to argue that all that the last diagram shows is that we need to characterize the top process, not just in terms of the highlighted causes, but also the enabling conditions for that process. So we must have a not-g condition, or conditions X such that, together with the laws, implies that g doesn’t occur. The difficulty with this response is two-fold. First, such a condition itself doesn’t present the same tidy intrinsic picture we had when just focusing on a to e. Second, if we must count in the enabling conditions, then the proper characterization of intrinsicness is the following.

   :  



If c, d₁, d₂, d₃, . . . and e is a sequence of the events ending with e and containing all the causes of e from the time of occurrence of c (call this the complete causal process from c to e) and another process c*, d₁*, d₂*, d₃*, . . . and e* is intrinsically identical to it in terms of the events which constitute it, and their spatiotemporal relations to each other, then, given that the same laws hold, and intrinsically the same enabling conditions P* hold as those which held for c, d₁, d₂, d₃, and e, viz P, the causal process from c* to e* is complete with c* being a cause of e* (Hall (b), p. , slightly adjusted to fit with my terminology). However, with this adjustment, we’ve lost the difference between cases of double prevention and cases of productive causation. b’s firing will be included as the enabling conditions of the process between g’s occurrence and e’s occurrence. It might be argued that there is an important difference. By contrast with those conditions for the top row sequence of events, the enabling conditions for the case of double prevention are not causes of e’s occurrence. This difference, though, just reflects the difference between productive causation and double prevention. It has nothing to do with the putative intrinsicality of causation. A more significant difficulty with the appeal to enabling conditions is that it seems to lose the significant feature of causation that the characterization of intrinsic causation was seeking to capture. What stops the enabling conditions from including that there are no competitor chains of the type characteristic of redundant causation cases? However, talk of the intrinsicality of causation was initially motivated by the thought that something doesn’t cease to be a causal process, if there are competitors around, so long as these competitors don’t mess with the structure of the target process. It was not supposed to wrap up the absence of competing chains in the characterization of enabling conditions. So it is better to think that the analysis of P causation, with its appeal to the -mechanism, is itself the proper characterization of the idea that causal processes are, in an important sense, intrinsic. If that’s right, then the issue is whether there are cases of redundant double preventions. We found that there were. The twin preventions of the instructions not to shoot down the bomber and the interceptor being shot down were a case in point. So in the only sense in which it makes sense to capture the intrinsicality of causal processes, they are as much a feature of non-productive cases of causation as productive cases. Where differences may arise in cases of non-productive causation is, as I have already urged, when one or both of the putative relata fail to exist.

. Bell Inequality and Relativity: The Options Experimental results predicted by quantum mechanics together with the special theory of relativity have been the basis of an objection to counterfactual theories of causation in favour of some more substantial idea of a causal process. I shall set out a highly simplified version of the experimental situation. I hope it is thought to be accurate in the relevant respects but the most important point is to get the structure of the challenge right. Indeed, since my theory of causation purports to be a necessary truth, the entire discussion can run at the level of a thought experiment concerning a possible but perhaps not actual situation. If the upshot of my



  

discussion were to use a counterfactual theory of causation to dismiss a certain treatment of the issue, then it would be inappropriate to run the discussion at this level. The fact that a situation is actual is of potential significance in itself. But I shall not use the counterfactual theory of causation in this fashion. Hence, the simplifications can be justified. In what is known as an Einstein-Podolsky-Rosen (EPR) experimental set-up (derived from a paper which set out the preliminary reasoning to which John Bell responded), two particles, α and β, with  angular momentum taken together, emitted from a source and travelling away from each other in, perhaps opposite, directions will conserve angular momentum (spin being a type of angular momentum). So if one particle, p₁, is measured and found to be spin up (i.e. it has the value + ½ with spin pointing in the direction of the positive direction of the z axis), then the other, p₂, will be found to be spin down (i.e. it has the value ½ with spin pointing in the negative direction of the z axis). Quantum mechanics does not predict for either particle that the probability of a certain angular momentum e.g. spin up is . Different values are given probabilities. If a measurement is made on a particle, Pr(spin up) = ., Pr(spin down) = .. These probability values are not taken to be a measure of uncertainty alone. According to the Copenhagen interpretation of quantum mechanics, the particles have no spin properties prior to measurement. Even talk of them being particles is misleading. However, the issue is how can these probabilities be the probabilities of the result of measuring angular momentum for either particle and yet, if the result is spin p for particle α, say, then Pr(spin down for β) = . Indeterminism prior to measurement should not guarantee conservation when measured. There seem to be two immediate options. First, the measurement of (say) α as spin up causes β, or its measurement, to be spin down. We can represent this as follows. α

0.5

0.5

1

β

0.5

0.5

Figure . The direction of the vertex of the triangle represents the particles being spin up or spin down respectively. The numbers represent the probabilities. The effect on β of the measurement of α is instantaneous and the measurements may be miles apart (or more). So we would have a case of superluminal (i.e. faster than the speed of light) causation.

   :  



Second, there is some feature of the source that has been left out which transmits itself down the paths of both particles, α and β, determining what the angular momentum of each particle will be, and hence, that angular momentum will be conserved. If the second option were the case, quantum mechanics is incomplete because it omits mention of such a feature and just gives probabilities to each of a range of angular momentum values. Really, the situation is like this. α

β

1

1

Figure . If the first option were the case, then there would be superluminal causation. This is ruled out by the special theory of relativity. Hence, if quantum mechanics is complete, then it is incompatible with the special theory of relativity. That, at least, is the preliminary conflict, to be qualified shortly (for more discussion, Lange (), pp. –). Reasoning due to Bell is taken to establish that the second option is ruled out. We can illustrate the issue as follows (drawn from Maudlin (), pp. –). Polarization is a particular form of spin that photons have. When light passes through a polarized filter, like sunglasses, about half the light is absorbed and the half that is emitted all have the same direction of polarization where, before, they might have any. Consider photons, α and β, emitted from the source passing down the two arms of the EPR set-up illustrated above which, at a certain point, arrive at a filter on each arm. Let L be the left arm filter and R be the right arm filter. Although the partner photons may have any direction of polarization before they arrive, if the filters have the same alignment with respect to the corresponding arm, either both photons will pass through or fail to pass through the filters. This is so for any angle relative to the arm at which the filter is set. If the filters are misaligned, then the photons still behave as if they have the same alignment. For example, if the alignment of R is L’s alignment + ° and the photon passes through L, then the corresponding photon is absorbed by R, and vice versa This is exactly what would happen if we were considering photons passing through a filter, having a particular polarization as a result, and then arriving at a second filter aligned ° to the angle of the first. The photons would be absorbed by the second filter. If, in the EPR set-up, the photon passes through L and the misalignment of R to L is between  and °, then the proportion of times the photons passes through R is



  

given by cos²Δ (the angle of misalignment). So, for instance, if the angle of misalignment is °, then there is . agreement, if °, . agreement. Once again, this is the behaviour observed if photons passed through a first filter, had a certain polarization, and then met a second, misaligned filter. The details of the present case explain why the second option—that the probabilistic relationships are to be explained by some feature of the source—is ruled out. The behaviour of the photons is settled by two factors: first, the angle of the filter relative to the photon’s path of travel; second the alignment of the filters with respect to each other. The EPR experiment puts the two filters on different arms and we observe the behaviour of one photon and its partner. So we know the polarization of the photons is determined by the filters and not by something at the source. This is not just because we know what does determine the behaviour of the photons. There is no feature that the source could have which could be sensitive to the angle of the filters and alignment between the filters. Indeed, we could set the filters after the particles have discharged from the source. The objection to counterfactual theories of causation arises as a result of the second option being ruled out. Consider the counterfactuals (EPR) If the measurement of α’s angular momentum had not been spin up + ½, then it would not have been the case that the probability that the measurement of β’s angular momentum is spin down ½ = . (EPR) If photon α had not passed through filter A, then it would not have been the case that the probability that photon β passed through filter B =  (in circumstances where the two filters are aligned). Both seem to be true because neither are backtracking counterfactuals in which the apparent counterfactual dependency holds in virtue of a common cause, some feature of the source. Equally, if the measurement of α’s angular momentum had been spin up + ½ (or if photon α had passed through filter A), then it would have been the case that the probability that the measurement of β’s angular momentum is spin down ½ =  (or it would have been the case that the probability that photon β passed through filter B = ). So the required probability fluctuation is present. The satisfaction of my analysis does not require that the candidate effect be absent when the cause is not there (so long as its chance is much lower). So it is not committed, as Luke Fenton-Glynn and Thomas Kroedel point out Lewis’ analysis is, to a causal relationship failing to hold in this case because maximizing perfect match would be achieved by taking β’s angular momentum to be spin down anyway. My revision to the similarity weighting to constrain the application of the perfect match condition means that it is not the case that the closest worlds are those in which β’s angular momentum is spin down anyway (Fenton-Glynn and Kroedel (), pp. –). There also does not seem to be any reason for supposing that the other conditions for causation wouldn’t be realized. Hence, my analysis is committed to claiming that there is apparently superluminal causation in this case. The charge is that a proper analysis of causation should not rule out the possibility of a non-causal connection between the photons and, hence, entail that the special theory of relativity is false (Butterfield (a), pp. –, (b), pp. –).

   :  



We can break responses to this line of objection into two parts. The first concerns the claim that the counterfactual theory of causation rules out the possibility of noncausal connections between the photons that preserve the truth of the special theory of relativity. One such account appears to avoid the difficulty in name only. Michael Redhead has argued that causation involves a robust dependency whereas, as the character of the relationship between the two photons can be altered by slight changes in their state as they emerge from the source, the connection between them is not robust (Redhead (), pp. –). He dubs non-robust dependencies passion. However, until we are clear about the problem with superluminal causation for the special theory of relativity, and whether superluminal passion shares in the important feature that gives rise to the difficulty, this is not a theoretical option we need to keep open. Either non-robust dependencies of this sort are called causation or they are called passion. If passion is unproblematic, the dependencies, as such, are unproblematic, and there is no immediate clash with the special theory of relativity. Another suggestion is that the quantum correlations are a dispositional property of the particles taken together. In other words, there is an intrinsic property of the particles—their standing in a certain relation to each other—that does not supervene upon particular features of either particle (Teller (), pp. –, (), pp. –). This would seem to imply that, for instance, a photon’s passing through, or being absorbed, is a relational property of passing through with the other photon passing through or being absorbed when the other photon is absorbed, with the polarizers having a certain alignment. If that’s right, then this option presents no difficulty for the counterfactual analysis of causation. There are two ways it might be developed: causal and non-causal. According to the first, the relational property holds in virtue of an underlying causal relationship. This can, itself, be developed in two ways. In one case, the relational property is possessed because one of the relata is a cause of a property of the other relata. For example, a torch can have the property of illuminating an object. Similarly, then, one particle polarizing may have the property of making the other particle a co-passer. This would not be an alternative to allowing that there is a causal relationship between the photons passing through the filters on either side of the apparatus. In the other case, the relational property is a manifestation condition of a disposition that is attributed to the two particles taken together. One photon hitting a filter is a cause of this manifestation condition that, as a result, is common effect. If this is the picture, then the counterfactual dependency would not be present. When we consider what would be the case if the first photon were not absorbed, we allow that something else may be different, for example, the photon deflected before it reaches the filter. Thus it doesn’t follow that the photon on the other arm would fail to be absorbed. The second way of developing the approach takes connection to follow noncausally from the nature of the dispositional property. One of the requirements of counterfactual analyses of causation is that the putatively causally related events must be distinct in relevant respects i.e. those responsible for the counterfactuals holding in the way I spelt out in .. The two photons passing through, or being absorbed, are not distinct and hence the counterfactuals concerning passing through the filter, or spin, don’t reveal a causal relationship. Moreover, given that Paul Teller has insisted that the dispositional property does not supervene upon properties of the particles,



  

there would be no minimal supervenience base of these properties that did not stand in a relationship of existential dependence to the other and which satisfied the analysis of causation. Uncertainty about the proper way to conceive of the non-supervenient dispositional property identified may be cited to explain how we can be ambivalent over whether the EPR phenomena involves causation. This answers a related objection to the counterfactual approach that is sometimes drawn from this phenomena, namely that it can’t explain our ambivalence (e.g. Fenton-Glynn and Kroedel (), p. ; Skyrms (), pp. –, seems to have a similar objection in mind). It might be argued that, even if we understood Teller’s proposal in the second, non-causal, way we could identify two distinct events that would still display a probabilistic counterfactual dependence. One pair of candidates would be some causal consequence of the joint passing through or absorption, for instance, a photon detector on each side that clicks if a photon has passed through the polarizer on that side. In such circumstances, shouldn’t we say that if a detector had not clicked one side, a photon detector would not have clicked on the other side? However, the reasons for rejecting backtracking in general would apply here too. It is not the case that if the photon detector failed to click on one side, that is because the common cause—the joint state of the two photons—would not have occurred. This is but one way in which the causal relationship may be disturbed. There are the other conditions that hold on either side that are required for a click. There will be much more discussion of this point in ..–. The second part of the response to the objection to the counterfactual theory of causation challenges whether concluding that there is causation in this case really gives rise to a conflict with the special theory of relativity. As Tim Maudlin points out, it is not superluminal causation that is the problem. It is rather the possibility of superluminal signalling. One consequence of superluminal signalling is that it is possible to define a notion of absolute simultaneity and a privileged reference frame (Maudlin (), pp. –). It has also been argued that, if superluminal signalling is possible, then there will be a reference frame in which a signal is sent into the past. This gives rise to a second consequence: the possibility of a signalling paradox such as deciding to send a signal if and only if I haven’t received it (Maudlin (), pp. –). I discuss the general possibility of such loops of possible causation in .. and conclude there need be no threat. The more important point is that quantum entanglements don’t seem to lend themselves to signalling in any event. What can be manipulated on one side to transmit a signal to the other side? It is not the case that we can determine whether or not a photon is absorbed on one side to signal to the other side. No matter what the orientation of the filter is, the chance of absorption is always  per cent. Nor does the correlation—existing as a result of setting up the apparatus—introduce a discernible change in the pattern of absorption and passing through looking purely at the photons on one side of the apparatus (Maudlin (), –). If one could, after setting the angle of orientation of polarization on one side, observe the state of the relevant photon on the other, then signalling is possible. However, the state of a photon cannot be observed (Maudlin (), p. , fn. ). The fact that these features are lacking doesn’t impugn the status of the connection as a causal relation.

   :  



Causation does not require that causes be means to ends (see . for further discussion). The possibility of the kind of manipulation involved in signalling is, thus, not a necessary condition for a causal relationship between photons passing through the polarizers on either wing. So there is no immediate conflict between these phenomena and the special theory of relativity. Although superluminal causation does not seem to be in direct conflict with the special theory of relativity, Huw Price has pointed out that there is an alternative: backward causation. The idea is that orientation of the polarizers is transmitted back to the source and the difference affects the photons as they leave the source and travel to the polarizers. One consequence of this view is that quantum mechanics is incomplete. It does not record the result of the backward influence of the angle of the polarizers on the particles at point of separation (Price (), p. ). The picture envisaged seems to be the following. e*

e

h

f

g

b

i

d

c

Figure .

a

Here e and e* are whether the photons are absorbed or not. Let us suppose that in this case, they are both absorbed. h, g are the angle of the polarizers. Thus, the input into c—the point of emission of the photons—is the difference between alignment that adds to the conditions in which the photons are emitted to cause a distinctive c event of two photon emissions. b, d, f, g are the photons travelling with a certain orientation because of the backward causation of h and i.



  

A feature of this position is that while there is no action between things that are separated by a space-like interval requiring superluminal causation—e and e*—there is action at a spatiotemporal distance. The angle of the polarizers affects the photons at point of separation first, giving rise to their respective orientations that persists up to the photons’ interaction with the polarizers. In this section we have seen two things. First, the favoured analysis is compatible with there being no causal relationship between the results of EPR phenomena if a position like one development of Teller’s is coherent or there is some kind of cosmic collusion whereby the positioning of the filters is causally determined by prior history in spite of the fact that the positioning seems to be the result of later experimental decision. Second, there are two ways in which there could be such a causal relationship that the counterfactual analysis successfully captures. This is compatible with distinguishing between the type of causation at work when there is a genuine causal process running between two events and a case such as the EPR phenomena. At this point, the question of whether to call the relationship causation because it satisfies the analysis of the counterfactual theory or something else seems largely verbal. There is no danger of the appeal to characteristics concerning genuine causal processes doing the work because of the difficulties with the formulation of these theories identified in . (as Esfeld suggests Esfeld ()).¹ The second way in which there is causation at work in the EPR phenomena involves backward causation. As we shall see in Chapter , the counterfactual theory can be developed in such a way that this is not ruled out. Thus, the counterfactual analysis of causation keeps most of the theoretical options alive in the discussion of the apparent conflict between quantum mechanics and the special theory of relativity.

. Concluding Remarks In the present chapter, I examined the claims of process theories to provide an account of causation more in tune with our intuitive judgements about when causation is present and the extent to which such theories supported the idea that there were different kinds of causation where they served to characterize the fundamental kind. I argued that process theories were subject to difficulties at precisely the point at which they attempted to characterize the nature of causation, that is, in distinguishing between genuine and pseudo-causal processes. This suggested that they were not successful in providing a theory of causation but rather identified certain kinds of causal process—through focusing on certain kinds of relata—where the causal character of these processes was understood in other, counterfactual, terms. This robbed them of the ability to demarcate a fundamental kind of causation and discredit the status of others. A new possibility thus opened up, namely that there are a variety of causal processes but one common account of what made them causal. I suggested that the analysis I put forward in Chapter  provided such an account. A threat to my position would derive from any of the following: first, a failure to capture our ¹ I would like to thank Michael Esfeld for making me think about this issue many years ago!

 



intuitive judgements regarding the difference between causation involving substantial causal processes and double prevention, omission, and the like; second, a failure to capture other features of causation such as intrinsicality or the rareness of action at a distance; and, third, a clash with the proper development of scientific ways to reconcile the special theory of relativity with quantum mechanics. I made, in brief, the following response to these threats. First, the rejection of negative causation together with an explanation of the truth of negative causal statements provides a better account of our intuitive causal judgements. Cases of double prevention are naturally thought of as causes and, hence, don’t favour an account of our intuitive causal judgements based upon an appeal to substantial causal processes. Second, my analysis captured the way in which causation is properly thought to be intrinsic. Third, cases of double prevention aren’t obvious cases of action at a distance. There is a spatiotemporally continuous chance-raising relation for standard examples. In any event, given our conclusions about process theories of causation, we should not look to the nature of causation but rather to the nature of the causal relata—for example, a transfer of energy—to identify what is puzzling about action at a distance when it is puzzling. There is nothing in counterfactual dependence or chance-raising itself that makes a dependency between spatiotemporally proximate events more intelligible than those more distant. Fifth, and finally, counterfactual theories are neutral regarding successful ways of resolving the apparent conflict between quantum mechanics and the special theory of relativity. In Chapter , I shall consider further the way in which causation may be various. Before that, I must turn at last to the nature of causal non-symmetry. Apart from the obvious central importance of causal non-symmetry in any theory of causation, my conclusion regarding the scientific neutrality of my proposed analysis rests partly upon material contained in that chapter.

 Causal Non-Symmetry The issues falling under the heading of direction of causation, causal priority, or asymmetry, are among the hardest in discussions of causation. It is often suggested that the direction of causation distinguishes causes from their effects (Mackie (), p. ). Causes explain, are means to, bring about, their effects, and not vice versa (Gasking (); Mackie (), p. ). Our topic is sometimes more or less stipulated to involve an asymmetry. It concerns that relation between a cause and effect that does not hold between an effect and a cause (e.g. Beauchamp and Rosenberg (), p. ; Ehring (), p. , (), p. ; Price (a), p. ). This is a mistake. The causal relation is non-symmetric rather than asymmetric. In the first section of the chapter, I will explain why. The account of causal non-symmetry to be offered in subsequent sections attempts to respect the following plausible constraints. The first is that there is an important connection between causal non-symmetry and temporal direction. At the least, it seems that the following is true Metaphysically necessarily, causes usually precede their effects. Although causation is non-symmetric, causal direction holds more often between earlier causes and later effects, and not vice versa, than otherwise. Backward causation in small doses may be defensible but, in every possible world, most causes precede their effects. The constraint is particularly important in the assessment of primitivist analyses of causal non-symmetry. If causal non-symmetry cannot be subject to further analysis, then the connection with time must be due to the character of time, rather than the character of causal non-symmetry (see .). As we shall see in the first section of the chapter, the claim that causes usually precede their effects will be moderated slightly to deal with the cases in which effects are causes of their causes. The second constraint is that causes are taken to explain their effects, and not vice versa. Any viable theory of causal non-symmetry needs to identify what is explanatory about causes. The answer to this question implicit in what follows is that causation involves non-symmetric chance-raising of the effect, characterized counterfactually. The type of explanation envisaged holds between distinct entities and relates to why one occurs. In this regard, citing something that increases the probability of its occurrence is a plausible response. This type of explanation does not detract from other explanatory projects. We can explain the features of supervening properties by citing the subvenient properties that determine their instantiation. We can explain the occurrence of a certain type of entity by showing how it is

A Variety of Causes. Paul Noordhof, Oxford University Press (2020). © Paul Noordhof. DOI: 10.1093/oso/9780199251469.001.0001

 -



the lawful consequence of another type of entity, a virtue of the explanation being the simplicity and systematic character of the system of laws of which the law to which we appeal is a part. We can also characterize the nature of the causal relationship between a target effect and its cause by taking them to be part of a process characterized in one of the ways we discussed in Chapter . Nevertheless, as we saw there, the processes cannot provide an independent understanding of the nature of causation and, indeed, have to draw on the materials of the analysis I have favoured. The second constraint records that there is a particular type of explanation that causes are naturally thought to provide and it is a constraint upon an account of causal non-symmetry that it shows how this is possible. The third constraint is that causes are means by which agents bring about ends. The last feature has been judged to be of such importance that manipulability or agency theories of causation have been built around this idea. It has proven hard to formulate an illuminating development of this idea and, in Chapter , I will argue that recent attempts fail. Nevertheless, a theory of causation should certainly respect the constraint and, we shall find, the idea of intervention can help to explain features of the proposal I develop (.). The second and third constraints are the reason why it is implausible to attempt to satisfy the first constraint by claiming that causes are temporally prior to their effects. If the only difference between events standing as cause and effect is a temporal one, then it is not clear why one is the explanation of the other and is the means by which the other may be brought about. By this point in the book, it will be no surprise that I will be offering an account of causal non-symmetry that is the basis for a corresponding non-symmetry in the truth of the counterfactuals we assert. However, it should be noted that counterfactual analyses of causation need only be partial. Proponents of such theories could urge that counterfactuals provide a proper analysis of the presence of a causal process yet not insist that counterfactual non-symmetry is causal non-symmetry. For instance, contrary to the reservations expressed, they might say that causes are simply temporally prior to their effects. Appeal to a feature like this would be a very minimal qualification to an attempt to provide a counterfactual analysis of causality. A striking fact, about many putatively alternative approaches to causal nonsymmetry, is the way that they appeal to facts that might easily be used to provide a counterfactual account of non-symmetry to develop an alternative theory. These alternative theories sometimes even appeal to the holding, or otherwise, of counterfactuals in virtue of these facts in the development of their own non-counterfactual theory. Just to provide two illustrations. Ehring’s characterization of the notion of condition—in virtue of which he justifies taking common effects of a cause to be causally connected but joint causes of an effect not—appeals to counterfactuals failing to hold one way and not the other in virtue of a certain kind of independence between causes characterized non-counterfactually (Ehring (), (), pp. –). David H. Sanford appeals to a notion of admissible circumstances— which might easily be modelled in terms of closeness of possible worlds—to characterize a non-symmetric notion of condition which, again, also draws upon a certain kind of independence between causes characterized non-counterfactually (Sanford (), (); Cover ()).



 -

The defence of none of these alternative theories is based upon flagging up different results that a counterfactual theory provides to their own, though sometimes it is noted that their own theory is not dependent upon a particular asymmetry that Lewis’ development of the counterfactual theory relies (with its denial of backtracking) (e.g. Ehring (), p. ). So a natural way to proceed is to consider the various alternatives that have been identified specifically as suggestions as to what features, or to what additional features, appeal should be made in giving a successful account of counterfactual non-symmetry. This is the most effective way of seeking to develop a more detailed account of counterfactual non-symmetry while, at the same time, identifying the points at which one might eventually have to conclude that such an approach is unsuccessful. This will be my approach in the next two chapters. In the second section, I shall discuss the role of context in the semantics for counterfactuals (for example, with respect to backtracking counterfactuals), different grades of counterfactual theory, and the features in virtue of which a counterfactual non-symmetry holds. A distinctive aspect of my position is that I allow that different features in different circumstances may be the basis for counterfactual nonsymmetry and, indeed, that different features combine to give rise to a counterfactual non-symmetry. One of these is Lewis’ asymmetry of overdetermination. I explain how the alterations to Lewis’ position I have adopted in previous chapters should be understood with regard to appeal to this asymmetry. A second is the independence condition, the fact that causal partners (as opposed to causes where one is an intermediary in the path to the effect for the other) are, in general, independent of each other. I explain how these two features relate to each other to provide a basis for causal non-symmetry and discuss cases where they prove insufficient to ground verdicts of causal non-symmetry. These provide grounds for looking at two other bases for causal non-symmetry that will be the focus of the second section of this chapter and Chapters  and . The first is a primitive non-symmetric notion of chance. It will receive preliminary formulation in . and be discussed further in Chapter . The second is a form of non-symmetry derived from agency. This will receive more extensive discussion in Chapter . I explain how these possible bases relate to the causal non-symmetry grounded in the other two at the close of the present chapter.

. Causal Non-Symmetry Rather Than Asymmetry The following definitions are pretty much standard. (I) A relation, R, is symmetrical iff, necessarily, if Rab, then Rba. (II) A relation, R, is asymmetrical iff, necessarily, if Rab, then not Rba. (III) A relation, R, is non-symmetrical iff, necessarily, it is neither symmetrical nor asymmetrical. (IV) A relation, R, is anti-symmetric iff, necessarily, if Rab and Rba, then a = b. Causation is not a symmetric relation. If e₁ causes e₂, it doesn’t follow that e₂ causes e₁. But it is by no means obvious that if e₁ causes e₂, it follows that e₂ doesn’t cause e₁. In which case, it is a non-symmetric relation. The cases below explain why, even if, as it turns out, effects aren’t also sometimes causes of their causes, we must recognize

 -   



that it is possible. They will also demonstrate that, unlike the case of ‘– is a part of –’, the causal relation is not anti-symmetric. Suppose that time is closed and that e₁ causes e₂ (for characterization and defence of closed time, Grünbaum (), pp. –; Newton-Smith (), pp. –). Then there seems nothing to rule out the possibility that, as time loops round, e₂ causes e₁. There may be differences in the way e₁ and e₂ stand to each other as cause and effect although there is symmetry with respect to their standing in the relation of cause and effect. Consider the following diagram. e1 e2

e5

e3

e4

Figure . e₁ is a cause of e₂ with no intermediate steps. e₂ is a cause of e₁ via e₃, e₄, and e₅. It is also hard to justify the claim that causation is asymmetric given earlier assumptions to which I have appealed in developing my theory. I argued that the question of whether e₁ causes e₂ is not settled by considering whether the various causal paths between e₁ and e₂ in toto involve chance-raising but rather whether there is chance-raising when we consider the paths in relative isolation. Thus suppose that there are two causal paths between e₁ and e₂. Along one path, e₁ conditionally raises the chance of e₂ by conditionally raising the chance ofP d₁—by ‘conditionally’ I, of course, mean conditional on the absence of the events in . Along the other path, e₁ combines with d₂ to raise conditionally the chance of d₃ which raises conditionally the chance of e₂. d1 e1

e2 d3

d2

Figure . I claim that e₁ is a cause of e₂ simply in virtue of either path (given the paths are complete). If one of the paths did not conditionally raise the chance of e₂ but lowered it, e₁ would still be a cause. In which case, it is hard to deny that e₁ would be a cause of e₂ if, instead, e₂ conditionally raised the chance of e₁ by the other path. I discuss causal loops further in .. The causal loop given earlier in the case of closed time is a special case of this. The two cases just given raise the question of whether e₁ can also count as a cause of itself. In .–, I placed restrictions on when satisfaction of my analysis revealed



 -

that e₁ is a cause of e₂. The analysis must be satisfied by instances of properties constituting e₁ and e₂ that aren’t modally connected in any of the ways specified. Obviously, in the case where e₁ and e₂ are identical, the only way to satisfy this condition would be if e₁ instantiated two modally unconnected properties that satisfied the analysis. Although this is correct for cases of piecemeal causation, the question of whether e₁ is a cause of itself in a closed time case intuitively shouldn’t depend upon whether this is so. Strictly speaking, we don’t have to resolve this matter to establish that causation is non-symmetric given my denial of transitivity. However, we may recognize that, where e₁ causes e₂, e₂ causes e₁, and the analysis is satisfied for e₁ with respect to itself, then we have an exception to the restrictions adopted earlier. They only apply where there is no intermediary between the candidate cause and effect such that the candidate cause satisfies the analysis with respect to the intermediary, the intermediary satisfies the analysis with respect to the candidate effect, and the candidate cause and effect satisfy the analysis. In the case at hand, e₁ satisfies the analysis with respect to itself. e₁’s satisfaction of the analysis is not by trivial counterfactual dependency on itself. Rather, if we assess the chance of e₁ after e₅ but just prior to e₁, the tell-tale probability fluctuation will reveal itself. A third kind of case that supports the claim that causation is non-symmetric stems from worlds, possibly including the actual world, in which the laws are time symmetric. Laws are time symmetric or, more precisely, time invariant, if the direction of time doesn’t matter to their application. We can apply them to present events in order to explain either future events or past events without any differences in how they are applied (Price (), p. ). If the laws are time symmetric, then the basis for the distinction between causes and effects derive from elsewhere. As far as the laws are concerned, there is straightforward two-way dependence and, thus, the possibility of two-way manipulation. Consider a world in which the basis for the difference between causes and effects are absent. How should we characterize the dependencies between events? We might say that they are non-causal nomic dependencies. However, each side satisfies many of the other features we associate with causes. A very natural alternative way of thinking of this case is to hold that it involves two-way causal dependence. If that’s right, then causation is non-symmetric rather than asymmetric for this reason too. Recognition of these cases qualifies the claim that causes usually precede their effects. Some worlds in which time is closed, or in which the laws are time symmetric with no further asymmetry, will involve effects preceding their causes as much as causes are prior to their effects. Nevertheless, even here, the proportion of causes that are posterior to their effects will not exceed those that are prior to their effects. So I add this claim for the special cases described in this section, which count as an exception to the claim about the temporal precedence of causes with which I began this chapter.

. Counterfactual Theories of Causal Non-Symmetry The most straightforward analysis of causal non-symmetry in terms of counterfactual non-symmetry would appeal to the different truth values of

    -



(F) If e₁ were not to occur, then e₂ would not occur, (B) If e₂ were not to occur, then e₁ would not occur, with (F) and (B) labelling candidate foretracking and backtracking counterfactuals, respectively. Foretracking counterfactuals are counterfactuals that mention the cause in the antecedent and the effect in the consequent. Backtracking counterfactuals mention the effect in the antecedent and the cause in the consequent. On those occasions when both are true, we would have a case of two-way causation. The putative backtracking counterfactual would not be a backtracking counterfactual after all. Unfortunately, it is plausible that there are true backtracking counterfactuals. Suppose I know that the house was filled with inflammable gas and that Michael was going to test his matches inside, out of the wind. I ask passers-by ‘Was there an explosion?’ ‘No,’ they say. ‘Ah,’ I reply, ‘the matches didn’t work. If there were an explosion, he would have managed to light one of his matches.’ Or, take Downing’s example mentioned by Lewis. Jim is a proud man but in need of help that only Jack can provide. I hear reports that Jack and Jim had a quarrel last week. Somebody asks me whether Jim asked Jack for help yesterday. I reply ‘If he had asked Jack for help, there would certainly have been no quarrel last week.’ Jim would never have asked somebody for help with whom he had had a quarrel like that (Downing (–), pp. –; Lewis (), p. ). In neither case do we suppose that the event mentioned in the antecedent was a cause of the event mentioned in the consequent. Although we can hear the backtracking counterfactuals as true, it is also possible to hear those very same counterfactuals to be false. Thus I can properly say that if Jim had asked Jack for help, then he would not have helped him because of the quarrel. We don’t conclude that he would have helped him because, if Jim had asked, there wouldn’t have been a quarrel. Similarly, I can say that if there had been an explosion, his matches not working would have been the least of his worries. A counterfactual theory of causal non-symmetry can draw upon these contexts and set aside those in which backtracking counterfactuals are true. It may be that the latter can be dismissed as only true in special contexts. However, all that we need is that, for any counterfactual used to state a causal relationship, there are contexts in which the corresponding backtracking counterfactual will be false. This was Lewis’ basic approach (also Loewer (), p. ). The talk of contexts should not be understood as talking about different situations. If backtracking counterfactuals are true in some situations but not others—for example, when we consider scientific experiments rather than everyday life—then the truth of backtracking counterfactuals would indicate the falsity of the counterfactual analysis of causation. Alternatively, the putative identification of the cause and effect are mistaken and the counterfactual in question not a backtracking one after all. We would have a case of backward causation if the event mentioned in the antecedent occurred later than the event mentioned in the consequent. Instead, talk of contexts concerns the way in which the truth or falsity of the counterfactual is evaluated. The standard way of evaluating the counterfactual is given by the similarity weighting laid out earlier. The non-standard way as a result of which backtracking counterfactuals come out true reduces, perhaps to insignificance, the appeal to perfect match as one weighting of similarity. In brief, the idea is that a



 -

particular way of evaluating counterfactuals reveals the dependencies that are the basis of causation. With this qualification made, the approach to be developed in the sections below reflects choices along three dimensions of variation regarding counterfactual theories of causal non-symmetry: first, the strength of the claim that causal non-symmetry is counterfactual non-symmetry; second, the bases for the non-symmetry and, third, the type of counterfactual non-symmetry in question. Under the first heading, the main options are either to take counterfactual nonsymmetry to constitute causal non-symmetry in all possible worlds or to claim that it constitutes it in some, but not all, possible worlds. If the second option is adopted, then it is plausible that causal non-symmetry comes in two forms: counterfactual non-symmetry and, as I shall discuss further, a kind of primitive non-symmetric chance-raising. I shall argue that there is no reason to deny that primitive nonsymmetric chance-raising can be one of the truth-bases for counterfactuals, given the type of counterfactual non-symmetry to which I appeal. If that argument is unsuccessful, the second option remains available and presents only the slightest qualification to the counterfactual analysis of causation. The link will be retained to counterfactuals in characterizing the dependency and many cases of causal nonsymmetry, with some exceptions to the latter. Under the second heading, and already prefigured in what I have just written, I shall argue that there are a number of distinct bases of counterfactual nonsymmetry. These need not always work independently. In some cases, counterfactual non-symmetry will be the result of two, or more at work, in the situation. Under the third heading, that concerning the type of counterfactual nonsymmetry involved, the main differences between Lewis’ theory and my own are that I appeal to, first, a revised similarityP weighting and, second, counterfactuals with probabilities in their consequent and a -set of excluded events in the antecedent. The options these dimensions generate look like Figure .a. The position that I will be defending in the rest of the chapter is the bottom left box. In more detail, the structure of my overall position will end up looking like Figure .b. I begin by discussing how two different non-symmetric macro-dependencies can be the basis for counterfactual non-symmetry. In the next section, I will review Lewis’ account of the non-symmetry of counterfactuals and argue that my revisions to the counterfactual theory present no problems to, indeed assist, its application. That does not mean there are no problems it faces. I address the main difficulties that have been raised. In subsequent sections, I shall discuss other bases for counterfactual nonsymmetry and how these support a counterfactual theory of non-symmetry in general. Recognition that there may be a number of distinct factors in play helps to deal with problems that each faces taken in isolation. It is also a useful reminder that we need to distinguish two enterprises. The first is: what provides us with a basis for counterfactual non-symmetry? The second is: what is the basis of counterfactual non-symmetry, if any, in this world? Thus an argument that a certain kind of nonsymmetry is not present in our world may either establish that there is another basis for counterfactual, and thereby, causal non-symmetry in our world or that there is no counterfactual and, perhaps, thereby no causal non-symmetry in our world. Sometimes these issues are run together in attempts to identify the basis for

    - Causal Non-Symmetry

Necessarily

Possibly Counterfactual Non-Symmetry

Counterfactual Non-Symmetry

Variable Realization

Invariable Realization

Simple Counterfactuals

Simple Counterfactuals

Probability Counterfactuals

Probability Counterfactuals

Figure .a

Probability Counterfactual Non-Symmetry

Non-Symmetric MacroDependencies

‘Asymmetry of Overdetermination’

Independence Condition

Figure .b

Local MicroNon-Symmetries

Primitive NonSymmmetric Chance Raising

Interlevel Non-Symmetry

Agency





 -

causal non-symmetry in our world. The plausibility of the counterfactual approach is enhanced when they are kept apart. An unqualified counterfactual approach is only refuted if there is a source of causal non-symmetry that is clearly not the basis for a counterfactual non-symmetry.

. Macro-Non-Symmetries .. Asymmetry of overdetermination One source of counterfactual non-symmetry is supposed to rest on the fact that events tend to leave many traces, that is, determine many events, in one temporal direction rather than another (Lewis ()). The idea of determination should not be thought of in terms of causation. If it were, then it could not be a source of causal non-symmetry but would presuppose it. Instead, the determination of one event by another should be understood roughly as follows. e₁ determines e₂ if and only if (i) metaphysically necessarily, if e₁ occurs and the laws, L, hold, and the circumstances are C, then e₂ occurs and (ii) it is not the case that metaphysically necessarily if L and C, then e₂ occurs (a similar idea occurs in Mackie (), p. ). The second clause is to ensure that e₁ is not redundant. In the case of indeterminism, the corresponding account concerns the probability of e₂. Thus we have p(e₂) = x, for a specific value or range of values of x, in place of e₂/e₂ occurs. A few comments and qualifications to this are needed. First, determination does not require laws in worlds where there is brute singular causation. In such worlds, whatever non-nomic determining facts hold should take the place of L in the formulation above. Second, if e₂ is causally overdetermined, then C will not include mention of the other, overdetermining, causes. Equally, if e₁ is linked by a chain of events to e₂ such that, if any of these events should fail to occur, e₂ would not occur and given that these events do occur, e₂ occurs, then none of these intermediate events should be included in C. The claim is not that e₁ is not redundant for any C. It is rather that there is some C such that it is not redundant. This will apply as much to the indeterministic case with respect to a probability of e₂. Third, C should not be taken to be restricted to matters of fact around the time of e₁. It may include facts around the time of e₂. This is a slight liberalization of Lewis’ idea since he seems to have had in mind circumstances just around the time of e₁ (Lewis (), p. ). It has implications I will discuss below. Let’s now begin with a simple case to illustrate. Suppose a particular event, e, determines many other events, including e₁, in a certain temporal direction but that e₁ does not in the reverse direction. e5 e4

e3

Figure .

e1

e e2

--



e’s determination of many events, in circumstances C, gives rise to an overdetermination of e in the reverse direction. For each ei, metaphysically necessarily, there are a set of circumstances C* (not necessarily identical to C) such that, given the laws and ei, e is the case. An asymmetry of overdetermination is derived from there being more traces of an effect one way than another. If we consider what would be the case if that event e were not to occur, it would not be possible to secure perfect match in particular matters of fact in that temporal direction without a fairly massive cover-up of the absence of e. Many other replacement events would have to be postulated to account for all the traces. So perfect match could not be secured without infringing the first condition of Lewis’ similarity weighting in the deterministic case. The third condition requires that we avoid even small violations of law. We avoid this by taking the determined events to be absent. Thus, according to Lewis’ weighting, we may conclude that, if e had not occurred, its determined events, including e₁, would not have occurred either. In the case of indeterminism, there would be no law violation if we supposed e₁ to e₅ present. However, perfect match achieved by these means is discounted by the revised perfect match condition. To recall, it now runs (B*) It is of the second importance to maximize the spatiotemporal region throughout which perfect match of particular fact prevails unless, in so doing, we fail to minimize departure from the distinct events (or their P absences) that the truth of the antecedent of the counterfactual makes more -probable given that their antecedent is actually false. So we can allow that these events may occur but we would not be forced to conclude they would occur. Consider now what follows if e₂, say, is absent. There are circumstances C which, given the laws, will make e₂ determine the absence of e. But instead of the diagram above, we have e e2

Figure . Since e₂ does not determine many events in the temporal direction of e, it is possible to secure more perfect match without requiring a fairly massive cover-up of e₂’s absence. So the first condition of Lewis’ similarity weighting is not brought into play. As perfect match is weighted more than small violations of law, e₁ would still be present. The discounting of perfect match in the revised condition is unlikely to apply. Since e has many consequences and we are only envisaging the absence of e₂, the chance of e will be high, whether or not e₂ is present, in virtue of the other determinants/probabilifiers. That suggests e would be present. My analysis ofP causation, though, does not depend upon the presence or absence of e₂ but rather its -probability. So even if it is concluded that e may be present rather than would be present, this would not undermine the basis of the causal nonsymmetry of my favoured account in itself.



 -

To consider whether my analysis can draw upon Lewis’ asymmetry of overdetermination as a basis for causal non-symmetry, the key counterfactuals we need to consider are these. P P (CN ) If neither e nor any of the events in were to occur, then for any time t, it would be the case that, just before t, the mean value of p(e₂ at t) = y. P P (EN ) If neither e₂ nor any of the events in were to occur, then for any time t, it would be the case that, just before t, the mean value of p(e at t) = y. To evaluate them we need to consider two factors: first, the move to probabilities; P P second, the implications of the -set mechanism. In the case of (CN ), we can expect the value of y to be lower than it would be if e were present because this is a standard case of causation we have already discussed. e and e₂ pick out events which reveal the expected differences of overdetermination as diagrammed previously. The P question is whetherP (EN ) displays the same pattern. Putting aside the -set mechanism for a moment, we have just seen that the same pattern is not reproduced. If there are many events determined by e and we are considering the probability of e when these events are still present save for one, e₂, then the chance of e looks as if it remains high. A complication in arriving at this judgement concerns the time of assessment of the probability of e. If it is assessed just after e, then e is in the past. Many find it plausible to suppose that past events have probability . In which case, trivially, the absence of e₂ would not result in a lowering of the probability of e. Alternatively, if we assess the probability of e just prior to e occurring, then at that point it has not been settled that e₂ is absent. Its absence at a later time just has a certain probability. In which case, one would not expect a probability fluctuation as a result of the presence or absence of e₂. The same reasoning would apply to assessing the probability of e just after e occurred if we rejected the assumption that the probability of a past event is . In that case, assessing the probability of e just before or just after e would be different ways of thinking about the influence of a candidate cause on the occurrence of e given that all of e’s other determinants are in place. One reservation I have with part of this reasoning is that it builds an asymmetry into the evaluation of probabilities that may not be legitimate. The reasoning relies upon it being the case that, outside of cases of backward causation, changes in future events will not influence the probability of past events and that past events have probability . Nevertheless, these orthodox ideas about probability and the past don’t presuppose the truth of a counterfactual approach to causal non-symmetry but are independent of it. Thus, it is perfectly legitimate to point out that, should these ideas be correct, then they do not undermine but support the claim that, where the asymmetry of overdetermination would have to become a putative asymmetry of probabilification, we would still successfully distinguish between causes and effects. That said, the asymmetry of probabilification does not depend upon this particular way of evaluating probabilities. Suppose that there is no difference between the past and the future of e in terms of how its probability is influenced. The fact of e₂’s presence or absence in the future (say) influences the probability of e earlier in just the way that the presence or absence of an earlier candidate cause of e may influence e’s probability later. The indicative probability fluctuation would still not show up in

--



the situation envisaged due to the multiple determinants of e in, we are assuming, the future: e₁, e₃, e₄, e₅. This is exactly what we would have to say in any event if the direction of e to e₁, e₂, e₃, e₄, e₅ was from future to past. We will consider further whether this is an option in .. Thus what we have seen is that, without appeal to particular ideas about the chance of past events and the time of assessment, the probability of e remains high. If we appeal to these other notions, then the verdict is reinforced. P P The -set mechanism may appear to change matters. Suppose we put in events e₁, e₃, e₄, and e₅. Then it might seem that, in the further absence of e₂, the chance of e must be very low. So the very mechanism that helps us provide an analysis of the cases of pre-emption and the like obliterates the difference between cause and effect from the counterfactual perspective. However, this is to overlook the fact that, in order for e₂ to count as a cause it must also satisfy the corresponding counterfactual in which e₂ is present. P (ES∑) If e₂ were to occur without any of the events in , then for some time t, it would be the case that, just before t, the mean value of p(e at t) = x (where x >> y). However, if e₂ were to occur without any of the other putative consequences of e, then the chances of e would seem low. It would be more plausible that e₂ occurred as a result of something else than e. Equally, if we appeal to the distinctive theses concerning the assessment of chance I mentioned earlier, we would have no probability fluctuation. So I conclude that both the adjustment to the similarity weighting and the proposed analysis of causation retain the benefits of an account of causal nonsymmetry based upon an asymmetry of overdetermination/probabilification. Note that the key feature, leaving multiple traces in a certain direction, is not by itself asymmetric but non-symmetric. It is compatible with multiple traces also being left in the other direction too. The feature becomes part of a theory of counterfactual asymmetry when it is coupled with the claim that there are not traces to the same degree in the other direction. When there is two-way massive overdetermination, there is either two-way causation or no-way causation. Given that causation is a nonsymmetric relation, the first option is both permitted and, independently, plausible. Causes and effects should only be differentiated from each other when there is a difference of determination in favour of the cause. Otherwise, both count as causes because each plays the other roles distinctive of causes, for example, being a means to an end. For this reason, we should distinguish between overdetermination which is a non-symmetric relation—and which, in this respect, makes it an appropriate basis for causal non-symmetry—and the asymmetry of overdetermination as hitherto used to capture the fact that, in a certain type of world, overdetermination does not hold both ways to the same degree. Hereafter, my use of asymmetry of overdetermination appeals to the latter and when I want to talk about the way in which overdetermination is a basis for the non-symmetry of cause and effect, I talk of the non-symmetry of overdetermination. This completes my discussion of whether the differences of my position from Lewis’ undermine appeal to Lewis’ asymmetry of overdetermination. I turn now to the question of whether it can successfully provide one basis for counterfactual, and



 -

thereby causal, non-symmetry. The objections I will consider break down into two types. The first type of objection denies that there is an asymmetry of overdetermination in our world. The second type claims that, even if there were, appeal to it could not capture the difference between cause and effect in certain cases. I shall turn to the latter in ..–. An objection of the first type is that the laws of classical mechanics and the conservation laws both entail that, for any event e at time t, there will be a unique necessary and sufficient condition for e at some later time t* (e.g. Pruss (), pp. –; Loewer (), p. ). For instance, consider the familiar case of a pebble dropped in a pond with the ripples spreading outwards. Lewis’ claim is that the presence of each segment of the advancing wave front determines, in circumstances that don’t mention the other segments in the wave front, the presence of the falling pebble (Lewis (), p. , taken from Popper (), p. ). S1

S2

S3

S4

S5

Figure . Thus if one of the segments were absent, S₁ say, the falling pebble would not be absent. There is massive overdetermination. By contrast, if we consider the various events that make up the causal circumstances of one of the segments, there is no massive overdetermination. Although each of these events, in the circumstances, determines the wave segment, it does so because the circumstances include the other events. They are joint determinants. Thus, suppose that c₁ (fall of pebble) and c₂ (presence of water) each determine S₁ (a specific wave segment) by my analysis, relative to conditions C₁ and C₂, respectively. Then, taking as our focus c₁, either C₁ includes c₂ or, metaphysically necessarily, if C₁ and the laws, L, hold, then c₂ occurs. The characterization just provided applies, to a particular case, the observations offered at the beginning of this section about the asymmetry of overdetermination. Pruss claims that this contrast is mistaken. The principle of conservation of energy requires that, if the energy of a certain segment of the wave front (Si) is reduced, then the energy in the source must be diminished. So it cannot be true that each disjoint segment of the wave front is sufficient for the presence of the falling pebble in the absence of the other (Pruss (), pp. –).

--



The objection seems to ignore the appeal to circumstances in the characterization of determination. Suppose we divide the wave front into five equal segments S₁–S₅ and let each have x joules of energy, the fall of the pebble at the outset supplying x joules to be dispersed (obviously this is a simplification to make a general point). If the energy at S₁ is reduced to x joules, by conservation of energy, one might think that the pebble’s fall should supply x joules of energy. However, in the circumstances where there is 
dissipation of energy into open water, that would suggest that the energy at each segment should then be  /x joules. In those circumstances, to get x joules of energy at S₁, you need a source of x joules. Lewis’ claim was that a segment together with a specification of circumstances (not including other segments) and the laws entail that there was a certain prior event of energy release. Part of the description of the circumstances will include the fact that the dissipation of the energy is in all directions in open water rather than being channelled. In which case, there being two joules of energy at S₁ is sufficient for x joules at source. We have the kind of local overdetermination that Lewis had in mind compatible with the conservation of energy. The application of conservation principles is one thing, the identification of the circumstances in which the quantities are dispersed and the resultant asymmetries (or otherwise) of determination another. It may be argued that we don’t have a case of overdetermination because in specifying the circumstances—that which allows 
dissipation involving no channelling—we have mentioned the other determinants, the other x joule segments, which, together with S₁, determine x joules at the source. So there is no asymmetry after all. However, this is not the case. Consider the causal circumstances that, together with the pebble dropping in the water, explain why there is a wave front segment at S₁. These will include the fact that the pebble hits open water (there is no channelling) plus facts about the local conditions of the water between the pebble hitting the water and that particular segment. These local conditions, for example, the absence of a barrier on the pathway to S₁, won’t apply for the other segments. Conversely then, the local conditions, plus the fact the stone was dropped in open water, plus x joules of energy being at S₁ will be sufficient to determine that the pebble drop involved x joules of energy. This is independent of x joules of energy at the other points in the wave front because we need not include the local conditions of the water in the other segments required to ensure x joules of energy at S₂, S₃, etc. An appeal to the particular character of the circumstances around the energy source—the falling pebble—also seems to apply to the related objection that there are no local facts about wave segments which, given the laws alone, determine the location and properties of the source. As Matthias Frisch seems to acknowledge, there may be such determination of the source by facts about the wave segments if our characterization of the circumstances also includes past facts (Frisch (), pp. , ). There is the danger that loosening our characterization of the circumstances will make overdetermination cheap, so losing the putative asymmetry. Take S₃. Is there not some characterization of the circumstances that will make a wave segment in S₃, along with circumstances around the source (Cs), determine a wave segment in S₁, and so on and so forth for the other segments, giving rise to overdetermination in the source to wave segment direction for each segment Si (e.g. Arntzenius (),



 -

p. , fn. )? This will only be so if, in addition to Cs, the circumstances include the circumstances, CS, that make the source sufficient for S₁. However these circumstances, Cs plus CS, are the minimal circumstances for every segment Si to determine S₁. There is no corresponding overlap between the minimal circumstances required for each Si to determine the source. We may appeal to this difference to characterize the crucial asymmetry of overdetermination. As I’ve already acknowledged, a substantial question is whether my characterization of determination identifies a genuine asymmetry of overdetermination in our world. Perhaps, in fact, many effects leave multiple traces in the temporal direction of their causes just as causes leave multiple traces in the temporal direction of their effects. It is certainly true that the characterization of determination doesn’t rule out the existence of an asymmetry. In a simple world in which events, either singly or (say) in pairs, cause a distinctive spread of other events, there will be an asymmetry of overdetermination. So there is no reason to resist the claim that it is one basis of counterfactual non-symmetry. The question is whether it provides any help with understanding counterfactual non-symmetry in our world, or worlds like it. According to Adam Elga, it does not. He illustrates the point by considering a world similar in many respects to our own in which the laws of Newtonian mechanics are true and argues that corresponding to any asymmetry of determination there need be no asymmetry of miracles required to cover it up (the key point in the application of the similarity weighting to ground a counterfactual asymmetry). He envisages that the point will extend to more complex cases (Elga (), S). I outline the argument below. Let S₀ be a state of such a world at t which evolves into S₁, a state of the world at t + n. Let Z₁ be the directional reverse of S₁ (e.g. where all the particles in Z₁ have reverse velocities to those in S₁) and Z₀ be the directional reverse of S₀. The process in which Z₁ evolves into Z₀ is a matter of running forwards (in terms of the velocities) the laws which, when run backwards, evolve S₁ into S₀. S0

S1 Laws

Z0

Z1

Figure . Suppose the world in question has our thermodynamic asymmetry. In the past, we have a low entropy state. Entropy increases over time. If we consider the set of states that are like S₁ and Z, thereby setting aside directional features, the Z₁-type states are a tiny proportion (most are S₁ states) and they are widely dispersed; similarly with regard to S₀ and Z₀-type states. That is, Z₁-type (or Z₀-type) states are very fragile and slight changes in the constituting particles, say, would change them into S₁-type (or S₀-type) states. The fragility of the Z₁–Z₀ process indicates the fragility of the S₁–S₀

--



process since the former just involves running the laws forward which would be run backward for S₁–S₀. One consequence of this is that slight changes in S₁ will result in radical changes in the past. A second consequence of this is that only a small miracle will be needed to achieve convergence to perfect match in the future rather than the past. Running the laws backwards from this small miracle will produce an anti-thermodynamic past in which entropy increases in the ‘area of infection’, that is, the area that is a consequence of applying laws to this small miracle and running them backwards. However, contrary to what Lewis says, this implies we don’t need a large and widespread miracle to obtain perfect match in the future (Elga (), SS–). To try to make this abstract point a bit more concrete, consider Elga’s counterfactual () If Gretta hadn’t cracked the egg, then at : there wouldn’t have been a cooked egg in the pan. The standard way of assessing this would be to suppose that there was a small miracle just prior to Gretta cracking the egg so that she doesn’t crack it. Since the future would contain many traces of her cracking the egg, Lewis would argue that there would be no possibility of achieving perfect match in the future without a widespread miracle. Therefore, we seek to avoid even small violations of law and hence would have no cooked egg. Applying the reasoning sketched above in abstract, first, consider the time reverse of the egg-cracking-egg-cooking world (W₁). Suppose the egg remained in the pan and rotted. Then, in the time reverse of that world, the sequence is recomposing, uncooking, flying out of the pan, restored, and sealed up in the eggshell (W₂). Only a small miracle just after the egg cracking in the actual world/prior to the egg cracking in the time-reverse world is required to keep the egg in the pan, rather than rising up to the point at which it was cracked, to give us the time-reverse non-cracking world (W₃). The time reverse of this in turn is one in which the egg de-rots from being in the pan, there is no egg cracking at :, a small miracle occurs after this, and we get the long sequence of the egg being cooked in the pan, cooling and rotting along with traces of the egg having been cracked (W₄). This sequence amounts to perfect match in the future. There would be many apparent traces of the egg being cracked into the pan, including apparent memories of it being cracked (as Lewis suggests) but these would result from a high entropy past in which no such cracking occurred. In summary, we have the following. Table . W₁

!

Whole egg

!

Egg cracking

!

Cooking in pan

Rotting

W₂

Whole egg

Egg cracking

Uncooking in pan

De-rotting

W₃

Rots in pan

Miracle stops cracking

Uncooking

De-rotting

Cooking in pan

Rotting

W₄

!

De-rots in pan

!

Miracle stops cracking

!



 -

In W₄, the antecedent of the counterfactual would be true not because the egg was left whole but because there was no whole egg to crack and the consequent would be false. There would have been a cooked egg after :. Because the perfect match condition has priority over the no small miracles condition W₄ is a candidate closest world. As a consequence, the counterfactual ‘If Gretta hadn’t cracked the egg, then at : there wouldn’t have been a cooked egg in the pan’ would be false. There is an equally close world to the one in which there is past perfect match, with future perfect match. So it is not the case that there would not have been a cooked egg (although there may not have been one). Future perfect match via a small miracle, as envisaged, can only be obtained by the violation of the Second Law of Thermodynamics: entropy increases in the future. It has been argued that this in turn relies upon what has been called the Past Hypothesis: the universe began in a low entropy state; together with a uniform assignment of probabilities to the physically possible initial conditions compatible with the past hypothesis (Albert (), p. ; Loewer (), p. ). One way of dealing with the possibility of future perfect match obtained in the way just described is to include the Second Law and/or these bases for it as important dimensions of dissimilarity (Loewer (), pp. –). Lewis himself canvassed this idea when he suggested that we should qualify the perfect match condition by saying it should not be obtained at the expense of the loss of de facto asymmetries of time (Lewis (b), p. ). His talk of de facto asymmetries reflects the fact that he didn’t take the past hypothesis to be a law. By contrast, the position put forward by David Albert, Douglas Kutach, and Barry Loewer is that both the past hypothesis and the probability distribution should be considered part of the laws, violation of which constitutes a dissimilarity (Kutach (), Loewer (), pp. –). Attributing to these elements the status of laws may be enough to break the tie between the two ways in which maximizing perfect match may be achieved in the Gretta case, and by analogy, all the cases of which it is meant to be an illustration. However, without giving these newly accredited laws special status, there is the natural concern that these are just two more laws that may have small local violations to achieve more perfect match. My adjustment to the similarity weighting and earlier defence of the asymmetry of overdetermination can deal with this concern. The key earlier adjustment of the similarity weighting was that perfect match which fails to minimize departure from the distinct events (orP their absences) that the truth of the antecedent of the counterfactual makesP more -probable (given it is actually false) is discounted. The way I characterized -probability is in terms of the mean probability value given the conditions in the antecedent were met. As we have already seen, the antecedent of the counterfactual concerning Gretta may be true in one of two ways. If there is a small miracle just before Gretta is about P to crack the egg, then events like the egg failing to cook, and so forth, are more -probable. There being a cooked egg—as there is in the actual world—is a kind of perfect match P that is discounted. However, the events prior to the small miracle are still highly -probable because of

--



the asymmetry of overdetermination. All of them are multiply determined by events that occurred at the time of the miracle. The counterfactual comes out true. The second way of making it the case that Gretta does not crack the egg was if there is a small miracle after the time of the egg cracking so that we have a process that creates an expanding area of infection from a lower entropy future to a higher entropy past. There would be no Gretta, the egg would de-rot in the pan, and then become cooked. There would be all the traces of cracking, etc. but they would be false traces. As Elga emphasizes, this is a highly fragile and unlikely situation to occur. In which case, the mean probability of there being an uncooked egg, taking both these ways in which the antecedent may be true into account, will be largely untouched by this second possibility and remain high. Perfect match thus achieved in the future by having traces of the egg cracking and a cooked egg is discounted. So the thermodynamic asymmetry interacts with the adjustment to the similarity weighting to make worlds in which there is perfect future match in this way further away. By the same token, because these worlds are the worlds in which the past is very different, counterfactual conditionals concerning chances relating to the past being very different will be false. The revised similarity weighting brings out a feature of Elga’s case. In effect, he argues that there is no straightforward asymmetry of miracles in the way that Lewis envisaged although there is an asymmetry in the chances to bring about perfect match in the two ways indicated. The revised similarity weighting is an appropriate way to reflect this weaker asymmetry. The latter asymmetry is an asymmetry in the incidence of the possibilities of covering up by a small miracle an asymmetry of overdetermination with regard to target causes and effects. This underlines the point that the original asymmetry of overdetermination does not drop out of the picture. First, when there is an asymmetry of overdetermination, then we have a straightforward basis for counterfactual asymmetry. Second, when there is not, the asymmetry can be a basis for the weaker asymmetry relating to the incidence of miraculous cover-ups one way rather than another. As Frisch has pointed out, appeal to the past hypothesis together with a uniform assignment of probabilities to physically possible initial conditions is not a sufficient basis for causal non-symmetry without the claim that there is overdetermination of the cause by its various traces. If there are only one or two consequences of a candidate cause, then one might expect that each such effect raises the chance of the cause in the way required for causation (Frisch (), pp. –, (), pp. –). If my argument in this section is successful, then Lewis’ appeal to the asymmetry of overdetermination is defensible. A failure in the reasoning, or other considerations as yet not identified, may show that counterfactual non-symmetry in our world does not depend upon the asymmetry of overdetermination. Even in that case, the asymmetry of overdetermination still counts as one basis for counterfactual nonsymmetry. We shall now consider others.

.. Independence condition and the transition period The independence condition characterizes those circumstances in which an effect is the result of two independent—that is, causally unconnected—causes.



 - e

c

c*

Figure . Some claim that this is the case for all causation and that it is the root of causal non-symmetry. That is not my position. I simply claim that it is one basis for counterfactual non-symmetry. There are counterexamples to the claim that all causation satisfies the independence condition which I shall outline below. The basic formulation of the independence condition appeals to a notion of causal connection that is neutral over which of two causally connected events stand as cause to effect. Thus e₁ and e₂ are causally connected if either e₁ is a cause of e₂ or e₂ is a cause of e₁. This would make the connection a symmetric one. Proponents of the independence condition differ over whether e₁ and e₂ are causally connected if e₁ and e₂ have a common cause (Hausman (), pp. – says ‘yes’, Ehring (), pp. , ‘no’). Obviously, they reject the idea that e₁ and e₂ are causally connected if they have a common effect (e.g. Ehring (), p. ). Many of those who appeal to the independence condition as the sole basis of causal non-symmetry appeal to an asymmetric or non-symmetric notion of condition, in turn partly understood in terms of counterfactuals or similar materials such as claims about admissible circumstances (e.g. Ehring (), p. , (), pp. –; Sanford (), pp. –, Sanford ()). For example, Ehring defines a condition of the causal connection between c and e as something that, if it were not present c and e would not be causally connected (Ehring (), p. ). Such approaches would not be appropriate for my purposes. So I shall eschew them and simply appeal to causal connection. The key point, then, for the independence condition is that a target effect, e, satisfies the independence condition if and only if there is some c* such that c* is not causally connected to c but it is causally connected to e. How should ‘causal connection’ be understood given that it characterizes a condition upon which my analysis of causation draws to provide an account of causal non-symmetry? It might look as if I can only provide an analysis of causal connection after having provided an analysis of causation. There are three distinct ways to respond to this challenge. The first is to take the counterfactuals in the analysis in both foretracking and backtracking contexts. Events satisfying the analysis in either a foretracking or a backtracking context are causally connected. The second is to argue that that e₁ and e₂ are causally connected if, in at least one order, they satisfy my analysis of causation, although the evaluation of counterfactuals is only in a foretracking context. The counterfactuals may rely upon the non-symmetry that is partly based upon the independence condition but the analysis of causal connection doesn’t draw upon this. The third is to argue that we can appeal to my analysis of

--



causation in providing an account of causal connection. There is no need to be able to identify an element characterizing a source of the non-symmetry independently of the success of the analysis. The important point in the understanding of causal nonsymmetry is understanding its basis in reality not displaying its priority in some kind of conceptual hierarchy. This brings us back to the question of common effects. Causes are not meant to satisfy the independence condition with regard to their common effects. However, if we stipulate that common effects are causally connected—but common causes of an effect are not—we write in a causal asymmetry rather than characterizing it. We need an independent basis for this choice of how to understand causal connection. The first, backtracking, response to the challenge of how to understand causal connection provides one such basis. If my analysis of causation may appeal to backtracking counterfactuals to capture causal connection, then two effects of a common cause will satisfy it. By contrast, without some anterior common cause, two causes of an effect would not. Put simply, there doesn’t seem to be any plausible context in which we claim that if c₁ hadn’t occurred, e wouldn’t have occurred and, thus, c₂ (another independent cause) wouldn’t have occurred. A related basis concerns screening off. Consider the following diagrams. (a)

(b)

e1

e2

c

(c)

e1

c

e2

e2

c

e1

e

c1

c2

Figure . It has been observed that the following probabilistic relations hold in the case of diagram A. Prðe1 =e2 Þ > Prðe1 Þ Prðe1 =e2 & cÞ ¼ Prðe1 =cÞ Prðe1 =e2 & not‐cÞ ¼ Prðe1 =not‐cÞ: However, it is not the case that, in the case of diagram C, Prðc1 =c2 Þ > Prðc1 Þ Prðc1 =c2 & eÞ ¼ Prðc1 =eÞ Prðc1 =c2 & not‐eÞ ¼ Prðc1 =not‐eÞ: The first set of relationships shows that c screens off the probabilistic association between e₁ and e₂. A problem with taking screening off as a basis for causal nonsymmetry is that it fails to distinguish between c being a causal intermediary (given in diagram B) and c being a common cause (given in diagram A) and, indeed, the direction of causation between e₁ and e₂. However, given that screening off occurs in an uncontentious case of causal connection (set out in diagram B), the screening-off



 -

phenomenon provides a motivation for taking common effects of a cause as causally connected too. By contrast, the failure of e to screen off a probabilistic association between c₁ and c₂ is a reason why causal connection should not be taken as present in the case of joint causes of an effect (diagram C). If c₁ and c₂ are independent of each other, then it is not the case that Pr(c₁/c₂) > Pr(c₁). Moreover, while Pr(c₁/c₂ & e) = Pr(c₁/e) may be true, Pr(c₁/c₂ & not-e) = Pr(c₁/not-e) is plausibly not true because, if not-e is the case and its other cause, c₂, present, then the probability of c₁ must be lower than it would be if it is just given that the effect is not present. A final point in favour of the extension of causal connection to include the relationship between two effects of a common cause is that, if the notion were not so extended, the independence condition would be in potential conflict with the causal non-symmetry supplied by the non-symmetry of overdetermination. By having many effects, the effects would satisfy the independence condition with respect to their causes and thus, there would be two-way causation in a huge array of cases. This potential conflict doesn’t occur if effects of a common cause are causally connected, because then they fail to satisfy the independence condition. The prima facie case in favour of the independence condition being a basis for the non-symmetric character of causation is that if there are two independent causes of a particular effect, the occurrence of the effect is sufficient for the presence of both of the causes whereas the causes are only circumstance-dependent sufficient conditions for the effect. Since the causes are causally unconnected, these independent causes can’t be replaced by a non-circumstance-dependent cause that causes them. The idea of sufficiency in play is that of nomic sufficiency where e₁ is nomically sufficient for e₂ in w if and only if, metaphysically necessarily, if e and L (= the laws that actually hold in w), then e₂. The circumstance-dependent character of causes has been thought to be one of their distinctive features which, to recall, Mackie sought to capture in the idea that causes are INUS conditions (discussed in .). A natural response to the prima facie case is that causes rarely stand in one–one relation to an effect so that the latter is sufficient for the former. There are many different possible causes that might give rise to a particular effect as set out in the diagram below. e

c1

Figure .

c2

c3

c4

c5

c6

--



The dotted arrow indicates that these other pairs aren’t realized in the circumstances. As a result, each causal pair is, in a certain sense, unnecessary for the effect. This is what led Mackie to say that causes were part of unnecessary but sufficient conditions (the US part of INUS conditions). Equally, though, it shows that e is not sufficient for any of c₁ to c₆ because it could have been brought about by any of the pairs (a fact upon which Honderich’s () account of causal non-symmetry is built, criticized by Sanford (b)). The non-symmetry identified in the prima facie case can be restored. Relative to conditions in which not-(c₃ and c₄) and not-(c₅ and c₆)—call these the exclusion conditions—e, is sufficient for either of the causes c₁ or c₂ and the latter causal pair are necessary for e. This might make it look like causes and effects are on a par. Just as there is a causal pair, so there is an effect pair—e together with not-(c₃ and c₄) and not-(c₅ and c₆)—such that each is a circumstance-dependent sufficient condition for one of the candidate causes. Indeed, Mackie notes that e will be an INUS condition for c₁ with these as the other conditions whenever there is some other effect of c₁, say e*, to make e satisfy the unnecessary component of the INUS condition (Mackie (), p. , (), pp. –). However, there are two important differences. First, relative to the negative condition not-(c₃ and c₄) and not-(c₅ and c₆), causes are only necessary for the effect whereas the effect is sufficient for the cause if the independence condition is the case. Second, and crucially, the effect pair includes one item that is not causally connected to either of the causes, c₁ or c₂, namely not-(c₃ and c₄) and not-(c₅ and c₆). So exclusion conditions are ruled out as conditions that enable effects to satisfy the independence condition with respect to their causes. Correspondently, we should not accept that effects are circumstance-dependent sufficient conditions for their causes in the relevant sense. So, in general, if an event is causally connected to another event e and it is a circumstance-dependent sufficient condition of e, it is plausible that it is a cause rather than an effect. The independence condition provides further support for Lewis’ position against Frisch’s criticism (Frisch (), pp. –). Suppose that Frisch is right that the segments of the wave front as displayed in the diagram below determine, but don’t overdetermine, the energy of the source. 2 2

2

10 2

2

Figure . Given that the independence condition holds, we know that there will be an independent cause, along with the pebble dropping’s x joules of energy, that are the causes of a wave segment having x joules of energy. In which case, from the argument of before, the wave segment’s possession of x joules of energy will be sufficient for the x joules of energy of the pebble drop. The fact that there is one way in which a collection of effects doesn’t overdetermine a source, does not establish



 -

that there is no way in which they do. But all Lewis needs is that there is a way of characterizing how causes are related to effects that reveals how the effects do overdetermine the causes. Moreover, there is no reason to suppose that there is overdetermination in the opposite direction—that different causes overdetermine the effects—because common effects of a cause fail the independence condition. The point just made is related to, but distinct from, Hausman’s claim that Lewis’ asymmetry of overdetermination follows from the independence condition together with the claim that causes are, in my terminology, circumstance-dependent sufficient conditions (and in his, drawn from Mackie, that causes are INUS conditions) (Hausman (), pp. –). The main point of difference is that my argument is not meant to establish an asymmetry but just the connection between the independence condition and the claim that there will be overdetermination of a cause of more than one effect (in the sense specified at the outset of .). My argument is neutral over whether there is no overdetermination of effects by causes. So it is not subject to the charge of trying to derive an asymmetry from something that does not involve an asymmetry (Frisch (), p. ). However, given what I argue below, the independence condition does involve an asymmetry because of the asymmetric characterization of causal connection and its incompatibility with mutual causation. So, in any event, Frisch seems mistaken here. Also, although Hausman doesn’t pronounce either way on this, my argument allows for the possibility that some sufficient conditions for the cause, namely those that just cite all the effects, need not involve overdetermination. My claim is just that at least one way of characterizing sufficient conditions for the cause will. An objection to the independence condition is that it seems inapplicable if all the events in the universe have a common cause, for example, the big bang. Hausman responds to this objection by claiming that the notion of causal connection, to which the independence condition appeals, is only relative to a certain set of events or system (Hausman (), p. ). However, he also notes that if there are probabilistic dependencies due to a common cause, then we should enlarge the system to include the common cause in order to keep the connection between causal connection and probabilistic dependence (Hausman (), p. ). So the real question is whether there are such probabilistic dependencies if all the events in the universe have a common cause. Defence of the independence condition should rest on the following points. First, just because everything might be an effect of the big bang, doesn’t mean that there are no independent events that make up this explosion. Second, the case for taking effects of a common cause to be causally related depended upon the truth of backtracking counterfactuals and the screening-off phenomena. The immediate suggestion was that this justified taking all effects of a common cause as causally connected. However, if the backtracking counterfactuals are false, or screening off doesn’t happen because the putative common cause is too remote, we can take the case to be correspondingly weakened. So although the independence condition was expressed in its strongest form, the role it will play in subsequent discussion only requires something weaker that reflects the basis for taking effects of a common cause to be causally connected. Finally, it should be recalled that my characterization of causation is not transitive and, thus, the characterization of causal connection is not

--



going to be transitive either. The big bang is obviously a special case. It is very tempting to suppose that without it, there would be nothing. However, it is possible that without it, the universe may have come about in different ways and there may be features of the universe that are just as likely, or perhaps more likely, under those different ways. So the case for the big bang being a cause of everything has to be made out and, thus, the case for saying that everything has a common cause. With this understanding of the independence condition, let’s now consider its implications for counterfactual non-symmetry. Suppose that c₁ and c₂ are independently causally connected to e in the sense just given. Consider the counterfactuals () If e were absent, c₁ would be absent. P () If neither e nor any of the events in were to occur, then for any time t, it would be the case that, just before t, the mean value of p(c₁ at t) = y (where y is much less than the value x that p(c₁ at t) would have if e were to occur). If e is absent, then even in a deterministic world, in the absence of any other candidates and barring miracles relating to e, only one of c₁ or c₂ would have to be absent. If there is no particular reason why we should select one rather than the other as a favoured absentee—the not-c₁-worlds and the not-c₂-worlds are equally close by—then () is false (Hausman (), pp. –). It is not the case that c₁ would be absent any more than it is the case that c₂ would be absent. Yet we have obtained this result without apparently appealing to any asymmetry of miracles. Similarly, with regard to (), setting aside an asymmetry of overdetermination, there is no particular reason why, if e is absent, the mean probability of c₁ would go down substantially because, intuitively, it may be that the absence of e is due to the absence of c₂. Both these points depend upon changes in one of the causes not implying changes in the other because of some connection further back. It is that to which the independence condition points. However, as remarked earlier, the independence condition cannot be the sole basis for counterfactual non-symmetry. Suppose there is a b such that b is a cause of c and c*, where these are on distinct paths. c b

e c*

Figure . Then, if we only appeal to the independence condition, one might think that if e did not occur, then c would not, hence that b would not, and hence that c* would not. Our resistance to this backtracking displays the independent role for the first non-symmetry we have discussed, that of overdetermination. Although I appealed to the independence condition to explain how there might be overdetermination in a particular case, it is no part of my position that the nonsymmetry of overdetermination only holds when the independence condition is satisfied.



 -

There are other advantages with a combined approach. First, and most obviously, my proposal allows for the possibility that there might be a single cause, at a certain point in a causal chain, of subsequent events in that chain. We might have an asymmetry of overdetermination when this occurs. Second, it will avoid the constraints placed upon the number of causal interactions that may take place. Suppose that there are n initial events. Then, as Hausman acknowledges, there can only be n(n –)/ effects of these events—on the assumption that only two combine together to be causes—before independence breaks down and there is overlap between the causal processes giving rise to two causes of a particular event (Hausman (), p. ).¹ An asymmetry of overdetermination can distinguish causes from effects, where the independence condition fails. My rejection of transitivity makes this a less pressing problem than it is if transitivity is retained but it would be unwise to assume that loss of transitivity resolved the issue here. Third, given what I have argued about the non-symmetry of causation, the independence condition fails to capture its non-symmetry because it is an asymmetric relation. If there is mutual causation between c and e, then any allegedly independent cause of (say) e, along with c, would not be independent of c because it is a cause of c (via e). So the condition fails to apply (Hausman (), p. ). Once more a combined approach avoids this problem. A combined approach doesn’t just deal with problems that face the independence condition. It also assists with issues concerning the asymmetry of overdetermination. First, when there is no asymmetry of overdetermination—for instance, when there are two causes, c₁ and c₂, of e without e having any effects (or only a single chain of effects) and without c₁ and c₂ having any other effects—then the independence condition supports the verdict that it is not the case that, if e had not occurred, c₁ would not have occurred. If e had not occurred, and it has two (or more) causes, then it may follow that at least one of these causes didn’t occur but it is quite unnecessary, and would plausibly reduce the extent of perfect match, if both didn’t occur. On the assumption that there is nothing to distinguish the non-occurrence from one, from the non-occurrence of the other, as far as perfect match is concerned, then the closest worlds in which e does not occur will be split between those in which c₁ and those in which c₂ doesn’t occur. So it is not the case that either would not occur, as opposed to may not occur. Second, and this in many ways constitutes its most important contribution, it enables us to deal with the transition period, those events which depart from the actual world in order for the antecedent of a counterfactual to be true. When we suppose that a possible world departs from the actual world to result in the truth of the antecedent, we don’t take the departure to be at the last possible moment. For example, I get a puncture from a pothole in the fast lane on the Westway flyover. The following counterfactual seems true. If I had been in the middle lane, I would have arrived in

¹ From the combinations formula n!/r!(n-r)! with r = .

--



time for lunch (the puncture delayed me). We don’t deny this counterfactual on the grounds that, had my car dematerialized from the fast lane and appeared in the middle lane, the driver coming up on the middle lane would not have seen me until it was too late and crashed into my car so delaying me anyway. Rather, as Lewis puts it, we envisage a graceful transition with me moving to the middle lane carefully and in good time. My being in the middle lane would make the later events of my being in the fast lane less Σ-probable and thus, given my qualification to the perfect match condition, not to be counted towards the extent of perfect match. Late miracles to bring about my shift in lane are particularly improbable and, consequently, the mean Σ-probability of the very latest events of my travelling in the fast lane is correspondingly unaffected by this way of realizing the antecedent. Nevertheless, a consequence of the emphasis upon graceful degradation stemming from this is that it can seem that there are a whole host of true backtracking counterfactuals concerning what would have happened just before the antecedent were the case. For example, if I were in the middle lane, I would have checked my mirror earlier to negotiate the manoeuvre from the fast lane into the middle lane. This is where the independence condition comes in. We can deny the truth of such backtracking counterfactuals because, while there will be a sequence of events giving rise to a graceful transition, there is no particular sequence of events which would occur. Rather there are many equally good ways (as far as the similarity weighting is concerned) each of which would give rise to the truth of the antecedent. While all the considerations lying behind the similarity weighting sets in which temporal direction the transition will occur, the independence condition ensures that we don’t have to accept backtrackers opposite to that direction. The perfect match condition requires that we try to secure as much perfect match within certain restrictions. Since the emphasis is on perfect match, a departure that brings about the truth of the antecedent by breaking an actual causal chain of events makes all other breaks in causal chains in the same portion of the world cost-free as far as this condition is concerned. In particular, it would make cost-free another departure that would also bring about the truth of the antecedent. However, if the independence condition holds, then there would be no reason why we should suppose that both departures occur. We just need one or the other. The closest worlds would divide between them. We get the truth of backtracking conditions with might-consequents but not would-consequents. This preserves a counterfactual nonsymmetry to which appeal can be made in the analysis of causation. Appeal to the independence condition to deal with transition-period backtracking relies upon it being the case that joint causes are such that, when the effect is not present, none of the joint causes would not be present but just at least one may not be present. Are there cases in which this requirement is not met? One case of apparently this type is due to Barker (Barker (), p. ). Consider a metal cylinder within which are two slabs, S and S, S on top of S, S supported by a copper wire (Figure .). S is attached to the side of the cylinder by solder bonds. Barker claims that if the copper wire is cut and S bears down on S, it is the cause of the downward descent of S and breaking of the bonds.



 -

S1 Solder bonds

S2

Solder bonds

Figure .

Nevertheless, the following appears true by Lewis’ similarity weighting and my own. () If S had not descended, S would not have. If we allowed that S descended anyway, we would have interpenetration of one slab, S, by the other, S. This would involve a sizeable miracle. Baker argues that, if () is true, we have backward causation. As Barker notes, it is not obvious that Lewis’ technical notion of miracles as involving a ‘wide, diverse violation of laws’ would imply that the interpenetration envisaged is such a miracle. The violation is relatively localized and the laws violated relatively few. This is not a point in favour of Lewis’ similarity weighting since the counterfactual () If S had not descended, S still would have, appears implausible. In any event, my restriction on the perfect match condition makes it much more likely the revised similarity weighting obtains the truth of () since S’s descent makes it much more likely that (S) descends. Appeal to the independence condition does not seem to change the verdict. Causes of S’s descent include S’s descent and S’s resistance to interpenetration. Yet when we consider which of the resistance of S’s descent would be absent if S failed to descend, it seems that we plump for the latter. Instead of taking the case to be a counterexample, it is more plausibly thought of as a case of two-way causal interaction and so the counterfactual correctly characterizes the fact that S’s descent is also a cause of S’s descent. S cannot descend if S is blocking its way. Impediments block certain kinds of causal relationships and their absence is part of the explanation of why something happens in the way that it does. Barker considers a line of response of this type. He argues that it is not

    - -?



S’s descending but its failure to resist due to the solder bonds and friction at each temporal point. Its failure to resist is a cause of the simultaneous descent of S and S (Barker (), p. , fn. ). Although the failure to resist is certainly a cause of the descent of both, it doesn’t follow from this that the descent itself is not causally implicated. For example, if I hold a bat in the line of flight of a ball, then the ball will strike the bat and go off in a different direction. My holding the bat may be a cause of the change in direction of the ball and of the bat being struck but it doesn’t follow from this that the location of the bat (as a result of my holding) is not a cause. Similarly, the failure to resist may explain why S descends but this does not mean that its descent does not also cause the descent of S. So the failure of the combined approach to result in a counterfactual asymmetry in Barker’s case can be considered a strength rather than a drawback. More generally, then, the success of the independence condition as a basis of causal non-symmetry depends upon the following conjecture. Problem cases of the type identified by Barker are better thought of as cases involving two-way interaction. This is a plausible source of the conviction that one type of candidate cause would not occur if the effect is not present.

. A Case for Primitive Non-Symmetric Chance-Raising? The two bases for causal non-symmetry hitherto identified appealed to macro-nonsymmetries in dependency relations. Objections to such approaches to causal nonsymmetry either present examples in which our attribution of causes runs counter to what they would proclaim or consider simplified scenarios in which these features are not present. As we shall see in .., the combination of the non-symmetry of overdetermination and the independence condition can remove the case for primitive non-symmetric chance-raising in many settings but not all.

.. Local asymmetry reversal Pruss raises the possibility that there might be particular circumstances in which future convergence involves fewer miracles than past convergence. For example, suppose that Nixon’s firing of the rockets to bring about a nuclear holocaust depended upon the firing of a single neuron, N, in Nixon’s brain. However, Nixon’s state of mind was very different from one in which N would naturally fire. In order for N to occur, there would have to be a widespread collection of miracles to produce the circumstances in which N occurs (Pruss (), p. ). By the same token, suppose that the initial consequences of the firing of the neuron are relatively local. Then we should conclude that the counterfactual ()

If N had occurred, then there would have been a nuclear holocaust

is false. Given that there isn’t a nuclear holocaust, if N had occurred, then there would not have been a nuclear holocaust because we could secure more perfect match in the future—where there are fewer consequences—than in the past where multiple changes would have had to be covered up. The diagram below presents what Pruss has in mind.



 -

N

Figure . With regard to any such case, it is always possible to disagree about the facts. Perhaps Pruss is wrong to suppose that the causal antecedents of the neuron firing require, for their occurrence, a multitude of miracles or that the initial consequences of the neuron firing are relatively local. The substantial question is whether we can be certain that, within a world in which there is a thermodynamic asymmetry (say), an asymmetry of overdetermination does not, on a few occasions, hold in the other direction. In those circumstances, would we be prepared to conclude that there would not have been a holocaust and, hence (say), that Nixon’s decision was irrelevant to whether the holocaust occurred? Pruss suggests not. The putative counterexample rests upon a mistake. The assumption seems to be that we should look for the most economical way to achieve perfect match compatible with a law violation to make the neuron fire. However, in the circumstances envisaged, we can just conclude that there is no perfect match in either direction because of the widespread miracles required in order to achieve it. Instead, there will be, let us suppose, a miracle after the actual timing of the neuron firing which both result in the neuron firing and, because perfect match isn’t an issue, a nuclear holocaust. Of course, it could be argued that a widespread miracle is not required to cover up the effects of the neuron firing and so there wouldn’t have been a nuclear holocaust. This makes the case more like a simple denial of multiple effects rather than the asymmetry. In that case, my remarks below are relevant. Perhaps the reason why it was assumed that there must be perfect match in one direction, at least, is that it is the basis for counterfactual, and hence causal, nonsymmetry. However, this is not so for the combined view I am seeking to defend. No counterfactual of the form ()

If N had not occurred, then there would have been no prior N- firing

    - -?



would be true because the multiple joint cases leading up to N shows that the causes of N satisfy the independence condition. Thus, while each of them may not occur it is not the case that one definitely would not occur if N had not occurred. By contrast, N is supposed to be sufficient in the circumstances for the holocaust. The combination of the non-symmetry of overdetermination and the independence condition removes the motivation for recognizing primitive non-symmetric chance-raising in this case. It is not needed to avoid the verdict that N caused the firing of one or more of the neurones in the past. Matters are not so easily resolved in other cases to be discussed below.

.. Simple cases Resistance to counterfactual non-symmetry being based or, at least, solely based, upon the macro-non-symmetries hitherto emphasized stems from simple cases. One famous micro-physical case due to Price runs as follows. Y

E

F

C

D

A

B X

Figure . X and Y represent directions in space. The lines are the possible path of a particle P that would not interact with anything else. In fact, the particle actually travels along path ACE and produces a small explosion by being at place E. Consider the counterfactual ()

If particle P had been at D, then the explosion would not have occurred.

Intuitively, the counterfactual is true. For the antecedent to have been true, there would be a small miracle to shift the particle from C to D. As a result, we may assume that the path of the particle is now ACDF. However, Price suggests we could secure reconvergence by thinking of the particle as having (instead) the past BD and going on to CE to secure perfect match in the future. The miracle required to move the particle from D to C is just the same as the miracle required to move the particle from C to D. If this is what happened, then the counterfactual would be false since, if P had been at D, then the explosion would have occurred anyway (Price (a), pp. –).



 -

It might seem as if the independence condition provides a way of dealing with simple cases. Another familiar case involves a universe with just two fundamental uncharged particles of the same type, a and b, revolving round each other in accordance with the laws of Newtonian physics. Each would be accelerated due to the gravitational effects of the other (Tooley (), pp. –, (a), pp. –). Ehring argues that if we recognize that causal relationships hold partly in virtue of negative conditions, the independence condition can capture the causal relationships involved. Consider the mass of a at t. It influences the rotation of b at t + Δ. If there had been some other force which does not affect the mass of a at t but did influence the rotation of b, then the rotation would be different. Hence, the thought runs, we have an independent condition—the absence of the other force—which explains why the mass of a at t is a cause of the rotation of b at t + Δ (and not vice versa) (Ehring (), pp. –). The problem is that this presupposes a causal non-symmetry rather than elucidates it. Suppose there was a force at t + Δ which influenced the rotation of a at t. Then, we have an independent condition—its absence—which would explain why the mass of b at t + Δ caused the rotation of a at t. Negative conditions are cheap. They hold as much one way as the other way if there is otherwise symmetrical dependence between the mass of one particle and the rotation of the other. Of course, if the point is that the dependency between mass and rotation is not symmetric, then there won’t be a negative condition that partly explains the effect of the later mass on the earlier rotation. But now the non-symmetry has come from elsewhere than the negative condition. Even if there were an answer to this concern, it would provide no help with regard to Price’s original case. The issue in that one was that we had two ways of securing perfect match. Each way survives the path of the particle having a causal direction to it given by application of the independence condition to negative conditions. One response is to embrace the symmetry and deny that () is just obviously true. It is more natural to hear the counterfactual ‘If the particle had been at D, there would not have been an explosion’ as true. That’s because we, in effect, take the counterfactual to have an unexpressed antecedent, namely, if the particle had been at D having travelled from A to C. With this unexpressed antecedent, one cannot maximize perfect match by supposing that the history is from B to D and we just need a miracle to get to C. Rather we would need two miracles to have the particle end up at C, one to get it to D as the antecedent insists and one to get it back to C again. It is our knowledge of the past and our taking it to be fixed that determines which counterfactual seems the most plausible. Nevertheless, it would be a mistake to suppose that we should ground causal nonsymmetry in terms of our non-symmetric response to these kinds of counterfactuals. If it is just a matter of what we take to be the unexpressed antecedent of the counterfactual, we could have easily taken the unexpressed antecedent to be if the particle had travelled from B to D instead. A second response is to reject the line that counterfactual non-symmetry can only derive from asymmetry in law or macro-non-symmetries in the straightforward way outlined above. This may be developed in two ways. The first is to recognize a

    - -?



primitive non-symmetry of chance to provide a direction of travel for the particle (e.g. Arntzenius’ asymmetric transition probabilities, Arntzenius (), pp. –). In this case, it is captured by taking the presence of a particle at position x₁, y₁, to raise the chance of the presence of the particle at further positions in the y direction with the value in the x direction being unchanged. The antecedent of the counterfactual thus raises the chance of the particle carrying on through points between D and F. We now consider the two situations. In the ACDF, the miracle occurs to move the particle from C to D. The miracle does not produce an outcome that is against what the antecedent makes more likely (that is raising the chance of the particle carrying on through points between D and F). By contrast, in the BDCF world, the miracle occurs after the particle is at D to move it to C. It runs counter to what the antecedent makes more likely. According to the revised similarity weighting, B*, perfect match is discounted if it fails to minimize departure from the distinct events (or their absences) that the truth of the antecedent of the counterfactual makes more Σ-probable given that its antecedent is actually false. So future perfect match—that secured by the BDCF world—is discounted. The counterfactual comes out true. It might be argued that the truth of the P antecedent would make both events subsequent to it and events prior to it more -probable. However, this overlooks the fact that we are recognizing a non-symmetry of chance. The truth of the antecedent raises the chance of certain events subsequent to it occurring. It does not raise the chance of events prior to it occurring in this case. Of course these prior events will have a chance, themselves, settled by the events prior to them. They will also have a probability that can be calculated based upon the distribution of chances both prior and posterior to these events. The latter probability will be derivative in a way I shall discuss further in Chapter . The similarity weighting, though, should be understood in terms of chance. The second way of developing an account of non-symmetry independent of law or the macro-non-symmetries identified earlier is to appeal to an interlevel nonsymmetry, with which the only one I am familiar is agency. This is the line pursued by Price and others in response to the case discussed. The basic idea is that, as agents, we remember the past and act towards the future. Causes are the potential means by which agents bring about changes to the world and, hence, are typically directed towards the future. In the case described, the suggestion would be that an agent would be able to remember the travelling of the particle from A to C and intervene to shift the particle to D as a result of which the particle would travel on to F. They would not be able to intervene to change the past keeping the future as it is. The truth of the counterfactual reflects this non-symmetry of agency (Price (a), p. ). This alternative will be the topic of discussion in .. Certain features, though, we can note now. The first is that, in its most plausible form, it takes the macro-nonsymmetries identified in previous sections as the basis for understanding a nonsymmetry of agency. For example, as Price notes, that we remember and, thereby, have knowledge of the past may be due to the prevalence of open forks—effects having common causes—towards the future and, thus, the satisfaction of the overdetermination asymmetry and independence condition by later events with regard to



 -

earlier events (Price (a), p. , drawing from Paul Horwich (), pp. –). These non-symmetries are the basis of a projected non-symmetry, due to agency, to cases where the non-symmetries are not found, for example, the micro-physical case. Hausman has claimed that the agency account of non-symmetry only applies in situations where the independence condition holds (Hausman (), p. ). In which case, it does not provide a genuine alternative. However, Hausman’s claim proves to be an overstatement with regard to the kind of case in which we are interested: token (rather than type) causation. His argument is that the agency theory implies the truth of a modal version of the independence condition. In our terminology, this would amount to the claim that if c causes e, then e might have a cause c*, which is independent of c. The possible independent cause, c*, would be the intervention by a human agent, or something akin to that (Hausman (), pp. –). This observation is compatible with a target effect, in fact, only having a single cause, in contravention of the independence condition. Moreover, in the simple cases we have considered, the modal version of the independence condition faces the same question previously raised concerning the appeal to negative conditions, as a way in which the independence condition may be satisfied. What settles that possible interventions hold for putative causes and not their effects? In general, possible interventions only go one way because of the non-symmetry of agency (derived from the macro-non-symmetries identified earlier). This shows that the non-symmetry of agency provides material that appeal to the independence condition for the relevant micro-events does not and, thus, the non-symmetry of agency does not depend upon the independence condition. Even so, it is hard to extend the agency approach from the micro-physical case when it occurs in worlds with the relevant macro-non-symmetries to simple worlds such as those discussed by Ehring and Tooley. In these worlds, there are no macro-non-symmetries and no agents to project onto the simple relations of dependence in those worlds that are claimed to be non-symmetric. While agency accounts of causal non-symmetry fail to apply to simple world cases, appeal to primitive non-symmetric chance-raising has its own version of a problem case. Consider a world in which there are the macro-non-symmetries discussed earlier but no primitive non-symmetric chance-raising. Then those who favour appeal to non-symmetric chance-raising as a treatment of the other problem cases are committed to denying that there is causation in the world just described at the micro-physical level when the other non-symmetries run out. However, one might argue, if there is the means–end non-symmetry distinctive of agency, then there is causal non-symmetry. Lack of primitive non-symmetric chance-raising is not enough to sink micro-physical causal claims about such a world. For this reason, we need to consider whether both constitute coherent ways of extending our account of the bases of causal non-symmetry. The agency approach will be considered more fully in .. Appeal to primitive non-symmetry of chanceraising will be considered in .. In the latter, we will consider the concern that, if a non-symmetry of causation is understood in this way, we won’t be able to explain why causes generally precede their effects. Before this, though, let us consider a problem case that raises the question of how these various approaches to causal nonsymmetry interact.

    - -?



.. Tooley’s inverse universes Consider a universe, U, made up of particles whose velocities determine the universe’s course of development over time according to Newtonian physics. U is like U except that it begins at U’s endpoint and works backwards with all the velocities of the particles thereby reversed. The Newtonian laws will hold in this universe too because they are time-symmetric. Tooley argues that if, in U, c causes e, then in U, e causes c. However, the very facts to which counterfactual theorists appeal, if they rely upon the macro-nonsymmetries discussed above, to explain why c is a cause of e in U won’t explain why e is a cause of c in U. Indeed, the facts would establish that c is a cause of e in U too (Tooley (a), p. , (b), pp. –). For instance, in U, let us suppose, causes have many consequences so making their absence hard to cover up. Effects have, in the direction of their causes, relatively few consequences. By contrast, in U, it is the putative effects that will have the many consequences in the direction of their causes and the putative causes that have relatively few consequences. So if we consider the counterfactuals (U) If e hadn’t occurred, c would not have occurred, (U) If c hadn’t occurred, then e would not have occurred, then Lewis’ similarity weighting would correctly proclaim that U is false and, incorrectly, that U is true. Given how the universes have been described and the ways that, in general, my favoured account of the similarity weighting replicates the verdicts of Lewis’, the result would be the same for my own approach. Equally, if agency theories of non-symmetry draw upon the macro-non-symmetries to capture the non-symmetry of agency, then they will not yield a different treatment of the two universes. If there are agents in the inverse universe, they will be facing backwards in time—towards their past—and, if they are able to take anything as a potential means to an end, they will take present events as a means to bring about things in the past of U. Such an approach would make the causal order the inverse of what it is specified to be in U and, if counterfactuals reflect agent non-symmetries, then (U) would be incorrectly pronounced true. One response to Tooley’s inverse universes case would be to insist that there is no reason to suppose that the causal direction is opposite to that which the nonsymmetries would support. Simple temporal order does not define causal order and the laws are time symmetric. What else could settle that the causal order is counter to the macro-non-symmetries? Tooley himself takes temporal order to be derived from causal order. He endorses a causal account of temporal precedence. This enables him to conform to the constraint identified at the start of this chapter that causes usually precede their effects. As we shall shortly see, such an account of temporal precedence is questionable. Without this, his preferred interpretation of the inverse universes case is open to further threat. Nevertheless, once it is accepted that there might be primitive non-symmetric chance-raisings, Tooley’s inverse universes seem a possibility and it is helpful to the development of the approach recommended here if we consider how we should deal with them.



 - Heat Off Wire

Button Pressing

Explosion

Memory

Time

Figure .

The case brings out the fact that there are two places at which a theory of causation might appeal to primitive non-symmetric chance-raisings: first, in the characterization of the similarity weighting of the counterfactuals (which I have presumed so far); the second, in the characterization of the consequent of the counterfactuals of any analysis of causation. The first deals with foretracking counterfactuals, the second with backtracking counterfactuals. To see how this works, consider Figure . that is an inverse of the familiar case of a button pressing causing an explosion (the nuclear holocaust). In U, heat off the wire, the explosion, and the memory are overdetermining causes of the button pressing. Consider the counterfactuals P () If there were not an explosion nor any of the events in occurred, there would not be a button pressing, P () If there were not a button pressing nor any of the events in occurred, there would not be an explosion, assessed in a U in which there had been an explosion and button pressing, and P () If there were an explosion without any of the events in occurred, there would be a button pressing, P () If there were a button pressing without any of the events in occurred, then there would be an explosion, assessed in a U in which there had been no explosion and no button pressing. These are counterfactuals that don’t explicitly mention probabilities in their consequents but which we might take to be relevant to whether there is a deterministic

    - -?



causal relationship between the explosion and the button pushing. () and () are foretracking counterfactuals, () and () backtracking counterfactuals. P In the case of (), with the memory and the heat off the wire in , the absence of the explosion very much lowers the chance of the button pressing. This is true without explicit appeal to primitive non-symmetric chance-raising. The adjustment to the similarity weighting discounting perfect match, if it would involve departure from Pthe distinct events (or their absences) that the truth of the antecedent makes more -probable, is sufficient to ensure that there would not be a button pressing. As we have noted, the explosion is an overdetermining cause of the button pressing in Tooley’s reverse universe U. We would expect this to show up in the truth of a counterfactual of the form of (). If there were an explosion without any of P the events in , the explosion would very much raise the chance of the button pressing and, hence, perfect match ensured by retaining the absence of the button pressing would be discounted. This brings the no local miracle condition of the similarity weighting into play and, thus, there would be a button pressing. However, to validate the line of thought just sketched, appeal to primitive chancemaking plays a role. In . when we discussed the problem of backtracking with the P P -set mechanism in play, I argued that, without the events in (the other effect events), the target effect would not be sufficient for the putative cause because the chance of the cause would be low. The effect would probably have been brought about by something else, given all the other hallmark effects were absent. This reasoning does not make sense in the reverse universe case, U, where it is built in that the explosion is a cause (as opposed to us considering whether this drops out of the similarity weighting for counterfactuals). We can only accommodate this if we take chance-raising in such a world not to be reduced to the non-symmetries hitherto mentioned and, instead, appeal to a primitive non-symmetric notion of chanceraising regarding the button pressing. Such an appeal explains how the verdict for the corresponding counterfactual is different. Matters are different with respect to the backtracking conditionals relating the button pressing to the presence or absence of an explosion (), (). The nonsymmetries that, in the normal universe, would establish their falsehood, in the inverse universe establish their truth. There is no perfect match to be obtained by retaining the explosion without the cost of a widespread miracle. Because the counterfactual is a backtracker, there is no succour from appeal to a primitive nonsymmetry of chance-raising either. So we must concede that, unlike universe (U), the inverse universe will have true backtrackers in standard circumstances. Nevertheless, this does not mean that we must recognize that causation is symmetrical in that universe. Rather the non-symmetry of causation shows up in the second place at which appeal to non-symmetric chance-raising might be felt: the characterization of the consequent of the counterfactual. The button pressing does not count as a cause of the explosion because it does not satisfy the clauses of the analysis understood as appeal to primitive non-symmetric chance-raising in its consequents. Effects may raise the probabilities of their causes in such and such a case but that is not, in these circumstances, sufficient for causation. The counterfactuals we would be looking at would be these.



 -

P (*) If there were a button pressing, without any of the events in occurred, then for any time t, it would be the case that, just before t, the mean value of p(explosion at t) = x. P (*) If there were not a button pressing nor any of the events in occurred, then for any time t, it would be the case that, just before t, the mean value of p(explosion at t) = y. For the button pressing to be a cause of the explosion in such a situation, it would have to be the case that x >> y where the probability values they express are the result of the primitive non-symmetric chances to which we have had recourse to characterize the inverse universe Tooley envisages. The failure of primitive non-symmetric chances to hold in the button-pressing explosion direction, which in U is the effectcause direction, explains why button pressing is not a cause of the explosion. A second matter that the case brings out, implicit in our discussion up to this point, is the priority ordering of the various non-symmetries. In worlds, or for that matter regions of worlds, in which there is primitive non-symmetric chance-raising, this will settle the question of whether or not there is causation, both by its role in the similarity weighting and in the characterization of the analysis. Where this is not present, the non-symmetries to which I have already appealed settle the matter. It is appropriate to group all these cases together as involving a univocal notion of counterfactual and causation because, in the circumstances in which primitive non-symmetric chance-raisings are not present, we still have an account that draws on non-symmetries of chance-raising. It is just that these non-symmetries are not primitive but derive from the counterfactual non-symmetries I have already identified.

. Concluding Remarks We have seen that there are various different sources of counterfactual nonsymmetry. The fundamental basis for such non-symmetries is a non-symmetry of chance-raising. The macro-non-symmetries I identified earlier provide a basis for the non-symmetry of the counterfactuals with probabilities in their consequent. There are other possible bases for non-symmetry drawing on other considerations, for example, a certain highly determinate characterization of event, taking causation to be spatiotemporally continuous and involving chance-raising but it involves assumptions that I would not want to make here (Kutach (), chs –). My aim has been to develop an account of counterfactual non-symmetry whose bases covered the range of cases that have been discussed to show the defensibility of the counterfactual approach. My defence of the asymmetry of overdetermination rested upon two moves. First, the recognition that the characterization of an effect’s determination of a cause may appeal to circumstances around the putative cause, rather than around the effect together with other effects of that cause. Second, that the introduced limitation of the perfect match element of the similarity weighting had the consequence that an asymmetry in the incidence of the possibilities for perfect cover-ups by small miracles in the cause to effect direction can be the basis for counterfactual non-symmetry,

 



when a simple appeal to an asymmetry of overdetermination is not enough for an asymmetry in miracles required for perfect match. In the case of this feature, I noted that, although discussion in the literature has been of an asymmetry, the feature of overdetermination is non-symmetric and, thus, the characterization of cause that it supports is non-symmetric too. It is just when the overdetermination holds one way but not the other that causes are distinguished from effects. In this respect, it is unlike the second macro-non-symmetry: the independence condition. My defence of the independence condition involved demonstrating that its formulation did not involve an illicit appeal to causal asymmetry—for example, by failing to count two effects of a common cause as causally connected—and did capture something distinctive about a range of causes with regard to their effects. The key idea was that causes were circumstance-dependent sufficient conditions for their effects whereas, relative to exclusion conditions, effects were simply sufficient conditions for their causes. A consequence of this is that no counterfactual of the form ‘If e₁ were not to occur, e₂ would not occur’ (or its probabilistic equivalent) would be true with e₁ as an effect and e₂ as a cause. This was significant for an understanding of the transition period. The grounding of counterfactual non-symmetry in these macro-non-symmetries showed that there is no need to presume that a primitive non-symmetry of chanceraising is at work. However, when they don’t hold, or when they hold but there is another factor at work—primitive non-symmetric chance-raising—then that factor has priority. It has the priority it does because it provides, in primitive form, the very same contribution that the other non-symmetries provide in its absence. The cases in which we need to recognize primitive non-symmetric chance-raisings may be extended if my arguments against the challenges raised to the macro-non-symmetries prove ultimately unsuccessful. My discussion of the non-symmetry due to agency—which I took to be a case of interlevel-non-symmetry—needs further discussion. This will be the opportunity to evaluate agency and interventionist analyses of causation more generally and return to the discussion of the desiderata on a theory of causal non-symmetry I mentioned at the outset of this chapter. In that context, we need to consider in more detail the relationship between causation and time. These issues will occupy us in Chapter .

 Agency, Intervention, and the Past The appeal to agency in order to understand causation can take one of, at least, three forms. Some take causation to be best understood in terms of the idea that causes are the means by which agents obtain what they want. With this notion at its heart, they either seek to develop a full-scale analysis of causation or, at the least, insist that vital illumination will be attained by these means. I shall review difficulties with this approach at the beginning of .. It is, in any event, partly motivated by difficulties that other analyses have had with causation that I have sought to deal with earlier. A second appeal to agency draws upon agency to understand causal non-symmetry. That is my more central interest. Agency accounts of causal non-symmetry are often proposed as the only source of causal non-symmetry. That will not be my approach. The suggestion, taking up the discussion of Chapter , will be that it is one way in which non-symmetry is realized. The task will be to explain how agency can be a source of causal non-symmetry, without appealing to another causal non-symmetry between the events for which agency introduces a non-symmetry, and how it should be integrated into my analysis thus far. ..– will address this issue. The central element of the discussion will focus on attempts to characterize how an action may be an effective means to a certain outcome and whether this can be done independently of appeal to causality. The final way in which an appeal to agency may be useful is as a partial account of what unifies the various bases of causal non-symmetry. That will be the focus of .. In ., I discuss how the various features upon which counterfactual nonsymmetry depends relates to the first constraint I identified for successful theories of causal non-symmetry, the fact that causes usually precede their effects. In the course of this section, I explain how our concept of the past seems to be partially perspectival.

. The Role of Agency Everybody can accept that causes are means by which agents achieve ends. But the trivializing thought is that they are means by which agents can achieve ends because they are causes of those ends. Those who appeal to agency in order to understand causation cannot rest happily there. Rather they should insist that we will understand causation better by thinking of what is involved in something being a means to an end. The latter comes first. As I noted above, my particular focus will be on a further A Variety of Causes. Paul Noordhof, Oxford University Press (2020). © Paul Noordhof. DOI: 10.1093/oso/9780199251469.001.0001

   



characterization of a chance non-symmetry, other than the three identified as potential bases so far: the overdetermination non-symmetry; independence condition, and primitive chance non-symmetry. However, to get to the proper characterization of this chance non-symmetry we must understand the role it plays in the connection between agency and causation. So I will start by focusing on that. A full-blown agency theory of causation is committed to something like the following explanatory schema. An event e₁ is a cause of a distinct event e₂ if and only if bringing about the occurrence of e₁ would be an effective means by which a free agent could bring about the occurrence of e₂ (e.g. Menzies and Price (), p. , also Gasking (), p. ; Von Wright (), p. ). The italicized occurrences of ‘bring/bringing about’ are two places in which an agency analysis of causation threatens to be circular. The third is in the talk of ‘effective means’ (Cartwright (), pp. –). Proponents of agency (or manipulability) theories of causation have had limited success in avoiding concerns relating to the occurrences of ‘bring/bringing about’. For example, Georg Henrik Von Wright suggests that the first occurrence of bringing about is non-causal (Von Wright (), p. ). Suppose I open a window to let air in the room (it is a warm day today). According to Von Wright, this action, e₁, is a process, or for our purposes, we can talk of a sequence of events, that ends with the window being open. Figure . provides part of the picture. The action is the complete sequence. So when an agent opens the window, there is no causal relationship between the agent and the action in question. The intention and the window being open are part of the action. A problem with Von Wright’s suggestion is that it is natural to conceive of the process indicated as a case of piecemeal causation in which the intention to open the window is a cause of other parts of the causal process ending up with the window being open (see e.g. Lewis (b), pp. –). In which case, the suggested manoeuvre doesn’t enable us to understand the first occurrence involving ‘bringing about’ independently of causation. The occurrence of the second ‘bring about’ also involves difficulties. As we have noted, an advantage of the agency approach is that it can reveal a non-symmetry where there isn’t one if we consult the laws of nature or pattern of events. Unfortunately, there is no guarantee that the non-symmetry is one that tracks our

Intend to open the window Nerves fire in brain

Figure .

Arm movements Nerves fire in arm, muscles activated

Moving arm/hand unfastens window lock, pushes up window Concomittant neural activity

Window open



, ,   

natural understanding of causation. What an agent takes to be means to an end may be different from the underlying causal direction (Taylor (), pp. –). To cite the familiar case, agents may bring about the firing of the nerves in their brains and arms by clenching their fist, rather than vice versa. Firing nerves is rarely a target of our intentions. Some are prepared to claim that cases like this involve backward causation (Von Wright (), p. ). A consequence of so doing is that causation has to be relativized to a particular system of understanding. From the perspective of agents, they bring about nerve firings by bringing about fist clenchings. From the perspective of neuroscientists investigating the connection between nerve firings and fist clenchings, they bring about fist clenchings by bringing about nerve firings. However, the perspective of neuroscientists has priority. They can intervene to stop the fist clenching by breaking the connection between the nerve firing and the fist clenching and this will be a phenomenon that shows up in the agent’s perspective (Mackie (), pp. –). These problems have doubtless led other proponents of the agency approach to suggest that we can understand the ‘brings about’ by some kind of ostensive definition without presupposing our notion of causation. It is doubtful whether this is available. For one thing, it is suggested that the ostensive definition should be in terms of our experience of our own agency: doing one thing and thereby achieving another event, which we desire (Menzies and Price (), pp. –). This would cover the case of fist clenching described above and yet, presumably, we are not presented with a case of causality in the right way. Even more important, the issue is not so much whether we can explain how we have a grasp of ‘bringing about’ without appealing to causal notions as whether we have an account of the ontology of causation in the target agent analysis. If references to bringing about are just references to causation then the appeal to agency seems to play no role. The agency approach to causation should be developed in a different way. The occurrence of ‘bringing about’ should appeal to whatever agent-independent notion of causal or nomological dependence is available. In worlds with the macro-nonsymmetries, or primitive non-symmetric chance-raising, then it will pick out the relevant notion of non-symmetric dependence. In worlds without such nonsymmetries, it will pick out symmetric nomological dependence. The appeal to agency is to provide an additional basis for causal non-symmetry where these other non-symmetries fail to provide it. The non-symmetry based upon agency relies upon a proper understanding of the agency analysis’ appeal to effective means. One qualification to the appeal is that we should focus on cases of effective means where agents are not looking to bring about the preconditions for their successful action, for example, nerve firings. We could exclude such cases by requiring that the relevant case of bringing about doesn’t involve as the target event part of the minimal supervenience base of action seen as a means to the target event. Of course, the issue does not arise, or is much reduced in scope if we understand actions as mental tryings which are causally related in the right way to the subsequent events in the causal chain such as nerve firings to count as means to them in the standard sense (e.g. Hornsby (), pp. –). If e₁ is an effective means for an agent to bring about e₂, then doing e₁ raises the probability of e₂. The increase of the probability of e₂ is a measure of the effectiveness

   



of the means. There are broadly three approaches to the development of this idea that are worked out in decision theory. All three approaches identify the rational action for an agent to undertake. Each supposes that agents are rational if and only if they choose the action with the maximal expected utility or value, assessed by looking at the action’s value and the value of its consequences. The effectiveness of a means is the expectation that a certain value is produced. According to one approach, Objective Decision Theory, the expected utility or value is calculated by multiplying the value of the consequences by the objective chance that the agent will bring these consequences about by a certain action (e.g. Mellor (), p. ). This is an implausible source of an additional non-symmetry of chance because it appeals to a notion of chance that is already supposed to display none of the three nonsymmetries identified in Chapter . The only way it might be a source of nonsymmetry is if agents have free will in the sense that they are the uncaused originators of action. I shall briefly touch on this option below but it will not be the centre of discussion. The other two options are types of subjective decision theory: evidential and causal decision theory. Each tries to capture the rationality of agents from their perspective, concerning the probabilities that hold and what they value. Agents decide upon the right action in the situation in which they find themselves if and only if their evaluation of the outcomes is correct and these are weighted by their credences concerning outcomes that conform to the objective chances of these outcomes, given these actions. However, even if there are no facts about the values of the outcomes, or only facts about how much these outcomes are desired, and the agents’ credences don’t conform to the objective chances, agents can be rational in how they act. Subjective decision theory seeks to capture this second way of evaluating agents. It should not be taken to claim that, given their perspective, they ought to act in a certain way (e.g. Ahmed (), p. ). Rather, it claims that if an agent departs from certain combinations of desires, credences in outcome given actions, and actions, then their mental states are not as they ought to be. As we shall see later, it is plausible that there is a connection between these two types of evaluation. Specifically, with regard to the agent’s credences, an agent does not act rationally if their action would demonstrate that their credences fail to conform to the objective chances of the outcomes. This point will become relevant later when we discuss an objection initially made to causal decision theory but, as we shall see, also applying to the most effective defence of evidential decision theory (..). Either form of subjective decision theory is a potential source of non-symmetry. Some have argued that we must understand the probabilistic measure of effectiveness in terms that require causation to be characterized independently of it (see e.g. Cartwright (), pp. –). This might seem to rule out a characterization of effectiveness in terms of causal decision theory. It is certainly true that evidential decision theory has been the more popular way in which this basis of non-symmetry has been characterized. I will begin by discussing the defence of evidential decision theory from Newcomb cases: supernatural and medical. We will see that much of the case for causal decision theory can be undermined if the defence is developed in a particular way combining the tickle response and an appeal to the nature of deliberation. Unfortunately, an objection raised against causal decision theory is more



, ,   

damaging to this way of defending evidential decision theory. The result is that, on balance, there is more to be said in favour of a development of causal decision theory. However, I will argue that this is compatible with developing an account of causal non-symmetry that draws upon it (..).

.. Evidential decision theory and causal decision theory At its simplest, evidential decision theory holds that Evidential Decision Theory: VðAÞ ¼ ∑PðOi =AÞ  VðOi AÞ where A is an action, V(A) its expected value, Oi an outcome of the action, P( . . . / . . . ) is conditional probability and V is the value (or utility) of Oi as a result of A. In other words, the expected value of an action A is the value of the various outcomes weighted by the probabilities of those outcomes as a result of doing A. The rational action maximizes expected value so defined. The approach faces a challenge from what are standardly known as Newcomb cases. Newcomb cases present a problem because they involve actions that can raise the probability of an outcome without being an effective means to it. This raises the question of whether we can appeal to the understanding of effective means captured by evidential decision theory. In the classic Newcomb case, there are two boxes, one transparent in which you can see £,, one opaque in which there may be £ million. If an almost infallible predictor predicts that you will only open the opaque box, then they have put £ million in it; if they predict you will open both, then they will put in nothing and you will only get £,. There are two ways we can conceive of the almost infallible predictor. Either they have almost infallible precognition or they have almost infallible knowledge of the way the subject currently is, and the laws that apply to him or her. So we have either Agent’s Decision

Agent’s Pre-Decision State

Predictor’s Prediction

Money Placement

Predictor’s Prediction

Money Placement

Agent’s Decision

Figure . The precognition case involves the agent’s decision being a (backward) cause of the prediction. This is not what is had in mind in the classic Newcomb case. Instead, the predictor’s prediction is taken to be caused by knowledge of the pre-decision state plus laws (e.g. Eells (), p. ; Joyce (), pp. –). Price has argued that socalled supernatural Newcomb cases (involving nearly infallible predictors) that cannot be easily understood in terms of the second model have to be understood in terms of the first because the evidential probabilities are, then, indicative of a causal relationship between the agent’s decision and the prediction (Price (), pp. –). However, this is the conclusion of an argument that is explicitly

   



envisaged to run counter to the standard understanding of Newcomb cases in order to avoid the problem they present. The importance of the difference is that whereas in the case of precognition the agent’s decision leading to action might be part of the means by which he or she obtains the money by influencing the predictor, in the case of prediction from the agent’s pre-decision state, it is not part of the means. Of course, an agent’s decision to open only one box is a means to obtaining whatever money is available in that one box and, thus, given that £ million is in the box, it is a means to obtaining £ million. However, this observation is compatible with noting that, although deciding to open only one box raises the chance of £ million being in that box, the chance-raising does not reflect the way in which the decision is a means to get the money. Raising the chance of £ million being in the box is not part of what the agent did but rather the causal circumstances that, in fact, hold in which the agent’s decision is a cause of getting the money available. Deciding to open only one box, or deciding to open both boxes, provides news about which causal circumstances operate. However, in this case, information about which causal circumstances operate does not affect what an agent should do. If your decision to open only the opaque box is a cause of the predictor putting £ million in it, then it is rational for you to open only that one box. If the predictor’s placement of the money is caused by the agent’s pre-decision state, then, by the time the agent is making the decision, whatever money is available has already been placed and what money has been placed is unaffected by the decision. Whichever causal circumstances hold, it would be better to open both boxes and take all the money that is there. In the very nature of the case, the agent’s decision cannot affect the causal circumstances that are actually in place. Those who object to the verdict given by evidential decision theory in this case accuse evidential decision theory of being unable to distinguish between ‘news’ value and ‘means’ value (e.g. Gibbard and Harper (), p. ). The news value of an act includes not just what the act may be a means to achieving but also the value of the information about the circumstances in which the agent finds him or herself. The charge is that this should not be part of the characterization of the value of the act and it has been counted as such because the appeal to probabilities is not sufficiently discriminating. Although the classic Newcomb case raises questions about evidential decision theory’s capacity to provide an account of effective means, because it suggests that making the decision to open only one box is the most effective means by which to get the most money, it leaves untouched its potential to provide a basis for a fourth causal non-symmetry based upon agency. Whether one should open one box or two box doesn’t affect the fact that whatever money an agent obtains is a causal consequence of their choice. However, it is unsurprising that, if evidential decision theory fails to provide an account of effective means, it will also yield the wrong verdict with regard to causal non-symmetry. Medical Newcomb cases illustrate how. Here is one example. It is commonly suggested that migraine tends to follow from the consumption of certain foods and drink, for example, chocolate and wine. These are causes of an attack. However, suppose instead that eating chocolate and drinking wine are joint effects, along with the migraine, of a pre-migrainous state. The pre-migrainous state increases the desire to eat chocolate. The diagram for this case is slightly different.



, ,    Eating Chocolate/Drinking Wine Pre-Migrainous State

Migraine

Figure . Let’s focus on the case of chocolate. P(Migraine/Eating Chocolate) is greater than P(Migraine/not-Eating Chocolate). Yet we wouldn’t want to say that, in these circumstances, eating chocolate is a means by which to get a migraine. Moreover, the difference between being a means to something and a common effect of it corresponds to a difference in what it is rational to do. If the circumstances are as diagrammed above, it seems irrational to deprive yourself of the pleasures of chocolate since whether you have it or not will not affect whether you get a migraine. Examples such as these have convinced many to move from an evidential to a causal decision theory. Instead of weighting the value of each outcome by the probability of the outcome given the action—as indicated above—the value is weighted according to the probability of the outcome given the action and a specification of the causal dependencies at work, itself weighted by the probability of these causal dependencies holding (Lewis (b), pp. –, also Hitchcock (b), p. ). Thus we have Causal Decision Theory: VðAÞ ¼ ∑PðOi =AKÞ  PðKÞ  VðOi AKÞ where A is an action, V(A) its expected value, Oi an outcome of the action and K the causal dependencies at work when the action takes place. Thus, for example, a specification of the causal dependencies will include the fact that, if a subject is in a pre-migrainous state, eating chocolate (A) won’t change the probability that they have a migraine. So P (Oi/AK) = P(Oi/not-AK). The expected value of each course of action will turn on the utility of consuming chocolate, namely V(OiAK) as compared with V(Oinot-AK). P(Oi/AK)V(OiAK) is weighted by P(K) rather than P(K/A) because when their values are different, it will be because the causal dependencies are different given A. Since the causal dependencies won’t be affected by an agent’s actions, P(K/A) would reflect the intrusion of news value rather than means value in the assessment of the expected value of A. Causal decision theory is developed precisely to remove this element. In .., we shall consider whether this is necessary. In .., whether it always yields the right results.

.. Evidential decision theory and the need for causal information Defence of evidential decision theory seeks to explain how agents will be aware of the causal information described above and, as a result, how evidential probabilities won’t reflect an additional news value attached to a decision. If this is correct, there would be no need to shift to a causal decision theory. The defence comes in two forms: the tickle response and the agency response. The first seeks to explain how the information about causal circumstances will invariably be available prior to an agent’s decision, the second urges that, when an agent is making the decision, the evidence about the causal circumstances that hold is superseded. As we shall see, while both have problems, there are grounds for thinking that combining them to

   



cover different elements provides evidential decision theory with an effective response to the challenge of causal decision theory. Unfortunately, part of the basis for the effectiveness of its response proves its undoing (..). Evidential theories don’t arrive at different conclusions from causal theories if subjects can be expected to know the relevant causal circumstances of their actions prior to their decision to act one way or another—by a tell-tale tickle in the taste buds for chocolate, for example, revealing that one is in a pre-migrainous state (canvassed but not endorsed by Skyrms (), pp. –). In that case, we would have the following situation. Eating Chocolate Tickle Pre-Migrainous State

Migraine

Figure . In those circumstances, P(Pre-Migrainous State/Eating Chocolate & Tickle) = P (Pre-Migrainous State/not-Eating Chocolate & Tickle) and P(Pre-Migrainous State/ Eating Chocolate & not-Tickle) = P(Pre-Migrainous State/not-Eating Chocolate & not-Tickle). In which case, eating chocolate is screened off regarding its capacity to raise the probability of the subject being in a pre-migrainous state, given that the subject notices the tickle. This preliminary version of the tickle response is subject to the objection that there needn’t be a tell-tale tickle. What then? Sophisticated versions of the tickle response seek to identify something that could not fail to be present in the relevant circumstances. If an agent’s action, or decision leading up to it, reveals whether they are in a pre-migrainous state, then the candidate ‘tickle’ that reveals the nature of the causal circumstances in which the agent is deciding are the mental states that are required for the agent’s decision or action. For example, if an agent is rational, then their eating of chocolate will follow the desire to eat chocolate and/or the belief that this will be a pleasurable thing to do without harmful consequences. The tickle is taken to be these decision-conducive states (Jeffrey (), p. ; Horgan (), p. ; Horwich (), pp. –). By ‘decision-conducive’ I mean the combination of beliefs and desires that favour the target action over others (Eells (), p. ). If a subject believes that a combination of their beliefs and desires reveals eating chocolate is to be favoured over other actions, then this belief will screen off the putative increased probability of being in a pre-migrainous state by so deciding to act. Likewise, the argument runs, if they choose not to eat chocolate this will be in the absence of the beliefs and desires supporting eating chocolate as the best outcome. So they will already have the causal information that they are not in a pre-migrainous state. This works fine for the fully rational self-reflective agent but doesn’t for a partly rational agent who either decides on the basis of something else in addition to his or her beliefs and desires or is inaccurate in his or her evaluation of their strength prior to their result in action (Lewis (b), pp. –). In either case, the decision-maker will not successfully identify a tickle.



, ,   

One response is to insist that, to apply any version of decision theory, an agent must know their relevant beliefs and desires. Any case in which they do not is not a proper test case (Horwich (), p. ). This is too strong. Agents can work out what there is to be said in favour of one choice rather than another on the basis of a rough appreciation of their beliefs and desires. Fully accurate knowledge of them is not required (Ahmed (), p. ). Arif Ahmed argues that it is reasonable to suppose that agents know, at least, the following (adjusting for the case I have been discussing). (A) Eating chocolate is worse news (makes it more likely) an agent is in a premigrainous state than not eating chocolate. (A) If an agent refrains from eating chocolate, then it will be for this reason (Ahmed (), p. ). (A) captures the idea that an agent will know enough about their beliefs and desires for evidential decision theory to be able to make a recommendation to eat or not eat chocolate. That would be a necessary condition for setting up a case to begin with. Call this the ‘tickle identification claim’. Ahmed says that (A) is a normal condition for being an agent, namely that you know what reason is behind an action. Call this the ‘operative reason claim’. If an agent knows both (A) and (A), then they already have the causal information concerning which state they are in. If their beliefs and desires favour eating chocolate, then they are in a pre-migrainous state. If they abstain then this will be because of their recognition of (A) and, hence, it does not show that they are not in a pre-migrainous state. So, either way, only the value of the causal consequences of the action will be part of the decision-making. Agents will be able to work out the tickle from noticing the beliefs and desires that favour the action that indicates that they are in a pre-migrainous state. If their action is indicative, then it is reasonable to assume that they are typical agents. Typical deliberating agents end up eating chocolate as a result of their beliefs and desires. So these beliefs and desires will be the tickle (Horwich (), pp. –). Agents may fail to go through this process, and indeed assume that their actions don’t raise the probability of any outcome except those that are causally dependent upon them, without this supporting causal decision theory. Causal decision theory can be viewed as supplying heuristics to approximate the correct verdicts that are, in fact, determined by evidential decision theory together with recognition of a tickle. These observations extend the tickle defence and, indeed, provide a partial explanation for why a causal decision theory seems so plausible—it works as a heuristic—nevertheless it is questionable whether it extends the tickle defence far enough to cover all but the original Newcomb case (say). There are problems with both (A) and (A). The problem with (A)—the tickle identification claim—is that the question of whether a particular combination of beliefs and desires is indicative of a pre-migrainous state may depend upon a wider context in a way that can only be resolved when a decision is made upon their basis. So while some combination, in some mental circumstances, may constitute a tickle, an agent may not be in a position to know precisely what. They can only conceptualize the supporting mental circumstances as whatever is responsible for the final decision to eat chocolate. As their role is not going to be revealed until the decision is made, it is hard for subjects to take them into account to screen off the probability of being in a pre-migrainous state (Price (), pp. –).

   



Consider the case of a rising young executive, Robert Jones, who will be promoted only if he beats his co-workers in a reliable test of ruthlessness. He completes the test but the results aren’t going to be announced until Monday—a whole weekend of fretting. If he sacks a worker going through a bad patch on Friday, even though sacking them is ultimately unnecessary, that will raise the probability that he will be getting the promotion on Monday because it shows he has the ruthless streak (Gibbard and Harper (), pp. –, discussed by Horwich (), pp. –). He observes that he is strongly drawn to fire the worker, which seems indicative of his ruthlessness. But if that’s right, then he needn’t sack the worker. He already has the good news. However, then again, his rapid shift to not sacking the worker is a sign he isn’t ruthless. To remove this anxiety, he decides he must sack him, and so on. It seems that only the final decision, or the sacking itself, will do. In which case, there may be no tickle available to support the application of evidential decision theory to produce the correct verdict that it is not rational to sack the man on Friday. (A)—the operative reason claim—is also open to question. As agents, we are familiar with the distinction between those beliefs and desires that we have and, indeed, which seem salient to us, and those that are actually operative (e.g. Davidson (), p. ). Suppose I have the desire to eat chocolate but also the desire not to do so because of a perhaps misguided concern about the health implications. I am aware I’m in a medical Newcomb situation and hence believe that if I decide to eat chocolate, then there is a greater chance that I’m in a pre-migrainous state. In fact, I decide not to eat chocolate. I may be in no position to know that my decision is the result of my concern for good news. Thus (A) fails to hold. Maybe the health concerns had a role, or were even solely at work. I can offer explanations to myself as to why I acted as I did without knowing that one or other is correct. The fact that the explanations I offer are possibly correct, and that one is correct, is enough to ensure that I’m an agent. In the circumstances just described, my decision not to eat chocolate is not screened off from lowering the chance of me being in a pre-migrainous state. The decision lowers the chance of me being in a pre-migrainous state because some of the reasons why I may choose not to eat chocolate are ones which are more likely to be operative in the absence of a pre-migrainous state state. However, because I don’t know which reason is operative, the decision bears on the question of whether I’m in a pre-migrainous state and not just on the question of what beliefs and desires are candidates for being the tickle. Even if I had a belief that it was highly likely I refrained because I wanted good news about being in a pre-migrainous state, this would not be sufficient to screen off the decision. The decision would still increase further the likelihood that I was not in a pre-migrainous state state. Of course, this is only one type of case. Others will satisfy the two conditions Ahmed identifies and the decision will be screened off. However, we only need one type of case (contrary to what Ahmed says) in which the verdicts depart in a way that favours causal decision theory. Causal decision theorists will rightly claim that such cases show that evidential decision theorists overlook the significance of causal information. This may not matter in some cases in which the verdicts are the same. However, in others it is significant. We cannot write off the type of case just described as one in which the relevant agent has just failed to go through the



, ,   

reasoning that would lead the appropriate belief to be formed about the operative reason. Instead, the charge will be, causal information needs to be built in. An alternative to the tickle defence draws upon features of agents’ perspectives on their actions. The fundamental idea is that when agents freely choose what to do, they conceive (accurately or otherwise) their decisions and actions as probabilistically independent of the antecedent conditions that hold, apart from, perhaps, the beliefs and desires that are, together, an input into the decision. Correspondingly, when agents freely choose to do A, there are no conditional probabilities relating to their internal states—for example, their likelihood of being in a pre-migrainous state—given they do A (to continue the example, eat chocolate) from the agent’s perspective (Price (), p. , (b); Ramsey (), p. ; Pearl (), p. , although Pearl is a proponent of causal decision theory). Instead of information about the causal circumstances being incorporated, it becomes irrelevant. The idea may be developed in different ways. I shall focus on how these are responses to Newcomb problems. According to one view, subjects’ knowledge of features of the Newcomb situation makes them an exception to the probabilistic relations used to define it (Price ()). According to another, subjects’ ignorance about the non-mental causes of their action is the basis for the probabilistic independence (Price (), p. ). However, it’s hard to see how this would explain what is going on in the medical Newcomb case in which knowledge of the causal antecedents is hypothesized. So I won’t discuss this further. A third view is that when agents deliberate over what to do, they must chose between actions that are options for them to do and, thus, can’t appeal to probabilities concerning what decision they are likely to make or action they are likely to engage in (Levi (), pp. –, (), pp. –, (), pp. –). As we shall see, for this view, there is probabilistic independence even from the agent’s beliefs and desires. A fourth view is that agents have first-person authority with respect to the contents of two sorts of beliefs: first, that they have decided to do A and, second, that they will do A. In which case, the probabilities that they assign to each proposition are independent of the probabilities that they have given to prior conditions of the world, or themselves, including the beliefs and desires that gave rise to the decision (Price (), pp. –). A fifth view is that when agents deliberate over what to do, they focus on the considerations in favour, and against, doing the things in question rather than any other considerations that might be in play for making the decision, for example, that they have such and such beliefs and desires (Moran (), pp. –). Their corresponding grounds for believing that they will do such and such are the considerations in favour of so doing it. In brief, deliberation, and our consequent belief about what we will do, is transparent. These views are all articulations of the claim that when agents decide what to do, the probabilities that they attach to an action on the basis of a decision swamp the probabilities attached to those actions, given antecedent conditions of the environment or the agent. They do not deny that there is a probability of the agent acting in a certain way given antecedent conditions. They just deny that these probabilities are available to the agent in deliberating. All are variants of a fictional approach to the probabilities that, from the agent perspective, attaches, or rather fails to attach, to what they do (as Hitchcock dubs it, Hitchcock (b), pp. –). There is, of

   



Free Choice: Probabilistic Independence

Fact

Conception/Fiction

Exception to generalization

Ignorance

Genuine Options

First-Person Authority

Transparency

Figure .

course, the option of claiming that no probabilities in fact do attach. This is the last position to be identified. The landscape is as in Figure .. Let me begin by focusing on the last position identified, represented by ‘Fact’ in the Figure .. It makes the agency account of causal non-symmetry depend upon a highly contentious claim about the world, which runs counter to what many suppose is the current state of our physics, namely that it gives probabilities for any particular event in time (either directly or by giving probabilities to its constituents) given a certain history. The only possible way to avoid this conflict is to appeal to agent causation but we have already found reason to resist this approach or, at least, its capacity to supply a viable line of resistance (.). On the other hand, the fact that I have cited a clash with an empirical claim about the world shows that the probabilistic independence of agents’ decisions and actions is an empirical matter. There may be worlds that satisfy this reading of the appeal to the perspective of agents. In such worlds, agents would introduce a genuine source of non-symmetry. The more important question is whether this condition is required



, ,   

for a non-symmetry due to agency. The subsequent options should be considered in this light. I will argue that the last, transparency, reading captures the crucial basis of the non-symmetry. Let’s go through the others in turn. Price argues that subjects who believe that if I decide not to eat chocolate, it is less likely that I am in a pre-migrainous state make themselves an exception to the statistical generalization that those who decide not to eat chocolate are less likely to be in a premigrainous state. There is an alternative explanation as to why they decide not to eat chocolate, namely the belief just mentioned. They would not count as a normal case (Price (), pp. –). More generally, take any probabilistic generalization assigning probabilities to subjects in certain states. Then, any subject who believes this generalization will make themselves a prima facie exception to the generalization. For instance, if we appeal to a more refined probabilistic generalization concerning all those who decide not to eat chocolate and who believe that, if they decide not to eat chocolate, they are less likely to be in a pre-migrainous state, then the same reasoning applies. Such subjects will have the belief that if they decide and have the belief about what is likely if they decide not to eat chocolate, they are (also) less likely to be in a pre-migrainous state and this (in turn) makes them a prima facie exception (Price (), pp. –). Therefore, there are no probabilities, to which one can appeal, relating to what one’s decision shows about one’s anterior state. We don’t have to move to a causal decision theory to obtain the same results as the causal decision theorist. There are two problems with this proposal. The first is that subjects who believe that if they decide not to eat chocolate, it is less likely that they are in a premigrainous state will do so on the basis of the corresponding generalization. If subjects decide not to eat chocolate, it is less likely that they are in a premigrainous state. However, as we saw, arriving at the conditional belief that if I decide not to eat chocolate, it is less likely that I am in a pre-migrainous state will make each of them an exception to that generalization. So they should withhold their belief from the proposition in question. But if they withhold their belief from the proposition in question, then once more the generalization applies so they have grounds to believe the proposition. The result is an oscillation between attributing and not attributing a certain probability to a pre-migrainous state state. This is no basis for reproducing the recommendation of causal decision theory from the agent perspective but providing no stable recommendation at all (Ahmed (), pp. –). Second, Price’s line of reasoning does not seem to apply to If subjects decide not to eat chocolate, then they are less likely to be in a premigrainous state whatever beliefs they have about the likelihood as a result of making that decision. If we want an intuitive basis for the generalization, we may say that it is one in which cognitive states concerning the connection between the decision and being in a premigrainous state fail to undermine the statistical generalization between making the decision and being in a pre-migrainous state. There seems no reason why this can’t be the case. Some subjects might take it that they are already in a pre-migrainous state, or not, regardless of what they believe, and thus beliefs concerning the

   



likelihood have no influence upon the decision to eat chocolate. For others, while the belief may add to the considerations in favour of not eating chocolate, they wouldn’t by themselves be sufficient to support the decision. The decision would still be evidence that they are less likely to be in a pre-migrainous state. The generalization is reflexive because it will cover the belief in that very generalization and, for that very reason, a subject who has this belief won’t be an exception to the statistical generalization it records. Maybe the particular case is a less plausible illustration of the point but the general structure of the point stands. The generalization just cited is also not subject to Price’s further argument that if we thought the connection between decision and being in a pre-migrainous state was invariable, whatever inducements offered, then we would have a case of causation (Price (), pp. –). I’m not claiming that the connection will be invariable whatever inducements are offered. Some might break the link. For example, if a concerned friend offers me a million pounds not to eat chocolate, I might decide not to eat chocolate. The point is simply that if I am one of the subjects mentioned above, I think my beliefs about the probabilistic relation are no basis for deciding not to eat chocolate. A subject responding to the million pound inducement, but not to the belief about the probabilistic relationship, demonstrates that the conditions of free choice are plausibly met. Therefore, it is not open to defenders of this evidentialist response to medical Newcomb problems to insist that we have lost sight of the idea that the agents are supposed to be making a free choice, unless more is built into the idea of free choice (Price (), p. ). This brings me to the next way of justifying the claim of probabilistic independence in terms of constraints on deliberation. Isaac Levi argues that when an agent is deliberating over what to do, they are choosing between subjectively feasible options. Subjectively feasible options are those options open to the agent given the agent’s information about the objective feasibility of different options and the circumstances in which the agent is deliberating (Levi (), pp. –). An option is objectively feasible relative to a particular (possibly incomplete) characterization of the circumstances and the agent’s abilities. If determinism is true, there is only one option that is objectively feasible given complete information concerning the circumstances. However, more than one option may be feasible according to other states of information and, certainly, more than one option may be subjectively feasible if the agent only has information about some aspects of the situation. Out of these subjectively feasible options, an option is admissible if it may be chosen given the agent’s values and principles of rational choice (Levi (), pp. –). With this understanding of deliberation, Levi argues that an agent will fail to deliberate over whether to do A if either of the following two conditions are met. (B-not-A) The agent believes that he or she will not do A. (B-A) The agent believes that he or she will do A. Deliberation occurs in a condition of uncertainty about the outcome to be chosen in both ways. If (B-not-A) is true, then A is not an option for the agent. If (B-A) is true, then there is nothing to deliberate. This gives rise to a prima facie problem. If an agent is fully aware of the considerations that go into settling their choice one way or another—for example, as given by the content of an agent’s beliefs and desires— and the principles of rational choice when applied to these considerations yield a definite outcome, then the conditions of deliberation cannot be met. Yet, it



, ,   

seems, the situation just given, albeit very possibly idealized, shouldn’t rule out the possibility of deliberation (Levi (), pp. –, (), pp. –; Schick (), pp. –). Levi’s general solution is that at the point of deliberation agents do not believe that they will choose the rational option (that is, they don’t believe what Levi calls the Smugness Assumption (Levi (), p. ). The consequence of failing to have this belief is that, even in the idealized circumstances described, agents will not have a belief about whether or not they will do A. Levi does not deny that agents might be justified in believing that they will choose the rational option prior to deliberation and, indeed, that there is one rational choice. Levi’s claim is that when an agent is rationally deliberating, this belief is no longer held (Levi (), pp. –). If deliberating agents don’t believe they will choose the rational outcome while deliberating then, conversely, their choice of outcome does not imply that such and such antecedent decision-conducive conditions held in themselves. This is, at least, part of the basis for the claim that there are no conditional probabilities to which deliberating agents can appeal for a choice that will make them purportedly learn they are not in a pre-migrainous state. However, on the face of it, the failure to believe that such and such decision-conducive conditions hold in themselves does not rule out there being a probabilistic relationship between choosing a certain outcome and a prior state. Even if you don’t believe that you will choose the rational outcome, then it might be more likely that you do and, hence, given a particular decision, more likely that this decision resulted from conditions conducive to it. An agent won’t believe that they are in a pre-migrainous state but they will attach a higher probability to it. At first glance, these are circumstances in which the tickle response will be appropriate. This brings us to the second element in Levi’s position. Levi argues that deliberating agents can’t, at the point of deliberation, attribute a probability of less than  to doing A, given that they favour A over not-A, and A is subjectively feasible. This is revealed by betting behaviour. If agents have the opportunity to bet upon A occurring (which he or she favours) with a reward of £ if A occurs, then they will be prepared to buy the opportunity to make such a bet up to £. Whereas if they thought that the odds of A occurring was -, then they would only be prepared to offer up to £ for the bet so that their maximal expected loss would be  (expected winnings minus cost of buying bet). Deliberators can make propositions concerning the occurrence of subjectively feasible actions true. If that’s right, then deliberation is incompatible with the only probabilities that there would be grounds to assign (Levi (), pp. –). The problem with this argument is that there are no grounds for supposing that the probabilities so attributed reflect the probability agents give to the action before making it rather than the probability they attribute to the action after having already, in effect, decided to do it. Agents would be rational to factor in what they can ensure is the case before setting the price of being able to make the bet. In which case, it is no surprise that they will attribute the probability  (or ) to the action. It doesn’t indicate that there cannot be probability values in between  and  for their actions prior to the decision (Joyce (), pp. –). In which case, these probabilities aren’t swamped by the probabilities revealed by the agents’ betting behaviour described above.

   



There is also a question mark over the first component of Levi’s position, namely his characterization of agents as not making the smugness assumption. He holds that, while agents may believe that they will make the rational choice prior to deliberation, when they deliberate they no longer believe that they will. Probabilities relating to what they may decide, given their decision-conducive beliefs and desires, on the assumption that they are rational don’t hold. How can this belief be so speedily abandoned when deliberation is undertaken and on what grounds? How is it restored when deliberation is over? These are questions we would do well to avoid if another position is available which captures the plausible features of deliberation to which Levi points. A more moderate position is that, when we deliberate, we set aside the belief that we will decide on the rational thing, although we still retain it. In case this seems implausible, consider the case of calculation for the sake of comparison. Suppose I calculate (by long multiplication) what  is. I do it rapidly and arrive at ,. Somebody asks me to check this working and predict what answer I will come to beforehand. I report correctly that I believe that I will come to the answer ,. However, when I check the working, I don’t appeal to this prediction about my belief but go through the working. In the case of deliberation, my deliberation concerns the facts in the world and the values we attribute to those facts. It does not, in general, appeal to a prediction about what the upshot of the deliberation is although, for some deliberations, the basis for the prediction may be taken into account. For example, it is not the fact that, if I am a gambling addict, I am likely to backslide that has a role in my deliberation but rather my recognition that gambling is very attractive. Just as undertaking the calculation doesn’t mean I have abandoned the belief about the answer to which I shall arrive, so the deliberation doesn’t mean I have abandoned the belief about the rational outcome of the deliberation. Instead, the process in which I am engaged in both cases does not draw upon it. The belief is available to be drawn on if one needs to deliberate about another issue at the same time upon which the outcome of the first deliberation bears (e.g. see Ahmed (), p. ). Just as these more specific beliefs that, according to Levi, undermine deliberation are set aside, so is the general belief that I will decide on the rational thing to do. It is not part of the explanation of why my deliberation has the structure it does. The more moderate position rests upon deliberation being transparent. It draws on the fourth source of the probabilistic independence of decision and action on conditions, outside of the agent’s prior beliefs and desires, from the perspective of the agent identified earlier. Indeed, although more moderate in one sense, this source of probabilistic independence applies to the agents’ beliefs and desires too. According to this position, we don’t take our prior mental states to provide evidence for a decision unless the decision concerns what we should do about being in those mental states. To go back to the case of the gambling addict, suppose they are deliberating over whether to enter the casino. The nature of the deliberation will focus upon to what the gambler attributes value and his or her means of obtaining it. Predictions about what his or her decision is likely to be, for example, based upon all the times he or she has backslid in the past, have no role in settling whether or not to go in (Moran (), pp. –). The exception will be situations such as whether it is wise for an



, ,   

agent to pass by a casino given that the question of whether to go in will then arise. Then a fact about one’s states, and what it is likely that they will engender, will be an input into the decision the agent should make. Recognizing that deliberation is transparent in this way doesn’t necessarily rule out there being probabilities of making such and such a decision from the agent’s perspective, even in the standard case. Something that is extremely attractive makes a decision in favour of it more likely to happen given certain beliefs. Dropping the assumption that you will make the rational choice, as Levi proposes, doesn’t remove the fact that, while one is deliberating, with such and such beliefs and desires as inputs and, in fact, inclined to rationality, the consequence will be that a certain decision seems more likely to occur. So, by itself, it is questionable whether the transparency of deliberation establishes the postulated probabilistic independence. All it does is reject a particular mode of presentation of probabilistic dependence, namely that expressed in terms of certain mental states making certain decisions and actions more likely. It explains why the smugness assumption plays no role. The particular type of first-person authority we have with respect to beliefs about our decisions and actions brings a second important element to the agent perspective. There are potentially two aspects to it. The first is that, given standard assumptions about the workings of the agent’s mind and body, if the agent believes that they will decide to do A and/or believes that they will do A, then the agent can make that belief true by so deciding or acting. Such beliefs are justified by agents’ capacities to decide and act. This is one sense in which the basis for the beliefs is partly non-observational and non-evidential even if some evidence is required in order for agents to know that they are capable of making these beliefs true in the circumstances (Anscombe (), pp. –; Velleman (), pp. –; Joyce (), pp. –; Price (), p. ). The beliefs are partly self-fulfilling. The second aspect of the first-person authority is that, in deciding and acting, we know what we are up to. It is part of having control over these activities that we know the direction in which they are going prior to them being fulfilled. As a result, prior evidence that we will be making such and such a decision, or act in such and such a way, is superseded, if we believe we will decide otherwise and, thus, from the agent’s perspective, the decision, and resulting action, is independent of the evidence that the decision will be made one way or another. For these reasons, we don’t take our decisions and actions as evidence for our prior states. The two aspects identified make the probability of the decision and action independent of the agent’s prior mental states (see Ahmed for scepticism about this second aspect of the agent’s perspective, Ahmed (), pp. –). The disagreement with Levi’s position is over whether betting behaviour is a means of accessing the probabilities that agents attach to actions in the way sketched earlier. The primary contribution of the two aspects of first-person authority identified is to characterize the sense of probabilistic independence of decisions and actions from the antecedent conditions that hold in agents. However, there is also a confidence in what we are up to that will be reflected in a high credence in the decision or action occurring even though it is unclear how this might be measured for the reason mentioned earlier with respect to Levi’s position.

   



These are observations about the perspective of the agent. So it is no objection to the position that if, in fact, such and such mental states make a certain decision have a certain (objective) probability, say ., then the self-fulfilling character of our beliefs about our decisions and knowing what we are up to, will not differ in the subjective probability they confer upon the decision and subsequent action in normal circumstances in which agents have the capacities they take themselves to have. The issue is what these features of agency do to the credence an agent has in the decision he or she will make given prior mental states and conditions in the world. The suggestion is that although the values may coincide, from the agent’s perspective, the probability of the decision and action will not seem due to antecedent conditions in the agent. Likewise, then, their decision, and subsequent action, does not change the probability of the agent being in a prior condition such as a pre-migrainous state. The observations provide an answer to the charge that the verdicts supplied by this appeal to the agent’s perspective in Newcomb problems, and elsewhere, would draw on the intuitive plausibility of the verdicts supplied by causal decision theory, that is, taking into account the value of our acts as means to ends rather than news about what is the case (Papineau (), p. ). While this may be a consequence of the observations, the intuitive background is a certain conception of ourselves as agents. Ahmed objects to this approach that we should distinguish between two readings of I will do O (or as he puts it, I am going to realize O). The first is as an expression of intention. The second is as a statement about the future. He suggests that the point about the transparency of deliberation applies to the first of these but not the second. In expressing what we intend, we should only focus on facts about the world and the values we attribute to them. By contrast, our credence concerning what will occur should also take into account the probabilities we attribute to what we will do in virtue of our prior mental states and extra-mental condition (Ahmed (), pp. –). Although predictions about our future states must play a role, it is a mistake to characterize it in terms of the distinction just given. If gambling addicts attach high credence to their backsliding, then their decision not to go inside the casino cannot raise their credence to their not going into the casino. The conditions under which deciding to do A yields high credence that one will do A are not met. On the other hand, when agents do not have high credence that they will backslide, then the credence they attach to, say, going in the casino is extremely high simply in virtue of the fact that they have decided it. The high credence is independent of any credence that the past mental events and extra-mental conditions of the agent might provide. So transparency applies to both senses of the proposition that Ahmed identifies. The role of predictive beliefs in deliberation is rather to be characterized by whether or not the subject gives credence to the conditions that indicate the failure of their agency (e.g. Hampshire (), pp. –). In combining these two aspects of the perspective of agents, we have a way of analysing the talk of effective means without relying upon it being the case that, in fact, an agent’s actions are probabilistically independent of their anterior states. Moreover, the conditions we have identified are ones that would also hold for agents in which it is a fact that their actions are probabilistically independent of their anterior states because there is genuine agent causation. So a common minimum



, ,   

condition for an asymmetry has been identified that does not rely upon the more substantial metaphysical picture with which we began discussion of the perspective of agents. Although I have focused upon these two elements—the tickle defence and the perspective of agents—separately, as I noted, they may be combined to provide a more effective overall defence of evidential decision theory. It is arguable that the agent perspective only reflects one central aspect of our experience of ourselves as agents. A second part of self-reflection is working out the consequences of the recognition that we may be addicts, prey to biases, and so on. This recognition often results in an attempt to adjust the activity of deliberation described above. For example, do different evaluations of the same behaviour in others as, in some way, attractive or otherwise reflect gender stereotypes at work concerning how individuals ought to behave? Should the gambling addict think again about their positive assessment of entering the casino to appreciate the architecture and attractive atrium? In these cases, though, reflection on how our addictions and biases may manifest themselves will be revealed in tickles that, antecedently, might not have been appreciated to be such. The combined approach is to adopt different strategies to different cases. To the extent that a tickle is obvious, then causal information is an input into agents’ decision-making so the verdict is no different from causal decision theory. When no tickle is obvious, then the features of the agents’ perspective I have characterized are in play and the antecedent conditions of the agents are taken to be probabilistically independent of the agents’ decision and action. The upshot of the discussion in this section is that there are grounds for supposing that we can capture the idea of an effective means via evidential decision theory. There are commitments involved in this defence that makes it advisable to look at the other side: causal decision theory. In fact, we shall see that a problem that causal decision theory faces is compounded for any evidential decision theory that draws upon the agent perspective as part of its defence.

.. Causal decision theory, ratification, and instability Causal decision theory draws upon agents’ information about the causal dependencies that hold in order to evaluate how an action raises the probability of an outcome. However, it faces problems when an agent’s decisions or actions seem to provide information about these causal dependencies (Gibbard (), p. ; Egan ()). One example is the following. I am deliberating over whether to push the button accurately labelled ‘Kill All Psychopaths’. I judge it would be much better to live in a world with no psychopaths. Unfortunately, I’m also convinced that if I were to press the button, I would be a psychopath. I prefer to live in a world with psychopaths than a world without psychopaths including me (Egan (), p. ). The problem for causal decision theory is that in pressing the button I don’t cause myself to be a psychopath. Learning that I am one is just news about what outcome will occur. So the comparison will be between a world without psychopaths and a world with one. In which case, the charge is that causal decision theory proclaims that it is rational, given my preferences, to press the button (e.g. Egan

   



()). This seems to be counterintuitive because it recommends what, by my own lights, is worse. This type of case has the following structure. Button includes me Psychopaths killed including me

Psychopathic state

Pressing button

Figure . It differs from the medical Newcomb cases described above by making the antecedent state also a cause of the outcome of the action. Interestingly, though, it makes this kind of case plausibly much more like the initial statement of the classic Newcomb problem. Here is how we might diagram it. Places £1,000,000 Obtains £1,000,000

One-boxer

Chooses one box

Figure . The reason why it seems rational to two-box is that, given that the money has been placed, one might as well take all that is available. Whether it has been predicted that the agent is a one-boxer or a two-boxer, they will get the most money by taking what’s in both boxes. The choice of two-boxing dominates the other option. However, the same dominance reasoning does not apply to the outcomes of pressing the button. From the perspective of causal decision theory, the right way to analyse the situation is as follows.

Table . Causal circumstances

One box

Two box

Predicted two box Predicted one box

 ,,

, ,,

Table . Causal circumstances

Push button

Don’t push button

Psychopath

World without psychopaths and your own death

World with psychopaths but you are also alive

Not-psychopath

World without psychopaths

World with psychopaths



, ,   

In both cases, we have two distinct causal circumstances causally independent of the agent’s decision, the prediction and placement of the money in the classic Newcomb case, the question of whether the agent is a psychopath in the psychopath’s button case. If the agent knows that probabilities generated by each causal circumstances remain relevantly the same for the acts in question, then they can use them to weight the expected values of the various actions in the different circumstances. Even if the agent knows that they don’t remain relevantly the same, this may not matter if dominance reasoning applies as it does in the classic Newcomb case (Joyce (), p.  also makes this point). However, if the agent knows that the relevant probabilities may change, for example, by increasing the chance of your own death, then causal decision theory provides no recommendation for the situation at hand (for example, Gibbard and Harper’s comments about the death in Damascus case, Gibbard and Harper (), p. ). The claim that causal decision theory implies pressing the button rests upon the assumption that it doesn’t take the agent’s knowledge that the relevant probabilities generated by each causal circumstance will be different as, itself, relevant to the rationality of the decision. This would be a strange position for a causal decision theorist. It is not implied by its rejection of appeal to the news value of actions as a contributor to determining an action’s expected value (cf. Lewis (b), pp. –). If it were taking into account news value, then causal decision theory would support one-boxing and not pressing the button. Instead, the point is that if, by the agent’s lights, there will be further information that undermines assignments of expected value given the causal circumstances presumed to be in play simply as a result of making what seems to be the right decision, then this needs to be taken into account. As dominance reasoning does not apply in this case, and the information about the causal circumstances that hold fluctuates corresponding to whatever decision is made, causal decision theory fails to make a recommendation to press or not press the button. Proponents of evidential decision theory may take the inclination to press the button (or otherwise) as a tickle providing information concerning the causal circumstances that hold for some versions of the case described. Such a response would be available to causal decision theorists too. However, the envisaged case is one in which only one’s final decision, one way or another, reveals whether or not one is a psychopath, not one’s inclination which may not be finally carried out. If evidential decision theory appeals to the agency perspective to deal with medical Newcomb cases resistant to the tickle response, then it has an exactly similar problem with the case just described. Since, according to the agency perspective, there are no probabilities attaching to a decision given the agents’ prior mental and extra-mental conditions, when I am deliberating about whether to press the button, there is no probability of my being killed as a part of the button pressing. Indeed, if anything, the problem is slightly worse because, if what I have said is right about causal decision theory, it makes no recommendation without additional reasoning such as the dominance considerations that favour two-boxing whereas it is plausible that this version of evidential decision theory recommends that I should press the button if I start with the assumption that I’m not a psychopath.

   



A distinctive feature of the psychopath button case is that either decision is not ratifiable in a certain sense. Consider the following principle of ratification. An agent can rationally perform act A if, if he or she supposes that he or she decided to do A, there is no alternative B which would then be preferable. B is preferable to A if its maximum expected value is greater than A’s (Jeffrey (), pp. , ; Joyce (), p. ; Egan (), p. ). My decision to push the button is unratifiable because the circumstances that would hold if I made the decision would result in a high probability that I would die (along with the other psychopaths). Likewise, though, my decision not to push the button would be unratifiable. If I decide not to push the button, and so I’m not a psychopath, then it would be much better to push the button and live in a psychopath-free world. From your perspective, however you decide, it will then seem the alternative would have been preferable. The principle of ratification just described is the most natural one to endorse to capture the idea that the credences upon which we act should not be shown, by that action to fail to conform to the objective chances of the outcomes. Rational action can only be understood in terms of a stable basis of causal information. My earlier suggestion was that while subjective decision theory captures something that objective decision theory fails to capture, there is a connection between the two. Satisfaction of this obvious principle of ratification is a plausible way of articulating what this connection should be. This is one reason for thinking that the failure of causal decision theory to make a recommendation in this case—given how I have described it—is the correct verdict. We have a case of self-undermining deliberation. Some are tempted by the thought that the correct decision is that I should not press the button. Sometimes it is conceived of roughly in the following way. If there is no ratifiable decision, then we should look to see which agent I’d rather be, the psychopath who pressed the button or the gentle soul who did not but lives in a world of psychopaths (Egan (), p. ; Gustafsson (), pp. – inherits this feature). Of course, the answer is the first. But my decision in this case can’t make me either the psychopath or the gentle soul. My preference for one rather than the other reveals to me what news I would rather have about the person I am. It is thus, if one is a clear-headed causal decision theorist, nothing that should be behind the evaluation of one’s decisions to act. News one would prefer to receive is no way to try to conform our subjective credences with objective probabilities. There is, let us suppose, a fact about the way I am. If the very low credence I attribute to being a psychopath reflects the objective chance of me being a psychopath, then there will be a correct decision for me to make by the lights of an objective decision theory. If I am not a psychopath, then even if the chances of me being a psychopath are high if I pressed the button, in fact, the right choice would be to press the button. Subjective decision theories of the form we have been considering try to capture what the right decision is from the perspective of the agent. In the circumstances of the Egan case, what we learn is that no decision will seem right from the agent’s perspective if one is a clear-headed causal decision theorist. Each attempt at getting one’s credences more in line with reality will seem, from that perspective, to be undermined.



, ,   

Some opponents of this defence of causal decision theory say that it leaves causal decision theory in a situation where it has no recommendation, just continual vacillation, in circumstances where it should make a recommendation. By the lights of the argument developed here, this is a mistake. There is no answer to the question of whether one should press the button from the agent’s perspective because agents can’t make themselves into a psychopath or otherwise by the decision and can have no grounds for supposing one way or another on the basis of their decision. The fact that any decision will reveal that their background credence for being a psychopath is in need of updating explains why there is no answer from their perspective. There is, of course, an answer from the perspective of objective decision theory. It is arguable that the intuition that there is a right answer draws partly upon this and the fact that the potential increased risk of death is so significant. In such circumstances, we should minimize the chances of the worst-case scenario looking at both possible assignments of credence in the unstable position. The more trivial the difference between the two outcomes, the more it seems that an unstable position is the right one without appeal to this way of resolving the situation. Another candidate characterization of the connection between credence and objective probability would appeal to full information or, at least, credences formed as a result of full easily available information. For example, James Joyce favours the following (slightly rephrased to avoid introducing all of his terminology): You should act on your current expected utility only if it is based upon beliefs that incorporate all the evidence that is both freely available to you at the time and relevant to the question about what your acts are likely to cause (Joyce (), p. ). The fact that information about causal dependencies changes with my decision as to whether to press the button shows that this is not a source of information that is freely available. However, further information is freely available concerning an equilibrium point for credences. Consider the following pay-offs to pressing the button. Table . Causal circumstances

Push button

Don’t push button

Psychopath Not-psychopath

 

 

Joyce argues that when faced with this situation, the only equilibrium point for the agent is if the expected value of pushing the button is identical to the expected value of not pushing the button. The expected value of pushing the button is given by the following. UðPushing the buttonÞ ¼ Pr ðPsychopathÞ: 30 þ Pr ðnot‐PsychopathÞ:10 The corresponding expected value for not pushing the button is  from the above table. In which case, the equilibrium credence in being a psychopath is given by 0 ¼ Pr ðPsychopathÞ: 30 þ Pr ðnot‐PsychopathÞ:10

   



which makes Pr (Psychopath) = .. Joyce’s suggestion is that the result of taking all the information about one’s chance of being a psychopath, from one’s decisionmaking, is that one’s credence will be .. At which point, the expected value of both options, or a mixed action that attributes a chance for both and chooses randomly by tossing a coin, say, will be identical. If in the state of full information, the rational action is to maximize expected value, then any of these choices are permitted (Joyce (), pp. –). The understanding of full information that derives from this notion of equilibrium is unrelated to the objective chance of being a psychopath. Even if one’s choices indicate whether or not one is a psychopath, we have no reason to conclude that the values attributed to the consequences of pressing the button or otherwise reflect this chance. The appeal to full information is plausibly justified by the fact that it is more likely that our credences will conform to objective chances. This is not what happens here. So it is better to view the situation as described as one in which no decision is recommended. We can choose arationally one or the other or, if the worst-case scenario is particularly bad, act to avoid that in the way I have indicated. The upshot of our discussion is this. Evidential decision theory can provide an account of effective means that is the basis for causal non-symmetry. However, the very thing to which evidential decision theorists appeal to defend their account has the result that evidential decision theory delivers the wrong treatment of the psychopath button-pressing case. Evidential decision theorists’ reliance, in crucial cases, on the probabilistic independence of decisions and actions from the conditions in an agent is responsible for the problem. When our decisions one way or another provide further insight into the causal circumstances that are in operation, then the appeal to probabilistic independence is inappropriate. It is prima facie unsatisfactory to draw upon a non-symmetry of agency characterized by evidential decision theory, with the additional assumptions we have considered, when these assumptions provide an approximation to something that explicitly involves causal notions. It may become the basis for the charge that, in fact, the non-symmetry of agency is a causal notion. So, in .., we will consider whether an analysis of causal non-symmetry can draw upon one based in causal decision theory. The response offered will deal with the charge I’ve just canvassed too.

.. Causal non-symmetry and agency The explanatory schema with which we began this discussion was An event e₁ is a cause of a distinct event e₂ if and only if bringing about the occurrence of e₁ would be an effective means by which a free agent could bring about the occurrence of e₂. If we understand the occurrence of effective means as proponents of evidential decision theory recommend, then the idea is that an agent’s credence Pr(e₂/e₁) >> Pr(e₂) when e₁ is brought about by a free agent. The agent’s credence is not understood in terms of an appeal to causal circumstances and causal dependencies. So there is no prima facie problem with an analysis of causation that draws upon this characterization of effective means.



, ,   

The situation appears different if a causal decision theory is true. In place of Pr(e₂/e₁) >> Pr(e₂), we have Pr(e₂/e₁K)  P(K) >> Pr(e₂) where K is a characterization of the causal dependencies in play. However, in fact, there is no damaging circularity in this for the following reasons. First, K picks out the causal dependencies that the agent is representing to be the case rather than the causal dependencies themselves. There’s no immediate circularity appealing to the representation of F in order to understand F. The conditions for the successful representation of F needn’t involve presupposing something about the nature of F. Indeed, it is a familiar fact that what is required to possess a concept of X need not involve all, or even a sizeable part of, a philosophical theory as to the nature of X (.). In which case, attribution of causal beliefs to a subject need not involve appeal to the very theory that has, as a part, mention of a subject with causal beliefs. Second, the causal dependencies may be characterized in terms of the counterfactual analysis of causation so far provided where it is simply presumed that the later event is the effect, the earlier event is the cause. To recall, agents are supposed to introduce non-symmetries where there is, in fact, symmetry. This can be just by a presumption of difference that, as a result, is a genuine basis of difference. Third, in fact, we already have three forms of causal non-symmetry and the characterization of the causal dependencies may draw upon the representation of these three forms. Agents were supposed to provide an interlevel basis for a microscopic non-symmetry. They can do this while working within the macro-nonsymmetry framework. For all of these reasons, appeal to an agency non-symmetry partly understood in causal terms is not, thereby, a threat to the analysis. Likewise, an appeal to a nonsymmetry of agency understood in terms of evidential decision theory, supplemented by the tickle and agency responses, may be related to something understood in explicitly causal terms. Nevertheless, because this non-symmetry of agency doesn’t rely upon causation for its characterization, no circularity is involved. The more substantial issue is the basis of the non-symmetry and how this relates to the other non-symmetries. For example, what is the explanation for why agents take causes to be prior to effects rather than subsequent to them? The answer to this question is that agents reflect the non-symmetries introduced by the macrophenomena of which they are an element. Their capacity to intervene in one direction and use some micro-events as a means to other micro-events reflects this. I have used an agency theory of causation to make these points so far. One of the challenges that such an approach faces is that it renders causation anthropocentric. Something can only count as a cause if an agent can use it as a means to a particular event. Those events that are unable to be used as means by agents—for example, because they are too big or too small—may count as causes if the relationship in which they stand to their effects resembles in the appropriate way the relationship between effects and the events agents can use as means to them (e.g. Menzies and Price (), pp. –). The question is how to characterize this resemblance given that there are a number of different bases for causal non-symmetry. My suggestion is that we can capture the relevant similarities by abandoning the agency theory of causation and, instead, embedding the appeal to agents in the

   



characterization of a particular kind of chance non-symmetry to which the similarity weighting for counterfactuals can appeal. It will apply at the same point as the previous appeal to a primitive non-symmetry of chance did, for example, in limiting the perfect match condition. By characterizing the relevant similarity in terms of the role played in the similarity weighting for the counterfactuals that are the basis for the analysis of causation, we both provide an answer to the challenge posed to agency theories of causation but, at the same time, show that it is a mistake to take causation to be understood in terms of agency alone. Indeed, in this respect, agency would be just one small element. The agent-generated probabilities will characterize a certain kind of relationship between micro-events in the world if agents’ decisions are probabilistically independent of their antecedent beliefs, desires, and other states, in the way envisaged by certain participants in the free will debate mentioned above. Otherwise the probabilities will characterize the agent’s perspective. In the latter case, causal statements would still be true or false. There is still a fact of the matter about what the agent’s perspective is due to tickles and the transparency of deliberation. The point is simply that the truth or falsity would not be due to a non-symmetry between the microevents that makes one a cause and the other an effect. Unlike the case of primitive non-symmetric chance-raising, appeal to agentgenerated probabilities does not have priority over the other bases of non-symmetry. There are two classes of case that illustrate this point. As we have already observed, there are some cases of causes—earthquakes, black holes, friction between continental plates, the consequences of supernovas, etc.—where it is just implausible that they could be means by which agents achieve certain ends. This does not mean that there is no causal non-symmetry. Instead, it is due to one of the other bases that, thus, have priority over the verdict of whether or not there is a non-symmetric relationship. Second, as the Tooley universes which partly motivated an appeal to primitive non-symmetric chance-raising showed us, causation may run in the opposite direction to the way in which agents face. Perhaps in such worlds, there will be no sense in which agents could exist. However, to be sure about this we need to examine our experience of the past and sense that we can influence the future. I will turn to this in .. Nevertheless, in the absence of other sources of causal direction, appeal to the nonsymmetry of agency comes into play. Take the simple case of the particle travelling to produce an explosion described in ... The case is supposed to be one in which, as far as the macro-non-symmetries we have identified are concerned, involves two-way dependence. In these circumstances, agency introduces a further source of nonsymmetry defined from the agent-generated probabilities that would characterize the perspective of the agent if they were intervening upon the course of micro-events. The direction of possible agent intervention would be settled by the macroasymmetries already discussed. This is one of the ways that the non-symmetry due to agency is derivative from the others and, thus, cannot supersede them. Nevertheless, it introduces a new non-symmetry given that, at the micro-level, the macro-non-symmetries are not present but intervention by agents is still possible.



, ,   

. Agency-Motivated Account of Unity and Intervention In the previous section, we saw how the role for an non-symmetry based upon agency was more limited than those who adopt agency theories of causation tend to insist. Nevertheless, it would be a mistake to suppose that this is the only way talk of agency might provide insight into the resulting shape of what we take to be causation. Consider the similarity weighting for counterfactuals that I have defended over the course of this book so far. One aspect of it is that it seeks to keep the circumstances fixed, against which the antecedent is varied, as much as possible. It is unsurprising that this reflects very much how we conceive of our possible interventions as agents in the world. We don’t assume our intervention might only occur in very different circumstances when we are evaluating what we should do. Another aspect of it is the limitation we introduced to the perfect match condition. Saying perfect match didn’t matter if achieving it went against what the truth of the antecedent made more likely to occur, we put the focus on evaluating possible changes that we might make and not on further match. Woodward argues that similarity weightings of the type I have defended do not invariably take the truth of an antecedent to involve an intervention. Suppose that c₁ is the common cause of c₂, c₃, c₄, . . . cn and a slightly later e. c2 c3 c4 . . cn c1

e

Figure . Consider the counterfactual () If c₂ and c₃ and c₄ and . . . cn had not occurred, then e would not have occurred (Woodward (), pp. –). The charge is that the no widespread miracles condition recommends that the absence of c₂, c₃, c₄, . . . cn be obtained by the absence of c₁. In those circumstances, e would not have occurred. Yet the antecedent is not an intervention. An intervention-inspired

-     



similarity weighting, in contrast to the one defended here, obtains the right verdict, namely that () is false. Woodward’s charge is mistaken for a number of reasons. First, the truth of the antecedent, the negation of a conjunction, only requires that one of c₂, c₃, c₄, . . . cn not occur. In those circumstances, there is no reason to insist that c would not have occurred and hence that e would not. Of course () can be rewritten to capture the scenario Woodward has in mind () If neither c₂ nor c₃ nor c₄, . . . nor cn had occurred, then e would not have occurred. However, this counterfactual is not one that we would use to test whether the conjunction of elements is a cause, nor would we use it to test whether any of the elements is a cause (as the previous discussion of the asymmetry of overdetermination in .. revealed). So it is no threat to the interventionist understanding of the similarity weighting. It is certainly true that the view of the similarity weighting I have defended will sometimes make the truth of the antecedent fail to count as an intervention in the strict sense to which Woodward appeals (Woodward (), pp. –). He insists that, if c₁ is an intervention that brings about an event e, it should not change the relationship between any of the other would-be causes of e independent of c₁ (see also Earman (), pp. –; Frisch (), p. ). This may happen if a cause of c₁ (the candidate intervention) is a common cause of some other element that is incompatible with how the actual causal circumstances are set up to operate. We can try to control for this or classify the intervention as including both elements. However, as it stands, there is no reason to think intervention must satisfy this strict standard. Of course, appeal to intervention in the strict sense may be a term of art used to provide illumination into the nature of causation. However, the discussion of Hausman’s nuclear reactor case in .. indicates that this is not the notion of intervention with which we work in causal reasoning. The additional differences in causal circumstances that would hold if the antecedent is true are an essential part of our assessment of what would happen. Interventionist approaches to causation often hold that e₁ is a cause of e₂ if and only if, (i) interventions on E₁ changing its value, result in changes in the value of E, (ii) e₁ is one value of E₁ as a result of an intervention, (iii) e₁ resulted in e₂, a specific value of E₂, (iv) interventions on E₁ are outside of the system which has as elements E₁, E₂ and independent of the causal history of values of E₁ and E₂ that are part of that system (e.g. Frisch (), pp. –; Woodward (), pp. –; although the notion of intervention is weakened in Frisch (), pp. – with regard to the ‘independence of causal history’ requirement). Here ‘E₁’ and ‘E₂’ are determinable types of cause in a particular causal network. A contrast is drawn between causation understood in terms of external interventions upon systems and making sense of causation in the universe where there is no external element. The interventions of free agents on the world is taken to be one example although the idea is then idealized and generalized.



, ,   

The question is whether this introduces something distinctive that my approach fails to capture. Interventions on a system S will be the result of its own causal history outside S. These facts about the universe are then related to specific facts about the relative isolation and independence of the system S, and the elements within it. It’s unclear why this fails to be captured by the perfect match condition and the independence condition. Both suggest that the change—the intervening cause—will have consequences that don’t affect other elements of the system. If identifying systems within the universe help in the characterization of the role of cause, there is no reason to reject the idea that facts about the universe, independently of talk of a system, may be the basis for causation. That is what I have sought to provide with the particular account of the similarity weighting for counterfactuals. Proponents of an interventionist view sometimes talk in terms of possible interventions that reveal the asymmetry of the causal model upon which the intervention is made. The relevant possible interventions are often envisaged to be counternomic (e.g. Frisch (), pp. –; Earman (), pp. –). If there is a non-symmetry in the causal model, then this will be captured in primitive non-symmetric chanceraisings. It is hard to see how the intervention plays a role in capturing the nonsymmetry over and above the non-symmetries of primitive chance-raising. In which case, given that the similarity weighting defended embeds the non-symmetries in question, there is no further role for appeal to interventions. Recognizing the way in which the similarity weighing reflects the character of interventions does not mean that it would be more illuminating to talk in terms of interventions. As Woodward acknowledges, if we did so, we would not have the possibility of a reductive analysis of causation in the sense that I have been defending (Woodward (), pp. –). Nor does an account which fails to talk explicitly of interventions fail to have an explanation of the significance of our notion of causality. The similarity weighting for counterfactuals simply articulates, in reductive terms, the weighting that is significant because it enables us to obtain the right results for our judgements about interventions. Any justification of the importance of the notion of intervention, and in particular, those interventions by agents, provides a justification for the similarity weighting together with the analysis of causation I have adopted. The distinctive contribution of intervention by agents, which I identified in my appeal to agent-generated probabilities in .., is far more limited than interventionist approaches urge.

. Causes Usually Precede Their Effects One of the platitudes about causation identified at the beginning was that (P)

Metaphysically necessarily, causes usually precede their effects.

Any theory of causal non-symmetry has to explain why (P) is true or provide good reason for revising this claim. If I had coupled my counterfactual theory of causal non-symmetry with the claim that counterfactual non-symmetry was just based upon a non-symmetry of overdetermination, the independence condition, and the non-symmetry of agency, then this section of the chapter could be quite quick. Appeal to the existence of irreversible thermodynamic processes would characterize

    



temporal direction and explain how this coincided with the other asymmetries. Causes would usually precede their effects because the counterfactual non-symmetry in terms of which they are characterized derives from something that is a plausible source of temporal direction. I don’t mean to suggest that this approach is without its critics, but I will focus my main attention on the consequences of allowing that causal non-symmetry may also derive from a primitive non-symmetric chance-raising. Here appeal to thermodynamic asymmetry does not help because it is not guaranteed to be present. The inverse universe is one example. Nor is it possible to adopt a temporal theory of causal non-symmetry and simply stipulate that causes precede their effects. Two points are relevant here. First, we would have no explanation of why this terminological decision also made causes means to, and explanations of, their effects rather than vice versa. Second, there would be no guarantee that such an appeal would pick out the same events as the other non-symmetries when they are relevant. Instead, I compare two ways of dealing with the problem with a third way that I favour. The first is a causal theory of temporal precedence—discussed and criticized in ... The second draws upon a de facto asymmetry of entropy. I discuss it and my preferred option in ...

.. Causal theory of temporal precedence According to proponents of a causal theory of temporal precedence, something like the following is true. (T) Metaphysically necessarily, t precedes t’ if and only if there is some event or fact c at t which causes some event or fact e at t’ (Mellor (), p. ). Taking causation as primitive, it is possible to construct a temporal ordering of events or facts. This formulation of the theory seems to be committed to time instants. It resolves the problem of the temporal relationship between events, or facts, which don’t stand in causal relations to each other by making them share the same time instant with those which do. I shall not be concerned to assess this part of the theory. I’m just interested in whether causation can be the foundation of temporal order. If a causal theory of temporal precedence were true, we could explain the fact that causes usually precede their effects in terms of it. When causal non-symmetry is based upon the non-symmetry of overdetermination or the independence condition, the causal theory of temporal precedence explains why these non-symmetries line up in the temporal direction they do. They are the basis of causal non-symmetry that, in turn, grounds temporal precedence. When causal non-symmetry is based upon primitive non-symmetric chance-raising, then we don’t line the non-symmetries mentioned just a moment ago with temporal direction. Instead, we explain why a primitive non-symmetry of chance generates temporal precedence. The causal theory of temporal precedence is incompatible with those who have argued that all causation is simultaneous. However, the arguments offered for this position are not plausible. One focuses on the explanation of the temporal gap between cause and effect. We may put it as follows. Let c₁, c₂, . . . cn be the direct causal circumstances for e. By that I mean, there are no causal intermediaries



, ,   

between c₁, c₂, . . . cn and e. Suppose, further, that by t, c₁, c₂, . . . cn have all occurred. Then either e occurs at t or later than t. No explanation is required for why e occurs at t because by then all of c₁, c₂, . . . cn have occurred. A further explanation is required if e occurs later than t. Therefore, all causation is simultaneous (Mumford and Anjum (), pp. –). First, let me make a general point about the need for explanation. If causation involves no more than a counterfactual supporting regularity between two distinct entities of a certain type, then there is no reason why this should require that the entities in question occur at the same time. When c₁, c₂, . . . cn have occurred, all the conditions are there for e to occur. However, e’s time of occurrence will be whatever time the regularity has involved. If e occurs at t + n, then the only explanation required for its occurrence at t + n is the fact that the regularity involves events of type C₁, C₂, . . . Cn occurring at t, and an event of type E occurring at t + n. Suppose, though, causation involves some kind of necessitation (or productive force) in a way we shall discuss in more detail in Chapter . There is no particular reason why this necessitation is any easier to understand if the cause exists at the same time as the necessitation operates. The fundamental puzzle is how one entity can have an affect on a distinct entity. When all c₁, c₂, . . . cn have occurred at t, why should some distinct thing, e, occur? There is no problem if e is the occurrence of a relational property that c₁, c₂, . . . cn have all occurred but that’s not what e is. Presumably, the answer involves appeal to the necessitation c₁, c₂, . . . cn supply, perhaps in virtue of the laws that hold of them or the powers they possess. But there is no reason to suppose that this necessitation is temporally limited to the moment that all of c₁, c₂, . . . cn have occurred. Necessitation now is no more explanatory than necessitation in five minutes’ time. In which case, the only explanation that is required is the nature of the necessitation itself (for a related but more circumscribed point about probabilistic laws Maslen (), pp. –, see also Ehring (), pp. –). To suppose otherwise is to take causation to be all about one entity making spatiotemporal contact with another. Causal theorists should not commit themselves to taking this to be a necessary truth about causation. Indeed, taking causation to be simultaneous in such cases implies a contradiction. Consider the case of one billiard ball hitting another stationary ball. The first ball has a certain momentum, m, it partly loses to the second ball in order for the second ball to move off. If this causal relationship is simultaneous, then all of this happens at (say) time t. In which case the first ball both has m and fails to have m at t, just as the second stationary ball both does not have, and then has, a certain momentum as a result. To avoid the contradiction, the time at which the first ball possesses m must be distinct from the time at which the second ball obtains a momentum. So this case of causation is not simultaneous (Le Poidevin (), pp. –, Le Poidevin (), pp. –). Huemer and Kovitz seek to avoid this argument by claiming that the impact is not a case of direct causation. There’s an intermediate event of ball one’s momentum continuously decreasing and ball two’s continuously increasing (Huemer and Kovitz (), p. ). They dub this the collision event. But, it is hard to see why this strategy won’t apply to any candidate case of direct causation. There will always be an interaction event. Allowing the existence of such an event doesn’t show that the case

    



is not a case of direct causation. It exists as a result of the direct causation in question. So the contradiction point stands for cases which involve impact in the way described above. To understand the temporal relationship between the first ball’s impact and the second ball setting off, let a closed interval of time from t₁ to t₂ include both t₁ and t₂. Following Mellor, we can represent it by [t₁, t₂]. An open interval of time that includes neither but all other times between would be represented by (t₁, t₂). Halfopen intervals are [t₁, t₂) and (t₁, t₂]. These reflect the fact that if time is dense, then there is no first instance of time after t₁ (Mellor (), p. ). With this machinery in place, we have the following relationship. Billiard Ball ’s impact [t₁, t₂) causes billiard ball ’s motion [t₂, t₃]. There will be no temporal gap between the impact and the motion of the balls since there is no instant of time separating them (Mellor (), pp. –). Nevertheless, they are not simultaneous and, hence, no contradiction arises. Another argument for all causation being simultaneous relies upon three claims. First, time is continuous: between any two instants of time, there is a distinct instance. Second, there is direct causation. Third, there is no action at a spatiotemporal distance. Suppose that a direct cause of e, c, is at t₁ and e is at t₂. By the continuity of time, there is an instant of time between t₁ and t₂. In which case, c and e involve action at a spatiotemporal distance. The only way that this can be avoided is if t₁ = t₂ (Huemer and Kovitz (), pp. –). We have already seen that there are no grounds for denying action at a spatiotemporal distance. In addition, the machinery we have used to characterize spatiotemporally contiguous causation can be used to explain how there is no instant of time between c and e. The claim is that for any such instant, the identified cause will occupy it. There is also a third objection to this argument. The argument takes time to be continuous but not causation. Why should we endorse this? An alternative is to take causation to be continuous too and deny that there is any direct causation (e.g. Maslen (), pp. –). The analysis I have provided deliberately avoided appeal to direct causation for this reason. This brings me to the standard objection against simultaneous causation: if causation is simultaneous, how can there be causal chains extended in time (Hume (), p. ; Taylor (), p. ; Ehring ())? Some have sought to avoid the problem by arguing that causal processes don’t involve chains of events but, instead, non-causal persistences which interact simultaneously (e.g. Dummett (), pp. –; Brand (), pp. –). For example, when one billiard ball is travelling at uniform velocity to hit another, this process is in need of no causal explanation, although its initiation by being struck by a cue is, and is a case of simultaneous causation. It is hard to see the motivation for this. While it may be true that the persistence of a process needs no further explanation, apart from the nonintervention of anything that might disrupt the process, the process would not persist at time t + Δ in the way it is, if the process had not been occurring in the way it was at t. We can decide not to call that causation if we like but all the same issues arise as to whether persistence must involve simultaneous links or can involve links to subsequent times.



, ,   

For these reasons, there is little to be said for the claim that all causation is simultaneous and, thus, a clean argument against (T) is not available. The principal difficulty for proponents of (T) is that while most are prepared to accept that, metaphysically necessarily, causes usually precede their effects, many think that sometimes causes may occur at the same time as their effects or temporally prior to their effects. Proponents of a causal theory of temporal precedence argue that these intuitions are mistaken. Here the argument takes two forms. First, there is the treatment of particular cases and appeal to the laws that hold in our world. Second, general considerations are offered. One case that has been discussed involves an electrically charged point particle’s influence upon an electrostatic field. Suppose the particle is at space-time point st. Then the worry is that in order for there to be no unmediated influence on all points absolutely later than st, the particle will have to influence the electrostatic field at st. This would be a case of simultaneous causation. A standard response is to argue that space-time is dense. Hence, for any point in the electrostatic field, say, st + Δ, there will be an intermediate point between it and st such that the electrically charged point particle interacts with it (Mellor (), pp. –, (Mellor (), pp. –). The suggestion will work in possible worlds in which space-time is dense but the density of space-time seems to be a contingent truth. In worlds in which spacetime is not dense, and there are electrostatic fields, the problem will still be there. If the causal theory of temporal precedence were right, we would have to conclude that both the particle at st simultaneously interacts with the field and temporally precedes the point of interaction. This is not possible. Given that (T) claims a metaphysically necessary connection between temporal precedence and causation, without a way of ruling out non-dense worlds with electrostatic fields, the objection stands. The case just discussed concerns alleged simultaneous causation between spatiotemporally coincident facts. For spatiotemporally distinct cases, proponents of the causal theory of temporal precedence may appeal to the special theory of relativity. Suppose I push a pencil on my desk at the blunt end and the other end of the pencil moves as a result. Mellor claims that this is not a case of simultaneous causation because objects aren’t perfectly rigid. If the pencil end moves at time t, the pencil compresses a little and the pencil tip moves at time t + Δ. However small Δ is, there will still be some time difference between the cause (the pencil end moving) and the effect (the pencil tip moving) (Mellor (), p. , (Mellor (), p. ). If the pencil were perfectly rigid, then pushing the pencil at one end results in a simultaneous movement at the tip only if a signal—the shock wave—is transmitted from one end to the other faster than the speed of light. But, given the special theory of relativity, accelerating a signal from rest to a speed faster than the speed of light would require an infinite amount of energy. As its speed approached that of light, the mass of the signal would approach infinity. Moreover, Mellor argues, whenever there is simultaneous causation between two spatiotemporally distinct facts in one frame of reference, there will be backward causation in another frame of reference and backward causation is impossible. I will come to Mellor’s argument for the latter

    



claim in a moment. But first I just want to underline the limitations of the points so far. They don’t establish that simultaneous causation is metaphysically impossible but, at best, that it is nomologically impossible, independent of special considerations drawn from the metaphysics of laws which I argue are, themselves, contingent (see ..). First, the reasoning depended on the special theory of relativity and there is no reason to suppose that it is metaphysically necessarily true. Second, there seem to be peculiar cases that avoid conflict with the special theory of relativity. A perfectly rigid pencil, which travels as a matter of law at a continuous superluminal velocity, would be one example. The velocity of the end of the pencil is a cause of the velocity at the tip. The relevant clauses of the analysis of causation would be satisfied. The causal connection in question would not involve acceleration through the speed of light transmission of signal from end to tip in the circumstances envisaged because the superluminal velocity is not changing. Mellor has contested the claim that he needs the special theory of relativity to be metaphysically necessarily true for his reasoning to be effective (Mellor (), p. ). His argument seems to be this. If simultaneous causation between spatiotemporally distinct facts is possible, then backward causation is possible. One such case would be a possible world in which the special theory of relativity holds. But backward causation is not possible. Hence simultaneous causation is not possible. There is no appeal to the metaphysically necessary truth of the special theory of relativity in this argument. The support for the proposition that backward causation is not possible is derived from the argument to be considered below. Nevertheless the argument appears to rely upon the following premise. If simultaneous causation between spatiotemporally distinct facts is possible, then simultaneous causation is possible in a world in which the special theory of relativity is true. It is open to somebody to deny that this is true. They could appeal to Mellor’s argument that backward causation is impossible to demonstrate that, in worlds where simultaneous causation would imply backward causation, simultaneous causation is not possible. As we shall see, though, the argument against backward causation is ineffective. The general considerations against simultaneous causation are due to Mellor. The most compelling train of thought draws on his rejection of what he calls loops of causability: the possibility of two-way interaction (of which backward causation is one case) (for further discussion of the other considerations see Mellor (), pp. – and Noordhof (), pp. –). Mellor’s argument relies on two claims. The first is that it is possible for two events, e₁ and e₂ (or, in his preferred ontology, facts) to interact, if they are spatiotemporally coincident, in virtue of e₁ being F and e₂ being G. The second is that, if that is possible then it is possible for there to be a loop of causability and, indeed, causation for some cases in which e₂ is F. For then, the conditions under which event e₁ is a cause of e₂ in virtue of being F will also make e₂ a cause of e₁. It is conceivable that there is some further factor that will make causation hold one way but not another. However, it is not the case that there must be a further factor. The properties of these events plus their spatiotemporal



, ,   

contiguity is sufficient, in at least some circumstances, for there to be two-way causation. The possibility of this kind of simultaneous causation turns on whether loops of causability are impossible as Mellor claims. The case against simultaneous causation collapses into the case against backward causation. His argument rests on the claim that (Chance Independence) For any cause c and effect e, the chances of e given c and not-c respectively are metaphysically independent of the chances of c, with and without its causes, and metaphysically independent of the chances of e’s effects, with and without e (Mellor (), p. ). It proceeds as follows. Suppose C-type events and E-type events stand in a loop of causability. Given (Chance Independence) we could assign arbitrary values for the chances which the presence or absence of a C gives an E and which the presence or absence of an E gives a C. For instance, suppose that there are  million Cs, and  million not-Cs and suppose that the chance of an E if there is a C is . and the chance of an E if there is not-C is .. The law of large numbers asserts that, for all p, p(X) entails f1 (X) = p. In other words, chances entail hypothetical limiting frequencies. This would mean that it is almost certain that there would be around  million Es and  million not-Es. Suppose, further, that the chance of C given E is . and the chance of not-C given not-E is .. That would mean that it is almost certain that there would be  million Cs and  million not-Cs. Mellor claims that this is a contradiction (I take the figures from Mellor (), pp. –). By our arbitrary assignment of chances (licensed by (Chance Independence)), we are faced with the conclusion that it is almost certain that the distribution of Cs and not-Cs is not what it actually is. Mellor concludes that, if C and not-C give independent chances of E, then E and not-E do not give chances of C. Hence, causal loops in general, and backward causation in particular, are not possible (Mellor (), pp. –, (Mellor (), pp. –). One problem with the argument is that, as we will see in ., on only some theories of chances do hypothetical limiting frequencies entail chances. Yet, if (Chance Independence) holds of anything, it holds for those theories in which there is no such entailment. In which case, with p so understood, it is not the case that p(X) entails f1 (X) = p. Given the full assignment of probabilities detailed above, the observed incidence of Cs, not-Cs, Es, and not-Es would be unlikely but not impossible. There is no contradiction involved even in Mellor’s extended sense in which two conflicting propositions are each attached a near certainty of holding. A second problem with the argument lies with (Chance Independence) itself. It will have to receive some modification to take into account what may be needed to make for a coherent, law-governed, world with a particular time order. If chances are metaphysically independent—as opposed to (say) a consequence of the laws that hold—then they may be distributed in any fashion so that there are no regularities in the world. If, as is highly plausible, chances are determined by laws, then chances will be distributed so that in like circumstances, there are like chances. If, in addition, laws settle the time order of events, then a further restriction upon chances will be that they should not set up incompatible time orders (Mellor (), pp. , –). If

    



Mellor were right that there is a genuine inconsistency between the assignment of probabilities detailed above, there is no reason why a further constraint upon their distribution could not be that they must be compatible with the probabilities that other chances assign to the relevant sequence of events (see also Earman (), pp. –, for appeal to consistency conditions regarding backward causation). If, in fact, there is no incompatibility, the constraint is not required. We will just have little reason to make such an assignment because the actual chances are those that would make the actual sequences that hold likely. In . I will explain how the most plausible development of a propensity account of chance must recognize the distinction between chances and derivative probabilities to avoid Humphrey’s paradox. The distinction also vitiates Mellor’s argument against loops of causability here. As a result, I conclude that loops of causability are possible and, hence, that there is no reason to reject either backward causation or simultaneous causation. The arguments offered in this section do not establish that the causal theory of temporal precedence is incorrect. It is possible that it is a brute metaphysical necessity the reason for which we will never understand. My purpose has been simply to undermine the arguments that purport to show that the counterintuitive consequences of the causal theory of temporal precedence are not counterintuitive after all. That is sufficient to justify a serious look elsewhere.

.. Time direction as preponderant causal direction: causal perspectivalism and past perspectivalism Many have been tempted to relate causal order to temporal order by appeal to a third, de facto, asymmetry: increase in entropy. As I have already noted, the overdetermination asymmetry and the independence condition can be rooted in it. One pressing question about such an approach is why low entropy lies in the past and high entropy in the future. A statistical explanation of change of entropy—appealing to the fact that there are many more possible states of high entropy than low entropy and so the former are more probable than the latter—does not explain why the unlikely kind of state (as it were) is located in the past and not also in the future (Horwich (), p. ). One response to this question is to accept that there is a further explanation that is needed but to deny that this involves anything specific about the past. From this point of view, what needs to be explained is that there is low entropy at one end of the temporal dimension. From this perspective, there is an independent characterization of the past and this is coupled with an explanation of why low entropy states occur there. There are two problems with such an approach. First, it does not apply to possible cases in which causal non-symmetry is rooted in something else and either the asymmetry of entropy is not present in such a possible world or causal direction (derived from primitive non-symmetric chance-raisings) runs counter to it. Second, it leaves open the question of how the past is to be identified. It is fair enough to say that the past just happens to coincide with low entropy in our world but this is no help with the claim that in other possible worlds, causes usually precede their effects as well. An alternative that addresses both of these concerns has an advantage.



, ,   

My suggestion is that temporal direction is determined by preponderant causal direction. We start with the de facto asymmetry that in one temporal direction—call it A—there is low entropy, in the other—call it B—there is high entropy. This then sets up a preponderant causal direction. Causes are usually B-directed. The past is defined by appeal to this characteristic of causation. The future is the temporal direction towards which causes are usually directed, the past is the temporal direction away from which causes usually act. So a de facto asymmetry—by two pieces of analysis—becomes the basis for the metaphysically necessary claim that causes usually precede their effects. Note that while this might explain which direction is the past, it does not explain why there is pervasive low entropy in the first place, that is, why the majority of almost isolated segments of the universe are in a state of low entropy in one direction (Horwich (), pp. , ). However, this is an explanation that both approaches—those which take the past to have low entropy and a position like my own—need. If preponderant causal direction fixes the direction of time, then we have an explanation of why there may be universes in which the direction of time goes from high entropy to low entropy. These universes are ones in which the primitive non-symmetric chance-raisings run in the opposite direction to the typical nonsymmetries in our universe. One interesting consequence of this is that those who argue that our universe is one that contains such primitive non-symmetric chanceraisings have to explain why these coincide with the macro-non-symmetries mentioned earlier. The proposed basis for the direction of time gains in plausibility by being related to various identified asymmetries of agency with respect to the past and the future. Perhaps the two most significant of these are the fact that agents are almost invariably unable to influence the past, but can influence the future, and that agents generally have more knowledge about the past and less about the future. Call these the intervention and knowledge asymmetries, respectively. If preponderant causal direction fixes the direction of time, it doesn’t immediately follow that agents are almost invariably unable to influence the past. It could be that agency is a pocket of backward causation. The non-symmetries that we have identified as behind counterfactual non-symmetry are the explanation of agents’ inability to influence the past. As long as they hold, then it won’t be the case that if an agent were to do A, then O would occur, where O is in the agent’s past. The asymmetries set up by a preponderance of non-symmetries in one direction are sometimes summarized as the point that there are few causal handles for agents to influence the past in the way that they can influence the future. Recognition that there may be primitive chance-raising non-symmetries does not change the picture. Agents can’t influence the past if the preponderance of these chance-raising non-symmetries line up to face the future and they will do so given the connection between past and preponderant causal direction identified. The knowledge asymmetry also has a role to play in the explanation of the intervention asymmetry but, before we get to that, we need to explain how it relates to the preponderant causal direction claim and counterfactual non-symmetry. Just as there have been attempts to root the intervention asymmetry in the universe’s initial low entropy state, so this fact has been suggested as the basis for the knowledge

    



asymmetry. The key idea is that it is responsible for the existence of records of the past (and absence of records of the future). For example, a footprint reveals order in a situation in which the entropy of the universe is increasing and so needs to be explained. This is the basis for the claim that it reveals information about the causal impact of a footfall (Grünbaum (), pp. –). There are problems of detail with regard to these explanations as well as a more general issue. On a point of detail, we can pick up information about the past—for example, a bomb blast or a volcanic eruption—without the effects themselves constituting a low entropy state (Earman (), p. ; Horwich (), pp. –). On the general point, the fact that we allow that causal non-symmetry is variably realized, and the appeal is to preponderant causal direction, means facts about a particular realization cannot settle the matter. Is there something more general that can be offered? Our knowledge about the past depends upon perception, memory, and the theories to which we appeal to go further than what is provided by experience, and remembered about experience afterwards. The appeal to theories will depend upon perception and memory for a significant portion of their justification so, for the sake of simplicity, we can focus on perception and memory. Both require that there are causal connections between the items perceived or remembered and states of the subject’s mind or brain. In recognizing this causal condition, I’m not suggesting that the perceptual or memory state itself is caused. For some, that matter will turn on whether perceptions and memories are relational states involving their objects as constituents (although even here, one might allow that piecemeal causation is going on) (e.g. Snowdon (); Child (), for discussion). The point at present is just that causal relations are required for the state to be present. If causation is required, then the asymmetry of our knowledge of the past relative to the future will depend upon the extent to which the causes predominate. The causal condition is only a necessary condition for these sources of knowledge. However, if a necessary condition for knowledge can be primarily met one way, then this will be the basis for the knowledge asymmetry. It might be argued that talk of perception and memory already builds in the asymmetry. The anterior question is why we don’t have non-causal sources of knowledge about the future. An answer to this question depends upon an analysis of knowledge. The latter issue is by no means resolved. Various necessary conditions on knowledge have seemed plausible, though, and these can be the basis of an explanation for why we don’t have corresponding states regarding the future that, for a handy label, we can dub clairvoyance. For example, consider the following candidate condition on knowledge. Sensitivity:

If p were false, S would not believe that p (e.g. Nozick ()).

Suppose that the truth or falsity of p is a distinct existence from the belief that p. If p concerns something in the future, then sensitivity would normally not be met. If the future is changed in some way to make p false, S would still believe that p by the similarity weighting for counterfactuals we have endorsed. Matters would be different for sensitivity if p were about something in the past. The failure of sensitivity, and the satisfaction of it in the past, is related (given our analysis of causation) to the failure of causation to hold so much running from future to past, as from past to our current states.



, ,   

Another candidate condition on knowledge is Safety: In most nearby possible worlds, if S believes that p, then p is true (see e.g. Williamson (), pp. –). Safety does not imply sensitivity because some conditions that are required for p to be false—for example, where p is that I am not a brain in a vat—are ones which would not hold in nearby worlds. So a belief may be safe but not sensitive. For our purposes though, the observation about sensitivity will come across to safety. For many of the things we believe about the future may be false in close-by worlds and we retain the belief. The points just made are unrelated to the question of induction, namely whether, given our observations and the laws at which we have arrived on the basis of observations, we can have knowledge about the future (or, for that matter, the unobserved past). Suppose the question of induction is resolved favourably. We have knowledge of the sort just indicated. The observations just made explain why we will have commensurately more knowledge about the past than the future. Perception is a source of knowledge, memory preserves knowledge, and nothing similar is available regarding the future. I have explained why we don’t have clairvoyance to correspond to perception and memory and how this relates to the causal requirement on each. The general diagnosis is that the failure of the relevant counterfactual to hold is due to a failure of causation. There might be a causal connection between some observation and a prediction about the future but it does not have the right direction. The thing observed is not caused by the something in the future that our prediction concerns. This point in turn relates to the various accounts of causal non-symmetry I have defended and proposals that have drawn upon them. I will go through the elements in turn. If the independence condition holds, then an effect provides information that all of its causes were in place. Information about what invariably gives rise to such an effect enables a subject to interpret that effect as a record of one or other of the causes in question. By contrast, any event that is a candidate for being a pre-record of a subsequent event is not information that the subsequent event will occur because other conditions are required. Subjects who seek to know the future will have to keep track of whether these other conditions are in place (cf. Grünbaum (), pp. –). Equally, the asymmetry of overdetermination provides us with many distinct traces of a past event in contrast to the situation with regard to the cause of a future event. Of course, the existence of many distinct traces is insufficient to explain how we know more about the past than the future. We need to interpret these traces (Horwich (), pp. –). But the important point is that the asymmetry provides a basis for the asymmetry of knowledge. In the case of primitive non-symmetric chance-raisings, the consequences for the causal condition is much more immediate. Events in the future don’t affect states of the subject as revealed by the corresponding counterfactuals. Let me turn to how the knowledge asymmetry helps to explain the asymmetry of influence. The idea is that the knowledge asymmetry explains the asymmetry of intervention for agents with regard to micro-symmetrical cases. There are two

    



dimensions to this. The first is that the predominant knowledge that agents have concerns the past and what seems open is the future. As we saw in the last section, if something is up to us, while deliberating upon it we cannot know what the outcome will be on the basis of evidence. Thus if we know facts about the past on the basis of experience, or judge that such facts are knowable on the basis of evidence, then the past will not seem up to us (Price (), pp. –). By contrast, the future will not be presented as fixed. If the conditions which settle whether or not I move my arm, say, have their best evidence my actually deciding it, then there is a clear cognitive efficiency in not attributing an evidential probability to my previous state until the decision is made. This will make the decision appear undetermined and the future open. As we have seen, this reflects the genuine and distinct knowledge asymmetry discussed above, rather than just an agent’s perspective, however, it gives agents an orientation that affects the direction in which they act (by contrast, Earman (), pp. –, takes the orientation of agents to be a prejudice in favour of forward- rather than backward-directed intervention). Knowledge about the past doesn’t help us to intervene in the past whereas knowledge about the past and near present does provide information about how we might intervene so changing the course of future events. Deciding to act one way or another also provides us with well-grounded beliefs about how the future will turn out. These features go across to circumstances in which, in fact, the conditions are symmetrical. The second dimension of explanation is that creatures orientated towards the future, and not seeking to intervene on the past, are the only ones that are likely to survive natural selection. It is unlikely that there are going to be more successful creatures who follow a mixed strategy and recognize those occasions where it might be possible to intervene on the past. A consequence of these points is that there may be circumstances in which the perceived causal order is different from the actual causal order. We cannot take the perspective of agency as primary in setting causal direction (causal perspectivalism). The plausibility of the perspectival position on causation is at its greatest when the other sources of asymmetry are not present for the events we are considering and there is no predominant causal direction that privileges the position of one of the agents over the other. In those circumstances, causation becomes a perspectival relation. Nevertheless, it is not essentially perspectival. Earlier I noted that the direction of the past is determined by the predominant direction of causation. It may be that this needs some qualification. Suppose that agents only existed at one point in the universe’s history, namely when there was a local decrease in entropy. So all the creatures that ever existed were orientated away from the predominant causal flow of the universe. In those circumstances, it seems quite unclear that the past should be taken to be their future and what they call the past a mistake. An essential part of our notion of the past is that we experience and take it to be fixed (for the most part) and suppose that the future is open. It is only when this is in harmony with the predominant causal flow of the universe that I think we have a past at all. When it is not, there is the perceived past and the predominant causal flow in the other direction. There is no past but just a temporal direction. So there may be an inescapable perspectivality to the past that causation does not share.



, ,   

. Concluding Remarks The importance of agency for the analysis of causation is revealed at two points. First, it can be a distinctive, generally perspectival, basis for causal non-symmetry. Second, because the similarity weighting for counterfactuals is the basis for an analysis of intervention, one subcategory of which are interventions by agents, we can appeal to this to provide a justification of the significance of this analysis, and motivation for its structure. The first role for agency depended upon a successful characterization, from the perspective of the agent, of how one event, perhaps an action of the agent, is an effective means to another event. I defended evidential decision theory against standard objections to it by a combination of the tickle defence, where the ‘tickle’ was the decision-conducive states favouring the target action (e.g. eating chocolate), and appeal to the transparent nature of deliberation. The tickle supplies causal information when it is obvious and, when it is not, the transparency of deliberation explains why evidential decision theory comes to similar results to causal decision theory in the other cases. Unfortunately, this defence made evidential decision theory more susceptible to a challenge raised, in the first instance, against causal decision theory involving an agent deliberating over whether to push a button that will kill all psychopaths. A decision in favour would have him or her among the people affected. I argued that the proper way to develop causal decision theory has the consequence that it is justifiable for decision theory to fall silent in such a case. By contrast, the favoured development of evidential decision theory has the counterintuitive consequence that the agent should push the button. Nevertheless, I argued, even if causal decision theory is correct, this does not introduce a damaging circularity in appealing to agency to characterize a fourth causal non-symmetry. In the light of this defence, I explained how appeal to agent-generated probabilities could be used to limit perfect match in the same way that primitive non-symmetric chance-raisings did, with the result that there is a projected non-symmetry on microevents where the other macro-non-symmetries are not in play. I noted that this is a much reduced role for agency in the analysis of causation but that this limited role has some plausibility. The second role for agency concerned the characterization of what is common to these non-symmetries. I argued that the similarity weighting of counterfactuals reflects what we might think of as a generalized, idealized form of intervention by agents. What we are inclined to hold fixed when agents act, in order to evaluate the consequences of their action, is what we more generally hold fixed in thinking of the cause as an intervention in the world to change it in various respects. Attempts to differentiate the similarity weighting from the notion of intervention proved to be unmotivated. The unifying feature of these various bases of non-symmetry is that the key counterfactuals of my analysis P () If e₁ were to occur without any of the events in , then for some time t, it would be the case that, just before t, the mean value of p(e₂ at t) is x, P () If neither e₁ nor any of the events in were to occur, then for any time t, it would be case that, just before t, the mean value of p(e₂ at t) is y, () x >> y,

 



is true if e₁ is a cause and e₂ the effect but not necessarily vice versa. In the final part of this chapter, I explained how the counterfactual analysis of causal non-symmetry can capture the truth of the claim that causes usually precede their effects. This involved relating the various possible bases of counterfactual nonsymmetry with temporal direction. I explained why a causal theory of temporal precedence is inadequate. It is not that all causation is simultaneous as some urge. Arguments in favour of this claim were unsound. Nevertheless, simultaneous and backward causation are possible. I defended this claim against Mellor’s argument to the contrary. Simple appeal to a de facto asymmetry such as low entropy couldn’t explain why causes usually precede their effects either if one basis for causation involves primitive non-symmetric chance-raisings. It also left open the question of how the past is to be identified more generally. So, I suggested that temporal direction is determined by preponderant causal direction. The platitude that causes usually precede their effects doesn’t reveal so much about causation as about the direction of time. I argued that if we put together the non-symmetries I had identified, with the analysis of causation and temporal direction, we had a basis for an explanation for why agents could generally only affect the future (the intervention (or pragmatic) asymmetry) and why we have more knowledge about the past than the future (the knowledge asymmetry). It followed from my semantics of counterfactuals, and familiar conditions upon knowledge, that agents would have more knowledge of the past than the future independent of causal assumptions. This provided a further basis for the intervention asymmetry. The discussion of causal non-symmetry has provided us with the second substantial way in which causation can come in a number of varieties. In Chapter , I will turn to the third. The target now will be the different ways in which laws may be realized.

 Causation and Laws What’s the relationship between causation and laws? For many, where there is causation, there is law, with the latter being viewed as fundamental in any account of causation. Thus, John Carroll writes For example, being extremely conservative, there is this much of a link between causation and lawhood: If there is any causation at all, then there is at least one law of nature . . . c can’t cause e unless any event exactly like c in precisely similar circumstances would have some chance of causing an event similar to e (Carroll (), p. ).

I take it that under the assumption of determinism, Carroll would insist that, in precisely similar circumstances, events exactly like c cause events exactly like e. According to this view, appeal to law is needed to capture the generality which is said to be involved in causation. Indeed, some take to be one of the desiderata for a successful account of law that it capture the implicit generality while, at the same time, recognizing that causation is an intrinsic matter. The intrinsicality of causation lies behind, in their eyes, the misguided intuition that brute singular causation is a possibility (e.g. Heathcote and Armstrong ()). Carroll’s conservatism rules out one of the motivations for adopting a counterfactual theory of causation, namely that brute singular causation is possible. Brute singular causation is a case of causation where the generality does not hold and there is no law that is, in some other way, implicated. If brute singular causation is possible, then, while law may have an essential role in helping us to understand some cases of causation, it is not necessary for causation. If the key feature of causation is a certain kind of dependency, then failure to recognize brute singular causation involves a confusion of three potentially distinct issues. (i) The question of whether causation explains regularities. (ii) The question of whether laws explain causation. (iii) The nature of causation. We need strong argument to collapse these into a single view in which all causation involves laws that, as a result, explains regularities. As we have already seen, for the counterfactual theorist, the vehicle for the proper understanding of the role of law in causation is the similarity weighting for counterfactuals. And here we arrive at a puzzle. In spite of the fact that Lewis cited the possibility of brute singular causation as a reason for rejecting the regularity theory of causation, his later characterization of the similarity weighting for counterfactuals in terms of match and law violations make it very hard to see how any counterfactual theory, which appealed to it, could allow for such a case. In ., I shall discuss this A Variety of Causes. Paul Noordhof, Oxford University Press (2020). © Paul Noordhof. DOI: 10.1093/oso/9780199251469.001.0001

  



problem and its solution within our framework. This is the first element in loosening the connection between causation and law. A successful law-based account of causation might hope to undermine the grounds we have for thinking that brute singular causation is a possibility. In ., I consider a recent argument which purports to show that laws are required to deal with certain cases of causation that no counterfactual analysis could discriminate and explain why this is not so. I go on to discuss three problems with law-based accounts that suggest that, at best, they need supplementation that lets in the possibility of brute singular causation. The possibility of brute singular causation is hard to make sense of if Humean supervenience is a necessary truth. The way in which the similarity weighting is adjusted to accommodate the possibility involves an element that fails to satisfy a natural understanding of Humean supervenience. I’m inclined to take this to be an early sign that, while Lewis was keen to defend Humean supervenience, his theory of causation was not intended to rule out the possibility of non-Humean causal relations. Once we allow brute singular non-Humean causal relations, the way is also opened up to allow for non-Humean causal relations in virtue of non-Humean laws. But how can there be both Humean and non-Humean laws? My suggestion is that, in place of a law-based analysis of causation, a causation-based analysis of law is preferable. Given my operating assumptions so far, such an analysis may seem like a non-starter since the similarity weighting for counterfactuals will persist in involving an explicit appeal to laws. That is not so. The similarity weighting may mention laws but the question is whether this mention describes what is ontologically (vertically) fundamental or whether it simply grouped things in a particularly appropriate and convenient way. I shall argue for the latter. Circularity can be avoided by giving a particular vertically fundamental characterization of each of the realizations of causal laws. However, by the end of the chapter, I shall give a formulation that appeals to elements that are naturally thought of as horizontally fundamental: chance fixings. The argument proceeds as follows. There are broadly three metaphysical types of accounts of laws in the literature: regularity accounts, accounts that appeal to a primitive nomologically necessary connection between properties, and accounts that appeal to a constitutive or metaphysically necessary connection between properties. Standard discussions point to weaknesses in one type as a way to support another type. In the third, and largest, section of this chapter, I begin by discussing issues of formulation for each theory of law, particular problems they are alleged to have with regard to some distinctive features of laws, and how they give rise to certain problem cases. Having given a preliminary defence of each and some of the issues that arise, I turn to questions that, it has been argued, substantially bear on the success of one theory over another in .., .., and ... I argue that the allegedly decisive advantages in favour of necessitarian accounts, and in .. the powers ontology in particular, are ill-founded. All accounts fail to satisfy the desire for an account of laws to make causation both intrinsic and general but, it appears, there is good reason for supposing that no account can succeed in this latter respect except by fiat. Unless we find some further ground for deciding between these accounts, it seems that we are left with mutually incompatible accounts that, as far



  

as we can tell, are equally correct. If that’s right, they cannot all be accounts of law. So my suggestion is that they are accounts of how laws may be realized. As it turns out, recognition of this can help with the problem cases specific to each account. In that way, we can arrive at a more successful theory of laws. If these three theories of law are all accounts of how laws may be realized, is there something that they share? In ., I argue that the unifying property is that they are all potential patterns of causation. It is in this sense that we have a causation-based account of laws. We have a similarity weighting of counterfactuals that—at a certain level of abstraction—appeals to potential patterns of causation and, yet, counterfactuals so understood can provide an analysis of causation. There is no circularity because, for any world, there is a characterization of the similarity weighting that does not appeal to causation. We can delete mention of laws in characterizing the similarity weighting for counterfactuals and appeal, instead, to the disjunction of these various realizations of laws. To allow for the possibility of brute singular causation, reference to laws in the similarity weighting is deleted and appeal to the idea of chance fixing is put in its place. Laws are the primary, but not only way, in which the relevant chances are fixed. The approach to laws defended here has some similarities in approach with Lange’s account of laws as invariants and John Roberts’ account of laws as guarantors of methods of measuring natural qualities (Roberts (); Lange ()). Neither attempts to give a metaphysics of laws but rather identify a certain role that they play. My approach does suggest a metaphysics—assuming that potential patterns of causation count as a metaphysics—but the metaphysics supplied is not vertically fundamental but grounded in something else, the various proposals concerning law realizers that is. Nor is it horizontally fundamental if causation and chance-fixing have greater generality across various possible worlds, albeit plausibly constructed from what is.

. Brute Singular Causation In spite of the fact that the possibility of brute singular causation is cited as a principal motivation for counterfactual theories of causation, standard attempts—such as Lewis’—to supply a similarity weighting for counterfactuals don’t seem to allow for it. The problem lies in the absolutely central role played by appeal to law. The easiest way to make the point is to consider possible, but not actual, brute singular causation. Let’s return to the example with which I illustrated brute singular causation in .. I reached out and touched my host’s favourite vase, which crumbled to dust. If my touch is a brute singular cause, then, my prospective touch of which I think better is a possible brute singular cause. The problem is that there would be no reason to claim that if I had touched the vase, it would crumble to dust since it failing to do so is not a local violation of a law. Brute singular causation involves no law. Let’s now consider, in abstract, a case of brute singular causation. Suppose that in the actual world c and e occur and, although there is no law relating c to e, c causes e. By hypothesis, the conditions in which c occurs are, by themselves, insufficient for e and the laws which apply to these conditions will not apply to c causing e. In the closest worlds in which c fails to occur, then, there are no grounds for thinking that e

  



will fail to occur, although it may. Its occurrence is not contrary to the conditions holding minus c, and the laws. As far as the similarity weighting for counterfactuals is concerned, straightforward counterfactual dependence is absent. An assumption behind the problem just raised is that laws are general. There cannot be brute single-case laws. It cannot be a law that if c, then ch(e) = . (say), where ‘c’ picks out a token event. The assumption is very natural taken within the context of the best system analysis of law detailed below, in which laws are those patterns expressed by the best set of systematizing generalizations. Nevertheless, it is open to question for other accounts of law that, as we shall see, don’t appeal to systematization in their characterization. Suppose we stipulate that something plays a chance-fixing role if it takes antecedent particular matters of fact—for instance, a cooccurrence of certain particular events—and attributes to this the chance that another event will occur. Laws are plausible candidates for being chance-fixers. If laws must apply to types of antecedent particular matters of fact and attribute chances to types of events, then they are a subcategory of chance-fixers. Another subcategory will be those that apply to particulars regardless of the type to which they belong, thus supporting attributions of brute singular causation. I discuss chancefixing in more detail in Chapter . If we recast Lewis’ similarity weighting for counterfactuals in terms of chance-fixers, then the first and third conditions will now talk of the importance of avoiding big widespread violations of chance-fixers and small localized violations of chance-fixers respectively. The case of possible brute singular causation would be captured by counterfactuals because, now, the failure of the vase to crumble into dust in those circumstances would involve a violation of a local chance-fixer. In a case of deterministic brute singular causation, matters are a little more complicated. The occurrence of c would involve, in addition, the holding of a chance-fixer: if c, then ch(e) = . Thus, e would occur. However, given that we are talking of what is actually the case, there is no need to appeal to violation of local chance-fixers to get this result. In the absence of c, the conditions that hold to ensure that e does not occur (which the token presence of c worked against) would be in operation. So we would have if not-c and D, then ch(e) =  (where ‘D’ adverts to the circumstances in which c operated). This would be the corresponding brute singular absence of causation. Because the case is one of brute singular causation, there may be other occurrences of events exactly like c, c*, in the same conditions in which e does not occur and these would be cases in which it is not the case that if not-c* and D*, then ch(e) =  (where ‘D*’ is the circumstances in which c* would occur). Achieving more extensive perfect match by, in spite of the non-occurrence of c, supposing that e occurred anyway, would be at the expense of widespread law violations so that D by itself resulted in e. Thus we move to the no local miracles condition of the similarity weighting and conclude that e would not occur. The idea that e may occur in the closest not-c worlds is ruled out. Indeterministic cases of brute singular causation involve no additional difficulties. If c and e occur, but if c, then ch(e) < , then c is the indeterministic cause of e if it raises the Σ-probability of e just before e in the way indicated by the analysis given earlier. In the absence of c, the Σ-probability of e would be very much lower. As far as the analysis of causation is concerned, e may still occur. The presence of



  

indeterministic causation does not require the absence of e when c is absent so long as the Σ-probability-raising relationship holds. We have seen how we might adjust the similarity weighting to allow for brute singular causation. But are there grounds for denying that such causation is possible? . focuses on whether it is, in principle, possible that there may be a successful lawbased account of causation that provides theoretical grounds for denying that brute singular causation is possible.

. Law-Based Accounts of Causation Law-based accounts of causation insist that something like the following holds. Metaphysically necessarily, c causes e if and only if (a) there is some F and some G such that Fc and Ge and (ii) the Fs are nomically related to the Gs. That is, if c is a cause of e, then there must be some properties of c and e in virtue of which a law holds. Some philosophers prefer to characterize the relationship in terms of descriptions of c and e and take c causing e to follow from these descriptions of them and a true causal law (Davidson (), p. , fn. ). Others talk in terms of laws involving a relation of nomic necessitation between the properties F and G (e.g. Heathcote and Armstrong ()). The above formulation can be made more precise in these ways but does not need to be for the points below. The intuition that brute singular causation is a possibility can be undermined if there are theoretical reasons for supposing that causation must be understood in this way. As we saw in .. and ., the existence of laws is related to property causation though, when one property is a cause of another, it doesn’t follow that there is a law holding between these properties. However, this is only a particular type of causation involving generality. The question is whether, even in the case of causation between particulars, there must be laws at work. Some philosophers seem to take it as an a priori matter (Davidson (), p. , fn. , ()). Others take it to be an a posteriori necessary truth (Heathcote and Armstrong (), pp. –; Armstrong (), pp. –). Thus Adrian Heathcote and Armstrong write ‘The success of repeatable experiments leads us to draw the meta-inference that singular causal processes are identical with the instantiation of strong laws’ (Heathcote and Armstrong (), p. ). The explanatory utility of their account of strong laws will come up later. The success of repeatable experiments may well entitle us to draw the meta-inference that there are laws at work concerning certain processes. Laws can have an explanatory value when they are at work. However, it does not follow that causation must involve law and can only be understood in its terms. The latter cannot be established by the observation they make. Many of the grounds for the appeal to laws—for example, accounting for the nontransitivity of causation—have been dealt with by earlier discussion and defence of the counterfactual theory (Paul (), pp. –; Tooley (), p. ; Davidson (), pp. , ). Let me focus, instead, on a recently forcefully argued case for the need to appeal to laws (Maudlin (), p. –). Consider a simple world—for aficionados, a world according to John Conway’s game of life—in which succeeding states of squares are given by the values of

-   



surrounding squares. These squares are either filled or empty. There are two distinct laws relating to the circumstances specified in the  x  grids below.

Pattern A

Pattern B

Figure . Each law says that subsequent to the respective patterns, a filled circle occurs in the centre square. Maudlin claims that there is a rational debate over whether or not the occurrence of a filled circle in the bottom centre square is a cause, or an essential part of the cause, in the first of the two situations specified. If the law relating to pattern A is in operation, it is. Yet there is no difference in counterfactuals. Regardless of which law holds, the following counterfactual is false. If the bottom centre square were unfilled, the central square would not have been filled. So it is laws rather than counterfactuals that settle whether or not the filled circle in the bottom centre is a cause of the filled circle in the centre. He concludes ‘it is laws, not counterfactuals per se, which underwrite causal claims’ (Maudlin (), p. ). Within the framework of the analysis I defended in Chapter , one might take Maudlin’s argument to show that the membership of Σ must include laws, and not just events. In which case, putting pattern B law in Σ would show up the required dependency of a filled circle in the centre on the filled circle in the bottom centre of pattern A. Since my development of the counterfactual theory of causation does not entail but is only compatible with Humean supervenience, there is no problem with treating laws in this way. Moreover, recognizing the importance of laws in settling the causal structure of certain cases is compatible with both the development of a counterfactual theory of causation and the recognition that, in other cases, as we saw above and will see below, appeal to laws is insufficient. Nevertheless, it is questionable whether such a move is necessary. There are two plausible ways in which one might interpret the case. According to the first, the right way to characterize it is by the following two laws. Pattern A: It is a law that if there are filled circles in the first two columns of row  and all three columns of row , then there will be a filled circle in row , second column. Pattern B: It is a law that if there are filled circles in the first two columns of row  and the first and third column of row , then there will be a filled circle in row , second column. Under this interpretation, the pattern B law would also be applicable to the pattern A situation. It is questionable whether the centre filled circle in row  should come



  

out as a cause then. There are no circumstances in which it could be an independent causal factor from the competitor process governed by pattern B law. Moreover, Maudlin emphasizes that (as far as the laws are concerned) patterns A and B have nothing in common at all (Maudlin (), p. ). In which case, it makes little sense to ask, subsequently, whether some subelement of pattern A is proclaimed a cause by the law. But this situation should be distinguished from the situation that Maudlin has in mind which gives the following characterization to the pattern B law. Pattern B*: It is a law that if there are filled circles in the first two columns of row  and the first and third column of row  and the second column of row  is empty, then there will be a filled circle in row , second column. It is the italicized emptiness condition that stops the pattern B law applying in A and captures his idea that the pattern B law is a back-up process. Recall that, as we saw earlier, it is sometimes necessary to put non-actual events in Σ. To consider whether the filled circle in row  column  is a cause, put in Σ the event of row ’s column  being empty (not to be understood as a negative event). When we consider what would be the case if the filled circle in row  column  were not present, we would not go to the square being empty—that would be in the Σ set. Instead, we might go to there being a filled triangle in the second column of row . In which case, neither law would apply and it would not be the case that the second column of row  would contain a filled circle. The world we would be considering as a result of putting the square being empty in Σ would differ from the world envisaged by not being one in which there are only two options for any square: filled circle or empty of filled circle. However, this is no different from any evaluation of a counterfactual where we recognize that the laws will be a bit different to bring about the conditions adverted to in the antecedent. So there is no problem with appealing to it here. To generalize, then, once we make clear how the laws independently govern the envisaged circumstances, then the counterfactual analysis provided will successfully characterize what are plausibly thought to be causes. If the conception of cause I have defended earlier is correct, this is exactly what we should expect. Thus, Maudlin’s case provides no grounds for supposing that laws, rather than the particular counterfactuals we have identified, underwrite causal claims. Law-based accounts of causation also face problems of their own. The standard one is that not every scientific law is a causal law—that is, describes a relationship between variables which holds as a result of causal relations between events instantiating the properties the variables concern—and, even amongst those which do, the causal relationship holds in a particular direction that the laws leave unspecified. Examples of non-causal laws may include classificatory laws like electrons have a charge of .
−¹⁰ esu, conservation laws (such as the conservation of momentum or energy), laws of thermodynamics such as that entropy is increasing, and phenotypical laws like if a child is the result of two blue-eyed humans mating, the child will have blue eyes, or all robin eggs are greenish blue (Fales (), p. ; Bunge (), pp. , ; Segal and Sober (), pp. –; Hempel (), pp. –). The last two are arguably laws that hold in virtue of a relationship between effects of underlying causes. Examples of laws that don’t make clear the direction of causation

-   



include laws of association or functional laws such as Boyle-Charles’ ideal gas law PV = nRT (where P is pressure, V volume, T temperature, n quantity of gas in moles, R a constant), the laws of optics that enable us to, for example, deduce the height of the Empire State building from the distance between the building and the shadow of the tip of the building and the angle of the ray of light at that point to the base of the building (Nagel (), p. ; Kistler (), p. ; Bromberger (), p. ). Even if it is obvious that the laws to which Maudlin adverts are causal laws, without an independent characterization of the features in virtue of which this is so, they can’t even begin to be the basis of an alternative account of causality. The account of causal non-symmetry developed over the previous two chapters is an indication of the materials involved. It is not just laws to which we must appeal but patterns of laws and particular matters of fact that hold to set up the non-symmetries. A second problem that specifically afflicts law-based accounts is the pairing problem (Ehring (), pp. –). Suppose that we have a law that implies the following generalization: for all x, if x has F, then there will be some y which is G ((8x)(9y)(Fx ⊃ Gy)). Let the antecedent be satisfied on a particular occasion by a token event, a, being F. The question is which of the events over which the variable y ranges is the event which is caused to be G by a. The law supplies no guidance on the matter. Introducing time and space into the characterization of the consequent does not help in cases of indeterminism such as that involving Ehring’s case A. Suppose we have (8x)(9y)(Fx ⊃ P(Gy at st) = .) and (8x)(9y)(Hx ⊃ P(Gy at st) = .). Yet it can be that, due to indeterminism, the causal chain starting with a being F completed and the one starting with b being H did not. This problem led Tooley to deny that particular matters of fact plus a relevant law are sufficient for causation (Tooley (), pp. –, (b), pp. –). I explained how my proposal could capture what is going on in this case in ... It relied upon the identity of the event that is G at st and the corresponding characterization of chance-raising. Drawing on such materials would abandon the distinctive character of law-based accounts. A third problem arises from the ontology of laws. Suppose that there are three events e₁, e₂, and e₃. Let e₁ be a cause of e₂ and e₂ a cause of e₃. The question is how does appeal to laws decide whether or not e₁ is a cause of e₃. If causation were transitive, the answer would come immediately. If there is a law covering e₁ and e₂ and a law covering e₂ and e₃, then e₁ is a cause of e₃. However, we have seen that causation is not transitive and, moreover, that the most obvious way in which we might appeal to law to distinguish the case in which e₁ is a cause of e₃, from the case in which it is not, doesn’t work (..). The only other option is to insist that when e₁ is a cause of e₃, then there is a further law at work covering e₁ and e₃. But then we would need an account of the relationship between the laws that covered e₁ and e₂ and e₂ and e₃ and that which covered e₁ and e₃. It would seem to introduce an unnecessary overdetermination. What reason is there to suppose that an extra law is needed if the succession of events is already settled because the other laws hold (Armstrong (), pp. –)? To summarize, the most significant recent case for taking laws to be primary is undermined by features of the analysis I have defended earlier. Moreover, law-based approaches to causality need to appeal to chance-raising, event identity, and so on to deal with difficulties with their approach. Exactly these features are behind the



  

possibility of brute singular causation. It seems possible, though inexplicable, that two distinct events may display the distinctive relationship of counterfactual dependency. So, as things stand, while much causation may involve law, there are cases that are not dependent on it. Here is our first inkling that we may understand laws in terms of their distinctive role in supporting a particular kind of causality.

. Three Accounts of Laws One way of thinking about the three main accounts of laws I’m going to consider is to view them as placing different emphases upon the role of generality in the construction of a metaphysics of laws. Regularity theorists focus on generalizations that hold within a particular possible world, the actual world. For them, the key issue is to distinguish between accidental and certain non-accidental regularities in that world, the latter being laws. They use this distinction, with other material, to account for a second sort of regularity, namely that which holds in a specified range of other possible worlds: the nomically possible worlds relative to our world. This provides them with an analysis, such as it is, of the necessity involved in laws. By contrast, necessitarians focus on generalizations across possible worlds, for example, whether two or more particulars or properties co-occur in just the actual world or whether they do so in a significant range of other possible worlds as well. Certain of these regularities across other possible worlds are laws. They use this feature to explain the regularities that hold in the actual world. As we shall see, some of the problems that these theories face relate to their attempts to extend, from the generalization upon which they put emphasis, to the other dimension of generalization. I shall structure the discussion of these accounts in the following way. I begin by examining some issues concerning their successful formulation and defence independent of the key areas for our discussion, namely, their support for counterfactuals, generalizations and induction, and the question of quidditism. I shall mention some standard counterexamples to these approaches with the aim of highlighting how a move to taking the approaches to be realizers of laws can provide a satisfying resolution. I then turn to the key areas. Having established the credentials of all three approaches, I explain how taking them to be realizers of laws can deal with the counterexamples. A fourth important issue, the relations between laws and probability, will receive separate treatment in Chapter .

.. Regularity theory: the best system analysis Regularity theories of law take laws to be particular kinds of patterns of property co-occurrence and law statements to be generalizations about these patterns. They need to distinguish between what we classify as accidental co-occurrences and those that are distinctive of laws. The most successful and, indeed, well-known way of doing so is that proposed by Lewis, following on from work by Mill and Ramsey: the Best System Analysis of Laws (Ramsey (), pp. –; Lewis (a), pp. –, ()). The basic idea is that laws are those patterns described by the axioms or theorems of the best system of generalizations concerning the pattern of co-occurring properties instantiated in our world. Lewis defines best system as follows: ‘The best system is one that strikes as good a balance as truth will allow between

   



simplicity and strength. How good a balance will depend on how kind nature is. A regularity is a law iff it is a theorem of the best system’ (Lewis (), pp. –). When he turns to consider the case of probabilistic laws, he introduces an additional constraint. He writes ‘some [systems] will fit the actual course of history better than others. That is, the chance of that course of history will be higher according to some systems than according to others’ (Lewis (), p. ). Probabilistic law statements are those that make the chance of the actual course of history higher than other candidates without too much expense of simplicity and strength. Other supporters of this type of position include Earman and Loewer (Earman (); Loewer ()). Theoretical strength is to be understood in terms of the capacity to entail all the particular matters of fact about the world. Take the conjunction of all the statements about these particular matters of fact and call it S. Then S is very strong, since it entails everything that is the case, but not at all simple. On the other hand, the axiomatization of logic can be very simple but, on the assumption it lacks any empirical entailments, not at all strong. Requiring a balance between simplicity and strength, in effect, requires us to form simple generalizations that, together with some statements about particular matters of fact, entail the remaining particular matters of fact. Suppose that S is the best system of generalizations for world w. Let F apply to objects in a world if and only if S applies to the world. Then we may formalize S as (x)Fx. This makes simplicity easy to obtain for any system. In which case, we may go for maximal strength. S will just be all the truths that hold at w (and hence all the generalizations). All the generalizations will count as law statements since they are consequences of the statement of all the truths that constitute the one axiom of S. The proponent of the best system analysis will be unable to make sense of the distinction between accidental and lawlike regularities (Lewis (a), p. ). Proponents of the best system analysis avoid this problem by restricting the kind of vocabulary with which we may formulate S. The terms should only refer to natural properties. Since appeal to the notion of natural properties is needed to avoid the conclusion that any generalization is a law statement, we cannot understand natural properties in terms of their figuring in laws. If we did, then we would have no reason to exclude (x)Fx because this would be a law of nature according to the proposed formulation. So instead, as we saw in ., a property’s naturalness is taken to be a primitive and it is in terms of this that duplication is characterized (Lewis (d), pp. –). Two objects will be duplicates if they share all their (perfectly) natural properties. Nature doesn’t make natural properties natural. It is not a contingent matter whether or not a particular property is natural depending on how things are. Natural properties are not simply intrinsic properties because amongst the intrinsic properties will be conjunctions and disjunctions of natural properties which are not themselves natural (Langton and Lewis (), pp. –). Instead, natural properties are thought of as a subclass of intrinsic properties in terms of which intrinsic properties are defined. My theory of intrinsic properties defended in . reduces the role of an appeal to naturalness in a definition of intrinsicality. It does not detract, though, from the role that naturalness is required to play in the best system analysis of laws. In brief,



  

we can’t obtain fake simplicity because a constraint upon the terms used to characterize the system is that they should stand for natural properties. Although it is open to question whether we can take the terms in which we have, in fact, formulated candidate laws as picking out natural properties, this concern does not specifically bear upon Lewis’ approach. Any metaphysics of laws is afflicted by the same issue. Do we have any grounds for supposing that creatures such as ourselves, the result of evolutionary selection, should have terms that pick out natural properties that capture the basic patterns of the universe? Perhaps not (Van Fraassen (), pp. –). This does not undermine the point that we have not achieved simplicity by generating a term, F, along the lines described above. Earlier discussion also bears upon the characterization of fit. As I noted in ., to deal with the problem that a particular infinite sequence of events has zero probability of occurring, we must understand best fit in terms of the higher likelihood that certain test propositions are true rather than simply whether the laws make a particular history highly likely (Elga ()). Although the discussion was in the context of providing support for a characterization of the similarity weighting for counterfactuals that we rejected, it does apply to the proper specification of the best system analysis of laws. Further detail may no doubt be provided about how we trade off simplicity, strength, and fit. It should not be supposed that we have explicit rules for such trade-offs. The thought is simply that, ultimately, the generalizations at which we arrive will stabilize around a particular, perhaps rough, trade-off. We should also resist concern that the analysis provides an anthropocentric account of laws. The regularities that are characterized are independent of human endeavour. The exact features these regularities possess will be independent too. Their status as laws, on the other hand, may not be independent of human endeavour, but our classifications in general are likely to reflect our purposes and activities. That is no particular problem for the best system analysis. The feeling that it might be a problem probably derives from something else, namely that—the charge will run—the account of laws provided does not pick out the kind of thing which is appropriately explanatory. According to this objection, which is expressed in many forms, laws are supposed to govern particular matters of fact and account for their development over time (e.g. Lange (), pp. –, Mumford ()). They are an explanation of the regularities we perceive. Sometimes the regularities may look, to all intents and purposes, like there must be a law explaining them but, in fact, there isn’t. However, when there is such a law, the explanation is not simply that the regularity in question is that picked out by a statement in the best system of generalizations describing the succession of matters of fact. Instead, there is an appeal to some kind of necessity. To this line of objection, the proponent of the best system analysis can give a threeprong reply. The first point is to remark that, as we shall see, all theories have difficulties with capturing the idea of laws governing the succession of particular matters of fact. Nevertheless, and this is the second prong, there is a perfectly clear sense in which the best system analysis, along with the similarity weighting of counterfactuals, can be part of the explanation of how, given a certain antecedent, such and such would follow. Proponents of accounts that appeal to necessity might

   



claim that this is not the notion of governing they have in mind but now they have moved from what might be fairly characterized as a datum, which a reasonable account of law might try to accommodate, to special pleading for a particular, hard to articulate, notion they prefer. It is sometimes suggested that laws—understood as proposed in the best system analysis of laws—cannot explain a particular regularity on the grounds that something cannot explain itself. The concern is that, since, according to the account, laws are just regularities, that is what the best system analyst must say. This is a mistake. What needs to be explained is a particular sequence of events in time. The regularity that a generalization in the best system expresses does not concern a particular sequence. The generalization may be true in a number of different ways. The explanation of the particular sequence is the joint work of the regularity expressed by the generalization plus the initial circumstances to which the generalization is applied. Neither of these independently, or taken together, is identical to the particular sequence of events although the latter may be entailed by the initial conditions plus the regularity expressed by the generalization. This brings me on to the third, and final, prong of the reply. If an account of laws fails to capture part of our intuitive notion of laws—the idea of particulars being governed by them—it does not follow from this alone that the account should be rejected, or that we conclude that laws don’t exist (e.g. contrary to Mumford ()). Instead, we can allow that the account in question is good enough. We can argue that the idea of governing is not essential to something being a law even if certain accounts can capture it. This is the familiar point that we should consider what would be enough for us to conclude that there is a certain kind of thing and not what we would ideally like them to be. Where the last objection to the best system of laws can seem like a simple insistence on a questionable conception of laws, and corresponding explanation, a closely related one seems rooted in scientific practice. We often envisage changed circumstances of particular matters of fact, indeed very simple situations, and consider what the laws would predict in such circumstances to happen. The objection runs that the best system of laws cannot make sense of this practice because in these changed circumstances a different set of generalizations will count as the best system of laws. Indeed, there are circumstances in which relatively trivial changes of particular matters of fact will result in laws failing to be laws. Here the idea of laws governing particulars is not so much about a particular kind of explanation involving necessity but rather a particular kind of insensitivity to changes of particular matters of fact and application to the widest possible range of circumstances. Some see this as of a piece with the previous idea of law governing (see e.g. Beebee (), pp. –, –). However, it seems more accurate to take it as a distinct idea of laws as invariants. As an illustration of the first point, note that scientists might consider what Newtonian mechanics would predict happening in a simple world in which there is just one particle moving at a uniform velocity. Yet Newtonian mechanics is much too complex for such a world. The point is not simply that we allow for the consideration of possibilities which, the charge runs, the best system analysis would rule out. It is also that this has a consequence for the semantics of counterfactuals. Consider the following



   Mirror

Y Field

U1

U2

Figure .a

() If the particle were travelling at uniform velocity in a simple world, then it would carry on moving without change in velocity indefinitely. Newtonian mechanics might secure its truth. But if the simple world is one in which Newtonian mechanics does not hold, there is no reason to suppose that the counterfactual is true. The intuitive truth conditions for counterfactuals allow for more independence from particular matters of fact than the best system analysis of laws can allow. As an illustration of the second point—that small changes in particular matters of fact will result in changes in the laws that hold, and the predictions consequent upon this—there is Carroll’s Mirror Argument. Suppose there are two possible worlds U₁ and U₂ containing X particles and Y fields. In U₁, all the X particles that enter the Y fields have spin up. One X particle, call it b, has a mirror close to the trajectory of its path into a Y field. In fact, the mirror does not block the trajectory and b passes into a Y field as the others do. In U₂, things are the same as U₁ in terms of particular matters of fact save for the fact that when b enters a Y field, it does not acquire the property of being spin up. Figure . might make this clear, the round circle being the b particle. Consider the following law. (L)

All X particles in Y fields have spin up.

In U₁ this law is true, in U₂ this law is false. U₁* and U₂* are identical to U₁ and U₂, respectively save for the fact that the mirror blocks b’s trajectory in each case so that b doesn’t end up in a Y field.

U1*/U2*

Figure .b

   



As a result, the generalization. G₁: All X particles in Y fields have spin up holds for both. Nevertheless, Carroll argues, in U₁* it expresses a law, in U₂* it is just an accidentally true generalization. There is a formal and an informal version of his argument. The informal version invites us just to consider the circumstances described and conclude that it is a very plausible thing to say about the case. The background thought is that the generalization in U₂* only holds by accident. The mirror blocked the possibility of it being disconfirmed. The formal version appeals to the following principles. (SC*) If it is nomologically possible that P and Q is a law, then if P were the case, Q would still be a law. (SC’) If it is nomologically possible that P and Q is not a law, then if P were the case, Q would still not be a law. Let’s start with U₂. ‘All X particles in Y fields have spin up’ does not state a law in U₂. (SC’) explains how, just because the mirror blocks the pathway in U₂* (that would be the P in this case) it doesn’t follow that ‘All X particles in Y fields have spin up’ is a law in U₂. The generalization is (now) true but the law doesn’t hold. Consider now U₁. (SC*) explains how, if the generalization is a law in U₁, the mirror blocking the pathway can’t change it to a true generalization but not a law in U₁*. These two principles together entail different verdicts about the laws U₁* and U₂* on the basis of the same set of particular matters of fact. There are two problems with the formal version of the argument. The first is that (SC*) and (SC) are false according to the most plausible semantics of the counterfactuals they contain. It is not true that any proposition, P, nomologically compatible with the laws that hold would not alter whether or not something is a law. This sets perfect match to nothing in the similarity weighting for counterfactuals (Beebee (), pp. –). The second problem is that according to the most plausible account of nomological possibility, (SC’) is false. Consider P is nomologically possible in W iff there exists a possible world having all the laws in W in which P is true (Lewis (c), p. ). P is nomologically possible if it is left open by the laws in W but this is compatible with the truth of P resulting in another law holding too. That is, it is compatible with a law being added to those that hold in W. If this is the case, then (SC’) which says that Q would stay not a law is false. If (SC’) is false, then we cannot conclude that U₁* and U₂* have different laws. While (SC*) entails that G₁ is a law in U₁*, it may also be a law in U₂* (Roberts (), pp. –). The informal argument remains though. The imposition of the mirror doesn’t seem the right kind of thing to add a law relating to X particles. That the best system analysis might seem to have this consequence means it is poor at capturing the idea that laws are insensitive to the particular matters of fact which hold and hence count as invariants.



  

Some proponents of a regularity approach to laws have suggested that they may fail Humean supervenience because law statements are the projections of a subject’s predictive capacities or theoretical model of an environment (Halpin (); Ward ()). They adopt a non-factive approach to laws. Others, as we have already noted, deny the force of the cases just given and attribute them to an illegitimate governing or necessitating conception of law (Beebee (), pp. –, –). Recognition that the best system analysis of laws is only one realization of laws allows for a third possibility. The possibilities envisaged hold when a different realization of laws is in play. I shall return to this point after I have discussed the other two approaches.

.. Independent necessitation accounts Independent necessitation accounts of laws take laws to involve relations of necessitation between universals in which the necessitation is independent of the properties in question. The most celebrated and discussed versions of such accounts are those championed by Armstrong, Dretske, and Tooley. Hence, they are called DTA accounts (in order of presentation in the literature) (Dretske (a); Tooley (); Armstrong ()). All three start with the idea that the structure of laws is, in Armstrong’s formulation, N(F, G) where F and G are universals and N represents the relation of independent necessitation. The existence of the relation of necessitation between these universals distinguishes nomic generalizations from accidental generalizations. They then hold—sometimes with qualifications—that Metaphysically necessarily, if N(F, G), then (x)(Fx ⊃ Gx) and, in particular, Metaphysically necessarily, if N(F, G) and Fa, then Ga (for all substitutions of a). The main controversy concerning these accounts is the extent to which they are entitled to these claims. I shall consider this matter, and compare the account with the others, in ... In .., I discussed the ideas that laws governed the succession of particular matters of fact and were relatively insensitive to the changes in those matters of fact compatible with the laws, dubbing the latter the invariance of laws. Given their denial of Humean supervenience, independent necessitation accounts of causation should hope to do better than the best system analysis of laws. But it is not clear that they do as well as might be expected. This reveals itself in two areas: first, the question of the conditions under which universals exist and the connection between this and uninstantiated laws; second, the question of structural universals and the account of causation developed from the DTA approach to laws. I take these in turn. A law is uninstantiated if there are no entities whose succession, in fact, involves the holding of the law. One illustration is Newton’s first law: an object stays at constant velocity unless acted upon by an external force. On the assumption that no object is free of the influence of external forces, it is never instantiated (Armstrong (), p. , although some contend that while the law is uninstantiated, there is no property of being acted upon by zero net force to be uninstantiated, see Mellor

   



(), pp. –). Another illustration commonly given before the Chernobyl nuclear power station accident in  involves the laws concerning the conditions in a nuclear reactor that would give rise to a nuclear explosion. The hope was that, with the right safety regime, the law would never be instantiated (Mellor (), pp. –). There may be controversy over particular cases but it is generally conceded that the possibility of uninstantiated laws must be accommodated. If F and G are taken to be platonic universals, then there can be fundamental uninstantiated laws in virtue of a relation of nomic necessitation between them (Tooley ()). Problems arise if, instead of taking F and G to be platonic universals, they are supposed to be Aristotelian universals bound by a principle of instantiation according to which these universals only exist if they are instantiated by some particular, or particulars, at some time (Armstrong (), p. , (), p. ). Armstrong can deal with some uninstantiated laws by his treatment of the relationship between standard formulations of law and his metaphysics. Consider Newton’s familiar F = ma. Armstrong takes F = ma to specify the existence of many laws of the general form N(F & M, A), laws for each value F, M, A may take, e.g. So we have N(F₁ & M₁, A₁), N(F₂ & M₂, A₂) . . . and so on. To illustrate, F₁ may be  Newtons ((kg) x (m/s²)), M₁ may be  kg, and A₁ thus  m/s². Since there are an infinite number of possible values F, M, and A may take, we may assume that some are never realized, let one be Fi. On the assumption that it is plausible, if Fi had been applied to a mass, a certain acceleration would have resulted, there is a law in virtue of which this counterfactual is true. It can’t be a derivative uninstantiated law involving Fi because that would infringe the principle of instantiation. Thus, Armstrong appears to recognize laws involving necessitation relations between determinable properties viz: F, M, and A. These he envisages to take the form N(Being a F-type property, being a G-type property such that G is a function, f, of that same F-type property) (Armstrong (), p. ) which he shortens to N(F, a G such that G = f(F)) (Armstrong (), p. ). As Armstrong recognizes, the proposal does not work for uninstantiated universals for which there are no determinables. Suppose that there is a possible world with only ten types of fundamental particles and that their pair-wise interactions depend upon the types of particles they are. Then there are fifty-five possible interactions (!/!(-)! + for those cases of particles interacting with particles of the same type). Fifty-four of these possible interactions take place in the history of the world but as things happen the fifty-fifth does not. The interaction in question is nomically possible. The laws of nature don’t rule it out from taking place. If the world is deterministic, its failure to occur might be because the circumstances, as a matter of fact, rule out two types of particles, say X and Y, moving in proximity to each other to interact. If the world is indeterministic, there might even have been a probability of their interaction. Nevertheless, their failure to interact means that its idiosyncratic consequence, say the instantiation of a universal K (for which there is no determinable), never occurs. Hence, there is no law of the form N(X & Y, K).



  

Tooley remarks that in such circumstances it is still reasonable to suppose that there is an underived law governing the interaction (Tooley (), p. ). This presents Armstrong with a problem since his preferred manoeuvre above does not work in this case. Adoption of the principle of instantiation also renders the theory incapable of fully capturing the idea that laws are invariants. It is not possible, for example, to consider a simple world in which Newtonian mechanics is still true. There has to be at least enough complexity to instantiate the universals. As Armstrong’s view of laws is supposed to be a necessary truth, the case cannot be dismissed as a merely possible case (though he does try this line, Armstrong (), p. , even though he is not averse to prosecuting the best system analysis for failing to deal with merely possible cases (e.g. Armstrong (), pp. –)). So, instead, he suggests that he can allow that the following counterfactual is true: if X and Y were to interact, then there would be some idiosyncratic consequence (though it is not determinate what) (Armstrong (), pp. –). It is not quite clear what grounds the truth of this counterfactual. The most immediate, though implausible, candidate is that there should be a law involving the determinables the property of being a pairwise interaction of fundamental particles and the property of being an idiosyncratic upshot and, indeed, that does seem to be what Armstrong had in mind in earlier work (Armstrong (), pp. –). By contrast, proponents of the best system analysis would seem to be in a better position. They can argue that the best system will include a law for the fifty-fifth interaction on grounds of simplicity. In any event, we have come to a peculiarity of Armstrong’s position. In the indeterministic case, the claim is that there is a certain probability that X and Y will interact and yet there will be no determinate probability of a particular product occurring. In which case, the law would not govern their first interaction if they were to interact since it would only exist after the first consequent occurred. This shows that, even in the deterministic case, the law would not exist until the first succession of particular matters of fact relating to it has been completed. Armstrong seems to be faced with a picture of laws in which the first interactions of any two fundamental entities giving rise to a yet uninstantiated type of consequence creates the laws regarding this interaction. At the start of the universe, where there have been no interactions, or instantiations of the relevant sort, the laws would be created as a result of the first interactions and, hence, these first interactions would not be governed by law. Thereafter, if an F is instantiated, then the existence of N(F,G) together with the instantiation of F can be said to govern the instantiation of G. Prior to that first instantiation, though, it is not clear whether F will be succeeded by H rather than G. So, in whatever sense of ‘govern’ Armstrong’s account of laws can claim to capture, that instantiation is not governed by the law. But if laws are not needed to govern interactions here, then why are they needed later? Perhaps it might be argued that the requirement that universals be instantiated at some time in order to exist does not imply that they don’t exist prior to that time to govern the interaction as it were. Unfortunately the distinction appears unmotivated. If you adopt the principle of instantiation in order to avoid having to allow universals an existence outside space and time, then you are in no position to allow that universals might exist prior to their instantiation: exactly where is this existence going on and how does it govern? Indeed, there is a general question concerning how laws so understood can govern if their existence depends upon the existence of instances.

   



It is hard to see how a commitment to eternalism about time would change the situation. Eternalists claim past and future entities exist in the same way as present entities (e.g. Sider (b), p. ). Correspondingly, a law exists if there is some spatiotemporal instantiation of it, say, in the future. However, consider a point in time prior to the law’s first instantiation. The existence of the law in virtue of the later time does not imply that it is in a position to govern the way things go prior to that first instantiation and, thus, in a position to govern what follows given its antecedent is instantiated. For this reason, those who wish to defend the orthodox DTA account of laws may seem better off rejecting the principle of instantiation and endorsing Tooley’s Platonist version but there are costs. Taking universals to exist outside space and time is not just naturalistically unfortunate but also, as Armstrong notes, threatens to remove one way of resolving the Bradleian regress concerning universal instantiation (Armstrong (), p. ). There will always be a question concerning the proper explanation of the instantiation of universals by particulars if it is possible for universals to exist independently of the particulars. The temptation is to introduce a relation of instantiation, perhaps participation by a universal. But if the grounds for supposing that there is a relation of instantiation are sound, then they also seem to be grounds for requiring a relation of instantiation to relate the relation of instantiation to the particular, and so on. This is not just a general and familiar point about the problems that a Platonic account of universals faces that proponents of Platonism can seek to brush off as part of a cost-benefit analysis with Aristotelian accounts of universals. It has more immediate impact. Without a theory of instantiation, it is quite unclear how the DTA approach can capture the idea that laws govern the pattern of instantiation of properties. Yet, this is taken to be part of the recommendation of the position (Armstrong (), p. ). The problem that structural properties pose for this account can be developed in two ways, first in terms of laws, second in the theory of causation that has been developed from this theory of laws. Structural properties include chemical compounds like methane (to cite the familiar example). The chemical formula of methane is CH₄. The prima facie most natural way to understand what all occurrences of methane share is a universal with the following structure. H

H

C

H

H

Figure . The problem is that this would seem to contain four hydrogen universals whereas there is only one hydrogen universal shared by its instances (Lewis (d)). So, if



  

there are any laws involving structural universals, then they contain instances of the universals rather than the universals. It is hard to deny that there will be laws of this sort because most laws concerning chemical compounds will be laws involving apparently structural properties. In which case, the explanatory role of laws in explaining the generalizations that are distinctive of them is threatened. This can be brought out by focusing on the theory of causation that was developed from this theory of law (Heathcote and Armstrong (); Armstrong ()). The final statement of it is that c being F causes e being G only if FC causes GE. That is, the token causal relationship on the left hand side is an instantiation of a state of affairs of type FC causes GE, where C, E refer to the types of which c, e are tokens. Laws are then given the form—₁ being F causes—₂ being G (Armstrong (), p. ). The reason for the revision to the analysis of laws is as follows. Let us suppose that F stands for the property of being on fire. Fire in one object can give rise to fire in another. How should we represent the law involved in this causal interaction. Appealing to the N(F, G) format gives us N(F, F). Now we face a dilemma. Either F is the same universal in both, in which case there is no relation of nomic necessitation between F and itself; or the two occurrences of F are distinct, in which case they are not universals. Armstrong’s solution is to suppose that instead of thinking of F as the same universal in each case, we should think of each occurrence as abstractions from two distinct states of affairs involving different objects. Armstrong dubs these ‘inviscerated states of affairs’. The question is whether invisceration de-particularizes the universals. If it does, then it would seem that the same universal occurs in—₁ being F causes—₂ being F and hence we face the first horn of our dilemma. If it does not, then the universals begin to look more like tropes or property instances and it is quite uncertain how something with this structure could explain the regularities of causation. Each such structure would be instantiated only once. Since it would only exist on completion of the relevant succession of particular matters of fact, once again the governing role appears threatened. I shall outline this problem in further detail and discuss solutions to it in ... The upshot will be that a radical revision of this approach to laws is necessary. But, for now, it seems clear that the DTA approach to laws ill serves those who search for the kind of explanatory role of laws that the best system analysis was said to fail to provide.

.. Dependent necessitation accounts: the powers ontology Proponents of a powers ontology claim that, as far as laws are concerned, fundamental properties are powers or, as they sometimes put it, potentialities. According to this approach, the modal force associated with laws is dependent upon the nature of these powers. Let Ri be the characterization of the causal profile of instances of a particular property. The characterization may be rather complex. Standard cases will include triggers and manifestations. The property of being fragile (to mention the familiar illustration) has a trigger—e.g. tapping the vase with a hammer—and a manifestation: e.g. cracking and breaking. Nevertheless, there may be cases of manifestation without triggers. When there is a trigger, it need not follow that

   



there must be a manifestation. There may be an intervention that stops the manifestation. Thus, if it is possible to give a characterization of the causal role in terms of conditionals, this will not be straightforward. Recognizing these qualifications, the minimal condition for the approach is ðPÞ □m ðxÞðFx iff Ri xÞ: Here ‘Fx’ should be read ‘x is an instance of F’ and ‘Ri,x’ should be read ‘x has causal profile Ri’. The causal profile is a set of potential causal relations in which possessors of a property may stand. They will be characterized in terms of the two elements identified above. The characterization will include properties whose instances are triggers and whose instances are manifestations. Thus, the simplest abstract characterization of the position is: Nm(TF, M) where ‘T’ is a trigger property, ‘M’ is a manifestation property, and ‘F’ the power or potentiality linking the first with the second by metaphysical necessity, indicated by ‘Nm’. Opinions vary over what must hold in addition to (P) in order for the relevant laws at a world w to be determined by the causal profile of F. Most proponents of a powers ontology allow that there might be worlds with different laws from the actual world if those worlds have different properties (e.g. Swoyer (), pp. –; Ellis (), pp. –; Bird (a), pp. –, ). Allowing such variation is compatible with the truth of (P). There is a prima facie problem with this idea. The following argument expresses the difficulty. () Properties are necessary existents. () If a property F exists in w, then the property’s causal profile fixes the relevant laws for w. Therefore, ()

The same laws hold for all possible worlds.

Platonists about properties divorce existence from instantiation. A property may exist at a world regardless of whether it is instantiated. If the position is to avoid the conclusion, one of two options are available. The first is that different possible worlds will have different universals populating Plato’s heaven. There is no reason to suppose that Plato’s heaven should be cross-world. In which case, premise () is false. Even if Plato’s heaven has the same members in every possible world, the Platonist can reject premise (). They can insist that the laws that hold are a matter of which properties are instantiated and not just which properties exist. Their moderate agreement with Aristotelianism about laws would have a drawback. It would make their position on powers prey to some of the problem cases detailed earlier for property-independent necessitation accounts (e.g. Tooley’s ten fundamental particles case). Nevertheless, it would avoid one ostensible difficulty for the Aristotelian position, namely how a property could have its character given by a causal profile mentioning properties that don’t exist when that causal profile is unmanifested in certain respects. The Aristotelian position insists that a property’s existence depends upon its instantiation (Tugby ()). This would not be the case if the causal profile is unmanifested. Platonists can say that existence does not require manifestation.



  

In point of fact, it may be possible to avoid both problems. The idea is that a universal exists if it is a member of the powers net in terms of which the causal profile of an instantiated universal is characterized. So an existing universal is either instantiated, or part of the causal profile of a universal which is instantiated, or part of the causal profile of a universal which is mentioned in the causal profile of the instantiated universal, and so on. Equally, so long as one property in w is instantiated from the powers net, all the other laws that serve to characterize the powers net hold too for w. The advantage of this position is that it provides a natural treatment of the problem cases. If certain universals are not instantiated because of particular intervening circumstances, the laws they would settle would still hold because the universals’ existence would be settled by appeal to the powers net of an instantiated property. This position also allows for us to characterize the causal profile in terms of relations to other uninstantiated but existing universals. The powers ontology takes the connection between a property and its causal profile to be one of metaphysical necessity. However, it is important to appreciate that appeal to metaphysical necessity alone cannot constitute the proper characterization of the target necessity of laws of nature. Consider a network with undifferentiated nodes and potential relations between those nodes. For the moment, let us set aside the question of whether a network can constitute the nature of the different properties in the network simply from their position in the network. The network could involve relations of coinstantiation or succession. Then, for something to be the property it is, it would have to be coinstantiated with such and such properties, and be succeeded by such and such other properties. Nevertheless, this claim concerning what is metaphysically possible and necessary for instances of a certain property doesn’t imply anything about whether there is causal necessitation between these property instances. For example, it is compatible with a certain kind of Humeanism. The point can be missed if the development of a dependent necessitation account of laws occurs within the context of independent necessitation accounts like Armstrong’s. It can appear mandatory that metaphysically necessary connections between the instantiations of properties must involve a strengthening of the N relation to which Armstrong appeals to yield Nm(TF, M). However, as Lowe pointed out some time ago, varieties of accounts of laws that involve metaphysical necessities need involve no more than a predicational tie between two existing universals, the second universal predicating an essential property of the first property, the first property characterizing a kind of thing (e.g. Lowe (), pp. , , ). For example, the putative law that salt is water soluble is understood to have the structure WS where water solubility is predicated of the kind salt. The present point extends the observation to the question of how properties may be understood structurally from a network involving undifferentiated nodes but distinct structural relationships. Proponents of a powers ontology take properties to be causal potencies. The characterization of the structural properties of the network should take its cue from such a characterization. Each property, F, should be specified by something like the following network property: all instances of F, fi are such that, if an instance of the property T (a triggering property) stands in such and such a relation S to fi,

   



then fi causes an instance of the property M. Here T, S, and M will themselves be characterized in terms of the powers net. Suppose S is a relation of spatial proximity. Then the causal consequences of the relation of spatial proximity holding between instances of two properties, G and H say, will figure as part of the characterization of S. Although there is a direct appeal to causation in the characterization of the network property, the notion of a causal potency should be distinguished from that of a cause. The causal potency is that which, when certain conditions are met, gives rise to causation. The potency itself is no more causation than, in the terms of Armstrong’s old theory, N(F, G) is causation. Appeal to causation is necessary because without it we will just have a pattern of coinstantiation characterization of the network that was earlier observed to be inadequate to capture the idea of causal necessitation. Properties as causal potencies, then, have their identity derived from the complex pattern of coinstantiation causally specified. What is the relationship between R (the causal profile) and F? The most natural characterization is identity. If that’s right, then it is a mistake to characterize R as a second-order property that constitutes F. If R is comprised of second-order relations in which F stands to other properties in the network, then an object cannot possess R. That would make R a first-order property. But an object can possess F. It does so when it stands in the network of causal relations I specified above. That’s what it is for an object to instantiate F. If F = R, then R is not a second-order property. There is also no further question about whether R itself is a power. It is a power because it is identical to one. Moreover, if R is taken to be a relation between properties, then R is not the potential for standing in various causal relations. Properties don’t stand in these relations, only their instances do (Barker (), p. ). That’s another reason for denying that R is a second-order relation. The powers ontology takes all fundamental properties (including relations) to be powers. So what about the causal relation itself? Cases of iterated causation indicate that the causal relation itself can be understood as a power. Someone causing pain in an innocent animal (say) can cause outrage. Earthquakes causing damage can result in building regulations to ensure that buildings survive such assaults. Nevertheless, it is open to the power ontologist to reject the question on the grounds that causal relations supervene upon a power plus a trigger for the manifestation of that power. According to this view, causal relations are not a fundamental part of the world, causal potencies are. Potency plus what makes that potency actualized is sufficient for the derivative entity: the causal relation. My earlier characterization of causal potency in terms of causation was to assist understanding and not to reveal ontological priority (in the vertical sense). Understanding properties as nodes in a network of causal potencies gives rise to a concern about circularity. I will focus on two ways in which this has been thought to arise relating to the network’s relational character and its capacity to provide identity and distinctness conditions for properties. The first concern is that if properties don’t have an independent characterization from the relational structure, then there is nothing to stand in the relations that are said to be constitutive of their identity and distinctness. For example, there is nothing to count as the manifestation of a power because any candidate is just another potentiality (e.g. Robinson (), pp. –; Armstrong (), pp. –; Martin ()). The mistake here is to overlook the fact that the network is of the



  

potential for causal relations. The instances of properties that stand in the nodes are causal potentialities whose manifestation is triggered when other instances of properties in the network stand in certain relations to them. The causal potentialities themselves are actually instantiated in the nodes—they are not just possibilities—and the potential for standing in various causal relations is a nature that is independent from the particular relations that are manifested when triggered. The characterization of properties as nodes in a network should not be understood as making these properties relational as opposed to having the potential to stand in relations. So there is no mileage to a ‘no relations without relata’-style objection for this approach. The second concern is of particular significance for my overall argument. According to this version of the objection, it is not possible that the identity and distinctness of properties should be understood in terms of the network because, if the properties aren’t differentiated prior to the network, there is nothing within the network from which identity and distinctness can be constituted. The identity of each property would depend upon its potential for relations to other properties whose identity, in turn, depends upon the potential for further relations. Nothing is available to fix the identity of them all (e.g. Lowe (), p. ). Alexander Bird shows that appeal to causal profile in a network can provide proper identity conditions so long as the structure of the relations is asymmetric (Bird (b), pp. –). That is, there is no way of mapping the nodes in a network of relations onto each other while keeping the same structure. This condition need not be met. To give Bird’s example, consider the following structure.

Figure .a A rotation of the nodes by ° would yield a network with the same structure. If the potential relations are the only things to which the power ontologist can appeal, the property at the top left hand side vertex cannot be distinguished from that at the bottom right. Such a network would not provide distinct identity conditions for the nodes. Nevertheless, there are other networks—in fact an infinite number of such networks—in which such structure-preserving mappings are not possible. These are the networks that can provide identity and distinctness conditions for properties. One of the simplest illustrations of such a network is (again taken from Bird) as follows.

Figure .b

   



Here there is no mapping that would preserve structure. In this case, the relationship between the nodes is asymmetrical. In the case of a powers net, further grounds for asymmetry are introduced by the fact that one property is the manifestation of another but not, generally, vice versa; one power may be the manifestation of itself in another object; where powers have triggers, they are part of the essential character of a power so we need a different connective from that which holds between a power and its manifestation; and, finally, while the manifestation property of a power is part of its distinctive character, that a power is a manifestation property of another property need not be. To deal with the last point, Bird notes that it is not the whole network which determines the identity and distinctness of properties but rather a subgraph: a ‘directed walk’ through the network which does not allow a move from a node which is a manifestation property of another node, back to the node for which it is the manifestation property. With all this in place, Bird’s intriguing claim is that a powers ontology can answer the identity and distinctness objection but only by restricting the network of causal potentialities to certain structures: those with asymmetries generated by these relations. Obviously the scope for asymmetry in this full picture is considerable. Let’s be clear about how the appeal to asymmetry works. The nodes will be defined in terms of their potential for relations to other nodes. Because the other nodes are mentioned, the definition is circular in one sense. There is no escape from mentioning the identity of other nodes in defining the identity of a node. However, the identity of each node will involve a different structure of potential relations to the other nodes. It is by appeal to these differences in structure that differences in node are characterized. So the issue is not whether node identity can be formulated in a node-independent way but rather whether, when giving a node-dependent formulation, the identity of each node is given by its place in the network of potential relations or whether some further network independent identity is required. The demonstration that nothing further is required discharges the concern that the identity of the nodes remains indeterminate. With all the different possible grounds of asymmetry Bird has identified, it is clear that there are no constraints on the number of fundamental powers there may be (as there were with the simple networks specified above). Nevertheless, this still raises the intriguing prospect that there are certain power nets that, if we discovered that they were the case, would involve certain symmetries. Such power networks would fail to distinguish between those nodes about which the network is symmetrical. Hence, if we took the nodes to be distinct, we would have empirical grounds for supposing that a powers ontology in the way that Bird developed it would be false. This accords nicely with the line I’m pressing in this chapter. In different possible worlds there may be different realizations of the laws. Our grounds for believing that one or the other holds should depend upon the evidence for, and explanatory utility of, the various approaches. In this light, the most significant argument against a powers ontology are the observations due to Jeremy Butterfield and Denis Robinson. Butterfield notes that there may be symmetrically related properties, L and L*, such as being right and left handed, that can only be distinguished by reference to L and L* particulars (reported by Mellor (), p. ). Robinson invites us to suppose that there are two



  

properties, F and G, such that they have the same causal profile except with respect to their interaction with each other. Two objects with the same property, that is both with F or both with G, will be repulsed. However, two objects one of which has F, the other has G, will be attracted. Since the identity of these two properties is not prior to their role in a network, these properties cannot be distinguished by the network. Each will have the same causal profile as the other (Robinson (), pp. –, for another example, Hawthorne (b), p. ). If such properties are possible, then the identity of causal profile does not imply identity of property. This, in itself, does not imply that properties aren’t the basis for the truth of law statements, and those upon which necessary connections depend. Nevertheless, introducing an additional distinguishing factor—for example, an internal qualitative aspect as some power ontologists do—brings with it a difficulty (e.g. Martin (), pp. –; late Shoemaker (), p. ); Heil (), pp. –). How are we to relate the distinguishing factor to the causal profile? There may be something that explains the connection but it is not clear what. That’s why a perennial objection to these ‘Janus-faced’ accounts of the individuation of powers has been: why isn’t it possible for the distinguishing qualitative aspect to be related to a different causal profile since the qualitative aspect and causal profile seem distinct existences (Armstrong (), p. )? Of course, there is nothing incoherent about two distinct things having the same implication. For example, two more determinate colours may imply the instantiation of a certain determinable colour, a chair and a table may imply that space is occupied, and so on. It is just that we find it hard to identify a model for how two different properties can imply the instantiation of a more general property without also seeing how those differences may give rise to differences in more specific ways in which that more general property might be. Thus we are inclined to think that if two properties with differentiating qualities implied the same causal profile, there is a way in which those different qualities should also show up in a difference in causal profile too. But that is the very thing that is ruled out in the cases to which appeal to qualitative aspects is a response.

.. Intrinsicality, generality, and induction In ..–, I have sought to deal with many of the main issues in the successful formulation of the three main types of theory of laws, independent of the subject matter of the present section. We saw that there were no immediate grounds for dismissal of any of them but that all had significant difficulties. Those who resist regularity approaches to law are apt to cite the issues in the present section as grounds for rejecting it. In brief, they hold that regularity theories such as the best system analysis cannot capture the intrinsicality of causation, they offer no explanation of regularities that they state and, as a result, provide no basis for providing a solution to the problem of induction. The task of the present section is to show that non-regularity theories have no such advantages. Regularity theorists’ best response to the charge that the approach cannot capture the intrinsicality of causation is to distinguish between two theses. They must accept that, if regularity theories are true, then whether two events, e₁ and e₂, stand as cause to effect in virtue of some of their properties, say F and G respectively, will turn on whether there is a regularity involving other Fs and Gs (that is, other events with F and G). So it does not just depend upon a local matter of fact about e₁ and e₂.

   



Nevertheless, they can insist on two other points. The first is that the proper characterization of the causal relationship—in terms of a complex kind of contingent probabilistic dependence as described earlier—is entirely local. The second is that this type of theory captures the claim that causation is intrinsic in another important sense, namely that it does not depend upon competing causal chains. If e₁ causes e₂, then the verdict doesn’t change if the same local facts hold but there is a pre-empted chain that would have caused e₂ or an overdetermining chain that also does. Let us now turn to the question of generality. Both property-independent and property-dependent necessitation accounts have difficulty explaining the generality of causation in their own terms. By that I mean that, just like the regularity theory, we can write in an explanation of the generality of causation by appealing to something explicitly general. But we don’t get it for free out of the ontological materials basic to either account. Consider the property-independent necessitation account first. The initial, and most famous, formulation of this approach takes the basic form of laws to be N(F, G). Armstrong’s provisional claim is that by metaphysical necessarity, if N(F, G), then (8x)(Fx ⊃ Gx). As many have observed, this creates a puzzle. N(F, G) is a distinct existence from (8x)(Fx ⊃ Gx). The first is a second-order relation between universals. The second is a universally quantified statement about the coinstantiation of those universals by particulars. How do we get from the first to the second (e.g. Lewis (a), p. ; Van Fraassen (), pp. –)? We need to get one complication out of the way. As Armstrong notes, for any candidate connection between the instantiation of F and the instantiation of G, it is plausible that there will be intervening factors that could result in G not being instantiated when F is. Suppose that the instantiation of I is an intervening factor. Then one way of characterizing the relevant law is not N(F, G) but N(F and not-I, G). Those who baulk at recognizing the existence of negative universals—not-I—take this argument to establish that proponents of property-independent necessitation accounts of laws face a choice. They could adopt a Platonist conception of laws along with a proliferation of nomic relations between universals. In which case, as Tooley urges, the relevant law is F without I necessitates G (where ‘without I’ does not involve a negative universal but rather a relation of being without a certain existing universal I) (Tooley (), pp. –). Aristotelians cannot appeal to this idea because, first, I may be uninstantiated and so, by their lights, not exist and, second, the instantiation of this law would involve a relation of nomic necessitation being instantiated between F and not-I on the one side, and G on the other. In which case, either the instantiation of negative universals has to be recognized or one element of one of the relata of the instantiated relation of nomic necessitation doesn’t exist viz the instantiation of not-I. The alternative to Platonism is to accept that there are few laws properly characterized as metaphysically necessitating the universal generalization—few steel laws as Armstrong calls them—but rather a looser association that Armstrong dubs oaken laws.¹ One way of characterizing it would be that, in the absence of ¹ Armstrong’s iron laws are those in which there is, as a matter of fact, no I that interferes between F and G. This leaves it open that it is possible that there is an I and, hence, the iron law does not metaphysically necessitate the universal generalization (Armstrong (), p. ).



  

intervening factors, the law necessitates the universal generalization (Armstrong (), p. , fn. ). Another way would be to take N(F, G) to metaphysically necessitate (8x)(Fx & not-Ix ⊃ Gx) (Armstrong (), p. ). For the purposes of the discussion to follow, I shall consider the best case scenario for the position, namely when there are necessarily no interfering factors and the candidate law would be a steel law. With the issue of intervention out of the way, Armstrong’s proposal concerning how we get from N(F,G) to (8x)(Fx ⊃ Gx) is that the latter is presupposed by the former (Armstrong (), p. ). It is part of what it is for N(F, G) to hold that (8x) (Fx ⊃ Gx). The idea seems to be something like this. Just like the relation of invariable coinstantiation, N, is something which does not hold between two universals in a world unless (i) there are Fs and Gs and (ii) all Fs are Gs. An implication of this is that, temporally local laws could not be represented by N(F, G). Suppose that a law holds only between  and  . Then the relevant law should be characterized as N (F & T, G) where ‘T’ stands for the time period. There are two related problems with Armstrong’s formulation of a propertyindependent necessitation account of laws with regard to the metaphysical necessitation of the truth of (8x)(Fx ⊃ Gx). The first relates to his idea that universals are wholly present in their instantiations. Their being wholly present in their instantiations is the basis for the explanatory utility of appeal to universals to characterize resemblances in nature. Qualitative identity in a certain respect is reduced to numerical identity of universals. A universal, U, is not identical to its instantiation, I(U), because the universal may be multiply located and, thus, be present in a number of different spatiotemporal regions, whereas the instantiation is not. Nor is the universal part of the instantiation, otherwise the instantiation may have a greater spatiotemporal extent than the particular spatiotemporal region it occupies because it has, as a constituent part, something that is also wholly present in the other instantiations of U. These observations make the relationship between universals and their instantiations a puzzling one. At the minimum, the instantiation of a universal seems to involve the loss of certain of the properties of a universal. The important point is that if a universal is wholly present at a certain spatiotemporal region, then its presence is independent of what holds at spatiotemporal regions that have nothing to do with its instantiation there. Consider, then, the claim that N(F, G) is wholly present at a certain spatiotemporal region. If, specifically, N is wholly present relating a particular instantiation of F and G, then this cannot turn on whether all other Fs and Gs are so related. Thus, it might be the case that an F occurs without a G instantiated but rather a H instantiated instead elsewhere. Note, my point is not the simple one that it is not legitimate for Armstrong to stipulate that there is a metaphysically necessary connection between N (F, G) and the truth of the generalization. I am prepared to allow that he can characterize an entity as explanatory in this way. My point is rather that there is a tension between, on the one hand, the characterization of an entity as explanatory in this way and, on the other, his further characterization of it as wholly present in its instantiations. Further, if Armstrong seeks to make an exception for N, and deny it is wholly present in a relation between an instantiation of F and an instantiation of G, he loses his claim that his approach to laws can capture the intrinsicality of causation in

   



the first sense. Making N(F, G) presuppose the truth of (8x)(Fx ⊃ Gx) robs it of any special advantage over the regularity theory. This might make us inclined to consider whether the thesis of universals being wholly present in the instances should be abandoned. We have already noticed that it makes the idea of instantiation have puzzling properties. But this brings us to the second problem with Armstrong’s formulation. As we noted at the end of .., to deal with the problem of structural universals, Armstrong had to revise his account of the structure of laws to—₁ being F causes—₂ being G. The crucial feature of this revision is that F and G are not straightforward universals but particularized universals. This was required to deal with the case of—₁ being F causes—₂ being F. The consequence of this revision is that his necessitation relation—now written in as causes—no longer relates universals but rather these particularized entities and so there is no reason why it should only hold between these entities if (8x)(Fx ⊃ Gx). These considerations don’t demonstrate that no property-independent necessitation account of laws can capture the link between laws and generality. The point is simply a question of formulation. An immediate way of establishing the link would be to write it in explicitly. Thus, the standard form of a law might be (8x)(Fx ⊃ N(F,G)x). Informally, if an object has F, then it has the property of F necessitating G. One problem with this quick fix is that it separates the generality from the necessity. The latter is no longer providing an explanation of the former. The second problem is that if N(F,G) is a relation between F and G, then the necessity is, at best, providing a redundant explanation of the instantiation of G since a relation can only exist if its relata exist. This ensures that G is possessed by x anyway. The problems can be fixed by the following adjustments. First, instead of appealing to a second-order relation between F and G, N(F, G), we should appeal to a potentiality characterized by a stimulus F and a manifestation G. We can write this PF,G. This deals with the concern that the explanation offered is redundant. The instantiation of PF,G does not imply the instantiation of either F or G. Appeal to potentiality does not mean commitment to a powers ontology. F and G need not be potentialities and they need not have their causal profile essentially. PF,G may have its causal profile essentially but it is analysed in terms of a certain kind of dependence between properties. Second, we should take the law to be something that holds of a world and gives a potentiality to objects or spatiotemporal positions in it. This gives us the following structure.
L w; PF;G ðst1 Þ; PF;G ðst2 Þ;:::PF;G ðstn Þ : The law is thus a polyadic relation which is implicated in the explanation of any causal relation involving a particular property dependency. ‘PF,G(sti)’ involves particularizations of the universals F, G at a spatiotemporal position sti. The crucial point to realize about this characterization of a property-independent necessitation approach is that, while it shows how the two explanatory roles— particular and general—are played by necessity, the extent of its application is written into the law. So PF,G(st₁), PF,G(st₂), . . . PF,G(stn) might include all the spatiotemporal positions of w or a subset of them. The generalization is explained but it is not an



  

inevitable consequence of the character of the law that a generalization in its widest scope is explained. This will be important when we come to the role such an account of laws plays in providing a rational basis for induction. Before we consider that let us turn to property-dependent necessitation accounts of laws and how those putatively relate to generalizations. At first glance, the potential for a satisfying explanatory relationship seems to be greater. No appeal is made to a contingent relationship of necessitation. Instead, the relationship between the instantiation of the relevant properties seems to hold in all possible worlds. Nevertheless, in fact, similar difficulties afflict the propertydependent necessitation accounts. First, there is the analogous problem of structural universals for the powers net. The characterization of a powers net will involve multiple appeals to the same universal. For example, consider the instantiation of universals involved in the process of burning. Part of their powers will involve further instantiations of the same universals in other objects. The powers net that seeks to characterize their place in a network of potential causal relationships will have to appeal to these universals on more than one occasion. Perhaps it might be said that the potential for causal relations between the instantiation of the same universals in different objects could be represented in a power net as follows.

Figure . There is only one occurrence of the universal represented by the filled circle. The connector just indicates that the universal has a potential for causal relations with itself. A problem with this suggestion is that causal relations hold between entities that are distinct in some sense. This constraint would be violated. The suggestion would have to be that the powers net should not be understood as claiming that universals had the potential for causal relations with each other but rather it was making a claim about the instances of the universals in the powers net. Furthermore, the violation of the constraint would not deal with the more general difficulty. If structural properties have the potential to engage in causal relations then part of the characterization of the web will include multiple instances of a universal standing in bonding relations to other universals, that would have the potential to stand in further causal relations with universals some of which may be the very same universals. If the powers net is a structure of potential causal relations between particularized universals then it seems that the fact that a particularized universal, F, has a certain causal profile which mentions, say, causing an instance of G in circumstances C, does not imply anything about the generalization that all Fs cause Gs in C. The second issue for property-dependent necessitation accounts concerns the characterization of the potential for causal relations. At first glance N(F,G) seemed

   



appropriately general. It was only when we looked at the details that we saw that this was not the case. But the corresponding element in the powers ontology doesn’t have the appearance of generality written into it at all. We might characterize the potential causal relations, in which F has to stand, in non-general terms, for example, it has the potential to cause x’s possession of G in C (where x is a particular object). Of course, regarding this second point, if a causal profile is characterized in general terms, then (bracketing the first issue), we have the requisite generality. However, that is because we have explicitly characterized the causal profile in general terms. It is not the property-dependent necessitation that is doing the explanatory work but rather the fact that we have claimed this property-dependent necessitation applies generally. The discussion up to this point has focused on whether accounts of laws that appeal to necessitation provide an explanation of the generality of law unavailable to regularity theories. We found they did not. Indeed, they had to write in the generality. The issue is related to the question of whether necessitation-based accounts of laws are a necessary condition for a successful treatment of the problem of induction. This was the second subject matter of the present section. We can be briefer. The role of appeal to necessity in the treatment of induction is often taken to go as follows. We have a generalization that all Fs, we have observed, are Gs. As an inference to the best explanation of this limited regularity, it is suggested, we should appeal to a favoured necessity-based account of laws (Armstrong (), pp. –; Foster (–), (), pp. –). For example, we should conclude that N(F, G) or the powers ontology is true. But if we have grounds to believe that the generalization is explained by the relevant necessity, then we have grounds to believe not just that all Fs, we have observed, are Gs but that all Fs are Gs. Necessity-based accounts of laws justify an extension of the observed generalization to all Fs. Of course, we might be mistaken in our characterization of the generalization and, indeed, the generalization may just be accidental. So the inference is defeasible. The point is simply that, when we observe a certain regularity and we are careful about getting the conditions right, then it is reasonable to conclude, as an inference to the best explanation, that a relevant necessity holds (characterized by our favoured account of laws) and, hence, that the generalization doesn’t just hold for all that we have observed but extends to the unobserved too. The inference to the best explanation does not have to be quite so direct. The focus does not have to be upon explaining a particular observed generalization. Instead, it may be argued that the appropriate inference to the best explanation is that the observed world is a world of regularities and, apparently, active interacting particulars. The best explanation of this, en bloc, is a powers ontology in which natural properties and kinds have essential natures on the basis of which our law statements hold. In which case, the problem of induction is transformed. When we have an observed regularity, we are just interested in the question of whether the characterization of the regularity is in terms of natural properties and kinds. That would justify an extension of the regularity where grounds for thinking that the regularity is not so characterized would undermine the justification (e.g. Swoyer (), p. ; Ellis (), pp. –; Ellis (), pp. –).



  

The upshot of our discussion is that the explanatory claims of necessity-based accounts of laws are illegitimate. It is not the necessity that explains the generalization. Rather the generalization has to be written in. It is a generalization of a necessity-based account of a particular interaction. So necessity-based accounts of law do no better than regularity theories. Indeed, as we have seen, in themselves, the most popular versions do worse and have to be supported by regularity conditions. That does not mean that our conclusion should be that the problem of induction is insoluble. We can suppose that it would be simplest and best if the pattern we are seeking to explain was one that held of the unobserved too. But this is something to which the best system analysis can appeal just as much as either type of necessitation account. The point is simply that the problem of induction is no more soluble under necessity-based accounts than it is under regularity accounts and hence putative successful treatment of it is not a differentiating factor between the various accounts of laws. The preference for necessity-based theories over non-necessity-based theories reflects a preference for explaining why one type of entity succeeds another type of entity in terms of necessity. This preference is not further justified by making the problem of induction more tractable (for related sceptical discussion, see Beebee ()).

.. Counterfactual support Laws are taken to support counterfactuals. Some proponents of necessity-based accounts of laws have suggested that these accounts are particularly well suited to play this role. Indeed, the suggestion seems to be that their preferred account of law can provide the relevant backing independent of the issues that led to the provisional drawing up, and subsequent development of, a similarity weighting for counterfactuals begun in Chapter . This is a mistake. In the case of Armstrong, the idea seems to be that the antecedent of a counterfactual should be thought of as instantiated in nomically possible circumstances, relative to a fixed property-independent necessitation law, and the law establishes the truth or falsity of the counterfactual by proclaiming whether the consequent is true or false (Armstrong (), pp. , –). The proposal faces the familiar difficulties that arise from adopting a similarity weighting which places no value upon perfect match. First, it is not clear that the counterfactual is true because we have not taken across the supporting circumstances in which it operates. There may be a law between F and G but something which is an F only causes a G in the right circumstances, in particular, if there is no interfering property instance I. Yet, by excluding appeal to match, such information does not contribute to the evaluation of the counterfactual. Second, we would get a host of backtracking counterfactuals since, if we keep the laws fixed and suppose that a contrary to fact antecedent is realized, the past will be very different. This indicates that the proposal is ill suited to capture our notion of counterfactual support by itself. Power ontologists suppose that the truth of counterfactuals is, in some way, supported by the powers themselves. A preliminary thought is that if there is an object with a power, F, whose manifestation condition is M and trigger condition is T, then the appropriate counterfactual ‘If T were instantiated, then M would be instantiated’ is true (e.g. Jacobs (), p. ).

   



The preliminary thought needs adjustment. First, there might be circumstances in which instantiation of T causes the possessor of F to lose F. The classic example involves reverse electrofinks that act so as to deaden a live wire when contact is made so that no shock is given off (Martin (), p. ). In those circumstances, the counterfactual is false. Yet, it is still the case that the wire has the power to shock if it is touched. Second, there might be circumstances in which the relevant manifestation of the power is masked. A vase may be fragile but it would not break if wrapped in bubble wrap. Bird’s proposed adjustment is to add in the antecedent that the circumstances are not of the two types indicated: that is, there aren’t finks or masks (or antidotes) (the terminology changes) (Bird (a), pp. –). While the adjustment may show that, with certain qualifications, there is a link between the attribution of powers and the truth of counterfactuals, it cannot count as an alternative proposal to Lewis’. It does not tell us, given how the circumstances are (which may include the presence of finks or antidotes), whether a counterfactual is true. In particular, it does not give us any insight into what should be held fixed, and what may change, in the counterfactual circumstances in which the antecedent is true. Yet any of this may have an impact upon whether the consequent is true. Indeed, in fairness, I should note that, while Bird shows how the possession of a power in certain circumstances may imply the truth of a counterfactual, he does not develop a full-blown alternative semantics for counterfactuals. The need for appeal to circumstances can sometimes be obscured. For example, Jonathan Jacobs’ version of powers-based semantics for counterfactuals takes the relevant powers to be ones identified in the antecedent of a counterfactual which are such that every exercise of them brings about the manifestation conditions, his example is ‘If these chemicals were mixed, then reaction X would occur’ (Jacobs (), p. ). This might mean that, either, he has in mind a subset of powers that are not susceptible to finks and masks or he is taking their absence into account by phrases like ‘mixed’. At first glance, though, cases in which powers are masked are ones in which the powers are not exercised. In which case, his approach is subject to the indicated problem. Even if it is true that, whenever the powers are exercised, the manifestation conditions occur, mention of the powers in the antecedent of the counterfactual will have to include all the material relevant to the powers being exercised—which is exactly what talk of possible worlds is meant to supply—in order for the consequent of the counterfactual to be true. In providing the required details concerning the circumstances in which the power operates, the proposed alternative to Lewis’ approach simply becomes one in which the references to laws become references to the power ontologist’s preferred candidate for laws: powers. Proponents of this approach cannot claim that they avoid what they perceive to be the unmotivated aspects of a Lewis-style similarity weighting or that appeal to powers succeeds in remedying them (Lange (), pp. –, for an expression of a similar concern regarding Ellis’ appeal to similarity between worlds, Ellis (), p. ). Even if necessity-based accounts of laws fail to support counterfactuals by themselves, it may still be argued that they are a necessary component of support for counterfactuals. Proponents of such accounts of laws will say that, if there is no necessity, then there are no grounds for it being the case that the consequent would



  

be true if the antecedent of the counterfactual is true. Any events mentioned in the antecedent and consequent would only be ‘loose and separate’ (e.g. Armstrong (), pp. –, (), pp. –). There are three things that might be said in response to this argument. The first is that if what I have argued in the previous section is correct, necessities don’t provide a basis for extrapolating to counterfactual circumstances without writing in that they have application. The fact that, say, f₁ necessitates g₁ does not mean that for some other instance of F, f₂, f₂ necessitates g₂. Once it is recognized that the laws may not hold in counterfactual circumstances, then their necessity or otherwise becomes irrelevant. Necessities only support the extension if one adds that they also hold for the f₂, g₂ instantiations. This is no different from claiming that there is a lawful regularity that, thus, covers f₂, g₂. In a phrase, the mistake is to move from necessity of instance to necessity that there are necessities of corresponding instances. Even if my conclusions regarding the explanatory potential of necessity prove to be more limited, the argument pays no attention to the fact that the laws that are taken to back the counterfactuals are not just any old regularities but have special features. They are those whose statement is part of the best system of generalizations that capture the pattern of events that occur in the universe. They constrain our understanding of what are the most similar universes to the actual universe given certain, counterfactual, changes in circumstances. This provides a basis for claiming that the relevant counterfactuals are true in the way the similarity weighting has tried to set out. We are prepared to assert counterfactuals in the absence of necessity. For example, as discussed in Chapter , we move from ‘Either A or B’, to ‘If A were not the case, B would be the case’. Counterfactuals don’t insist upon the freight of necessity for their truth and they are inappropriate to convey a commitment to it. This brings me to the final point. The issue is not whether necessities provide a particularly satisfying grounding for the truth of counterfactuals. The issue is rather whether, in the absence of such necessities, it would still be legitimate to assert the counterfactuals. In brief, whether the legitimacy of our counterfactual talk may survive in a Humean world. The burden is on those who insist upon necessities— especially given their explanatory difficulties—to establish otherwise. A more significant issue, for the position I am ultimately developing, is whether necessity-based accounts of laws can be plugged into the general framework set out in the similarity weighting for counterfactuals I have outlined earlier. There is the concern that its formulation presupposes a particular view of laws, roughly the Humean picture. The concern expresses itself in two ways. First, there is the idea of law violation. The standard thought is that, for the antecedent of the counterfactual to be true, there will be some law violations. This is characterized as the laws relating the properties being a little different. However, the powers ontology rejects the idea that the laws may be a little different and the properties remain the same (Bird (), pp. –). Second, there is the appeal to perfect match. Consider the simplest version of the property-independent necessitation account in which laws are N(F, G). The claim is that these laws are instantiated in the causal relations between instances of F and instances of G. However, if the laws are a bit different, then different laws will be instantiated and hence there won’t, simply because of this, be perfect match. In the

   



case of the powers ontology, difference of laws implies difference of property. However, this again has the implication that there won’t be perfect match.² It’s important to be clear about the second of these points. It’s not simply that, where there is law violation, there won’t be perfect match. That’s true for regularity approaches to laws too. The issue is that since the laws are instantiated either as different properties having different causal profiles or different relations of property independent necessitation, the changes just before the antecedent won’t just apply there but will imply complete absence of perfect match prior to this. By contrast, regularity accounts of laws don’t have this implication because they take laws just to be patterns of property instantiation. A change, just before the time in which the antecedent is made true, does not imply that the past need be radically different since, antecedent to this time, there are just patterns of property instantiation and not further, instantiated, nomic facts as necessity-based accounts envisage. An initial response would be to note that proponents of both propertyindependent necessitation and property-dependent necessitation accounts of law are prone to take the basic laws as oaken. So it doesn’t follow from it being a law, say, that N(F,G) or that Nm(TF, M) that all Fs are Gs or that Ts always result in Ms. In which case, the laws may remain the same and yet intervening factors make it the case that there is no instance of G, or of M, just before the antecedent of the target counterfactual as a result of which the conditions under which the antecedent is true are realized. However, unless oakenness is taken to imply the falsity of determinism, relying on this feature alone looks to be inadequate. Determinism still requires that identity of past history plus laws entails identity of future events. So even if each law is compatible with the possibility of an intervention breaking the indicated connection between property instances, in order for the antecedent of a counterfactual to be true in a deterministic world, some extra-intervention law violation, or other, will be needed. For the purposes of illustration, in the case of the powers ontology, there may, perhaps, be a non-triggered manifestation of a power. So what we need to recognize is that proponents of these approaches to laws may have to adopt a slightly different way of conceiving of a change in the past in order to make the antecedent true. For example, they will have to suppose that the closest world involves a spontaneous indeterministic intervention or change which is not incompatible with any of the actual deterministic laws but involves a new feature. The more standard ways of imagining departures from the actual world in order to make the antecedent of a counterfactual true should be resisted in the deterministic case. Alternatively, perfect match might be understood as perfect match in non-nomic facts. This would easily deal with the case of property-independent necessitation approaches to law. The fact that N(F,G) would not be instantiated all through the past but N(FI, G) would not count as a relevant difference for the perfect match condition. In the case of the powers ontology, the closest world might involve a slight indeterminism that, though it shows up in law, does not plausibly result in a

² I’m grateful to Helen Beebee for making me think about this issue she notes in an unpublished paper of hers.



  

difference of different properties being said to be instantiated. For example, if we had not Nm(TF, M) but Nm(TF, P(M)= .), it is quite unclear that we should conclude that a different property is instantiated. The one thing proponents of necessity-based accounts of laws should not do, though, is reject the similarity weighting framework. In order to assess counterfactuals, we need some notion of keeping the circumstances fixed. Thus my conclusion is that, while neither property-dependent nor property-independent necessitation accounts fail to support counterfactuals, they have no claims to perform better than the regularity analysis. There are no grounds for differentiating in favour of one account of law or another with regard to their success in supporting counterfactuals.

.. Quidditism Both the best system analysis and property-independent necessitation accounts allow for the possibility that properties may have a different causal profile to the one they actually have. Indeed, so far as these theories go, they are committed to what Robert Black has recently dubbed quidditism: cross-world identification of fundamental properties is primitive (Black (), p. ). Black contrasts this position unfavourably with a powers ontology that claims that cross-world identification is a matter of shared causal profile. An attack on quidditism is, therefore, an attack on the viability of the first two accounts of laws offered above. The present section is aimed to turn the attack. One argument in favour of quidditism runs as follows. We have seen that an account of the identity and distinctness of properties cannot be made in terms of a causal network unless there is at least one source of asymmetry in the network. However, it seems possible that there are symmetrical causal networks. A good example of such a network is one in which there is simply a distinction of handedness, the left hand objects and the right hand objects, over which a symmetrical network of powers is characterized (mentioned at the end of ..). The distinction can only be captured by non-structural properties. This does not automatically mean that these non-structural properties fail to entail a certain causal profile. There may be distinct properties that entail a causal profile they share. Nevertheless, once the need for non-structural properties is recognized, then it seems that the way in which the two properties are distinct should be independent of their causal profile. Thus quiddities are introduced. The argument just given is not an argument in favour of their actuality but rather their possibility. That is all I need for the development of my position that putative accounts of laws committed to quiddities are one possible way for laws to be realized. It also throws into question many of the standard arguments against quiddities. In brief, my strategy in the rest of this section will be to show that either, in the light of the argument, a charge against quidditism is unfounded or a comparison or contrast alleged to be unfavourable to quidditism is illegitimate. Most immediately, the argument throws into question concern about the methodological utility of quiddities. It might be argued that science has no use for a notion of properties that makes them independent of the character of the causal structure in which they are situated and allows that, say, mass might play the causal role of electric charge in another possible world (e.g. Hawthorne (b), p. ; Eagle

   



(), pp. –). However, this is a mistake if the reason for the postulation of properties with this character is to make sense of causal networks with symmetrical structures. Another objection is that quidditism is as unacceptable as haecceittism about individuals. Regarding the latter, the charge is that it makes no sense to suppose that there is a distinct possible world in which I have all your properties and you have all mine. All we have done is swap the names over. So, likewise, it makes no sense to say that the property of inertial mass has the complete causal role of the property of charge and vice versa (Bird (a), p. ). The first point to make is that the question of whether or not some component of the causal role of a property is essential to it is distinct from the question of whether quidditism is true for the fundamental properties of the universe. Suppose that the objector is right about the property of inertial mass. Then the property is not a fundamental property of the universe, although it is related to one, viz the one that occupies the causal role distinctive of inertial mass. Second, and more significantly, there is an important sense in which haecceittism and quidditism are not on a par. Haecceitism requires that we recognize primitive individual differences rather than simply qualitative differences. Quidditism is not fairly described as recognizing primitive qualitative differences where a powers ontology does not. The powers ontology has its own primitive qualitative differences, viz. difference in the potential for causal relations. Since the power ontologist takes properties just to be these differences, it is not the case that one is primitivist about qualitative differences and the other is not. Rather, the difference is over which differences are primitive. On the assumption that there is no limit on the number of qualities independent of causal profiles, if quidditism is true then there will be an infinite number of worlds precisely the same as ours, in terms of causal profiles and patterns of causal relation specified in terms of causal profiles, and yet constituted from different properties occupying the causal profiles. Black suggests that this would involve ‘distinctions without a difference’ (Black (), pp. –). However, this matter should turn on whether there are reasons for supposing that the occupants of a causal profile should be contingently connected to it and not on any antecedent conviction that the distinctions drawn are not genuine. We have seen the circumstances in which this would be appropriate. So we have reason to suppose that there are at least some worlds in which the occupants of causal profiles are contingently connected to the causal profiles. That means that we have reason to believe that there will be an infinite number of worlds with the character that Black suggests. Since the differences Black dismisses are a consequence of independent theoretical considerations, we have reason to allow that they are present. A third line of objection to quidditism is epistemological. This comes in various forms. One worry is that it makes the fundamental properties of the world inaccessible to us. If quidditism is true, we don’t know which properties exist, merely, that some property or other occupies the causal role. This worry is misguided. On the assumption that there is a certain property which is causally responsible for our theorizing, and which we can think of as the occupant of causal role R, we know that that property exists, as opposed to some other property which, in another possible



  

world, may occupy the same causal role. The standard considerations in favour of not having to rule out every sceptical alternative apply here too. If it is insisted that the inability to rule out sceptical alternatives threatens knowledge in this case, then it threatens knowledge everywhere. We don’t, in general, take this to imply that our characterization of the physical world should be neutral over whether it is a physical world, a vat world, a demon-produced world, or the like. So there is no particular reason to suppose that we should adopt a powers ontology for this reason. Other treatments of knowledge yield a similar upshot (Schaffer (b), pp. –). A second epistemological concern takes a semantic twist. Suppose that each property is identified as the occupant of a particular distinctive causal role. Quidditism seems to allow for the following possibility: there are two properties that occupy a particular causal role. In which case, there would be no unique property and hence our term for the property in question would fail to refer (Bird (a), p. ). If our actual world is not such a world, then there is no reason to suppose that this kind of two (or more) occupant worlds counts as close and, hence, in need of ruling out. The laws would be significantly different. The similarity weighting developed in Chapter  supports this conclusion. So any account of knowledge appealing to a similar standard of closeness—as many do—would allow that we know that our property terms refer if the causal role is instantiated. Moreover, there is no reason to believe that the powers ontology brings with it significant epistemological advantages in this case, even if the desirability of these advantages could be motivated. The quidditist allows that there may be two properties that occupy causal role R. The worry is how we could distinguish between them. However, some power ontologists allow for the possibility of inaccessible causal potentialities: causal potentialities that we cannot detect (e.g. Bird (a), p. ). The specification of R will not include the hidden powers. So, by their own lights, there may be two properties that occupy a certain causal role R and the condition for successful identification of a property is not met. Quiddities are simply one way in which distinctions can be hidden for us. The merits of being able to rule out this way, given the existence of others like the one just described, are far from clear. As a result of this discussion, we should conclude that there are no good grounds for supposing that quiddities are impossible. Whether they are actual may turn on the structure of the causal network we have reason to identify in our best theories of the world. We are now in a position to turn to the implications for a proper account of laws of my defence of these three kinds of theories.

. Laws as Variably Realized: Structuralism about Laws My conclusion from the discussion in . is that each of the three approaches to law are defensible. Each captures the main features generally attributable to laws. There is no objection that seems to dish one candidate in favour of another. Each seems a good candidate for what the laws might be. But they can’t all be what laws are because they are radically different from each other. We might put the argument like this. Let L be laws and LBSA, LN, and LP be what laws are according to the three accounts

   :   



I have discussed: the best system analysis, the property-independent necessitation account, and the powers ontology. () () ()

◊ L = LBSA and ◊ L = LN and ◊ L = LP. ☐ LBSA ≠ LN ≠ LP. If ◊F = G, then ☐F = G (where ‘F’, ‘G’ are rigid designators of properties).

Therefore, by transitivity of identity and necessity of identity. ()

Not ().

In effect, I am using the strength of the individual accounts of law against them to show that none of them could count as identifying laws. Instead of taking the accounts as accounts of laws, we should take them as accounts of the different bases for the truth of law statements. It is helpful to compare the argument just provided with the argument for the variable realization of mental states. The standard argument starts with the plausible premise that, in different creatures, different kinds of physical state play the distinctive causal role of pain, or love, or belief, or the like. These different kinds of physical state are not identical to each other. So, by transitivity of identity, these mental states are not identical to kinds of physical states but realized by them. The difference between these arguments is that the argument concerning laws has a premise based upon the possibility of laws being identical to one or other of the accounts rather than claiming it is so identical. That’s because it is implausible that each account of law represents one way that laws are realized in the actual world. Nevertheless, that’s just an artefact of the most plausible way of developing this kind of argument concerning our mental life. The argument from variable realization could have rested on the possibility rather than the actuality of different kinds of mental states playing the distinctive causal role of pain or belief (say). In the argument, I took ‘L’ to be a rigid designator of a certain kind of property— laws—in the sense that, in every possible world in which the property is instantiated, ‘L’ refers to it. If L is identical to LBSA in one possible world, then it picks out LBSA in all possible worlds. But it doesn’t because there are other properties that would be just as plausible candidates for law. There would be just as much reason to suppose that ‘L’ picks out these other properties. Thus, it is not possible for L to be identical with any of LBSA, LN, and LP. Suppose it is argued that, although there is no reason to favour the identification of L with LBSA rather than LN, in fact L is identical with LBSA. By analogy, although there is no reason to identify pain with human pain rather than what looks to be octopus pain, in fact pain is human pain. This would seem to rely upon an additional hitherto unidentified factor to be the basis for the identification. I can’t rule out that there is such a feature. The argument depends upon all the central features of laws being accounted for and I have drawn on the features generally identified to be distinctive of laws. Perhaps there is still something to take into account that somehow differentiates between the three accounts. It is hard to see what this would be since I have been discussing the main ways in which each of these accounts is taken to be favoured over the others. Similarly we would question whether there were grounds to deny that an octopus is in pain.



  

It is not mandatory to think of ‘L’ as a rigid designator. Instead, we can think of ‘L’ as an abbreviation for the various features we plausibly attribute to laws, central ones of which we discussed under the headings of generality and induction. ‘L’ would then have variable reference picking out whatever had those features in a possible world. In which case, ‘L’ need not pick out the same property in every possible world. () is false. The necessary non-identity of LBSA, LN, and LP is compatible with it being possible that L is identical with LBSA, possible that L is identical with LN, and possible that L is identical with LP. In each of the possible worlds described, different types of thing play the law role and these types of thing count as the laws for that world. Nevertheless, the property of being a law—on this perspective, a second-order property—is none of these things. Either way of formulating the point will enable us to develop an alternative way of dealing with the problem cases for the three putative theories of laws discussed above. To keep things brief, I will adopt the first. The possibility of the complex laws of our world holding in a simple world is the possibility that a different realization of laws— than that of the best system analysis—holds in that simple world. The possibility of uninstantiated laws without commitment to Platonism—the Tooley case is an example—is the possibility that a powers ontology hold of that world. The possibility of symmetrical causal networks is the possibility that some networks are supported by a realization of laws other than the powers ontology. So we have a situation in which the central features of laws are supported by all three realizations of laws and the problem cases by the existence of the distinct realizations. The success of this treatment is a further consideration in favour of the approach recommended here. If the accounts of different bases for the truth of law statements described above are not the laws, then what are laws? If they are accounts of laws but not of the second-order property of being a law, then what is this property? Should we conclude that laws as such—or the second-order property as such—don’t exist? There are just best system analysis laws, property-independent necessitation laws, and the powers ontology laws. It is natural to wonder whether there is something common to all three types of laws that make them all types of laws. If there were, then we might take the various putative accounts of laws discussed in the previous section to be different realizations of this common feature. My suggestion is that laws are potential patterns of causation (or the second-order property is the property of being a potential pattern of causation). The conditions for the manifestation of the potential are expressed by the antecedent. The basis for the potential are the various accounts of laws understood as realization conditions. The general form of a deterministic law is: for all x, there is some y such that if Fx, then Fx causes Gy. The general form of an indeterministic law is: for all x, it is probable that there is some y such that if Fx, then Fx causes Gy. The characterization of causation in the consequent would be provided by my counterfactual analysis. One obvious objection is that the account seems circular. The similarity weighting for counterfactuals is partly understood in terms of laws. Now counterfactuals are being used to elucidate laws. My response is that the appeal to laws in the similarity weighting should be understood in terms of law realizations. These do not rely upon the analysis of causation. The analysis can then be used to explain what is common to the three accounts of law realizations.

   :   



A second objection concerns the possibility of conflict. Consider a world in which property-independent necessitations are present in a way which conflicts with what would count as the best system of generalizations covering events. What then are the laws? My answer is that the property-independent necessitations have primacy. Just because the best system analysis identifies something that is good enough to count as laws does not mean that it should be given equal privileges to the richer theories. The primacy reveals itself in the counterfactuals we are prepared to assert concerning simple worlds. This does not undermine the claim that the best system analysis provides us with one way in which laws are realized. We should just recognize that the realization base has a minimal duplication requirement. Thus Any world that is a minimal duplicate in terms of patterns of particular matters of fact to a world w for which Humean supervenience holds, is a nomological duplicate of w (cf. Jackson (), p. ). A world in which there are property-independent necessitations is not a minimal duplicate. The situation is comparable with what physicalists say about the possibility of non-physical accounts of the mental. If physicalism is true, then a minimal duplicate of our physical world is a duplicate simpliciter (e.g. in terms of the mental properties instantiated). Nevertheless, there might be worlds in which the mental properties instantiated vary in virtue of the existence of non-physical mental properties. There is no need to suppose that, because, in a world without necessities, there are laws, in a world with necessities the laws still be patterns of particular matters of fact (contrary to what Briggs argues in favour of the claim that the best system analysis if true, is necessarily true (Briggs (), pp. –)). This also means that the best system analysis supervenience base of laws must have a ‘there are no necessities’ condition. In worlds in which there are, this is not the supervenience base of laws. Since the best system analysis takes laws to be settled globally anyway, with a ‘and nothing else’ clause, this doesn’t seem to be a particularly problematic part of the position.

. Concluding Remarks In the course of this chapter, I have defended three approaches to laws: regularity, property-independent, and property-dependent necessitation theories. In the case of property-independent theories, significant reformulation of those most popular in the literature proved necessary. Each approach has, through the history of philosophy, found favour. For example, elements of a property-independent necessitation account can be found in Descartes, and of a property-dependent account can be found in Aristotle (Ott (), pp. –, –, –). Given the argument of the last section, we can now see that these are three realizations of laws (or three different players of the law role which possess the second-order property of being a law which is not to be given an account in terms of them—call these realizations of laws in an extended sense). The fact that these realizations can be characterized independently of causation explains how we can appeal to them to provide a semantics for counterfactuals that allows for a counterfactual analysis of causation.



  

The existence of these three options significantly weakens the strength of objections against each. For example, we noted that the idea that we can consider how our laws might apply in a simple world, which would not make them the best system of generalizations to characterize what is going on, was a prima facie objection to the best system analysis. We take laws to be invariants in this sense. Equally, the case of symmetrical power nets presented a problem for explaining how certain powers are distinct from other powers in the net for a powers ontology. Such objections, we argued, are a case for one of the other realizations of laws for the possibilities envisaged to be problematic. Each type of realization brings with it a particular characterization of the kind of potential pattern of causation that constitutes laws. Matters would be different if there were compelling reasons to favour one approach to laws over others. However we found that was not so. The distinct accounts of the realizations of laws reflect preferences about how regularities can be explained. We saw that the preferences could not be justified by, centrally, providing a better basis for a solution to the problem of induction. Each realization of laws had to write in the requisite generality rather than provide a successful basis of it. Similarly, no realization of laws had a particular advantage in explaining the truth of counterfactuals because all three needed to appeal to the possible worlds framework and similarity weighting. Finally, there were no metaphysical or epistemological issues raised by the truth of quidditism under non-property-dependent accounts of laws. Laws are one way—perhaps the primary way—in which, given a certain state of the world, the chances are fixed. However, in Chapter  (see especially .., .), we allowed for the possibility of primitive non-nomic chance-fixing (if nomic chancefixing implies generality) and in the present chapter (.) we discussed how this should be understood to allow for the possibility of characterizing brute singular causation in terms of counterfactuals. This requires an adjustment to the similarity weighting previously defended which I mentioned in . but set out here. (A) It is of the first importance to avoid big, widespread, diverse violations of chance-fixers. (B*) It is of second importance to maximize the spatiotemporal region throughout which perfect particular matter of fact prevails unless, in so doing, we fail to minimize departure from the distinct events (or their absences) that the counterfactual events required for the truth of the antecedent of the counterfactual makes more (non-derivatively) Σ-probable given that their antecedent is actually false. (C) It is of the third importance to avoid even small, localized, simple violations of chance-fixers. (D*) It is of fourth importance to maximize similarity of particular fact which is (non-derivatively) Σ-probabilistically independent of the truth or falsity of the antecedent. The chance-fixers mentioned in the similarity weighting are those that, we have seen, are potentials for patterns of causation in the case of causation involving law. As noted earlier, brute singular causation is accommodated by the similarity weighting because (B*) discounts perfect match which fails to minimize departure from

 



the distinct events (or their absences) that the truth of the antecedent makes more (non-derivatively) Σ-probable, and we have accepted that there can be non-derivative singular chance-fixers. The resulting picture of causation and laws is that causation is not to be reduced to laws because additional facts are required, in addition to laws covering the relevant events, to settle whether or not they stand in a relation of cause and effect and the most substantial argument in favour of appeal to laws was unsound, given features of my analysis of causation (.). Similarly, although laws are to be understood in terms of causation—laws are potential patterns of causation—an understanding of a particular realization of laws, and its contribution to causal facts, can be stated without appeal to causation. Nevertheless, the fact that different realizations of law are grouped together by being potential patterns of causation displays one way in which causation is horizontally fundamental. Although I have appealed to chance-fixing, one matter which I have not discussed in any detail in this chapter is what Lewis has called the big bad bug for the doctrine of Humean supervenience, namely the nature of chance. Probabilistic laws have also figured only in passing, subjected to little scrutiny. I shall focus on this also in Chapter . The other issue which immediately arises is the connection between the position defended here on law and the metaphysics of modality in general. This returns us to the matter raised in the opening chapter, namely the implications of taking Humean supervenience to be a contingent truth, for reductive approach to modality. I shall be considering this in Chapter .

 The Ontology of Chance The nature of chance is relevant to my analysis of causation because it involves appeal to chances in the consequents of the counterfactuals that make up the analysis and also in the similarity weighting for the counterfactuals themselves. Chance is a big topic in its own right and not something of which I can hope to provide a significant treatment in the present work. Some discussion of the nature of chance is necessary, though, to provide further defence of the position I outlined in Chapter  on laws. If a key element of laws is their chance-fixing capacity, and only one or other of the accounts of laws outlined in Chapter  proves adequate to the task, then laws may not prove to be variably realized after all. The discussion of the present chapter will focus upon this challenge to the different candidate realizers of laws (by my lights). It will involve two charges. The first is that the best system analysis of laws cannot accommodate the natural link between chance and credence (the degree to which we believe something) because it allows for the possibility of undermining. The best system analysis retains an explicit, though complex, link between chances and frequencies (that is, the link between, for example, chance of a coin coming up heads and the frequency of heads as a proportion of the results of coins tossed). As a result, there is a chance that a certain pattern of events occurs which would, if it were to occur, imply that a different theory of chance held, where this means a different assignment of probabilities to kinds of events. When coupled with a natural way of relating chance to credences, the principal principle, (for details, p. ) the upshot is that the latter will (counterintuitively) recommend that we have contradictory beliefs for a range of cases. The second is that propensity accounts of chance cannot explain why it is rational to conform our credences to chances. The second charge affects property-independent and property-dependent necessitation accounts of laws. Although they differ in the precise ontology they ascribe to dispositions and powers, they are united in taking chances to be propensities rather than, as the Humean does, some refinement of frequencies. However, in so doing, this breaks the link between chance and limiting relative frequencies and, indeed, makes the connection between chance and long-run frequency, of whatever form, problematic. The long-run frequency of a type of event is the proportion of this type of event compared with a more general type of event over a significant number of cases. The expectation is that long-run frequency will approximate to the chance of an event, although may not according to some propensity theorists (e.g. Fetzer (), p. ; Gillies (), p. ). As the number of cases approaches infinity, it is said that the proportion tends towards a certain limit given by the chance of the type of event in question. This is its limiting relative frequency. A Variety of Causes. Paul Noordhof, Oxford University Press (2020). © Paul Noordhof. DOI: 10.1093/oso/9780199251469.001.0001

   



The potential break between propensities and these notions of frequency is bad enough in itself. However, since the most plausible defence of the rationality of conforming our credences to chances relies upon chances being related to the frequency of kinds of events and, thus, to outcomes which would constitute successful action, the charge is that propensity accounts face the second challenge mentioned. In the worst-case scenario, the charges are that of inconsistency (in the case of Humean accounts) and irrationality (in the case of propensity accounts) respectively. Given my previous aim, the minimal condition for success in this chapter is to establish that there is no consideration drawn from chance that favours one realization base of laws over the other. If there were, then this would be a consideration in favour of this realization base not just being a realization base of laws but, in fact, the proper account of laws. As we shall see, no such consideration is forthcoming. Nevertheless, I shall seek to do a bit more. I shall try to provide preliminary grounds for supposing that both approaches count as a reasonable account of chance. . will focus on undermining. I shall argue that the correct treatment of this possibility is to revise the principle principal and, with this revision in place, the best system analysis does not face a problem. Although it is said that the motivation for revising the principle is one that only proponents of the best system analysis will feel, in fact adjustment is needed to accommodate many non-Humean propensity theories too. The purported challenge to the best system analysis is, in fact, more general. In ., I will turn to the proper formulation of a propensity account of chance. This comes in roughly two types. According to the first, the fundamental case for propensity theories is single-case probabilities. Many such theories have difficulty relating the single case to limiting relative frequencies and, indeed, frequencies generally. They avoid the problems of undermining but make the second issue— that of providing a rational justification for the principal principle—especially intractable. Those that do not face this problem become prey to objection from undermining. According to the second type of propensity theory, the fundamental case for propensity theories is long term or limiting relative frequencies. Such theories have difficulty showing their application to the single case and, depending upon how they are characterized, are more open to the objection from undermining. The result is that the objection from undermining is a cost theorists pay to avoid other difficulties. It is not something that decides matters against Humean theories of chance and the best system analysis specifically—especially once it is recognized that a revision to the principal principle is appropriate. The extent of the application of the objection from undermining has been obscured by different ways of understanding the dispositional nature of propensity theories. In the course of the development of propensity theories, I will discuss the so-called Humphrey paradox. I argue that it shows that propensities are the truth-base for objective probability statements but not all objective probability statements have specific corresponding propensities concerning them. Taking propensity theory as a global supervenience claim also helps with the proper way to understand the connection between an event having chance  or , and it occurring or not. With this material on the formulation of propensity theory, and the objection from undermining out of the way, I then turn to the justification of the principal principle. My conclusion will be that propensity theory suffers a slight disadvantage obscured



   

by the error about induction and laws I identified in ... Nevertheless, this does not decide matters in favour of the best system analysis. It just underlines the point that the theories are finely balanced between costs and benefits and thus equally appropriate as realizations of laws.

. Undermining and Contradiction Suppose that Tw is the true theory of chance about the world w. It is the conjunction of all the conditionals that take a complete specification of the world’s history up to t in the antecedent, for variable t, and give a chance of a particular event in the consequent, for every such event in the world subsequent to t (Lewis (), p. ). Let Htw be the history of a world w up until time t. The conjunction TwHtw gives the history of the world up to a certain time t and the chances of all events subsequent to t conditional upon that history, for every possible value of t. There will be certain ways in which the world might develop, Fu, after any t that would be incompatible with Tw being true. If, as the best system analysis claims, candidate statements of law are tested for fit, where this is understood to be making the course of events in w more probable than another candidate law statement, then certain attributions of chance will fail to hold if the future develops in any of these ways. So Tw will give chances concerning its own undermining, that is, a chance to there being a course of events, Fu, which would mean that Tw is not the correct theory of chance. Yet, also, if Tw is the correct theory of chance, then the chance of an undermining sequence will be zero. In itself, this is peculiar but not an immediate problem. Nor is it a problem that only afflicts the best system analysis although it is more limited in its application to other approaches. Any propensity theorist who is committed to chances entailing limiting relative frequencies (e.g. long-run propensity theorists or certain proponents of the single-case approach) must concede that, in worlds with an infinite number of events, the correct theory of chance will allow that there may be an undermining future that is inconsistent with the theory (e.g. Hacking (), p. ; Hempel (), p. ; Mellor (), pp. –, (), pp. –, ; Schaffer makes a related point, Schaffer (b), p. ). The chance attributed to this, and, indeed, any, future will be either infinitesimal or 0 depending upon your views of how probabilities of infinite sequences of events should be measured (Elga ()). However, even the attribution of 0 chance to the sequence of events is compatible with this future happening (as we shall see in .). So some propensity theories cannot make the complete theory of chance fail to allow for the possibility of undermining while at the same time entailing, if it is the correct theory of chance, that this does not happen. It would be better not to insist the correct theory of chance must be otherwise (see Bigelow et al. (), p. , here I agree with Lewis (), p. ). The problem arises as a result of the natural link between chance and rational credence. By Lewis’ lights, chance is objectified credence. The motivation for making the link concerns the particular role that knowledge of chance is meant to play in our beliefs about the world, and consequent action upon it. In order to succeed in what we do, it would be most useful to be omniscient. For example, if I have to bet on what face of a die will come up next, the best information will include the true proposition

  



that the die will come up . That will make me successful. Hall has characterized this as being a database expert. The second best information will be that the actual frequency of the various faces of this die in the future of its existence is such and such. Both bits of information concern the future. If chance is distinct from the actual frequency, then it is a candidate for being the third most useful piece of information. The latter involves what has been dubbed analysis expertise. Chance is that which takes you from a limited data set of particular matters of fact, not including the fact you desire to know, and outputs a chance of that fact holding. If we conform our credences to this aspect of the world, then our actions based upon them are most likely to succeed in the absence of the other information. This view of the matter is naturally enshrined in Lewis’ Principal Principle and it is through this that the phenomenon of undermining generates a contradiction. Lewis formulates it as follows. CrðA=XEÞ ¼ x: Here Cr is a reasonable initial credence function, A is the target proposition concerning a particular event, X the proposition that the chance, at time t, of A’s holding is x, and E any other admissible proposition (Lewis (), p. ). In brief, the principal principle says that we should attach the same credence to A as the chance of it holding under certain conditions so long as we only conditionalize on admissible propositions. Admissible propositions are those which, if they are relevant to the credence we attach to A, are relevant by being relevant to credence concerning the chance of outcome stated by A. So once the chance of the outcome is given, admissible propositions have no further impact. Some deny that credence should track chance. Beebee and David Papineau have argued that credence should track relative probabilities instead, where these are probabilities of particular events happening relative to those features of a situation known by the agent (Beebee and Papineau (), pp. –). Chances are a subclass of relative probabilities where the features the agent knows are all the relevant features of the situation. Given that they accept that chances are a subclass of relative probabilities that our credences should track, it is unlikely that their position avoids the difficulty discussed below but let me defend, briefly, the focus on the principal principle. Consider a deterministic world in which we are tossing a fair coin. What credences should an agent attach to the coin coming up heads, and the coin coming up tails respectively? According to one plausible line of thought, the answer is the relative probability of /. But if the world is deterministic, the chance of heads (or tails) is  and the chance of the other . Beebee and Papineau take the basis of the answer / to be that the agent has knowledge of only some of the features of the situation, those in which it seems equally likely that the coin will come up heads and tails. The suggestion seems unsatisfactory. If we characterize situations by proper subsets of their relevant features and consider the frequency of outcomes, then the proportion of the outcomes may reflect the envisaged probabilities assigned: one half heads and one half tails. However, they eschew a frequentist interpretation and, for the reason identified below, it would have difficulty applying to the particular case (Beebee and Papineau (), pp. –). According to their position, relative



   

probabilities are fixed by laws that attach to subsets of the relevant features of a situation (e.g. Beebee and Papineau (), p. ). The problem is that the connection between these features and the probability in question may be disturbed by the presence of other features. There is no straightforward connection between a set of conditions and an effect, or probability of an effect, without some kind of exclusion clause such as the probabilities in question are relative to such and such features and there is nothing else to disturb the connection. Whatever features of the situation are required to result in, eventually, a head or a tails, will disturb the connection since they will alter the probabilities. Yet, if they are excluded, then they will alter the situation too because, in that case, there will be no probability of either a head or a tails, for example, because it is excluded that the coin is travelling through the air. The only relative probability for which this is not true is chance because that is relative to all relevant features and so there are no features which are both required for there to be a chance of the event but at the same time need to be excluded to keep the relative probability fixed. So there is a problem in understanding what Beebee and Papineau have in mind by such probabilistic laws. It is, in any event, implausible that, where T is a proper subset of the relevant features of the situation, ‘In such and such type of circumstances T, the probability of heads is one half ’ expresses a generalization required in the best system of laws to describe the pattern of events in the world or that ‘It is a law that in such and such type of circumstances, the probability of heads is one half ’ records the presence of a necessity, property independent or dependent. Perhaps more importantly, there is also no motivation for moving from chances to relative probabilities. The phenomenon to which Beebee and Papineau appeal can be explained by the general principle from which the principal principle specified above is a special case. According to the general version P P Cr(A/E) = x Cr(Xx/E)Cr(A/XxE) = x Cr(Xx/E)x (Lewis (), p. ). Here Xx is the proposition that the chance at t of A is x (for different values of x). Cr(Xx/E) is our credence in that particular hypothesis concerning the chance at t of A. Cr(A/XxE) gives the credence we should have in A at t under that hypothesis. So, overall, our credence in A, given admissible evidence, is given by the weighted sum of particular hypotheses as to the chance of A given the evidence. The subject who is about to toss a coin is in a state of knowledge whereby there are two equally likely theories of chance, one which puts the chance of the coin turning up heads as  and one which puts the chance of the coin turning up tails as . So looking at the formulation for the general principle Cr(Xx/E)Cr(A/XxE), Cr(Xx/E) is / and Cr(A/ XxE) has the value . Relative probabilities, which are not chances, are conditional credences about which theory of chance is correct. Consider now Beebee and Papineau’s case of Elspeth in a deterministic world. She has performed a large number of coin tosses on a newly manufactured coin and found it came up heads  per cent of tosses. Beebee and Papineau claim that her credence for heads in the next toss should be . and that this reflects a relative probability. It is not something that might be justified by the principal principle (Beebee and Papineau (), pp. –). Once again, the general principle can explain what is going on here. In this toss, as in all previous tosses, the chance of heads will be either  or . The issue is which theory of chance is correct for this

  



particular case. The evidence of previous tosses suggests that the theory of chance which is correct will be the one which attributes chance  to the event of coming up heads. We should believe that this theory is correct with credence .. If the first difficulty, relating to the status of relative probabilities, could be resolved then there would be little harm in taking agents to be seeking to conform their credences to relative probabilities regarding which theory of chance is correct. However, the case of Elspeth reveals there still may be costs. She may find nothing untoward in the coin or the manufacturing process. According to Beebee and Papineau, the appropriate principle relating credence and relative probabilities is as follows. The Relative Principle: The correct subjective probabilities for an agent to attach to outcomes {oi} are the probabilities of the {oi} relative to the agent’s knowledge of the set-up (Beebee and Papineau (), p. ). In the present case, the known features of the situation might well support there being a / chance of heads and tails. The  per cent of heads from previous tosses is not a feature of the current set-up although it might support the view that there is a feature of the set-up to explain it. How are Beebee and Papineau to explain their verdict that Elspeth should believe with credence .? Shouldn’t Elspeth be attaching credence to the outcome, by their lights, weighing relative probability suggested by the known features against those suggested by the frequency? There is no reason to suppose that the credence in these circumstances should be .. By contrast, as we saw above, it is reasonably straightforward why we should take the credence to be . within Lewis’ framework. We have grounds to conclude that credence should track chance in roughly the way that the principal principle suggests. There are other candidate principles, and criticisms of the principal principle’s formulation in other respects, concerning the relationship between chance and credence. I shall not consider these since they are independent of the points I wish to make. Our focus is on how the principal principle, together with the point about undermining made earlier, has been turned into an argument against theories of chance for which Humean supervenience is true. Recall that in Cr(A/XE) = x, E is a placeholder for any admissible proposition. Two candidates for admissible propositions are propositions about the history up until a certain time t and propositions about chances. An example of an inadmissible proposition would be a proposition about some future event. For instance, A itself is inadmissible. With this understanding, a special case of the principal principle is CrðA=XHtw Tw Þ ¼ x: The problem posed by undermining now becomes obvious. Given that Fu is a proposition to the effect that a particular undermining future occurs (that is, it is a detailed specification of such a future, not that it is specified to be an undermining future), then since Tw gives it a non-zero probability, Cr(Fu/XHtwTw) = x > . On the other hand, if it is an undermining future then Cr (Fu/XHtwTw) =  since, given Tw, the undermining future does not occur (Lewis (), pp. –, see also Lewis (b), pp. xiv–xvi, –, ).



   

The second claim—that Cr (Fu/XHtwTw) = —isn’t true if this world is a nonHumean world in respect of chances. No pattern of particular matter of fact in w entails that Tw can’t be true of w so long as Tw doesn’t attribute probability  or  to finite sequences of events in a non-Humean world. Since I hold that there may be non-Humean worlds with different ways in which laws are realized, and hence different ways in which chance is realized, the argument is, as it stands, vitiated (Vranas (), p. ). Some reject this approach on the grounds that the best system analysis is necessarily true, or that this is certainly Lewis’ view (e.g. Hall (c), p. , fn. ; Schaffer (b), p. , fn ; Briggs (), pp. –). I demur for reasons made clear earlier. Nevertheless, I am not happy with relying upon this response since the challenge might be reformulated. First, recall that I have argued that one may have empirical grounds for adopting one view of how laws are realized rather than another. These can figure as part of the material on which Fu is conditionalized. We may well attach different credences to the different possible realization bases of laws. In which case, our credence in Fu although not  will be a function of the weights of these different credences. This would result in a credence value which is less than the assignment of chance, x, given by each theory of chance but greater than . It would still be inconsistent with the claim that the credence should be x (from the principal principle and theory of chance, Tw’s, assignment). Indeed, the idea that we should weight the different credences attached to Fu by our different credences in the realization bases of laws looks to be an objection to the approach to laws I have recommended. The link between what the theory of chance says and what our credence should be is not straightforward in the way that is envisaged. Second, and this is a related point, the application of the principal principle both to particular cases, and more generally, to whether it should be endorsed in our world becomes an a posteriori matter. It will depend upon empirical considerations about the correct realization basis of laws and considerations about whether or not a certain sequence counts as an undermining future. This is a counterintuitive status for the principal principle to have. It is plausible that, if it is a rational constraint upon credence, it should be something that is known a priori. Another line of response to the contradiction generated by the application of the principal principle to undermining is to claim that we will never be in the situation in which one of the pieces of evidence we have tells us which theory of chance holds to tell us what the chance of an event is. At best, we will have various hypotheses about what the chance of an event is relative to certain evidence (Roberts (), S– S). In which case, the general version of the principal principle rather than the particular version stated above will apply. There are two reasons why such a response is inadequate. The first is that since the special case is entailed by the general principle, if the special case results in a contradiction, then that impugns the general principle. Second, as we saw above, if the general principle is true, then ∑x CrðXx =EÞCrðA=Xx EÞ ¼∑x CrðXx =EÞx: That is, for each candidate hypothesis that the chance of A is x, the credence— Cr(A/XiE)—should be x. However, if A is an undermining future for some theory of

  



chance that attributes x to A, then Cr(A/XiE) will be . In which case, for the equality to hold, the credence Cr(A/Xi*) (where i* ≠ i) should have a value greater than x, the chance according to a distinct theory of chance, since the right hand side of the equation has no cases in which Cr(Xx/E)x is . Roberts holds that there is every reason to suppose that this will be the case. But there is no reason to think so. If A is not an undermining future for a particular theory of chance, then the whole point of the principal principle is that Cr(A/XxE) should be x. Even if it could be argued that Cr(A/Xi*E) should have some other value, there is no reason to think it should be compensatorily large to make up for the times when Cr(Xx/E)x is . So we can’t argue that the circumstances in which we find ourselves will be ones in which no contradiction is generated. Instead, it looks like the principal principle needs to be adjusted to remove the recommendation to have contradictory beliefs. According to the old special case of the principle: CrðA=XHtw Tw Þ ¼ PðAÞ ¼ x: That is, our credence in A, given X—the proposition that P(A) = x—should be the value of the P(A), x. Lewis and Hall’s thought is that we should replace it with CrðA=XHtw Tw Þ ¼ PðA=Htw Tw Þ; dubbed the New Principal Principle. By conditionalizing the chance of A on HtwTw we are, in effect, throwing away the undermining futures. These get the value  because we are presuming that HtwTw holds and so the undermining future has not taken place (Lewis (), pp. –; Hall (), p. , Hall (c)). Lewis justifies the conditionalization upon Tw by appeal to the issue of inadmissible information. In the case of an undermining future, the truth of a theory of chance, if Humean supervenience holds, provides information that the future does not occur, independent of the chance that the theory of chance provides it. So, in this case, straight appeal to the theory of chance involves inadmissible information. By conditionalizing on the theory of chance, undermining futures are given a  chance and, thus, no contradiction arises. A problem with this justification is that it is motivated by a commitment to Humean supervenience. As a result, those who deny that Humean supervenience is true for chance have a consideration in their favour. They can retain the old principle. A theory-neutral motivation for the new principal principle would be preferable. Hall argues that one is available derived from thinking through the idea that chance is an analyst expert (mentioned earlier), formulated as follows.   Cr A=Cht ðA=EÞ ¼ x ¼ x: The chance, at time t, of A on the basis of evidence E is the best advice one can obtain regarding what credence one should attach to A on the basis of E (Hall (c), p. ). He argues that taking chance to be an analyst expert removes the need for restricting E to admissible information. Analysts just take whatever evidence we have and yield the best possible advice about the credence we should put in P. In addition, he claims that such experts don’t make claims about their own expertise. The first



   

element vitiates Lewis’ motivation for the new principal principle, the second element points the way to the revision. Both face problems. The problem with the first element is that it claims that chance is a general analyst expert whereas it is plausible that, in fact, its expertise is more specific. By Hall’s lights, the theory of chance covers all assignments of probability relative to a time, including events in the past or the future about which we have evidence (for example, by clairvoyance, if that were possible). Suppose that the evidence includes one of the following about a time or times after t. (Occurrence) The coin comes up heads at t +  (where the coin tossing is an indeterministic process where the chance of heads and the chance of tails is / respectively). (Frequency) The frequency of heads and tails after t until the end of the universe is / heads and / tails. Clairvoyance, an all knowing demon, etc. are possible sources of such evidence. In these circumstances, the chance analyst doesn’t change its view about the chance of the coin coming up heads at t +  or, in the case of frequency, the chance of the coin coming up heads later than t. Chances don’t reflect a general analysis of such evidence about outcomes for our credences. So, whatever kind of analyst is providing guidance here Cr(A/Cht(A/E) = x) = x, they are not a straightforward chance analyst. Supernatural Newcomb cases provide another illustration. If I decide to two box, then the credence I should attach to the supernatural being placing £ million in the opaque box is very low. If I decide to one box, then the credence I should attach to the supernatural being placing £ million in the opaque box is very high. Price argues that if causation involves chance-raising, the correct way to interpret supernatural Newcomb cases is that the subjects’ decisions cause the prior predictions of the almost infallible being (Price (), p. –, ). In other words, we have a case of clairvoyance. Part of the motivation for his position is drawn from Hall’s idea that chance is an analyst expert. However, the same doubts I raised a moment ago about whether chance is a general analyst expert applies here too. We should distinguish between raising the evidential probability attaching to the proposition ‘The supernatural being placed £ million in the opaque box’ and raising the chance. The latter is captured by counterfactuals with probabilities in their consequent. It is not true that if I had chosen to one box, the supernatural being would have placed £ million in the opaque box. Instead, the supernatural being may have gone wrong. The credence subjects have in a proposition is partly a consequence of their subjective feelings of certainty potentially unconnected with chance, evidence as to frequency, and so forth. However, if subjects’ credence does try to reflect features of the environment, then this on the basis of three kinds of credence-related input (rather than simply chance), each of which constitutes some kind of evidence that a certain proposition is true. I dub these inputs to the evidential probability of the proposition believed (Figure .). First, there is the information provided by the theory of chance itself: a certain kind of expert input into credence. It does not cover information about the likely truth of the proposition derived from simply being a database expert—those relating simply

  



Credence

Evidential Probability

Chance

Derivative

Data about Occurrences

Figure .

to the knowledge of the occurrence of events, or their frequency of occurrence. I have grouped those under ‘data about occurrences’. Nor does it include the evidential probabilities that result from derivative probabilities, for example, effects providing good evidence of their causes in the medical Newcomb cases or common effects in supernatural Newcomb cases. These are additional elements. Of course, there may be an argument against recognizing these distinctions between distinct sources of evidential input into credence but it shouldn’t be thought of as a natural move that needs no further defence. The motivation for Lewis’ appeal to admissible information is intact. We can agree that chance is objectified credence without taking these other sources of information as part of our understanding of chance. To see this, consider an analogy. Those who adopt a dispositional account of colour might suggest that colours are objectified colour experiences. In normal conditions, for normal perceivers, if a subject has a certain colour experience of an object, then the object itself has the colour in question. There are complexities but they don’t impact on the basic point. Suppose we were seeking to provide a characterization of when our colour visual system was working appropriately. We might put the relationship like this. ExðOc =Tc ERo Þ ¼ c: Ex is for experience, Oc picks out a particular kind of experience content concerning the colour c of objects O, Tc is the theory of colour, E is any other admissible facts about the world, and Ro the relevant subject standing in the appropriate causal relationship to the object O. So the formula says that the colour experience we ought to have is that which the theory of colour says the object has, the subject stands in the right relationship to the object, and any other facts hold whose sole relevant impact is via what colour the object is. Obviously there are disanalogies with



   

the principal principle. For example, the material upon which a certain type of experience is conditioned is not amongst the beliefs of the subject but rather facts in the world. However, there is an illuminating analogy. We would not suppose that the thesis that colour was objectivized colour experience implied that inadmissible facts—such as the actual colour we will experience O to be, perhaps under nonstandard illumination conditions—are also contributors to the colour the objects should be taken to be. In the case of colour, the inadmissible facts give us correct information about the colour the objects look to be but, in so far as they attribute colour to the objects, nonveridical information about the colour the objects are. In the case of chance and credence, matters are a bit more complex. The inadmissible facts—facts about future events and their frequencies, the (evidential) probabilities of the Newcomb cases, and indeed, facts about the occurrence of past events when related to their earlier chances—don’t give rise to mistaken credences. Rather they fix credences otherwise than by the theory of chance. This distinction will prove important for non-Humean theories of chance that also, as we noted, involve the notion of derivative probabilities. Although there is this difference, it does not vitiate the analogy. Chance is still one kind of objectification of credence. The second element of Hall’s justification of the new principal principle is that it is no part of something being a certain kind of expert that it makes claims about its expertise. A particular theory of chance says that, for example, the chance of a die coming up  is /. It does not claim that because it is the expert, the chance of a die coming up  is /. Suppose, then, that there are two candidate theories of chance, TW and TW, and we currently have no grounds for choosing between them. The evidence is equally balanced. Our credence in A should be given by Cr ðAÞ ¼1=2 CrðA=XHtw Tw1 Es1 Þ þ1=2 CrðA=XHtw Tw2 Es2 Þ: Here Es and Es are the respective conditions that should hold if the respective theories of chance have expert status (Es—for expert status claim). The initial contradiction arose because the theory of chance both specified a non-zero value for an undermining future and a zero value for the undermining future given the theory of chance’s correctness. The dual contribution has been split off. In the situation in which we take one theory of chance to be correct, we have CrðA=XHtw Tw Es Þ ¼ PðA=Htw Tw Es Þ: If the chance attributed to past history is  and there is no chance of an undermining sequence of events, for example, because a non-Humean account of chance is true, then we get CrðA=XHtw Tw Es Þ ¼ PðAÞ; since P(Es) =  entails P(Tw) = . This is the old principal principle. However, if A might be an undermining future and, thus, inconsistent with the theory of chance upon which we are conditionalizing, then we have CrðA=XHtw Tw Es Þ ¼ PðA=Es Þ:

  



This is the new principal principle. This is formulated in terms of Es to emphasize the fact that its role is to conditionalize upon Tw’s status as an expert (which is what Es asserts). For Lewis and Hall, Es will be the laws that hold, in terms of the best system analysis. The possibility of an undermining future fails to yield a contradiction because P(A/Es) is 0 in those circumstances. At the outset, we said that an ontology of chance was not to be rejected on the grounds it gave a probability to it failing to hold. If that’s right, then we shouldn’t pick, as our fundamental formulation of the principal principle, one that discriminates against this kind of theory of chance so long as contradiction can be avoided. That’s what the new principal principle succeeds in doing (Hall (c), pp. –). Questions arise over whether this revision to the principal principle is well motivated concerning both elements. Briggs argues that the characterization of chance as an analyst expert implicitly involves an anti-Humean metaphysics. A theory of chance is a tentative database expert about the future rather than an analyst expert if a Humean metaphysics is true. It conveys information about how the future must have developed in certain ways rather than others for the theory of chance to remain true (Briggs (), p. ). From the other angle, it might be thought that the distinction between what a theory says the chances are and the claim that the theory is expert cannot motivate the right hand side of the new principal principle: P(A/Es). There is, of course, an issue for the believer as to whether a particular theory of chance is correct but having P(A) on the right hand side is sufficient for the claim to be made that a particular theory of chance is the correct theory of chance. The salience of the distinction only becomes relevant when there are particular matters of fact, those that constitute an undermining future, which, if they held, would mean that the theory of chance in question was not an expert. In other words, the charge is that the particular motivation for the new principal principle derives from taking Humean supervenience to hold for chances. To this, there are two replies. First, the objection against talking of an analyst expert seems overstated. Appealing to chances given by the best system of laws involves an analysis of data that combines simplicity, power, and fit. It is perfectly appropriate to characterize this as an analysis of the data and not simply the provision of data. Second, as we have noted already, there is a good case for supposing that the new principal principle is the more general, neutral principle, from which we can derive the old principal principle as a special case. Moreover, it isn’t true that the motivation for the new principle is an entirely Humean one. Consider those propensity theories that take propensities to entail certain limiting relative frequencies or approximations to long-run frequencies. In either case, there is the possibility of undermining futures. For example, an undermining future for such a propensity for P(heads) = / would be either a limiting relative frequency of / or, supposing in the long-run case / counts as approximate, long-run frequencies of / say. Consider the old principal principle CrðA=XHtw Tw Es Þ ¼ PðAÞ: In the limiting relative frequency case, the recommendation may be to, depending upon how the chance of infinite sequences are measured, take the probability to be infinitesimal or 0. If the former, then contradictory beliefs would be recommended



   

since conditionalizing upon Tw would give the probability of the limiting relative frequency of / to be 0. If the Tw states that the probability of an infinite sequence is 0, there would be no immediate conflict. However, Tw would take that 0 to be compatible with the possibility that the limiting relative frequency of / occurred (since the limiting relative frequency of / would also have probability 0). By contrast, conditionalizing on Tw makes that limiting relative frequency impossible because, if it were instantiated, the propensity of P(heads) = / would not be. Thus we have a contradiction in this case too. Propensities entailing approximations to long-term frequencies just expand the range of undermining futures and allow for the possibility of non-zero probabilities for the long-term frequencies other than what the propensity is in favour of, against the impossibility of these occurring because then the theory of chance would be false if they did. So the old principal principle counsels believing in contradictions in this case too. The new principal principle can be justified by dealing with an entirely general problem for some theories of chance—not just Humean theories—albeit the issue with which it is dealing is potentially more extensive in the Humean case than the non-Humean case. However, the fact that one style of theory is the greater beneficiary does not make the motivation for the revision a Humean one. Some propensity theorists ostensibly avoid the problem from undermining because they insist upon a weaker connection between propensity and the two types of frequency mentioned. As we shall see in . (amongst other things), their avoidance of the problem does not have secure foundations. To see that, we need to be clearer about propensity theories.

. Propensity Theories of Chance Most propensities are best thought of as triggered dispositions of states of affairs or circumstances. A propensity is not a property of that for which it is a propensity—for example, the propensity for heads of / is not a property of coming up heads— because the propensities—the chances—can, indeed, invariably do, exist prior to the outcome (Mellor (), p. ). Triggered dispositions are not standard dispositions (although what is triggered may be a standard disposition). Something may have a disposition to do A (e.g. dissolve) and yet not dissolve because it has not been triggered (e.g. by being placed in water) nor have any chance of dissolving because it is kept away from water. It is a mistake to consider chances to be that feature of a set-up such that, if a certain trigger were to occur, then it would be the case that ch(e) = x. Suppose we consider a coin-tossing machine. Without activation, it is not the case that a particular fair coin has a  per cent chance of coming up heads. It is only upon activation that this chance exists. In this case, the trigger is the machine tossing. Cht(e)—the chance of the coin coming up heads as a result of being tossed— only exists when the coin has been tossed and not before. When it is said that a coin has a  per cent chance of coming up heads, people don’t really mean that there, sitting in the purse, the coin has a chance of coming up heads. What they mean is that if the coin were tossed, it would have a  per cent chance of coming up heads. The proper connection between standard dispositions and chances is that dispositions are dispositions to have chances (Mellor (), pp. –, (), pp. –).

   



In an extended sense, though, propensities can be taken to be dispositions. The circumstances including the trigger can certainly be described as having the disposition to have a certain outcome in a way to be refined shortly. There will be some occasions when chances may exist without triggers being included in the state of affairs they characterize. A familiar example would be the chance that a certain particle has of radioactive decay. Although bombardment may increase the chance of emission, there is a chance of emission anyway. The existence of chances that are triggerless dispositions should not obscure the fact that most chances are triggered dispositions. If we want a collective name to cover both cases we could call chances primed dispositions: some needing triggers and some not. Included in the conditions required for priming would be the absence of any masks that would stop a particular disposition from being manifested. If chances are primed dispositions, then the values we attribute between  and  serve to characterize the manifestation of these dispositions. According to propensity theorists who take the single case to be primary, these values are measures of the strength (or weights of physical possibilities) of the primed disposition with regard to the target event (e.g. Giere (), p. ; Fetzer (a), p. , ‘strength’; Giere (), p.  ‘weight’). Those propensity theorists who take frequencies to be primary take the primed disposition to be a disposition to produce a certain long– run frequency (e.g. Popper ()). Others take the single case to be primary but the limiting relative frequency to be the proper characterization of the nature of the disposition (Mellor (), pp. –). In developing an account of propensities in one of these two ways, propensity theorists face a dilemma that vitiates the putative difficulty for Humean approaches detailed in .. Let’s begin by focusing on the single case. If chances are primed dispositions for a certain upshot with a certain strength, then the connection between chances and limiting relative frequencies cannot be R (L) Ch (e occurs) = p entails 1(an E occurs) = p (e.g. Giere (), p. ). The proportion of E-type events relative to a reference class of n events (where ‘n’ is a number) tends towards a certain limit as n gets larger and larger, namely p. If 0 < p < , then it is possible that an infinite sequence of Es occurs (or any other proportion of Es), and hence the proportion of Es does not correspond to the limiting relative frequency. Therefore, Ch (e occurs) = p cannot entail a certain limiting relative frequency. A weaker connection would be the counterfactual connection (L*) If there were an infinite series ofR events or circumstances in which Chc (an E occurs) = p, then it would be that 1(an E occurs) = p (e.g. Mellor (), p. ). Lewis denies that (L*) is true on the grounds that there is no infinite sequence of outcomes that would occur if E (say coming up heads) had a certain chance. There are all kinds of sequence that would have a very small, perhaps infinitesimal, chance of occurring (Lewis (), p. ). The reasoning Lewis offers is questionable bearing in mind that he is willing to allow that there are cases in which we would be correct in saying that something



   

would not occur, even though it might occur because there is some chance of it occurring or, putting it positively, something would occur even though there is some chance of it not occurring (Lewis (b), pp. –). I will go through the reasons he offers for rejecting the connection between there being some chance of A and it not being the case that A would not happen. They are not equally effective. First, if the centring assumption is true, then a counterfactual of the form ‘If it were that A, it would be that B’ is true if both A and B are the case, even if the chance of B is less than  (see ..– for discussion of centring assumption). So, it cannot be the case that both of the following are true (Chance-Might)

If Chance (B) > , then it might be the case that B.

(Might = not-would-not) It might be the case that B =df it is not the case that it would not be the case that B. If the chance of B is less than , then the chance of not-B is greater than . So it might be the case that not-B (Chance-Might). It is not the case that it would not be the case that not-B (Might = not-would-not). In which case, it is not true that if it were that A, it would be that B. But that’s wrong. So one of the assumptions must go and it is plausible that it is the second. Lewis’ second line of reasoning runs as follows. Suppose that B has some chance of obtaining and failing to obtain in worlds u and v. In fact, it is true in u and false in v. A holds in both u and v and no other worlds (let us assume for simplicity). Then given both the (Chance-Might) and (Might = not-would-not) assumptions, then it is both false that ‘If it were that A, it would be the case that B’ and that ‘If it were that A, it would not be the case that not-B’. This could only be the case if u and v were as close as each other to the actual world. Only then would it fail to be the case, for example, that it would be the case that B holds in the closest A worlds (and similarly for it would not be the case that B). However, u and v may differ substantially in particular matters of fact apart from this. So we can’t endorse both assumptions. This line of reasoning isn’t very convincing. If there is a world u in which A and B holds, where not-B has some chance of occurring, then, by Lewis’ own similarity weighting, and for that matter my own recommended adjustment, it should be the case that there is a world v which is judged as similar to the actual world as u, in which B does not occur. Even if the actual world is a not-A, B world, the similarity in virtue of B will be discounted as only approximate by Lewis’ weighting or as irrelevant in mine. So Lewis has failed to establish that holding both assumptions are unacceptable in this second case. Third, consider counterfactuals that mention chances in their antecedents. We can reason as follows. If there were an unfulfilled chance that B, then it would not be the case that B. Nevertheless, if both the (Might = not-would-not) and (Chance-Might) assumptions hold, then, since it might be that B, it is not the case that it would not be the case that B. The counterfactual with chance mentioned in the antecedent would be false (Lewis (b), p. ). Fourth, and finally, we have seen that we assert certain counterfactuals on the basis of hindsight which would turn out false if the assumptions held. Recall the counterfactual concerning the winning number of a lottery: . I note, in hindsight, that

    ()



If my number had been , I would have won the lottery.

The chance of my winning the lottery is very low and, yet, because the winning lottery number is probabilistically independent of it being mine, the consequent of the counterfactual concerning the fact that I would win is true. At least three R out of the four considerations show that Lewis can’t argue that ‘It would be that 1(an E occurs) = p’ is false because there is some infinitesimal chance of other proportions of Es in the infinite case. So we have no reason to reject (L*) if a single-case propensity theory is true. Nevertheless, we do not have an explanation for why it is true. For instance, we can’t take it as a consequence of the centring assumption given that there aren’t the relevant infinite sequences of events. For some theories of law, an explanation is possible. For the sake of a simple contrast, consider the following two schematic laws. (L) All Fs are Gs. (L) All Fs have Pr(G) = .. If there is an F that is not a G, then (L) is violated because F failing to be a G is inconsistent with it. By contrast, if only . Fs are G, then this is not inconsistent with (L). However, if the best system analysis is true, then (L) would not express a law in those circumstances. This is a second way in which we can have a law violation. The explanation of (L*) If there were an infinite series ofR events or circumstances in which Chc (an E occurs) = p, then it would be that 1(an E occurs) = p is that, if a different proportion held, then it would not be a law that, in those type of circumstances, Chc (an E occurs) = p. By contrast, propensity theories—developed within an account of law for which Humean supervenience fails—cannot claim that the failure of the connection is a law violation in this second sense. A very different pattern of events of the kind envisaged doesn’t imply that a different law holds because laws don’t supervene upon the particular patterns that hold. So if propensity theorists appeal to law, they would have to appeal to an additional law, the result of which would be that, in fact, although departures from limiting relative frequencies have some chance of occurring, they would not occur. It is very hard to see why this second law doesn’t undermine the chance fixed by the propensity. If the law ruled out there being some chance of a departure from a limiting relative frequency occurring, then there is no chance of that happening. It would seem, then, that if propensity theorists want to hold that (L*) If there were an infinite series Rof events or circumstances in which Chc (an E occurs) = p, then it would be that 1(an E occurs) = p, then they have to appeal to typicality and not law violation. They must claim that, in (non-actual) circumstances in which there were an infinite Rseries of events in which Chc (an E occurs), then what would occur is a typical run: 1(an E occurs) = p. Yet we saw in . that there was little motivation for appealing to such a notion and it gave rise to significant problems. Moreover, while the appeal to typicality secures the



   

counterfactual connection, it appears to do so by stipulation. There is no further ontological grounding nor considerations to be drawn from the semantics of counterfactuals. This also has an impact upon the explanatory pretensions of propensity theorists. Some claim that propensities are postulated as causes, perhaps by an inference to the best explanation, of the limiting relative frequencies (e.g. Popper (), p. ; Fetzer (), p. ; Mellor (), p. ). Success by stipulation is not a plausible candidate for the best explanation. Propensity theorists who take the single case as fundamental are better off claiming that they cannot secure the connection between propensities and limiting relative frequencies (e.g. Giere (), pp. –). Instead, long-run frequencies are just evidence for propensities. Nevertheless, its proponents go on to say, their notion of strength of primed disposition still has an explanatory role to play. Propensities are just whatever is the case that makes the frequencies suggested by the numerical calibration of the strength of the propensity more likely to occur. As the number of times they are manifested approaches infinity, the corresponding frequency is closer and closer to the value of the propensity (a very informal statement of Bernoulli’s Limit Theorem, see Giere (), pp. –, (), pp. –, Fetzer (a), p. , (b), p. , (), p. ). We have reached explanatory bedrock at this point. It is easy to understand how propensities make frequencies more likely to occur if their strength is, at least partly, a strength measured by their production of the appropriate frequencies (in the way given by either (L) or (L*)). As we might put it extremely metaphorically, the force that an event of type E₁ has to produce an event of type E₂ is the very same force that makes E₂-type events have the frequency they have in the presence of E₁-type events. However, if strength or weight is understood to be distinct from the frequencies in question, how are we to understand the idea that they make the frequencies more likely (for similar concerns Schaffer (b), pp. –)? Is this likelihood to be understood in terms of propensity? Is there a law relating propensity strength to frequency that might fail to hold? Or what? Proponents of a powers ontology will resist the idea that there needs to be a property-independent law relating strength to frequency. The disposition whose strength is measured by chance is the disposition for the corresponding limiting relative frequency. But this would bring us back to the idea that there is an entailment between primed propensities and limiting relative frequencies. If the limiting relative frequency failed to hold, then the disposition would not be instantiated because it lacked its essential manifestation. It’s hard to avoid the impression that silence on this point lies at the heart of the apparent attractiveness of propensity theories of probability over the best system analysis. But this attractiveness is not well founded. The very feature that gave rise to the undermining objection in . has, as a consequence, an explanatory cost with regard to capturing and explaining the connection between chance and limiting relative frequencies. As we have already seen, the alternative development of the propensity approach takes chance to be a primed disposition to produce a certain limiting relative frequency. One difficulty with this position is that it is unclear how such a disposition could be possessed by individual cases and yet have, as its manifestation condition, the limiting relative frequency envisaged. For example, consider a particular die, its physical structure and so on, just rolled. Does this have the disposition to recur an

   



infinite number of times and result in a certain limiting relative frequency? It is not clear that it does. One might expect the die would crumble to dust long before. And what kind of property could this primed disposition be? In any event, if propensities are dispositions to produce certain limiting relative frequencies then, they entail those frequencies and, thus, are susceptible to the argument based upon undermining discussed in . (Fetzer (), p. , notes the point about entailment). Concern about the kind of property that a primed disposition to limiting relative frequency might be makes more modest long-run frequency propensity theories attractive. The suggestion is that if a primed disposition is to a long-run frequency, then that particular frequency ‘is or would be or would have been’ (Hacking (), p. ; Hempel (), p. ; Fetzer (), p. ). But we now have even a sharper version of the same question we considered with regard to (L*), namely what is the explanation for its truth? The obvious answer is to appeal again to the nature of the disposition itself. However, if the disposition to a long-run frequency would not be instantiated without the manifestation of that frequency in the appropriate circumstances, then once more the position becomes susceptible to an undermining argument, except that now the argument’s application is more extensive. A hybrid propensity theory would seek to combine the merits of the two types of propensity theories without the disadvantages. Suppose it is argued that chance is a backward-looking measure of something else—let us call it proto-probabilification— that those who take laws not to supervene upon particular matters of fact attribute to the Cs. Chance is a proto-probability that faces a limiting relative frequency defeater. The proto-probabilification of Cs explain why a certain limiting relative frequency holds but are only properly called Chc (an E occurs) = p if, in fact, the limiting relative frequency of p holds. Chance laws are violated when the limiting relative frequency does not hold because a different chance law would hold instead. Evidence concerning frequencies are, thus, evidence concerning whether the proto-probability in question will support the relative limiting relative frequency its numerical assignment requires. In which case, the explanatory role of propensities is moderated. They don’t fully explain the frequencies. Instead, there is a combination of explanation and stipulation. Supervenience of laws is introduced by hand in response to the difficulties of relating single-case propensities to limiting relative frequencies. The hybrid view just canvassed also has a familiar drawback. It will be susceptible to its own undermining objection. Whenever some alleviation is achieved as to the connection between propensities and limiting relative frequencies, the putative objection that afflicts the Humean position applies to it too. This is part of my case that there is a costs trade-off which, as a result, does not favour one of the views of laws over another. In Figure . I characterize the various versions of the propensity theory outlined above and how they relate to the issue that has been our main focus here. Only theories in the first box to the left escape the undermining objection and they struggle to explain any relationship between propensities and the frequencies they are taken to explain. Two remaining difficulties for propensity theorists remain, first, to explain how the adoption of the principal principle is a rational strategy for agents and, second, how to accommodate the fact that, on pain of inconsistency, not all the objective



   

Propensities

Single Case: Strength of propensity to realize singular events/makes likely frequencies (Giere, Fetzer)

Long-Run Frequencies (Popper, Gillies)

Hybrid Theory: Chance as backward -looking classification of strengths

Disposition to Limiting Relative Frequency (Mellor)

Figure .

probabilities of target events are grounded in primed dispositions for those target events. I will focus on the second issue first and use it as one motivation for a certain development of the propensity view, a global supervenience account of objective probabilities based upon propensities. In .., we saw in abstract how, if C-type events probabilistically cause E-type events, there will be objective conditional probabilities of C-type events given E-type events. Let me give an illustration of this. I take it from Paul Humphreys who derived the contradiction (Humphreys ()). Let It: event of photon impinging on mirror at time t₂. Tt: event of photon being transmitted through mirror at t₃ where t₃ > t₂. Bt: background conditions including the emission of the photon. The following three assumptions are plausible. First, impingement gives transmission a positive probability: Prt(Tt/ItBt) = p > . Second, the impingement given background conditions including emission has some positive probability:  > Prt(It/Bt) = q > . Third, there would be no chance of the photon being transmitted if it did not impinge on the mirror: Prt(Tt/notItBt) = . The theorem on total probabilities is that ðTPÞ PðA=CÞ ¼ PðA=BCÞPðB=CÞ þ PðA=not‐BCÞPðnot‐B=CÞ: That is the probability of A given C is given by each way we might get A given C—in this case B and not-B—weighted by the probability of that way occurring. Those who are more familiar with the language of probabilities will talk of these ways as partitions. Applied to the case in hand, we have ð1Þ

Prt1 ðTt3 =Bt1 Þ ¼ Prt1 ðTt3 =It2 Bt1 ÞPrt1 ðIt2= Bt1 Þ þ Prt1 ðTt3 =notIt2 Bt1 ÞPrt1 ðnotIt2= Bt1 Þ:

The total probability of transmission given the background conditions specified is the sum of the mutually exclusive and jointly exhaustive partition between impinging and not-impinging. We know that there is no propensity for transmission without impingement. Hence Prt(Tt/notItBt)Prt(notIt/Bt) = . Thus we get ð2Þ

Prt1 ðTt3 =Bt1 Þ¼ Prt1 ðTt3 =It2 Bt1 ÞPrt1 ðIt2= Bt1 Þ ¼ pq:

It is very plausible that, while there is a propensity for impingement to give rise to transmission, there is no propensity for transmission to give rise to impingement.

   



Impingement is independent of transmission because there is no backward influence. Hence ðCIÞ

Prt1 ðIt2= Tt3 Bt1 Þ ¼ Prt1 ðIt2= not‐Tt3 Bt1 Þ ¼ Prt1 ðIt2= Bt1 Þ:

This gives us Prt(It/TtBt)=q. The multiplication principle for conditional probabilities is ðMPÞ

PðAB=CÞ ¼ PðA=BCÞPðB=CÞ ¼ PðB=ACÞPðA=CÞ ¼ PðBA=CÞ:

Applied to the case in hand, we have ð3Þ

Prt1 ðIt2 Tt3 =Bt1 Þ ¼ Prt1 ðIt2 =Tt3 Bt1 ÞPrt1 ðTt3 =Bt1 Þ ¼ qðpqÞ ¼ pq2 :

But also ð4Þ

Prt1 ðIt2 Tt3 =Bt1 Þ ¼ Prt1 ðTt3 It2 =Bt1 Þ ¼ Prt1 ðTt3 =It2 Bt1 ÞPrt1 ðIt2= Bt1 Þ ¼ pq:

Hence ð5Þ

pq2 ¼ pq:

The values for p, q must be either p =  or q =  or p = —contrary to our assumptions (Humphreys (), p. ). A contradiction can also be derived from the three assumptions together with Bayes’ Theorem. The latter holds that ðBTÞ

PðB=ACÞ ¼PðA=BCÞPðB=CÞ

½PðA=BCÞ PðB=CÞ þ PðA=not‐BCÞPðnot‐B=CÞ: Putting in our example once more, we get ð6Þ Prt1 ðIt2= Tt3 Bt1 Þ ¼ Prt1 ðTt3 =It2 Bt1 Þ Prt1 ðIt2= Bt1 Þ=½Prt1 ðTt3 =It2 Bt1 Þ Prt1 ðIt2= Bt1 Þ þ Prt1 ðTt3 =not‐It2 Bt1 Þ Prt1 ðnot‐It2= Bt1 Þ ¼ pq ½pq þ 0 ¼ 1: But this is contrary to (CI) which gives Prt(It/TtBt) = q (< ). On the assumption that the standard theorems of probability are correct, the problem is (CI). There are going to be backwards probabilities. So either propensities aren’t simply those which work in the direction of causation or the propensity account of probability is incorrect. My response to this argument is not that we need a special set of theorems for causal probabilities (Fetzer (), pp. –, –). We can capture the nonsymmetries sufficiently by counterfactuals as we saw in Chapters  and . We do not have to claim that the (causally) forward propensities have corresponding backward propensities either. Instead, the proper way to develop a propensitybased account of objective probability is to take propensities to be part of the minimal supervenience base for objective probabilities that result from the global pattern of propensity instantiation (see .– for relevant notion of supervenience). This avoids potentially inconsistent attributions of probabilities. In the present case, it allows the backward probabilities to be generated from the arrangement of (forward) propensities.



   

Understanding the connection between objective probabilities and propensities also assists with the following problem. Consider the claims that (N) Ch(e occurs) =  entails e occurs. (N) Ch(e occurs) = 0 entails e does not occur (Mellor (), pp. –, see also Lewis (b), p. ). Suppose that the chance of heads if a fair coin is tossed is /. Each particular causal circumstance of a coin tossing has a certain property which we represent by Ch(h occurs) = /. It is compatible with this that an infinite number of heads is not ruled out. Yet, as we have already noted, according to one measurement of probabilities, the probability of an infinite number of heads is zero (since lim n ! ∞ (¹/₂)n = 0). In which case, we have a counterexample to (N) with ‘∞H’ in place of E. If Ch(∞H occurs) = 0, then Ch(not-∞H occurs) = . Since an infinite number of heads is possible, we have a counterexample to (N). Ch(not-∞H occurs) =  does not entail not-∞H (Mellor (), pp. –). Mellor suggests that such counterexamples may be avoided by denying that there are conjunctive truth-makers, and hence, a conjunctive truth-maker for Ch(∞H occurs) and Ch(not- ∞H occurs). Let ‘ci’ stand for the causal circumstances relating to the ith toss and ‘Ch(hi occurs)’ stand for the chance of the ith toss coming up heads. Then the state of affairs is Ch(hi occurs)ci, a state of affairs with the same atomic structure as Fa. Mellor denies that, for Ch(∞H occurs) (say), there is a corresponding truth-maker Ch(h₁ occurs)c₁ & Ch(h₂ occurs)c₂ & . . . & Ch(hn occurs) cn (where n ! ∞). All he allows is that there are the independent individual truthmakers: Ch(h₁ occurs)c₁, Ch(h₂ occurs)c₂, . . . Ch(hn occurs)cn. (N) and (N) only hold for probabilities for which there are chance truth-makers. He suggests that ∞H is logically possible rather than having any non-zero probability of coming about (Mellor (), p. ). In fact, he might say something stronger. It is not simply logically possible but physically possible: possible given the circumstances which hold and the laws. In any event, Mellor is denying that (N) and (N) hold for certain kinds of derivative chances. Earlier in the book I argued that there are no truth-makers. I don’t propose to rely upon that argument to raise difficulties for Mellor here because I think his overall point could be reformulated in my framework. Something I won’t seek to do here. I will talk in terms of truth-makers. Instead, I have two reservations about Mellor’s proposal. The first relates to the conditions under which it is appropriate to conclude that a chance property is instantiated by c (say) as a result of individual chance properties possessed by constituents of c. For example, ruling out conjunctive truth-makers does not rule out a truth-maker of the following form: Ch(∞H occurs)(c₁ & c₂ . . . cn) (where n ! ∞). This is not a conjunctive truth-maker. It is true that there is a conjunctive object—all the various causal circumstances—that is a constituent of this state of affairs. Nevertheless, the chance property is a property of the conjunctive object and not the conjuncts. Suppose he denies that such a property is instantiated in the case of an infinite number of independent coin tosses. What about throwing two sixes on a pair of dice. Each die throw, we may assume, is probabilistically independent of the other. If die throwing is genuinely indeterministic with each face of each

   



die having an equal chance of coming up, the chance of two sixes is /. Is this a genuine chance, or not, and why? There is no denying the existence of truth-makers of the general form of Ch(∞H occurs)(c₁ & c₂ . . . c∞) because this would just be a rejection of macro-properties. Rejection of such macro-properties would bring problems of its own. First, it threatens to make macro-properties, in general, inefficacious when combined with a chance-raising-based account of property causation (as outlined in .–). Second, the blanket denial of propensities as macro-properties may be a denial of propensities in general. The chance of a target event is plausibly thought of as a consequence of the various factors that make up a causal circumstance and possessed by them in toto. In which case, all propensities are macro-properties. The problem is to identify a feature of the infinite case Mellor wants to rule out that does not imply that all these other cases lack corresponding chance truth-makers too. The feature has also got to provide an explanation for why it is legitimate to deny the connection between P(e) being 0 and e not happening in this case. My second reservation about Mellor’s proposal is the familiar point that the denial of conjunctive truth-makers presupposes that the world is not ultimately conjunctive (or mereologically composite). Reality is fundamentally conjunctive if it doesn’t bottom out into atomic truth-makers (or mereological simples). We have been given no reason to suppose that reality can’t be like that. Is there any reason for taking such a possibility seriously? It is not a consequence of reality being such that, for any property we identify, F, we will discover that it is instantiated in virtue of being G₁ and G₂; that G₁ is instantiated in virtue of H₁ and H₂, and so on. F may be infinitely decomposable into other properties in this way and yet there are fundamental properties not subject to decomposition. Call them the Z properties. If there are an infinite number of properties, we will never reach the Z properties and yet each property we identify we will find decomposable into other properties. Nevertheless, something does not have to be a live possibility in order to be taken seriously. It is worthy of taking seriously if it points out the inadequacy of a particular solution with which we might otherwise be satisfied. Suppose that, whenever we decomposed something, we found a conjunctive property. We might otherwise consider the possibility that, at bottom, reality is fundamentally conjunctive. It is true that reality could be infinitely decomposable without being conjunctive in the way described above. However, equally, while there might be an infinite sequence of conjunctions of properties in the composition of F, there might be other properties for which there is a finite sequence. So persistently finding that reality is only decomposable into conjunctions of properties receives a more satisfying explanation if reality is fundamentally conjunctive. In which case, it would be a mistake to deny the existence of conjunctive truth-makers. Unfortunately, Mellor’s solution involves denying precisely that. So what’s the alternative? The proper adjustment to deal with the counterexamples is to argue that, while (N) and (N) are false, the following are true (N*) (N*)

Ch*(e occurs) =  entails e occurs. Ch*(e occurs) = 0 entails e does not occur.



   

Where Ch*(e occurs) = 0 only if it is not the case that there are constituents c₁, c₂, c₃, . . . cn such that they completely constitute e and, for each of these constituents, ci, Ch (ci occurs) > . c₁, c₂, c₃, . . . cn completely constitute e only if there is no constituent of e that does not overlap with any of c₁, c₂, c₃, . . . cn and is not identical to one of c₁, c₂, c₃, . . . cn. In the finite case, Ch*(e occurs) ≠ 0 because a finite probability of each constituent does not result in a zero probability of the complex. In the infinite case, Ch(e occurs) = 0 but the complete constitution condition rules this out as a case of Ch*(e occurs) = 0. Ch*(e occurs) =  holds only if Ch*(not-e occurs) = 0. This is not committed to the denial of an ultimately conjunctive reality. Ch* generally coincides with Ch except in the infinite case. In the infinite case, chance values may differ from chance* values in that the latter fail to hold. By failing to hold in these circumstances, (N*) and (N*) are preserved from counterexample. The success of the response depends upon there being a valid distinction between propensities and objective probabilities. If there were none, then it would be unclear why Ch(e occurs) = 0 fails to settle that e does not occur. However, if we allow that the relationship is true of propensities—taking Ch* to stand for them—but false of objective probabilities, then we can preserve the intuitive link. An infinite sequence of events with positive chances in the propensity sense does not entail that there is a 0 chance in the propensity sense that e occurs. This latter objective probability supervenes upon the propensity chances. In brief, the proper development of a propensity theory takes them to be primed dispositions upon whose joint instantiation—subject to certain constraints— the truth of probability statements depends. If chances are taken to be objective probabilities of some kind or another, then chances are not propensities. The character of primed propensities—in particular, the fact that probabilities serve to characterize their manifestation—makes it legitimate to call them chances in a more substantial sense so long as this is not taken to rule out the possibility of objective probabilities for which there is no corresponding propensity concerning the target events. With this more defensible understanding of the propensity theory, let me turn to the question of whether Humean and non-Humean approaches to chance differ in their capacity to justify the principal principle. To recall, the new principle states CrðA=XHtw Tw Es Þ ¼ PðA=Es Þ: It relates a certain variation in attitude—strength of belief—towards a proposition, A, to a proposition about the chance of A, given a certain context of information. Justification of the principal principle thus cannot be epistemic: explaining how the propositional content of one cognitive or perceptual state grounds another. Credences need not, indeed usually are not, an attitude towards a proposition about chance. Instead, the relevant place to look has been the role of such attitudes in rational action. If we find credences related in a certain kind of way to successful action, then the principal principle may receive an appropriate, as it is often called, pragmatic justification. So we should look to see whether one or other account of chance can better explain why, in terms of the success of our actions, our credences should reflect chance in the way set out by the principal principle.

   



As the format of the principle already recognizes, the occurrences of events, and not the chance of events, determines the success of actions. Credence, thus, would ideally track occurrences rather than chances. Of course, chance is naturally understood as related to occurrence. It is likelihood of occurrence. Nevertheless, they can potentially come apart and do in the cases where we have inadmissible evidence. Suppose an agent is considering whether or not to bet on heads as a result of a particular coin being tossed. The chance of heads is /. Nevertheless, suppose further, that as a matter of fact, the frequency of heads for the coin up until the time it is destroyed is  out of , tosses (at that point it is destroyed). Then, as far as success is concerned, it would be better if the agent had a higher credence in there being heads rather than take heads and tails to be equally balanced. In most cases, though, it might be argued that we don’t have access to future frequencies except via chances, so how could this be relevant? The answer is that the two approaches to chance differ in the closeness of their notion of chance to this fact about the success of actions being about frequency of occurrence. Propensity theories that, at most, claim that propensities make the frequency of a certain type of event more likely (whatever concerns we may have about the explanatory utility of such a move) are the most distant. Closer are those theories that take propensities as primed dispositions to relative limiting frequencies or long-run frequencies. However, closer still is the best system analysis. It is not simply committed to chances being related to limiting relative or long-run frequencies. Rather, chances are attributed which best fit the actual finite patterns of events when weighted in with other factors. Since it is the events, which occur, that are the relevant factor, any pragmatic justification of the principal principle within the framework of this notion of chance will be the most successful. It might be argued that there is a way in which chances according to a propensity account are more suitable. If we successfully conform our credences to chances understood in these terms, we will have latched on to something that is explanatory of future patterns. Whereas, as far as the best system analysis is concerned, current chances only hold in virtue of the presence of future patterns. The explanatory credentials are backward. We have seen that this reasoning is unsuccessful before. It is nothing but a repetition of the claim that non-Humean approaches to law and chance are in a better position to answer the problem of induction (see ..). This is not so. Both appeal to the idea that what is identified in the past will continue to play the same role in the future. The particular metaphysical character of what is identified plays no role. The limitations of the point about pragmatic justification should be recognized. I am not saying that there is no pragmatic justification of the principal principle from the perspective of propensity theory. My claim is just that it is less satisfactory than that provided by the best system analysis. When this is added to the previous discussion, it should be clear that respective claims of the two approaches are pretty evenly balanced. It is for this reason that I don’t believe that the question of chance pronounces matters in favour of one metaphysical view or another regarding the nature of laws. The preliminary conclusion of the previous discussion relating to the undermining objection not only stands but is reinforced.



   

. Concluding Remarks In this chapter I surveyed the traditional tension in the development of theories of chance between being open to undermining on the one hand and being divorced from the frequencies of events on the other. With proper adjustment of both kinds of theories, it seemed neither had a decisive advantage over the other. Both kinds of theories can produce viable theories of chance and, hence, they fail to provide grounds for preferring the distinctive view of laws of nature upon which they are based. The suggestion that causation and law may be realized in different ways across different possible worlds finds further reinforcement. Part of my defence of a Humean approach to chance involved arguing in favour of a revision of the principal principle, to the new principal principle suggested by Lewis and Hall. However, I differed from them in two respects. First, I motivated it by noting that many non-Humean propensity theories required adjustment to the principal principle too to deal with the relationship between propensities and frequencies. Second, I rejected Hall’s characterization of chance as, simply, an analyst expert. Chance involves a distinctive kind of analysis expertise that, for example, is related but distinct from information about frequencies and derivative probabilities. Turning to propensities, I argued that chances were primed dispositions that were, in some way, related to long-term or limiting relative frequencies. Propensity theories that avoided the undermining objection did so only because they struggled to explain the connection with frequency, appealing to poorly understood notions such as strength or making likely that then needed to be related to frequency. Those that did not suffer from this failing were more prone to suffer from the undermining objection. If a propensity theorist gave up on the connection between the primed disposition and frequency, then they had the weakest defence of the rationality conforming one’s credence to the principal principle. Schaffer has outlined a related position to the one I have sought to defend. He notes that propensity theories of chance (he calls them necessitarian theories) can allow that, for any E, if at t, after history h, Ch (E) > , then there is a world which has h, E occurs, and the theory of chance remains true. By contrast, Humean theories of chance cannot allow that a theory of chance remains true when E is an undermining future (Schaffer (b), pp. –). On the other hand, Schaffer argues, propensity theories cannot constrain rational credence because they float free of frequencies. By our lights, this is an overstatement. Schaffer’s conclusion is that our notion of chance is semantically vague (Schaffer (b), p. ). On one precisification, chances are propensities, on another chances are probabilities attributed by the best system analysis of laws. This doesn’t seem to be the right way to characterize the issue. Precisifications involve adopting one sharp boundary or another for something to be an F for things that, otherwise, are good candidates for having the distinctive features of the property. By contrast, in the case of chance, we have a notion of something for which the most obvious characterization of the principles concerning it show it to possess explanatory failures or counterintuitive consequences, such as credences that reflect probability values that are the consequence of ruling out undermining futures, to a greater or lesser extent depending upon the theory of chance involved. Instead, we are considering a successor

 



notion to chance as characterized by these principles or, and we could equally put it this way, we are considering which principles need adjustment to arrive at the proper characterization of chance. My claim is that we have, at least, two candidates that seem equally good realizations of chance. Whether they are realizations of different kinds of chance—different determinates of chance—or point to a more abstract characterization of chance that we have not characterized exactly right, remains to be seen. For our purposes, the crucial point is that this issue will not undermine the case for the variable realization of laws. The question remains whether there are other reasons why we cannot allow ontological variation in this way across possible worlds. In Chapter , I will refine our understanding of the doctrine of Humean supervenience and then evaluate the reasons offered for denying that one source of its contingency may be the possibility of necessary connections between distinct existences. It constitutes the final component of my justification of the idea that matters are advanced if we take the counterfactual theory of causation as characterizing what must hold if causation is to be realized in a world.

 Humean Supervenience and Possible Worlds The previous chapters have developed a counterfactual theory of causation and shown the merits of divorcing this development from the truth of Humean supervenience. In this final chapter, I will consider the question of whether it is coherent to take the doctrine of Humean supervenience to be contingent. This might be denied either because it cannot be true or because it can only be coherent to take it to be necessary. In . I will consider its proper formulation and how it relates to Hume’s famous denial of necessary connections between distinct existences. I identify two kinds of Humean supervenience: quality supervenience and modal supervenience. The full-blown doctrine combines both in an attempt to articulate a reductive account of modality. The denial of necessary connections between distinct existences is a necessary but not sufficient condition of the full-blown doctrine. This brings us to our first problem. Can we identify a supervenience base of non-modal entities upon which modal truths supervene? Some have argued otherwise. To deal with this concern, amongst other things, I distinguish between two ways in which the supervenience base may involve entities modally understood. The first is that certain properties of these entities imply certain modal truths. The second is that a proper characterization of these properties can only be modally specified. For example, consider the property of being a square. Two modal properties implied by it are, first, it is not possible that it is instantiated in virtue of an object being three-sided and, second, it is possible that there are two objects which instantiate that property. But we have given it a non-modal specification that properly characterizes its nature: the property of being a square. By contrast, being essential, necessary, possible, the supervenience relation, the causal relation. These are candidate properties and relations that can only be given a modal specification. Recognition of the distinction may be one way of, in Fine’s terminology, keeping one’s modal mania in check (Fine (), p. ). Those who are looking for a reduction of modality would not want to deny that the entities that constitute the supervenience base of modal properties imply certain modal truths. Indeed, the relevant reductive account of modality will be relying upon it. The problem is whether the supervenience base can be specified without reference to entities whose properties can only be modally understood in the second sense. I argue that an acceptable supervenience base can be found and so, as far as this matter is concerned, the doctrine of Humean supervenience may be contingently true.

A Variety of Causes. Paul Noordhof, Oxford University Press (2020). © Paul Noordhof. DOI: 10.1093/oso/9780199251469.001.0001

    



The contingent truth of the doctrine of Humean supervenience has been developed within the context of Lewis’ concrete modal realism: the view that other possible worlds exist in precisely the same way—as concrete entities—as our own world does. The existence of other possible worlds is required to analyse necessity. Their concrete character—and the denial of actualism that goes with it—I shall argue, in ., is required to avoid intra-world necessary connections between distinct existences. That does not mean that there could be no necessary connections between distinct existences. These may be part of a world. It is just that concrete possible worlds remove one motivation for them. There may be other reasons why the doctrine of Humean supervenience should be necessary even within this framework. One relates to whether it is possible to combine understanding necessity in terms of possible worlds with taking there to be intra-world necessary connections. I explain how it is. A second is when we turn to the delimitation of the extent of possible worlds by the principle of recombination. It has been argued that the only way this can be coherently done is if it is a necessary truth that there are no necessary connections between distinct existences. In ., I reject this argument. The principle of recombination is not required, and does not succeed, in playing, the designated delimiting role so there are no grounds to claim that the doctrine of Humean supervenience must be a necessary truth from this quarter. This completes my defence of the claim that Humean supervenience need only be contingently true. I then consider Wilson’s argument that the distinct existences principle and, thus, Humean supervenience is false, perhaps necessarily false. Her argument takes the claim that I have conceded—that properties may imply certain modal truths, indeed, constitutional necessities, as she dubs them, and purports to show that this implies that properties possess their causal powers necessarily and, thus, there are necessary connections between distinct existences. I draw on the material of ... to explain why this argument doesn’t work. This completes my defence of the theoretical approach to the doctrine of Humean supervenience taken in this book. A final challenge to my approach may come from another angle. It may be argued that both causation and laws have no application in a Humean world. Proponents of this objection place great emphasis on the importance of some kind of necessity, or a weaker notion of inclination that still involves some sense of directedness from cause to effect, to our understanding of causation and law. The question is whether this emphasis is best captured by denying that causation and law is present in such worlds as opposed to allowing that we are inclined to suppose that this additional feature—some kind of necessity or inclination—is very naturally associated with causation and, perhaps, constitutes a central important case of it. Here a relevant model might be the question of belief or thought. We might think that humans with standard mental abilities are the primary possessors of beliefs and thoughts while recognizing that it is also appropriate to attribute beliefs and thoughts of a somewhat lesser character to non-human animals of various kinds. Natural association—or primacy of case—should not be transformed into a necessary requirement. Thus, in ., I present a different kind of argument in favour of the possibility of causation in a Humean world, perhaps even as true of our world. I develop it by



    

drawing a connection with the debate over the possibility of zombies and the explanatory gap in the question of physicalism. There are those who think that consciousness must be more than simply an arrangement of narrowly physical properties and there are those who deny that it is something more. The latter provide various accounts of why we should be misguided into thinking that consciousness involves something more. I argue that the same approaches have application to the debate about whether causation and law must involve something more—necessity or inclination—than patterns of events of a distinctive kind. Indeed, there is good reason for thinking that the familiar approaches in philosophy of mind for dealing with recalcitrant insistence that consciousness involves something in addition are more successful when we turn to causation and law. Thus, I end with this challenge. If you think you have good grounds for being a physicalist, you should think that you have even better grounds for adopting a Humean approach to causation and law. With the defence of the claim that causation may be present in the Humean world complete, I consider the proper way to understand the claim that causation comes in varieties as the book title indicates. The main idea was that causal non-symmetry and laws are variably realized. I distinguish this from other ways in which we might understand the claim that there are varieties of causation and relate it to current thought that some metaphysical terms are neutral picking out something whose nature we directly grasp rather than whatever plays the role associated with that term (Chalmers (), pp. –). I then give a final statement of the overall position I am defending. My concluding remarks consider the extent to which the overall theory defended in the book meets many of the goals of a traditional analysis of causation. I point out the ways in which it does and how its merits may be overlooked. Its relative success suggests that recent scepticism about such analytic projects has been overdone.

. Varieties of Humean Supervenience and the Reduction of Modality The characterization of Humean supervenience suggested in Chapter  is that it is true of a world, w, which meets the following condition. Any world which is a minimal duplicate of w in terms of the qualities instantiated and their spatiotemporal arrangement, is a duplicate simpliciter of w. It is supposed to be an articulation of the idea that there are no necessary connections between distinct existences but it is, in one way, stronger and, in one way, potentially weaker than this idea requires. Consider the necessity of identity: If a = b, then necessarily a = b. Here ‘a’ and ‘b’ are candidate singular terms that pick out the same object, and not just whichever object satisfies a certain description, in all possible worlds. Suppose that it is possible that a world is different without being qualitatively different: haecceitism is true (Lewis (c), pp. –). For example, in two qualitatively

      



indiscernible worlds, exactly the same events which involve Fred in world , involve Bill in world , where Fred and Bill themselves are qualitatively indiscernible. Let us also assume either that there is no individual property that is necessarily uniquely possessed by one object or, if such properties are countenanced, then they are not qualitative. In such worlds, there need be no necessary connections between distinct existences and yet modal properties would not supervene upon the qualities instantiated, and their spatiotemporal arrangement. In world , it is necessarily the case that Fred = Fred, in world , it is necessarily the case that Bill = Bill. According to the characterization of Humean supervenience given above, Humean supervenience would not hold although the distinct existences principle still may in such worlds. So packaged in this formulation of Humean supervenience is not only a denial of necessary connections between distinct existence but also an anti-haecceitism. Haecceitism is only relevant to our interests if it involves the commitment to primitive modalities. It is not obvious that the combination of primitive identities plus the necessity of, at least, some of them has, as a consequence, that there are primitive modal properties. In any event, we can formulate the issue that concerns us in terms of the truth or falsity of Modal Supervenience: Any world which is a minimal duplicate of w in terms of the non-modal particular matters of fact, t is a duplicate simpliciter of w. Particular matters of fact should not be taken to be facts, given what I have argued earlier. They may involve more than the spatiotemporal arrangement of qualities instantiated. In particular, in addition, they may involve the existence and location of objects, and the properties (or qualities) they possess, if that is otherwise unsettled by the spatiotemporal arrangement of qualities. Modal supervenience is compatible with allowing that identity across time is a primitive further fact and that there may exist non-supervenient non-modal relations other than spatiotemporal relations, e.g. the relation which captures the succession of stages that make up a natural object of reference as opposed to some gerrymandered object from stages of different natural objects. The formulation claims that if you seek to duplicate world w in terms of the nonmodal particular matters of fact and stop right there, then you will have a duplicate of the world simpliciter including all its modal properties. This allows for the possibility that there might be other worlds—unlike our own—that contain intra-world necessary connections (for example). The formulation also suggests that we need one kind of fact—facts concerning the extensiveness of worlds or of totality (see .)—in addition to non-modal particular matters of fact, to determine whether or not propositions concerning chances are true or false (for instance). Hence, it avoids Scott Sturgeon’s objection that the truth of propositions concerning chance cannot supervene upon local particular matters of fact even in our world because in a world very like it with more stuff of the same kind the propositions will not be true (Sturgeon (), p. ). This does not make the proposal ill suited to express what Lewis had in mind. The crucial point is that, if the non-modal particular matters of fact are all that there is, then a proposition about chance will be true or false in virtue of the character of these alone.



    

The original formulation of Humean supervenience we might now dub Quality Supervenience. It captures the metaphysical vision at work in passages like the following. in a world like ours, the fundamental relations are exactly the spatiotemporal relations: distance properties, both spacelike and timelike, and perhaps also occupancy relations between point-sized things and spacetime points. And it says in a world like ours, the fundamental properties are local qualities: perfectly natural intrinsic properties of points, or of point sized occupancy of points. Therefore it says that all else supervenes on the spatiotemporal arrangement of local qualities throughout all of history, past and present and future. (Lewis (), pp. –)

As I said earlier, it is also, in one sense, too weak. Without further information about the character of qualities, quality supervenience does not imply modal supervenience. For all that has been said, the qualities may be potentialities. Upon most accounts of the nature of the intrinsic, including the one I recommended, there is nothing to rule this out (.). If potentialities are the basis of the truth of law statements, then there is nothing external to them that settles their potentiality (Noordhof (b); Ellis ()). The fact that quality supervenience may be true when modal supervenience is false shows that quality supervenience is not a version of Humean supervenience. The fact that modal supervenience may be true where quality supervenience is false shows that the latter adds constraints upon the supervenience base not present in the former and which, we saw, is in potential conflict with modern physics (.). Lewis’ own position is best described as the assertion of both modal and quality supervenience. I will dub this Non-Modal Quality Supervenience. We have seen that it is stronger than strictly necessary to formulate the idea that modal truths may be reduced to non-modal truths. It certainly involves more than the straightforward denial of necessary connections between distinct existences. So I will set quality supervenience, and this even stronger doctrine, aside. One concern to have about modal supervenience relates to the idea of non-modal particular matters of fact. Is there such a thing as a non-modal basis upon which we can consider modal facts supervening? For instance, monadic properties cannot relate distinct things, particulars cannot be instantiated, necessarily particulars only instantiate universals, every particular (universal) is necessarily a particular (universal) and so on (MacBride (), pp. –, (), p. ). Fraser MacBride presents those who claim that they can appeal to objects and properties without implicitly appealing to modal truths with a nice dilemma. First, there is no non-modal conception of universal or object that fails to allow that there is a possible world in which a universal/particular may satisfy the characterization of the other. For instance, consider the spatial model of the differences between universals and particulars an entity x is a universal iff x is wholly present in many distinct locations at a time. an entity y is a object (or particular) iff either y is wholly present in only one location at a time or y is partly present in many distinct locations at a time (MacBride (), p. ).

      



Suppose that there is a possible world w with a single negatively charged point particle. Then the particular—the point particle—and the property of being negatively charged are both wholly present at only one location at a time. So the property would be classified as an object and, thus, we would have to allow that some objects are instantiated in other objects. The possible world just described also presents a difficulty for the multigrade/ unigrade account of the difference between objects and properties according to which: an entity x is an object iff it is multigrade; an entity y is a universal iff it is unigrade. An entity is unigrade if and only if there are the same number of constituents in each atomic fact of which it is a constituent. Thus monadic properties have only one other constituent, dyadic properties have two other constituents, and so on. An entity is multigrade if and only if it is not unigrade. Objects are multigrade because they occur in facts with just one other entity (a monadic property), two other entities (another object and a dyadic property), and so on (MacBride (), p. ). In world w, both the point particle and the property of being negatively charged are unigrade. In which case, the point particle is not a particular but a universal. Of course, in other possible worlds, the point particle will be multigrade. The idea that an entity may be contingently unigrade or multigrade is incompatible with the claim that particulars are essentially particulars. Modal versions of these two accounts would avoid the problem presented by world w. The property of being negatively charged would not be classified, by the spatial account, as an object because it may be wholly present in many distinct locations at a time. Likewise, the point particle would not be classified as a property, by the multigrade/unigrade account, because it may figure in atomic facts with different numbers of constituents. However, these accounts of the difference between objects and universals mean that we cannot appeal to such entities to characterize the non-modal supervenience base for modal properties unless the modal properties in question can be accounted for in non-modal terms (MacBride (), pp. –). Now we come to the second horn of the dilemma. Reductionist accounts of modality appeal to a principle of recombination to settle the range of possibilities allowed. For example, to recall from ., Lewis endorses the following Principle of Recombination: ‘a duplicate of anything can coexist with a duplicate of anything so long as they occupy distinct spatiotemporal regions—size and shape permitting’ (Lewis (c), pp. –). This is very permissive about the possibilities it allows. Consider the point particle. It is a distinct existence from another point particle and it is a distinct existence from the relation of instantiation. Therefore, as far as the principle of recombination is concerned, one particle can stand in the relation of instantiation to other point particles. Hence it is not true that it, an object, cannot be instantiated. If it can be instantiated, there is no reason why it cannot be instantiated in more than one thing. In which case, it is not an object by the above conception of objects (MacBride (), pp. –). It seems that we can resist this conclusion only by abandoning or restricting the principle of recombination. Without something like this, we cannot appeal to properties and objects in order to characterize Humean



    

supervenience (MacBride (), p. ). However, if we do restrict by appeal to modal features, or abandon, the principle of recombination, we can no longer use it, and don’t have anything else to hand, to specify all the possible worlds as part of a reductive account of modality. That’s MacBride’s challenge. There are three points to make in reply. The first is to note that we can accept MacBride’s conclusion and reformulate Humean supervenience in terms of nonmodally differentiated entities (MacBride (), p. ). This means, in the present context, not drawing upon the distinction between properties and objects. Particular matters of fact might just be entities at spatiotemporal locations of whatever kind. We may note that some are instantiated and some possess entities that are instantiated in them without committing ourselves to any claims about whether these entities can only possess other entities or can only be instantiated. It might be wondered how, with this basis, we could ever hope to generate all the modal properties that are alleged to supervene upon them. This brings me to the second point. There is no problem with appealing to kinds of entities distinguished by modal properties so long as these modal properties are not taken to be brute as opposed to a consequence of their non-modal properties and one or other counterpart relation in which they may stand (Lewis (d), p. , (), pp. –). The possibilities concerning when a square is instantiated that I mentioned at the beginning is an illustration of the point about non-modal properties. The appeal to counterpart relations is suggested by the way in which Lewis moderated his earlier resistance to truth-makers. He suggested that truth-maker necessitation could be modelled by entities under a particular kind of counterpart relation. The truth-maker of ‘a is F’ is a qua F. By the same token, the non-modal entities I have just mentioned can generate the modal properties of particulars and properties by picking out certain counterpart relations. For example, d qua property instance P would pick out all the counterparts of d that were instances of P and d qua object O would pick out all the counterparts of d that are counterparts of O. The preferred modal characterization of the difference between objects and properties—for example, unigrade/multigrade—would be taken to be analytic truths characterizing a certain counterpart relation. So, any putative modal properties in the supervenience base can be treated in the same way as other troublesome modal properties. Although the appeal to distinct counterpart relations is a viable way to go, it is not clear that it is necessary. This brings me to the third point. Consider the claim that universals may be wholly present in many distinct spatial regions at one time. One way of reading it is to suppose that there is a property—it being possible for the entity to be wholly present in more than one spatial region at any one time—that can only be characterized in modal terms. Understood this way, we have a threat to any attempt to reduce modality by appealing to such an entity. Another way of understanding the claim is that the nature of a universal is taken as primitive. This nature implies a certain modal property: the one just specified concerning the possibility of being wholly present. Nevertheless, this is not a threat to a reduction. If it were, then there would be a quick argument against any apparent reductive account since any successful account will imply modal claims. MacBride moves too quickly from the claim that a certain property has modal implications to the claim that it cannot be the basis for a reduction of modality.

      



Even if modal supervenience can be given an effective formulation, it may appear too weak to capture the denial of necessary connections between distinct existences. A supervenience claim does not involve, or certainly need not involve, the denial of the supervening properties. Compare the corresponding formulation for the truth of physicalism in w. Any world which is a minimal physical duplicate of w is a duplicate simpliciter of w (Jackson (), p. ). It holds that mental properties (for instance) are, in fact, broadly physical. So, likewise, if modal properties supervene upon non-modal particular matters of fact, these modal properties are still instantiated. In which case, modal supervenience by itself doesn’t involve the denial of necessary connections between distinct existences. Maybe the only modal properties the supervenience base supports fail to hold between distinct entities but there is nothing in the formulation that guarantees this fact. The comparison with physicalism may give rise to puzzlement. In the case of physicalism, the supervenience of the mental upon the physical is taken to show that the mental is physical broadly conceived. The corresponding claim would be that the modal is shown to be non-modal broadly conceived. How is this possible? The distinction between properties whose nature can only be given a modal characterization and properties that imply the instantiation of modal properties provide the basis of an answer. If modal properties supervene upon non-modal particular matters of fact, then properties given a purely modal characterization are implied by entities whose nature can be given a non-modal characterization. Talk of modal properties being non-modal broadly conceived is only meant as shorthand for this latter claim. With that clarification, let’s return to the question of whether modal supervenience implies the denial of necessary connections between distinct existences. Lewis’ particular brand of realism about possible worlds lends itself to the following response to this concern. The key point is that the truth of modal propositions partly depends upon other worlds than w (the world in which Humean supervenience is supposed to hold). Thus we have (P) It is possible that A in w iff there is a world accessible to A in which it is the case that A. (N) It is necessary that A in w iff, for all worlds accessible to A, it is the case that A. (C) ‘If it were that A, then it would be that C’ is non-vacuously true at w if and only if some (accessible) world to w where both A and C are true is more similar to w, overall, than is any world where A is true but C is false (Lewis (), p. ). The supervenience of modal truths of the form necessarily p and possibly p hold just in virtue of the fact that w is a member of a set of worlds. It does not depend upon any particular matters of fact in w unless, I presume, the accessibility relation for worlds does not make the complete set of worlds accessible to w. This distinguishes the interpretation of modal supervenience from that of the mental upon the physical.



    

Matters are a little more complicated with counterfactuals. For Lewis, the supervenience of counterfactual truths, and causal truths, holds in virtue of particular kinds of similarities between worlds that define closeness. If particular matters of fact in our world determine the closeness of w to other worlds, and if the total particular matters of fact settle the laws which hold in w as the best system analysis says, then why do we need other possible worlds at all for causal truths? It seems that all the work is being done by actual particular matters of fact. As far as causal truths are concerned, isn’t it enough that we can identify the laws by patterns of particular matters of fact and work from there? Lewis discusses this concern in the following passage. It’s the character of our world that makes some A-worlds to be closer to it than others . . . why bring the other worlds into the story at all? To which I reply that . . . it is only by bringing the other worlds into the story that we can say in any concise way what character it takes to make what counterfactuals true. The other worlds provide a frame of reference whereby we can characterise our world. By placing our world within this frame, we can say just as much about its character as is relevant to the truth of a counterfactual: our world is such as to make an (A-and-C)-world closer to it than any (A-and-not-C)-world is. (Lewis (c), p. )

His answer seems to be that, although w alone is such as to make its counterfactuals true, we need to make reference to other possible worlds in order to characterize the respects in virtue of which w does make the counterfactuals true. His answer is weaker than the general case he makes in favour of the existence of concrete non-actual worlds. His line there is that we obtain reduction of the number of things we must take to be primitive and improve the unity and economy of our philosophical theories about a whole range of matters (Lewis (c), p. ). For example, if properties are natural classes of possible individuals, then the other possible individuals must exist for the properties to exist. Focus on actual individuals would not serve to differentiate properties that we take to be distinct (e.g. having a heart and having a kidney—assuming all creatures have either, neither, or both). All that he emphasizes in the passage quoted above is the possibility of concise statement of relevant counterfactual truth-supporting features. Nevertheless, as we shall see in ., even if the truth of counterfactuals depends only upon facts in our world, recognition of the existence of other concrete possible worlds avoids the introduction of necessary connections between distinct existences.

. Other Possible Concrete Worlds and Humeanism As I noted in ., supervenience claims are not naturally thought of as claims that banish the supervening properties from this world. My answer to the question of why Lewis thought that the doctrine of modal supervenience established that there were no intra-world necessary connections, or for that matter, any modal properties instantiated in our world, was that it made modal truths depend upon how things were in other possible worlds. There was nothing in our world that was the whole

     



basis for a truth about, say, a causal connection between distinct existences. Although, as we saw, what Lewis says about counterfactuals raises the question of whether he is in a position to appeal to this answer in the case of causation. In any event, the answer just canvassed leaves one matter open. Even if there are no modal properties instantiated in a world, and thus no intra-world necessary connections between distinct existences, it is still possible that there are necessary connections between distinct existences understood in the manner Lewis favours. By that I mean, it has not been ruled out that two wholly distinct existences co-occur in every possible world. In this context, Lewis’ account of possible worlds seem to play two roles. On the one hand, it is meant to offer a reductive account of modality that has, as a consequence, that there are no modal properties instantiated in the actual world. On the other hand, it is part of a programme that explains how our world is one in which we don’t have to recognize intra-world necessary connections between distinct existences. Whereas, alternative accounts of modality make this almost inevitable. As we shall see, Lewis’ account may not be essential to the first, but it is for the second. Lewis’ position is a combination of two theses. A denial of Actualism about possible worlds and an assertion of Concrete Particularism. Actualism holds that everything that exists is actual. Actualist realist accounts of possible worlds take these worlds to be part of the actual world in different standing to the world of which they are a part (Divers (), pp. –, –). Concrete particularism holds that the possible entities corresponding to spatiotemporal particulars in the actual world are also spatiotemporal particulars. It does not have to say that all that possibly exists are spatiotemporal particulars: numbers, alien properties, etc. may be an exception (for Lewis’ reservations concerning how to formulate his position which, hopefully, this avoids, see Lewis (c), pp. –). If you deny actualism while being a concrete particularist, then you must take possible individuals and worlds to be non-actual things of the same kind as the actual world. A standard observation is that actualist forms of modal realism (sometimes given the friendly title Ersatz Modal Realism) fail to support a reductive approach to modality. They are forced to appeal to modal notions in their articulation. There are differences of opinion as to what these possible worlds are, for instance, structural universals, maximal sets of consistent propositions, and the like. The intrusion of modal facts in the actual world comes at, correspondingly, various different points as a result. First, they are used to characterize possible worlds themselves. If our building blocks of possible worlds are propositions, then they are plausibly thought of as maximal sets of consistent problems. The definition of maximality doesn’t seem to provide a problem. A set of propositions, S, is maximal if and only if for every proposition, one of either it or its negation is a member of S. It is hard to escape an explicit mention of possibility in the definition of consistency though. According to the standard formulation, A set of propositions is consistent if and only if it is possible for them all to be true together (see e.g. Adams (), p. ).



    

It is possible that p comes out true if p is a member of a maximal set of consistent propositions (Adams (), p. ). Similarly, if possible worlds are uninstantiated world properties, thought of as universals, and you want to capture the idea that it is possible that there are talking donkeys, then you are committed to something like the following. There is a property such that necessarily any particular that instantiates it has a talking donkey as a part (Lewis (d), p. , or pp. –). Lewis’ thought is that while structural universals might provide the basis for a nonmodal treatment of claims about possible instantiations of simple properties, because they are part of the specification of the structural universal, they won’t be able to give a non-modal treatment for anything which is not part of specification of the structural universal but an implication of it. A similar worry afflicts Rosen’s actualist anti-realism—modal fictionalism—in which, for the non-spelt-out bits of his possible world fictions, he appeals to the idea of according to the fiction of possible worlds, p. Here, again, the assumption seems to be that if a certain fiction holds, p must be the case even if it is not explicitly mentioned (Rosen (); Sider ()). For this reason, I will not consider the possibility of avoiding irreducible modal truths by treating possible worlds as fictions whatever the merits might be of these theories for avoiding commitment to possible individuals. Armed with the distinction between entities that imply modal truths from entities whose properties can only be characterized in modal terms, we can see that some of the objections to actualist theories may be unjust. For example, we can argue that the nature of an uninstantiated world property implies that there is a talking donkey in just the sense that the property of being a square implies certain modal truths. As Fine has argued, there are grounds for supposing that notions like essence and grounding cannot be explicated in modal terms but imply modal truths. To cite a familiar example, it is no part of the essence of Socrates that there is a singleton set of Socrates, {Socrates}, and yet Socrates could not exist without such a singleton. Thus the essence of Socrates is not to be explained in terms of the modal characterization that it is made up of the properties that Socrates could not fail to have. Equally, intuitively, the singleton is grounded in Socrates rather than vice versa, and yet there is a two-way necessary connection (Fine (), pp. –). Fine suggests that metaphysical necessity is a special case of essence, advancing a particular reductionist thesis: ‘The metaphysically necessary truths can be identified with the propositions which are true in virtue of the nature of all objects whatever’ (Fine (), p. ). In later work, he tentatively reverses the priority to which he seems committed here arguing that an entity’s essential properties are those properties it has of metaphysical necessity that are ungrounded in other properties it has of metaphysical necessity (Fine (), p. ). I am focusing on the earlier proposal. A consequence of Fine’s earlier proposal seems to be that an actualist account of possible worlds can be the basis for a reductive approach to modality. There is a further question as to whether a reductive approach to modality can do away with possible worlds and individuals. Fine favours a positive answer (Fine (), p. ). However, there is a reason not to go along with Fine on this if our interests are a reductive account of modality.

     



As Fine acknowledges, he needs to appeal to characterizations of the nature of properties, in terms of what they are grounded in, to capture how one property is grounded in, and thereby necessitated by, another. To illustrate the point. The basis for the truth of ‘Necessarily, red objects are coloured’ is the fact that the nature of red includes, as part of its characterization, that it is a colour. However, this makes the nature of redness depend upon being coloured. To capture the fact that, if you are a physicalist, somebody being in pain is dependent upon being in a particular neural state, we can’t appeal to, say, the fact that the nature of pain includes, as part of its characterization that it is c-fibre firing and/or A-δ fibre firing because either of the latter include aspects of their nature that are not part of the nature of pain. We can’t appeal to the nature of, say, c-fibre firing including that it is pain because that would make c-fibre firing dependent upon pain rather than vice versa. So, Fine argues, we have to appeal to something like the following thesis. The nature of pain is such that, if a subject has c-fibre firing, then c-fibre firing is a ground of pain, if a subject has A-δ fibre then A-δ fibre firing is a ground of pain (and so on for all realizations of pain). Given that grounding is, itself, a modal notion, although not a purely modal notion, such natures cannot be the basis for the reduction of modality. We can avoid this problem if we retain the appeal to possible worlds. Let me set aside the question of whether we need to appeal to grounding rather than straightforward supervenience. Instead of giving the property of pain a modal nature of the sort described above we can characterize the relationship in terms of supervenience with the modalities involved understood in terms of possible worlds in the standard way. The connection between the properties will be captured by what the relevant possible worlds entail. If you want something more than a pure modal account to capture the grounding element, then this can be done by drawing upon various different notions of construction non-modally conceived (for further discussion Noordhof ()). In any event, this is why I suggest that the first role, the reduction of modality, may not require Lewis’ account of possible worlds. Let’s turn to the question of intra-world necessary connections between distinct existences. A common consequence of any actualist realist position is that the truth of modal supervenience will not depend, in part, on the actual world’s membership of a set of worlds that are not part of the actual world. By contrast, as we noted above, Lewis’ concrete particularism avoids commitment to the instantiation of modal properties in the actual world by understanding them in terms of what happens in other worlds that are not part of the actual world. It is, therefore, almost inevitable that there will be intra-world necessary connections. The only question is whether they hold between distinct existences. In fact, it seems clear that an actualist account of modality will struggle to deny their existence. The point can be made in, at least, two ways. First, suppose that you deny that a powers ontology is true of the actual world but accept that it is possible. Consider a non-actual possible world at which a powers ontology holds. If other possible worlds are complex properties corresponding to worlds, then the powers ontology world will be a complex, but uninstantiated, powers net. Let a component of it be, say, a power P to manifest M given a trigger T. Then



    

there will be a necessary connection between P & T and M. Since this world property is part of the actual world, then there will be an intra-world necessary connection between distinct existences at the actual world even if these are not amongst the properties instantiated. A problem with evaluating this first point relates to whether we can understand possible worlds in terms of world properties, with constituent properties, for reasons Lewis identified, discussed in .. regarding methane (Lewis (d)). The danger is that the position faces a dilemma. Either it has to recognize that the world properties don’t have properties as constituents and, thus, conclude that they have no constituents. The thought here is that properties are the only suitable constituents for complex properties since complex properties are understood to be universals wholly present in each object resembling others in the relevant respect. But if world properties have no constituents, then the connection between the world properties and the modal truths for which they are supposed to be a basis is magic. On the other hand, if the constituents are not properties but particulars capable of multiple instantiation as part of the world property, then the difference between this position and concrete particularism seems to diminish. Such an actualist will say that these world properties are uninstantiated partly particular-like entities that are part of the actual world. What does uninstantiated get you, in terms of plausibility, that denying that possible worlds are part of actuality does not? It seems very little. Taking possible worlds as maximal sets of consistent propositions doesn’t seem to avoid the difficulty. There will be a necessary connection between apparently wholly distinct propositions, namely those relating to the possession of a power and the instantiation of the trigger on the one hand, and concerning the instantiation of a property that is the manifestation of that power on the other. A proposition concerning the latter doesn’t have to mention the power in question, if it is thought that this might undermine the claim of the propositions I mentioned to be wholly distinct. This first way of making the point that actualist positions will struggle to deny that there are necessary connections between distinct existences relied upon the possible truth of a powers ontology. A similar line of argument could be constructed for the other non-Humean metaphysics we have considered involving propertyindependent necessitations. Determined Humeans may reject even the possibility of such positions. This brings me to the second way of making the point. Suppose that the actual world is one in which a Humean account of causation holds. Let c be a candidate cause, k be the relevant circumstances, and L the Humean law relating c in k to e (the target effect). Recall the best system analysis allows for uninstantiated laws. In this respect, the proper analysis of the basis on which law generalizations are true cannot be the same as that which makes any accidental generalization true, for example, the aggregate of events that fall under it plus some totality fact. Thus L is not committed to the existence of any instances. In particular, it is not to be taken as the complex pattern of events that includes c and e. Then c in k and L are distinct existences from e. Nevertheless, the relationship between c in k and L and e is one of metaphysical necessity. If non-actualist concrete particularism were true, this modal fact would be a fact about the actual world’s membership of the set of worlds not part of the actual world. But for the actualist realist, this modal fact supervenes upon the set of worlds that is a part of the actual world.

         



In the abstract case just described, L is not an uninstantiated law given that c and e fall under it. However, if L may be true, as a result of its position in the best system of laws, then its truth need not be understood in terms of these entities that fall under it. The best system of laws depends upon the pattern of events in the world. Some of the events of that pattern, perhaps the vast majority, will be part of the basis upon which the best system of laws is true. However, if uninstantiated laws may be true, then it follows that there may be a law which is, in fact, instantiated but which relies for its truth not upon its instances but other factors together with there being no counterinstances. The argument I just gave rests upon the assumption that L is such a law. A standard line favoured by Humeans, to support their position, is to invite us to consider a world involving the arrangement of distinct particular matters of fact, and suggest that there are no necessary connections to be observed, or conceived of, between such particular matters of fact. As we have seen, though, unless modal properties are rejected completely, their supervenience upon non-modal particular matters of fact leaves open the possibility that some of these modal properties are relations of metaphysical necessitation between distinct existences. Indeed, actualist approaches to modality find it difficult to avoid them. So it seems that the contingent denial of metaphysically necessary connections between distinct existences depends upon Lewis’ account of possible worlds where the contingent truth of modal supervenience need not. If that’s right, then there was a good reason why the most prominent recent Humean courted the incredulous stare (Lewis (c), pp. –). That said, modal supervenience is not, by itself, an expression of the denial of necessary connections between distinct existences and it was a mistake, by Lewis, to suggest otherwise.

. Can Humeans Afford to Allow That the Denial of Necessary Connections Is Contingent? Let me now turn to the two issues I raised at the beginning regarding the question of whether Humeans can afford to allow that denial of necessary connections between distinct existences is only contingently true. The first issue was whether allowing for the possibility of intra-world necessities vitiated the attempt to analyse necessity in terms of possible worlds. The second issue concerned the role of the principle of recombination either as a principle of plenitude, or as a reduction of modality, if there are modal constraints.

.. Do intra-world necessities vitiate the analysis of necessity in terms of possible worlds? At its simplest, one way of putting the concern is as follows. Intra-world metaphysically necessary connections between distinct existences are particular matters of fact with the following structure (or something like it) NM ðFa; GbÞ: Here ‘NM’ stands for the putative relation of intra-world metaphysical necessity. The possible worlds analysis of necessity holds that



    

It is necessary that (Fa, Gb) = df in all possible worlds (Fa, Gb). We have an intra-world fact and a fact across possible worlds. What determines that they are aligned? One could argue that the second fact is the result of the first. Possible worlds are allowed recombinations of entities in the actual world. If there were facts of the form NM(Fa, Gb), it would not be allowed that there were a world in which Fa held but not Gb. This would not be conducive to the kind of naturalistic reductive combinatorial account of possibility that Armstrong, for example, has in mind. For this reason, he endorses Hume’s denial of necessary connections between distinct existences (not always consistently since he allows exceptions) (Armstrong (), pp. –, for exceptions, see pp. –). Nevertheless, shorn of its reductive ambitions, restricted recombination could explain how these two elements are integrated. Proponents of the powers ontology often reject possible worlds and talk in terms of what is possible being that which is left open by the powers (Bird (), p. ; Jacobs ()). Nevertheless, if they wanted to explain how the two pictures might be integrated, given the powers ontology were only a possibility, this is how they could do it. Although we can say that the claim about possible worlds is the result of NM(Fa, Gb), that still doesn’t quite explain what is going on. Consider by analogy the identity statement David Cameron is identical to David Cameron. If it is a necessary truth, it seems to be because, if that man is in a possible world then the very same man would also be there or, in counterpart terms, ‘David Cameron’ on either side of the identity term picks out the same counterparts in all worlds. What’s the equivalent kind of explanation to that for NM(Fa, Gb)? In the case of the powers ontology, an appeal to the identity of properties— specifically their causal role—will play a similar role. Matters are a little different for property-independent necessitation accounts. Unlike the best system analysis or the powers ontology, the laws don’t supervene upon the properties that are instantiated. For them, the solution is to recognize that the laws and particular matters of fact that give rise to intra-world necessary connections are to be understood as potential changes in the similarity weighting from those that would be licensed by the best system analysis. To illustrate, recall the example in .. in which the generalization all X particles in Y fields are spin up held in a universe, U₂*, because a X particle’s journey into a Y field was blocked by a mirror. This was the only difference between U₂* and U₂, in the latter the mirror did not block the particle’s journey and the particle’s failure to be spin up falsified the generalization. For U₂*, the best system analysis would hold that, if the mirror had let the particle pass, it would be spin up. A property-independent necessitation account of laws—which would not take the generalization that all X particles in Y fields were spin up as a law in U₂*—would deny this counterfactual concerning the mirror. The difference would be reflected in which possible worlds were counted as closest to the world in which the mirror blocked the particle, given by the similarity weighting. As far as I can see, then, with this understanding of the implications of intra-world metaphysically necessary connections between distinct existences in place, there is no further problem posed by the mixed picture entertained here.

         



.. Principle of recombination There are two types of appeal to the principle of recombination: as a principle of plenitude and as a reduction of modality. I’ll take these in reverse order. To fix ideas, let me focus upon Lewis’ version slightly adjusted. Any number of duplicates of anything can coexist with any number of duplicates of other spatiotemporally distinct things size and shape permitting (Lewis (c), p. ). The italicized phrase shows that Lewis already accepts some restriction on the range of possibilities. He didn’t want the principle to be the basis for an argument that there can be space-times larger than one with an infinite cardinal number of points (a denumerable infinity). The maximum number of wholly distinct individuals in an infinite space-time would be one individual for every space-time point, that is, Aleph₀. An unrestricted principle of recombination would allow duplication of these individuals so that there were , , an infinite number of them for every space-time point. A space-time to contain them would have to be larger than one with Aleph₀ number of points establishing the possibility of a spacetime the size of which we have no other reason to countenance. To avoid this conclusion, Lewis adopted the ‘size and shape permitting’ condition. The appeal to duplication addresses two issues. First, Lewis denies cross-world identity for individuals. In different worlds, there are different individuals although they may be counterparts of each other. So recombination cannot be understood in terms of recombination of individuals. Second, recombination cannot be understood in terms of recombination of counterparts either because, as Lewis recognizes, the individuals we recognize may have certain relational features essentially. A duplicate of an individual is one that shares its perfectly natural properties. Suppose that I could not exist unless I had come from my parents. Then it is not possible for there to be a world in which I exist and my parents do not. Nevertheless, according to Lewis, there is a possibility not ruled out by this, namely that a duplicate of me exists and my parents do not. It is the possibilities inherent in duplication to which the principle of recombination appeals. As we saw in ., it is not clear that the properties that characterize duplicates support maximal recombination. There may be some restrictions in the case of a powers ontology. The principle of recombination in its first role—as a principle of plenitude—determines the space of possibilities. It is supposed to provide a way of determining the different possibilities there are—understood as possible worlds— rather than providing an account of the nature of possible worlds themselves. As Lewis remarks, saying that every way a world could possibly be is a way that some world is cannot count as a principle of plenitude because it just says that every world (i.e. way the world could possibly be) is identical with some world. This is true whether there are three worlds or an infinite number of worlds (Lewis (c), pp. –). The fact that the properties that characterize duplicates may not support maximal recombination shows that, as it stands, the principle is false. The restrictions derived from them mean that not any old recombination of duplicates is possible. However, the principle can be reformulated to



    

a duplicate of anything can coexist with a duplicate of anything so long as they occupy distinct spatiotemporal regions—size and shape and nature permitting. Since some constraint was already present, it is not clear that an extra source of constraint immediately undermines the role of the principle of recombination in a reductive account of modality. We have seen in . that recognition that natures may have modal implications—this time in the form of restraints—is compatible with a reductive account of modality. After all, intrinsic properties permitting maximal recombination have modal implications: the extensive possibilities they allow. Power ontologists who insist that their potencies have natures that imply their causal profile, rather than are expressed wholly in terms of it, can claim, in good conscience, that any appeal to the principle of recombination that they make is still compatible with a reductive account. Those convinced by Lewis’ original restriction on the principle of recombination are in a weak position to resist the additional restriction envisaged. The motivation for the restriction is that it is not possible for two or more duplicates to occupy the same space-time point. Power ontologists’ appeal to the causal profile of properties rule out, or insist upon, certain other instantiations. This is not a different order of restriction on the principle of recombination. We saw in . that commitment to a powers ontology may involve a commitment to necessary connections between distinct existences, although not in a straightforward fashion. The adjustment and defence of the revised principle above shows how this is compatible with an appropriate principle of recombination. So our preliminary conclusion is that there is no sound argument from the significance of the principle of recombination to endorsement of the distinct existences principle. There is also a question mark over whether the principle of recombination can serve as a principle of plenitude, and is needed for this purpose. I shall discuss the issue first in terms of the context of Lewis’ approach and then generalize. John Divers and Joseph Melia argue that the principle of recombination does not succeed as a principle of plenitude. The argument proceeds in two steps. The first step involves considerations in favour of there being an infinite number of alien properties, that is, properties uninstantiated in our world and not constructed from properties that are instantiated (Lewis (c), p. ). One line of thought rests upon the claim that there is at least one possible world, w₁, that instantiates an alien property in addition to all the properties of our world (by the principle of recombination). On the assumption that our world is not special, the same would hold of w₁, let that world be w₂. Again, it would have all the properties of w₁ plus a further alien property. There is no stopping point in this sequence. So there will be a world w1 that has all the properties of our world plus an infinite number of alien properties. A second line of thought starts with the observation that we might discover that what appears to be one kind of structureless particle breaks down into two sorts: those which attract each other and those which repel each other. Scientists thus claim that there are, in fact, two kinds of particle characterized by different fundamental properties that explain this behaviour. But there needn’t just be two kinds, there could be three that stand in this pattern of relations, the third kind repelled by the other two kinds, and so on. As before, there is no natural

         



stopping point in the argument. So there are an infinite number of alien properties (Divers (), pp. –; Divers and Melia (), pp. –). The second step is to note that since we don’t have names for all the infinite number of alien properties, all that we can do is appeal to a principle such as (OAN) There are worlds such that, for any n, n objects exist across those worlds and n distinct α-alien natural properties are instantiated among those objects (Divers (), p. ). to state that there are enough alien properties to capture all the truths about them. However, this principle does not enable us to specify the complete set of possible worlds. Let S be the complete set of worlds. (OAN) together with the rest of the principles for concrete modal realism establishes that there are infinitely many alien natural properties instantiated across worlds in S: P₁, P₂, P₃, . . . Pn. Delete all the odd members of that set of properties, and the worlds in S which instantiate them, to form a new infinite set of worlds S-. Then the principles of Lewis’ modal realism together with (OAN) are true of S-. So (OAN) cannot ensure that we have a set of worlds with all the natural alien properties there are (Divers and Melia (), pp. –; Divers (), pp. –). The earlier arguments in favour of an infinite number of alien properties don’t secure that we can specify the deleted properties, P₁, P₃, etc., because they only establish that there is an infinite set of alien properties, which is S- as much as it is S, and not all the alien properties that are included. Both S and S- are closed under recombination (Divers and Melia (), pp. –; Divers (), pp. –). If the principle of recombination fails as a principle of plenitude, then it does not matter if it requires the denial of necessary connections between distinct existences. There is no motivation for such a denial to be drawn from the principle. Nevertheless, it is not clear that a failure to be able to state the completeness of the space of possible worlds undermines the claim that a reduction of modality has been provided. A reduction of modality requires we have a non-modal ontology to make modal statements true. Whether we are in a position to state that this non-modal ontology suffices is a distinct matter. Our insight into the extent of the space of possible worlds is given by the combination of the principle of recombination plus the modal claims we are inclined to think we have good grounds for supposing are true. We don’t need any further specification of the extent of the space of possible worlds for the completion of a reductive project. In ., I explained how it was possible to develop a reductive account of modality within an actualist framework. An actualist with such ambitions potentially faces the same kind of argument that Divers and Melia developed above. In this case, though, it wouldn’t be formulated in terms of alien properties as opposed to uninstantiated properties. Once more, the argument would show that the principle of recombination fails to do its job. So it does not matter if it requires the denial of necessary connections between distinct existences. But once again, this failure to specify the complete space of possible worlds does not undermine the reductive project. As a result, we may conclude that there are no theoretical reasons to be drawn from the principle of recombination to conclude that the denial of necessary connections between distinct existences must be true.



    

. Wilson’s Argument against the Distinct Existences Principle Up until this point, I have been defending the claim that the distinct existences principle may be a contingent truth. If it is a contingent truth, then there may be non-Humean worlds in which there are necessary connections between distinct existences. The favoured property-independent necessitation account developed in Chapter  and the powers ontology would be two examples. It is time to discuss an argument that the distinct existences principle is false, indeed, necessarily false if all worlds meet a certain assumption. The argument is offered by Wilson and runs as follows. () There are constitutional necessities such as all red things are colours, anything with a certain mean molecular kinetic energy has a certain temperature. () The Subset Thesis: Property F is realized by Property G if and only if a subset of the causal powers of G are the causal powers of F. () If F and G did not have their causal powers necessarily, then the subset thesis would not explain the constitutional necessities. () F and G have their causal powers necessarily. Therefore, () There will be necessary connections between distinct existences i.e. the triggers of F’s manifestation and property instances wholly distinct from F that are part of the characterization of F’s manifestation (Wilson (), pp. –). The assumption I mentioned is that there are constitutional necessities. In worlds where there are no constitutional necessities but just simple maximally determinate properties, the argument would have no application. If there are such worlds, then the distinct existences principle may still be true in some possible worlds and, hence, the argument would not show that the distinct existences principle is necessarily false. That said, there are three problems with this argument even if the assumption holds for all worlds. The first, and most centrally, as we saw earlier, is that the subset thesis is false (...). So there is no need to, as part of an inference to the best explanation, conclude that the causal powers of F and G are necessary. The various forms of necessary relationship we have discussed between properties involved the supervening properties having causal powers that, in certain respects, outstrip their bases. So the issue of constitutional necessities arises as much for the powers themselves as it does for the purportedly problematic natures understood in non-causal terms. The second is that the subset thesis does not capture the distinctive character of at least some of the constitutional necessities. It is a familiar point that we can’t point to, say, those distinctive features that are added to colour to make it redness. There is no red residue factor. The subset thesis, though, suggests that these things are entirely separable. In particular, that it is possible to identify the causal powers of redness, which is over and above what is involved in simply being a colour, and this can be taken as the red residue. I’m all for the introduction of clarity into relationships of

  



constitutional necessity but the concern is that this mischaracterizes the nature of the relata. The third problem is that, strictly speaking, all the argument requires is that it is necessary that there is a subset relation and not that the properties so related are modally stable. So constitutional necessities don’t imply causal necessitation. It may be the case that a property’s powers are modally stable. It may also be that this is linked to the fact that properties’ causal profiles are the basis of our actual world identifications, though note that there is a well-entrenched practice of imagining that the laws relating to properties may vary. But all of this is just to provide a distinct argument in favour of causal necessitation, and hence for the falsity of the distinct existences principle, drawn from general considerations that have been offered in favour of a powers ontology. We don’t have an argument from neutral premises that even Humeans can share relating to constitutional necessities. My treatment of the powers ontology in ..– is the basis for my rejection of this independent argument.

. Physicalism and Humeanism I have sought to defend my acceptance of the merely possible truth of Humean supervenience by explaining how there were no successful arguments in favour of taking it to be a necessary truth. I will now focus on those who take it to be fundamentally implausible. In particular my interest is in those who would argue that if the counterfactual theory of causation allows that there may be causation in a Humean world, then that is a consideration against it. Often they combine this with the thought that, once it is recognized that causation requires some sort of necessitation or inclination, then the only interesting theory of causation will be one which goes into more detail about the necessitation or inclination envisaged. My argument will be that this is a mistake. Causation does not need to involve anything more. That does not mean we won’t have grounds for supposing that there is something more. Just as symmetries in the causal network might provide grounds for supposing that a powers ontology is not the case, so our experience of causal necessitation, or some as yet unidentified inference to the best explanation, might support taking our world as non-Humean. The current issue is simply whether we are mistaken in supposing that there can be causation in a Humean world and not whether our world is a Humean one. In particular, it is productive to look at the parallels between what people are inclined to think about causation and similar claims about phenomenal consciousness and physicalism. The parallel I want to explore is that Humean worlds are one realization of causation in much the way that arrangements of narrowly physical properties are one realization of mental properties. The analysis of causation provided in terms of counterfactuals plays the same role as the putative functional analyses of mental properties are meant to play in the development of functionalism about the mind. If there are different ways in which the causal relation may be realized, of which a Humean world is one, then two different interpretations are available of the analysis offered so far, in much the same way as two different versions of the functionalism in



    

philosophy of mind are available, occupant functionalism (e.g. Lewis (), ()) and role functionalism (e.g. Putnam (); Shoemaker ()). According to the first, the analysis picks out a certain role, and causation is whatever property occupies that role. The analysis concerns the attribute of causation distinct from whatever property is causation (in Lewis’ framework, Lewis (), Lewis ()). According to the second, the analysis is the property of causation. All the occupants of the causation role are just the various ways in which causation can be realized by properties that, themselves, aren’t causation. Consider our target case then. Let there be two events, e₁ and e₂ and that e₁ is F and e₂ is G. Suppose that a certain kind of regularity holds, all Fs are Gs, and this regularity is picked out by the best system of laws. Finally suppose that e₁ and e₂ stand to each other in the appropriate relationship—spatiotemporal continguity would be an example—so that the law statement is relating e₁ and e₂ rather than some other event ei which is G. Call the combination of the regularity and the relation—which involves no necessitation—R. Then one way of posing the question is to consider whether R can be causation. Another way of posing the question is whether R can realize causation. However we interpret R, if the similarity weighting for counterfactuals draws upon it so that, as a result, the proposed counterfactual analysis holds between e₁ and e₂, is this the right upshot? The discussion of Chapter  supported the view that a necessary, and I would argue sufficient, condition for realization is metaphysical necessitation (Noordhof (b), (), () for a defence of this). I will adopt the second way of framing the issue, take R to be the realization of causation, and relate it to the question of physicalism. Those who resist the claim that causation is realized in Humean worlds can fairly be characterized as endorsing one of the following. (R) (R)

It is possible that R and not C. There is an explanatory gap between R and C.

Here ‘C’ stands for causation. So (R) holds that it is possible that R holds between e₁ and e₂ say and yet e₁ does not cause e₂. In our world where, let us suppose, there is causation, R may hold and there is causation. But, the concern is, in a Humean world where there is only R, there is no causation. Similarly, there is an explanatory gap between R and C because C is something over and above R if causation is absent in the Humean world. The most well-known recent expression of the view that causation is absent in a Humean world is due to Galen Strawson. He writes Imagine a true randomizing device determines the colour value of each pixel on a  pixel, computer screen, running on a ten-times-a-second cycle—so that each pixel can take any colour value for each /th second period. On the screen it appears that there is a film showing. A woman enters a house, walks over to a stove, and puts on a kettle. Life—a world, as it were—goes on in an ordered, regular fashion, exactly as regularly as in our own world. But the image is being generated by the true randomising device. It’s pure fluke that what happened on the screen appears to tell a coherent story of a regular, ordered world, rather than filling up with—or suddenly switching to—a fizz of points of colour . . . The analogy is an attempt to convey some idea of the true (and astonishing) nature of the regularity theory of causation as applied to our own world (Strawson (), pp. –).

  



Strawson takes himself to be describing in as vivid way as possible how things are in a Humean world in which R is instantiated but with no causation. The regularity is described as a pure fluke, generated by a randomizing device, in which, for example, the prior colour values of the pixels have nothing to do with the subsequent values. It is a mystery how causation could be instantiated as a result of the regularities described. The two claims (R) and (R) have much more familiar corresponding claims in the discussion of physicalism. (P) (P)

It is possible that P and not M. There is an explanatory gap between P and M.

Here M is a subject being phenomenally conscious and P the full physical story of his or her brain and related environment in virtue of which, a physicalist will say, the subject is phenomenally conscious. The modal claim, (P), is an expression of the claim that zombie worlds are possible. There may be worlds physically exactly like ours and yet the relevant subjects are not phenomenally conscious. Thus the challenge of the Humean world for the counterfactual theory of causation is equivalent to the zombie world for physicalism. My argument will be that the proponent of the counterfactual theory of causation who allows that Humean supervenience is a contingent truth has a more effective answer than the physicalist. The first point to observe is that the proponent of Humean supervenience has a better story about how the gap can be closed between R and C than the physicalist. Analyses of phenomenal consciousness have been relatively imprecise and highly controversial. It is not possible to put forward an analysis of phenomenal consciousness that people are willing to concede, if it is satisfied, then there is phenomenal consciousness. Reflect now on your attitude to the counterfactual theory of causation defended here. Counterexamples were offered to a previous analysis that, primarily, made you think that the analysis could not be a necessary condition and, when (if) you were satisfied that the new analysis dealt with the case, then you were prepared to judge that there was causation when its clauses were satisfied. So there is no explanatory gap in the same way. Instead, the concern arises when it is noted that the similarity weighting for these counterfactuals need not presume a non-Humean account of law and that, as far as the actual world is concerned, ‘If it were that A then it would be that B’ is true if A and B. These are theoretical concerns generated from a semantics of counterfactuals and not concerns initially identified as a failure of the analysis of causation. So we have a prima facie closure of the explanatory gap about which we, then, begin to have some concerns. The question is how may these concerns be articulated and addressed. To be more explicit, in the case of physicalism, the following argument is run. () Metaphysically necessarily, if P then M (Physicalism). (P) It is possible that P and not M. Therefore, ()

Physicalism false.



    

Responses to this argument have emphasized how features of our epistemic access to these properties, P and M, or differences in the character of our concepts of them, would give rise to the illusion of possibility expressed in (P) which is, in fact, misplaced. Let me mention a couple to provide the basis for a comparison. One of the main physicalist responses is to say that we don’t actually conceive/ imagine that possibly P and not-M but rather possibly E(P) and not-M where E(P) is our mode of presentation of physical property P. Our mode of presentation of a phenomenal property is plausibly thought to be that phenomenal property (that is, E(M) = M). So the focus has usually been on the physical property. We imagine the grey matter that makes up the brain and suppose that this may be present and phenomenal consciousness absent. There is no problem with this possibility because, of course, the physicalist’s claim is not that grey matter, even in squidgy brain formation, is sufficient for consciousness. The details matter (Peacocke (), pp. –; Boyd (), pp. –). Nevertheless the claim is only semi-plausible. Anti-physicalists aren’t against squidgy greyness as a basis for phenomenal consciousness. They hold that, however you fill out the details in physical terms, it will still seem possible for phenomenal consciousness to be absent and we can’t explain why. A second significant line of response is what has been known as the phenomenal concept strategy. Although there are variations in details between the different approaches, there is a significant point of similarity that I will bring out. The principal focus is on a standard model of theoretical identification. It is taken to have the following general structure. () T has role RO (an a priori truth). () O occupies role RO (an a posteriori truth). Therefore, () T = O. In the case of physicalism, T = phenomenal property, O = occupying (i.e. physical) property. The standard model is argued not to work in the case of phenomenal properties because our concepts of them directly refer to these properties without intermediary description of the role they play. Philosophers differ over their reasons for this. For example, Sturgeon says that the canonical evidence for the presence of phenomenal properties is simply their instantiation (Sturgeon (), pp. –). Others, such as Kati Balog, claim that our phenomenal concepts have, as a constituent, the very phenomenal properties, to which they refer, quoted as a means of reference (Balog (), p. ). Some claim that it is our ability to imagine what an experience is like which enables us to make direct reference to the phenomenal properties that characterize it (Papineau (), pp. –). Others again claim that phenomenal concepts are recognitional concepts like demonstratives (Loar (), p. ). The absence of a priori descriptive material attached to our concepts of phenomenal properties, or phenomenal consciousness more generally, explains why we are under the illusion that it is possible for something to satisfy any physical description

  



and yet it is still possible that our phenomenal concepts do not apply. Moreover, this observation about phenomenal concepts is taken to be the basis of the explanatory gap. So no ontological distinction need follow from the fact that there is this gap. This physicalist response is inadequate in at least two ways. First, although one can’t infer from a set of descriptions to a demonstrative mode of presentation, one can work out that a certain individual demonstratively identified satisfies the relevant descriptions. For example, when John Perry records the discovery that, as he would express it, I am the messy shopper whose flour in the shopping trolley is spilling over the supermarket floor—having originally only noticed that somebody was making such a mess—he is not concerned that there is some explanatory gap between the person satisfying the description ‘the messy shopper’ and himself (Perry (), p. ). Whatever gap there is in the case of the application of demonstratives and indexicals is, clearly, of a very different kind to that which arises in the case of our concepts of phenomenal properties. Second, note that if O has R is an a priori truth then T has R need only be an a posteriori truth. So if a priori dispositionalism about properties turns out to be true or if the proposed identity is with functional properties, then there should be no explanatory gap. This is manifestly not the case. Consider now the corresponding treatment of causation (C) and regularities of a certain kind (R). Strawson’s particular way of developing the point that possibly R and not-C seems susceptible to the response that we are not really conceiving/ imagining possibly R and not-C but rather possibly E(R) and not-C. The equivalent to talk of squidgy grey matter seems to be Strawson’s characterization of the regularities as flukes produced by a randomizer. This is certainly a contentious way of characterizing them. To simplify, suppose that there are ten possible colours that might fill the pixels. Then their production by a randomizer gives the probability of each as P(colouri) = /. Contrast this with what a Humean will say the probability of, for example, water boiling when heated to  C at sea level is: approximately . Strawson will have to say that all these probabilities attributed within the Humean framework are, in fact, a mistake and the probabilities are really some value that gives equal probability to every option (Strawson (), pp. –, fn. ). There’s no reason why this should be accepted, especially given the play-off between Humean and non-Humean theories of probability. Thus it is easier to resist Strawson’s characterization of R as a proper grounding for judging that possibly R and not-C than the corresponding claims about whether phenomenal consciousness may be absent from squidgy grey matter. Setting aside the peculiarities of Strawson’s particular justification for the modal claim, the equivalent Humean response, to the first line of response to the argument against physicalism outlined above, is more plausibly that we don’t actually conceive/ imagine that possibly R and not-C but rather possibly R and not-E(C). This time, unlike in the case of phenomenal consciousness where E(M) = M, we can identify a distinct mode of access to causation. What is E(C)? Drawing on the material of ., it is plausible that it is the specified resilient cognitive grip, characterized in terms of the similarity weighting, which makes us conceive of the F-G connection as necessary. But if that is correct, then there is no problem seeing how we might be mistaken about this possibility since E(C) is the way we identify causation but not a way we must identify causation. So we can conceive of regularities for which we are not in E(C) and note that it will not seem like causation to us.



    

A version of the same point will also account for the apparent explanatory gap. E(C) does not involve a mediating description. Rather it picks out causation via the presence of a certain kind of cognitive grip that generalizations relating to F-type things and G-type things play in our cognitive lives. Since we can think about R without the cognitive grip being present, it will always seem there is a gap between the apprehension of R and the apprehension of it via E(C). The latter will seem like an additional accomplishment. The charge is that we take this cognitive difference and presume that it reflects an ontological difference. A popular defence of physicalism recently has been the ignorance approach (e.g. Stoljar ()). The key element of it is that the modal claim appears plausible because of our ignorance of a particular physical property or connecting principle and the explanatory gap is present due to the same ignorance (Stoljar (), pp. –, –). The immediate application of the approach to a defence of causation in Humean worlds is obscured because the focus on the regularities present in the Humean world, as the basis of causation, suggests that the Humean does not take us to be ignorant of the basis of causality in the way that the physicalist might say we were ignorant of the basis of the connection between physical properties and phenomenal consciousness. In fact, analogous points can be made in defence of causation in Humean worlds. It can be argued that we are ignorant of a non-modal property—in the present context, this means a property that does not involve necessitation—that is possessed by those regularities that involve causation. The features that have been attributed to regularities involving causation up until this point have been rather thinly specified, for example, by generalizations characterized by their membership in the best system of generalizations combining simplicity, strength, and fitness. Our ignorance might concern some feature of the entities that are part of the regularities or some feature of the regularities themselves in question. These options are analogous to those identified by Daniel Stoljar in the case of phenomenal consciousness. The first corresponds to talk of categorical properties or qualities (Stoljar (), pp. –). Stoljar’s emphasis here is on some physical property that it is not a causal-structural property. The second corresponds to the idea that causal-structural properties identified by physicists may explain, in ways we are not yet clear, structural properties of consciousness experience (Stoljar (), pp. –). The corresponding idea is that causation involves special kinds of regularities we have not yet identified. Let me emphasize the overall structure of the point. My claim is not that these defences of Humean worlds involving causation are without problems, although some of them have significant plausibility. The point is rather this. Commitment to causation in Humean worlds has considerably more plausibility than like commitment to physicalist accounts of consciousness. The defence of the latter position against arguments to the contrary is less successful than corresponding defences of the former. The extended argument in favour of a counterfactual theory of causation developed here is, equally, more plausible than attempts to secure physicalism by appeal to the overdetermination argument or provide a functionalist analysis of mental states (see ..). But perhaps there is a consideration in the opposite direction. Many physicalists claim that physical objects are not just a construction out of various possibilities of

  :    



experience but go beyond that. Instead, physical objects are taken to explain why there are these possibilities. By the same token, Strawson argues, we should accept that there is an explanation of the regularities we find in the universe: natural necessity. Acceptance of the physical object explanation while eschewing the natural necessity explanation is an unwarranted asymmetry (Strawson (), p. ). There is an important disanalogy. Explanations citing natural necessities have no positive content. Natural necessities are just specified to be those which explain the regularities. By contrast, physical object talk sets our pattern of experiences in a framework. We are located in space and stand in such and such relations to objects as a result of which we have experiences. This framework gives us an explanation of what is going on with independent content. In addition, it makes predictions about future experience. For example, if my position changes towards an object so that I go round to its back side, I will have such and such experiences of it. Natural necessities have no additional content and provide no additional predictions about future experience. They are simply characterized as what explains the regularities, whatever they are, and the regularities that, in fact, hold exhaust the experience, or indeed the possible experiences, we can have of the world. The only qualification to this is that, as we have seen in the mirror case, their failure to hold can result in a distinct prediction from the regularity that they fail to back. The relevant parallel is not with physical objects but with Kantian things in themselves. Kant’s things in themselves are not meant to have any distinctive implications for the pattern of our experiences but just, by affecting us, explain why we undergo the experiences we do (e.g. Kant (/), A/B). Philosophers concerned about entities whose sole characterization is that they are explanatory of something—experiences of objects—will find a ready additional candidate of concern in Strawson’s natural necessities. So it is perfectly legitimate to argue that physical object talk is the best explanation of the course of our experience but withhold the honour to natural necessity with regard to causal regularities. In which case, the point stands. Allowing causation in Humean worlds is easier to justify overall than physicalist accounts of consciousness. Resistance to allowing that there is causation in Humean worlds should be seen in this context.

. Varieties of Causation: Concluding Picture and Implications for Methodology of Metaphysics In the course of this book, I have developed a univocal analysis of causation while acknowledging that causation comes in varieties. On the univocal side, various indicative, potentially conflicting, features of causation were, in fact, with some adjustment, drawn into a single complete account. Consider the following list from causal pluralists (C) (C) (C) (C)

Causes raise the chance of an effect. Causes explain the effect. Causation involves the transfer of a quality/conservation of a quantity. Causes are means to ends.



    

(C) Causation is intrinsic. (C) Causation involves regularities. (C) Causation involves counterfactual dependence (drawn from Skyrms (), p. ; Psillos (), p. ). I have argued for qualifications for some of these. Instead of taking causes to raise the chances of effects—something that ignores the presence of potentially pre-empted competing causal chains—I have suggested that (C*) Causes are entities, for example, an event e₁, which (independently of its competitors) both make the mean chance of an effect, e₂, very much greater than its mean background chance and actually influence the probability of the effect in this way at the time at which the effect occurred via a complete causal chain. The characterization of this kind of chance-raising has been provided in terms of counterfactuals although not in terms of straightforward counterfactual dependence. Instead, the claim is that (C*) Causation involves a condition-relative probabilistic dependence characterized in terms of counterfactuals. The resulting picture explains how causes are means to ends (C). Indeed, part of the justification for the characterization of causation provided is that it captures a natural way of understanding means to ends. Combining (C*) and (C*) with the fact that the condition-relative chance-raising involved in causation is non-symmetric is the reason why causes explain effects (C). One way in which causation is intrinsic is that whether or not something is a cause is settled by the nature of the causal chain leading from that cause to the effect regardless of whether other potentially competing causal chains are present. Call this the ‘independent from competitors’ sense. This leaves open the possibility that some aspects of the causal chain may involve properties extrinsic to it, for instance, in the case of Humean accounts of law. Call this the ‘nature of the properties’ sense. Recognition of these distinct elements resulted in a qualification to (C) to yield (C*) Causation is essentially intrinsic in the ‘independent from competitors’ sense and is contingently intrinsic in the ‘nature of the properties’ sense. Just as there is this qualification to the intrinsicality condition so there is also a qualification to the claim that causation involves regularities. The proposal I have defended is that (C*) Causation involves regularities in virtue of the fact that one essential element of the basis of its analysis in terms of a notion of condition-relative probabilistic dependence implies regularities. Condition-relative probabilistic dependence is characterized in terms of counterfactuals, the similarity weighting for counterfactuals refers to ‘chance-fixers’, and central cases of chance-fixing involve laws, together serving to capture the appropriate relationship to regularities.

  :    



Although causation does not involve the transfer of a quality/conservation of a quantity in the sense that every cause is something for which this is true, the position I have defended is compatible with the plausible thesis that (C*) Causation involves causal circumstances some elements of which involve the transfer of a quality/conservation of a quality, which can be understood in terms of my analysis. In this last respect, the analysis undermines the case for saying that we have a variety of causes in the sense favoured by the causal pluralist. Nevertheless, the analysis has recognized important senses in which causes, and causation, is various and in what follows I will outline how we should understand this a bit further. A preliminary contrast between two ways of understanding the nature of the variety compatible with commonality is helpful: the determinable-determinate relation on the one hand, and the species–genus relation on the other. The latter is taken to have the following distinctive features. First, a species is obtained from a genus by adding an independently specified differentiating feature (Prior (), p. ). By contrast, it is argued, determinate properties cannot be analysed in terms of the determinable for which they are a determinate and an independently specified additional property. For instance, it is said that, in the case of colour, a specific shade of red cannot be analysed in terms of the property of being coloured plus some other property. All there is is redness. Second, species may have instances with properties that are not part of the dimensions of variation of the species or genus under which they fall. Call this their instances’ capacity for additional properties. For example, a human being can be an accountant or have a suntan neither of which, we may safely assume, are part of the dimensions of variation distinctive of being human (Funkhouser (), pp. –). Talk of genus-species may convey the impression that these distinctive features apply to biological kinds rather than some more extensive kind relationship. For this reason, I’m inclined to talk of the substantial kind–subkind relation. It characterizes one side of what Lowe puts forward as a fourcategory ontology (Lowe (), p. ). The determinable-determinate relation has other distinctive features that open up the possibility of a further discrimination between it and the idea of realization more generally. First, to every determinable there are dimensions of variation with regard to the determinates that fall under it. For example, in the case of a standard reference point of this discussion, colour, the dimensions of variation are hue, saturation, and brightness. Particular colours are combinations of these (Funkhouser (), pp. –). Call these the characterizing dimensions. Second, determinate properties are ways of being their determinable properties whereas, in the case of the relationship between realizing and realized properties, it is argued that this is not so. For example, a particular shade of red is a way of being coloured. Call this the ways of being condition. By contrast, the neural states that realize pain (if they do) are not a particular way of having pain. Particular ways of having pain will be the various phenomenological features relating to its intensity, characteristic profile of stabbing or throbbing, and the like. The latter do not realize pain but are determinates of it or, in Eric Funkhouser’s terminology, specifications (Funkhouser (), pp. –).



     Varieties Capacity for Additional Properties?

Yes Independently Specified Differentiating Property?

Yes Substantial Kind/ Subkind

No Independently Specified Differentiating Property?

No Ways of Being? Characterizing Dimenions?

Yes Ways of Being? Characterizing Dimensions?

Yes DeterminableDeterminate

Yes DeterminableDeterminate

No/Not necessarily Realized-Realizer

No/Not Necessarily Realized-Realizer

Figure .

So we seem to have the characterization of the territory as in Figure .. Funkhouser takes the realized–realizer relation to exclude the determinable– determinate relation because it only holds when the distinctive features of the determinable–determinate relation do not hold. That is reflected in the lower right boxes by ‘no’. By my lights, the realized–realizer is a more general relation of which the determinable–determinate one is a subcategory. This is captured by the fact that they both satisfy the minimal metaphysical necessitation base condition for the relationship between the realizer/determinate and the realized/determinable properties respectively (..). In which case, ‘not necessarily’ is the more appropriate characterization of realized–realizer. The most straightforward application of the determinable-determinate relation is that much of our causal talk in terms of pullings, pushings, digestings, gun firings, and so on seem ways in which the causal relation is instantiated. Causing, or causes, is the determinable relation for which these are the determinates. However, there are two points of disanalogy with standard cases that raise interesting issues. First, if there are characterising dimensions of variation in the case of causation, they are certainly more complex. The causally relevant entities identified by different sciences themselves differ substantially in the kinds of variation that are causally salient. Are we to view these dimensions as in some way integrated into a one-dimension system, are the dimensions relative to a particular type of subject matter—as studied by, for

  :    



example, physics, biology, or the social sciences—or are the apparent dimensions in biology and the social sciences, say, to be understood in terms of the dimensions identified by physics? Second, given that I have provided an analysis of causation, it is possible that a determinate of a causal relation may be analysed in terms of this analysis plus an additional independently characterized property or properties. For example, the transmission of energy may involve quantities of energy at distinct space-times satisfying the analysis of causation provided. This might suggest that the appropriate characterization of the relationship is realized–realizer but it would be a mistake to take the observation just made as conclusive. A pushing is still a way of being a causing. It is better to take the point about the analysis of determinate properties to hold for some such properties but not necessarily all. Those determinate properties falling under a determinable for which there is an analysis are a potential exception. An exception to the application of the determinable-determinate relation to causation in the respect we have just been considering involves the relationship between causation between particulars, which has been the main subject of analysis, and property causation. Instead, causation between particulars is part of the minimal necessitation base, and may be thought of as a partial realizer of, property causation. Another component of the realization is set out in the generality condition (see ..). Property causation is not a way of being the relation characterized by the analysis of causation between particulars I have provided. Equally, it does not seem appropriate to characterize causation as something common to causation by particulars and property causation. Instead, the latter holds if there is a pattern of instantiation of the former. A second exception relates to what I have argued about the nature of causes and causal circumstances. There are two ways in which causes are various which we need to recognize. The first relates to the different roles that causes may play in constituting a particular causal circumstance, for example, whether the cause is a producing cause linked to an effect by a genuine process or whether it prevents some preventing condition upon an effect; whether the cause triggers the effect, or whether it is an enabling condition, and so on. I leave open the possibility that there are other roles I have not identified. Some aspects involve a determinable-determinate relation as I have already indicated above: specifically, the presence of genuine processes or preventing conditions are two different ways of being a cause. However, the fact that a cause explains the timing of an effect or counts as an enabling condition (which itself may be a consequence of its time of occurrence relative to the presence of other causes in the causal circumstances) seems to be something that can be specified independently of the operation of the cause. We can take these temporal features to be part of the realization, along with determinate causal properties like being linked by a genuine process, for the realized property of being a triggering cause or an enabling condition. The second way in which causes are various relates to their metaphysical category: events, facts, continuants, properties, and so on. I have given a characterization of



    

each of these types of entities in a way that is independent of their role in causation. This suggests that these various kinds aren’t ways of being causal entities but rather, together with their satisfaction of the analysis, they are simply part of the realization of a causal entity. None are determinates of the determinable cause. Nevertheless, some are fundamental to our understanding of causation, specifically events and properties. If there are continuants and facts, they are causes because of the efficacy of events and properties to which they stand in some relation. For example, as I argued in ., continuants are causes in virtue of the fact that a specified duration of their existence and certain of their properties figure in a correspondingly efficacious event. Let’s move from the varieties of causation recognized in the first half of the book to those ways in which causation may vary in the second. The first concerned the different bases for causal non-symmetry: the non-symmetry of overdetermination, the independence condition (an asymmetric relation), primitive non-symmetric chance-raisings, and the non-symmetry of agency. The second concerned the different ways in which laws may be realized: the best system analysis, propertyindependent necessitation views, and the powers ontology. The third, following on from the first and second, concerned the different ways that chance is realized. There seem to be two models of how we may understand these relationships. According to the first, the various bases of causal non-symmetry and of laws realize but are not determinates of causation. They are not ways of being causation in the relevant respects. The study of causation may include the study of its realization but it still involves a shift in subject matter in much the same way that, according to the functionalist picture, a study of the realization of minds is not a study of their nature. According to the second, the connection is more intimate. The various realizations are actually determinate causal non-symmetries, laws, and chances. In studying their nature, the subject matter does not shift but becomes more specific. Causation does not stand to these various realizations of it as determinable to partial determinate. I say partial determinate to recognize that these realizations cannot be candidate determinates for causation as opposed to causal non-symmetry, laws, and chance respectively. Consider, first, the various realizations of causal nonsymmetry. The different realizations can work both independently and together as the basis for a particular causal non-symmetry. They are not mutually exclusive as, for example, determinate colours are of each other. For example, the non-symmetry between cause and effect may be the result of both the independence condition and the non-symmetry of overdetermination. Their success in realizing causal nonsymmetries may also depend upon the non-occurrence of other realizations. For example, the case of Tooley’s inverse universes, which was used to motivate recognition of primitive non-symmetric chance-raisings, relied upon the other macro-non-symmetries running in the other direction from the primitive nonsymmetric chance-raisings. So the macro-non-symmetries’ realization of causal non-symmetry depends upon there being no primitive non-symmetric chanceraisings present in competition. Similar points apply to the realizations of laws. The patterns picked out by the generalizations in the best system are present in worlds with a non-Humean metaphysics. In such worlds, these patterns aren’t laws unless in accordance with the laws of the non-Humean metaphysics. The response

  :    



I offered to the mirror argument against the best system analysis of laws is a case in point. The picture just sketched about the relationship between causation and its realizations has more general metaphysical implications. When metaphysicians talk about investigating the fundamental structure of reality, they usually envisage identifying something necessary that, in its own terms, settles what is possible. This is traditionally understood in the vertical sense I characterized at the beginning of Chapter . On this conception, the fundamental things are the constituents of the world from which everything else is constituted. It naturally goes with the truthmaking picture. Even when it does not, the fundamental constituents are those things in virtue of which the truth of propositions concerning non-fundamental things turn. (Sider (), pp. –). Fundamental structure vertically understood concerns, with qualifications, the identification of an austere class of natural properties (Sider (), pp. –, –). When the fundamental is conceived of in the vertical sense, it follows that the comparison between various metaphysical pictures should be a cost-benefit analysis of various accounts of what is vertically fundamental. The debates between various accounts of properties, persistence, and whether the world is a world of fact or things, have taken this form. Perhaps inspired by the case of physicalism, some participants in metaphysical disputes have allowed that the vertically fundamental may not be necessary. As we have seen, Lewis took Humean metaphysics in this way although his non-Humean opponents were not so concessive. However, there is an alternative, horizontal, conception of the fundamental that concerns how a world must be structured or formed, which may be realized in different ways. Debates over the horizontally fundamental can’t be resolved by the kind of modal considerations that are in play on the working assumption that we are trying to settle what is vertically fundamental. An illustration from a more familiar domain in which the distinction is tacitly in play might help to convey the point. Suppose we have two observations about the mental. The first is that phenomenal consciousness seems very unlike matter in certain respects. The second is that it seems possible that phenomenal consciousness could be present without a particular kind of body. In the grip of the vertical fundamentality picture, we might think of the issue as to whether there were two fundamental kinds of substances, or properties, rather than one, and take these observations to pronounce in favour of the former. As is familiar, there was another option. Functionalism suggested that minds, and the phenomenal consciousness they possess, were a certain functional structure (variably) realized in physical material with the potential for certain causal relations. The possibility of variable realization explained how it is possible that phenomenal consciousness could be present without a particular kind of physical body. Functional structures are rather different things to the matter from which they are composed, for example, as was remarked, this fundamental structure could be realized in immaterial things too (Putnam (), pp. –; Shoemaker (), pp. –, –; Shoemaker (), pp. –). The point I’m making does not rely upon the functional picture being successful. It is very likely that it is not—at least, not wholly so. The point is rather that evaluation of phenomena that were supposed to pronounce one way or another with regard to a particular account of minds, had a different possible evaluation once the resources of variable realization were brought into play. The modal properties of the realization



    

were not attributed to the realized. Indeed, the fact that something could be variably realized was taken to yield modal properties distinct from those of the realizing. Outside of an idealist or solipsistic metaphysics, minds don’t seem to be as fundamental as the matter in which they are putatively realized. Since, according to the story, there may be matter without minds, there is not the same pressure to suppose that delving into the nature of a particular realization will provide us with insight into central aspects of the nature of mentality in general. It might, but the option is there that it need not. By contrast, causation has a greater claim to be thought of as part of the fundamental nature of the universe. If the fundamental is understood vertically, that implies that thinking more about the character of a Humean metaphysics, property-independent necessitation, or a powers ontology gives us a greater insight into the nature of causation. However, if the way in which causation is understood to be fundamental is horizontally, the patterns of the Humean metaphysic, the various kinds of necessities, etc. are just different accounts of the way a causal structure may be realized. Any possible world with constituents, either fundamental or derivative, requires something to explain how these constituents are part of a world rather than isolated worlds in themselves. Appeal to laws is not necessary in the case of worlds of brute singular causation and not sufficient because their holding is no guarantee that integration has been achieved. There must be something or other that plays the causal structure role. Nevertheless the occupants, while settling how the structure is realized, are less fundamental in the key sense. I presume that’s what people have in mind by saying that causation is the cement of the universe—albeit something slightly different from Hume. The minor modification to this picture is that just as the universe may be constructed from different building materials, so different types of cement will be used. From this perspective, the debate concerns what is to be regarded as, although vertically fundamental, contingent. The theories currently put forward regarding various metaphysical entities become potentially contingent and the constraints that they must satisfy—the structural features—become necessary. According to one way of viewing the matter, the functional-structural properties are the fundamental necessary features of worlds. It strikes me that this has considerable plausibility. If the fundamental metaphysical categories concern the basic structure of reality, then it is no surprise that the occupants of the nodes of the structure prove to be contingent but the structure itself, at a certain level of generality, proves to be necessary. This observation, though, does not serve to identify any more substantial difference between the metaphysical categories. All of them would involve necessary structures and contingent realizers. This raises the question about the extent to which this type of procedure has application. For example, are there books to be written on the varieties of substance, the varieties of properties, the varieties of time, and the varieties of possible worlds . . . to name but four? Or is there a difference between these cases and the case of causation? Here is one way to sharpen the question. There is a familiar distinction between the primary intension and secondary intension associated with a particular referring term, or sentence, in two-dimensional semantics. Both are derived from how reference is fixed. Let RF be the way in which the reference of a particular term T is fixed, for example, ‘water’ having the reference-fixing description the liquid which falls from the skies, collects in lakes and seas, flows through rivers, (unsaltened) quenches thirst, and so on (hereafter, ‘the watery stuff ’). The primary intension of T given by RF is the

  :    



set of possible referents determined by RF taking each possible world as the actual world in which RF is applied. Thus if, in another possible world, a different liquid is the watery stuff, then that liquid is a member of the set. The secondary intension of T is given by the set of possible referents determined by applying RF to the actual world and taking its referent there to be its referent in all possible worlds. In the case of ‘water’, the second intension is standardly presumed to be H₂O. The corresponding primary and secondary intensions for sentences are given by the sets of worlds in which the sentence is true in virtue of the primary and secondary intensions of their referring terms respectively. Primary intensions are normally associated with a priori knowledge. Whenever a sentence expresses an a priori truth, the primary intension of the sentence (the primary proposition it expresses) will be necessarily true. In ., we noted that the reverse is not true. A combination of the material we need to possess a concept plus our everyday knowledge may fix the referent of a term. The latter knowledge may be something that is now available from the armchair but, if it is not part of what is required to possess the concept, it is not known a priori. A natural question which is suggested by this framework is under what circumstances should we take the characterization of the primary intension as describing a property that is variably realized by the different referents the primary intension fixes in different possible worlds considered as actual? The answer seems to turn on whether the reference-fixing description aims to be an articulation of the nature of a property or just a means by which we pick out something with a nature currently obscure to us. The primary intension of cause involving as it does a collection of claims about causation that holds for the most part, various observations about the presence of causation in particular cases, and so on, is not an attempt to characterize the nature of the property. However, the development of an analysis of causation from the material available in the primary intension of cause is a different matter. The possibility of doing so in a systematic and informative way indicates that we have a characterization of the nature of a property that may have various realizations the details of which are not a further characterization of the nature of causation itself. The question relating to other metaphysical categories is whether they display the same combination of features: (i) the development of an analysis in a systematic and informative way and (ii) further details about realizations do not add to the distinctive features of the target category. Requiring an analysis is not to presume that certain metaphysical categories cannot be primitive but there is a tension between taking a category to be primitive and yet holding that further details are available about its various realizations. It would seem that the latter shows that the category is not primitive after all. Sometimes something that aims to be the articulation of the nature of a property at one level is compatible with there being a deeper nature that the reference-fixing description fails to articulate. Consider discussions about the possibility of being in a matrix or a brain in a vat, one’s brain, amongst others, being fed electrical impulses that together constitute an experienced world. Look at statements like (Matrix Hypothesis) I am in a matrix and have always been in a matrix (Chalmers (), p. ). (PH) There is a physical world. (W)

Water is H₂O.



    

Chalmers has argued that the first is a metaphysical hypothesis about the nature of reality and that, arguably, the second and third remain true if the first is true. The primary intensions attaching to the second and third have the consequence that, in a matrix world, what these sentences express is true. In the case of ‘physical’ our notion may be neutral over the latest developments of physics. Whichever way they go, the world is still a physical one (barring certain views in quantum mechanics). In the case of ‘H₂O’ we have something whose primary and secondary intensions coincide around a particular scientific understanding of the chemical structure of water (or, at least one isotope of it). The matrix hypothesis implies a different account of the nature of physical reality, and molecular kinds that are a part of it, and not a sceptical hypothesis that, given our experiences, throws into question our knowledge, or entitlement to believe, such propositions (Chalmers (), pp. –, –; Putnam (), pp. –). Chalmers argues that for other propositions—those expressed by what he calls semantically neutral concepts—we have a direct grasp of how the world must be for them to be true independent of whether or not we are in the matrix. Included amongst these are concepts of mental states, mathematical and categorical concepts like object and property, and the subject matter of our investigation: causation and law (Chalmers (), pp. –). However, although these introduce more substantial constraints upon the way the world must be for them to be instantiated, they are sufficiently weak that they are satisfied in a matrix world. We can see that the additional account of how they are instantiated in such a world provides no further information about their character. The greater insight into the fundamental nature of reality vertically understood is no further insight into the fundamental nature of reality horizontally understood. Metaphysical categories appear, in general, candidates for horizontally fundamental entities but they may differ in the ways I have outlined concerning the extent to which they are realized in various ways. The extension of the approach favoured here for causation and law is certainly an open possibility. It suggests the following outlook. For entities with good claims to be horizontally fundamental, we should be careful about taking an account of their nature, which apparently provides more vertical depth, as a further contribution to the subject at hand. In particular, we should be cautious when we find that certain hitherto attractive possibility claims about the structure at hand are abandoned in the cause of vertical depth and fundamentality. It is likely that we are changing the subject matter and focusing on features of a particular realization. Equally, we should be very careful with regard to a particular account of a metaphysical entity within a programme not to mistake objections to a particular realization to be objections to an account of its structure that, as a matter of fact, has been developed within that programme.

. Concluding Remarks My primary purpose in this book has been to defend the counterfactual theory of causation. I have been much less concerned with the truth or falsity of the doctrine of Humean supervenience. Of more importance has been tracing through the consequences of the recognition that it is a contingent truth, at best, for the proper

 



development of a counterfactual theory. Nevertheless, my counterfactual theory is, I hope, of help to the Humean programme in two ways. First, I have explained how there may be causation in worlds without causal necessitation. I have emphasized that those who insist that there must be such necessitation, or inclination, have put the matter too strongly. Their position is hard to defend bearing in mind the close link between counterfactual dependency and causal dependency in our minds. Moreover, as I sought to explain in Chapter , if the similarity weighting for counterfactuals can also, when rethought of as an account of our attitude to laws and causal facts, be the basis for our idea of necessary connection, then we have an explanation of why we mistakenly insist upon necessary connections in nature as part of what is involved in causation. Second, by explaining the conditions under which we need to postulate modal facts and take them into account in our similarity weighting for counterfactuals, I have provided a relatively clear basis for settling the question as to whether the doctrine of Humean supervenience is contingently true in our world. In this chapter, we have seen how the rejection of Lewis’ theory of possible worlds may also bring with it the need to recognize the existence of modal facts and intra-world necessary connections between distinct existences. So if Lewis’ metaphysics of possible worlds proves unacceptable, establishing the falsity of Humean supervenience may not be far off whether or not its falsity is revealed in the causal character of our world. In such circumstances, it will be of particular importance that the fate of the counterfactual theory of causation is not tied to the Humean programme. Otherwise, its many virtues may be obscured. We have seen that it provides a genuine analysis of causation compatible with recognizing its variety. This variety reveals itself in, at least, two ways. First, there is the various types of causal relation involved in processes, double prevention, and the like. Elevation of one type of causal relation over the others proved unmotivated given the general character of the analysis provided. Second, there are the various ways in which the truth of the counterfactuals making up the analysis are realized. There we saw that different accounts of law, for example, were in fact different accounts of the way laws were realized and, hence, different ways for the causal relation to be realized. My preferred counterfactual theory of causation has general application to all the problem cases while on occasions drawing on the resources of a richer metaphysics, than one in which modal supervenience is true, in order to capture what we are inclined to say. The problem cases for which this is true are based, though, upon an intuitive verdict drawn from a richer metaphysics so this is unproblematic. The counterfactual theory reveals that the nature of causation is more minimal than it sometimes seems. But the inadequacy that some feel attend this can be explained away more plausibly than with regard to more widely held theories such as physicalism in the philosophy of mind. Alternative accounts of causation either fail to have the ambition of the counterfactual theory—by being tied to empirical conditions in this world or being non-reductive without there being a substantial motivation for this—or have their own difficulties. Richer accounts have failed to recognize that the counterfactual theory can draw upon their resources and that the real challenge to



    

their plausibility stems from what they are inclined to say in more austere metaphysical situations—those in which modal supervenience is true. The analysis that has been developed does not appeal, in its vertical fundamentals, to causation as a primitive. As a result, it has claims to be reductive. Failure to recognize the possibility of an alternative notion of fundamentality— horizontal fundamentality—and how vertical metaphysics may distort discussion of its character was one of the lessons of .. The counterfactual theory of causation was felt to face difficulties because it was allied to a particular, contingent, account of vertical metaphysics. Keeping these two strains separate enabled us to get a clearer idea of the merit of a theory that is meant to be a contribution to the former— horizontal—account of metaphysics. For these reasons, I think that a counterfactual theory of causation should meet with far wider agreement than seems to be current. Far from its popularity waning since the sad death of its most famous proponent, it should be seen as a theory that is more entitled to our firm belief than many philosophical theories. It still seems to me one clear area in which the merits of philosophical analysis are likely to bear fruit and, hence, one area which will support a certain style of philosophy which is, mistakenly, in danger of becoming unfashionable.

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Index a posteriori , , , – a priori , , –, –, , , –,  ability to change the laws – absences , , , – accessibility, unrestricted see possible worlds, accessible accidental associations see regularity, accidental accidental generalization see generalisations; regularity, accidental accidental regularity see regularity, accidental accidental intrinsics – accompaniment independence –, – action/actions , , , –, –, , –, –, –, –, –, , , – as mental tryings  action at a distance see causation, action at a distance actual needs – actualism ,  actualist anti-realism  actuality ,  Adams, Robert – admissible information –,  agency see agency response to medical Newcomb cases; agency theory of causation; agent causation; causal non-symmetry, non-symmetry of agency agency response to medical Newcomb cases , – exception to statistical generalization – first-person authority , , . free choice ,  ignorance – options, subjectively feasible , – smugness assumption – transparency of deliberation –, –, ,  agency theory of causation ,  circular , ,  effective means , –, –, –, ,  agent causation –, , ,  Ahmed, Arif , , , – Alexander, Joshua – Alexander, Samuel  Alexander’s Dictim  Alicke, Mark D. –

analysis –, , , – conceptual – nature of – reflective equilibrium  triviality of  Anderson, Norman H.  angular momentum – Anjum, Rani Lill  Anscombe, G. E. M , , , , , antecedent/antecedents , –, –, , , , , –, –, –, –, –, –, –, , –, , –, , –, –, –, , –, –, –, , –, ,  anti-catalysts, see catalysts and anti-catalysts anti-instantiation  anti-realism ,  antidote see powers, antidotes antidote case (delayer)  April rains and forest fire case –, , ,  armchair ,  Armstrong, D. M. , , –, , , –, , , –, –, , , , , , –, –, –, –, ,  Arntzenius, Frank ,  Aronson, Jerrold L. –, , ,  asymmetries of time, de facto , , –,  asymmetry in incidence of the possibilities of covering up  asymmetry of miracles –, , –, – asymmetry of overdetermination , , –, , –, –, , –, , , ,  P (CNP )  (ENP )  (ES )  relationship to causal non-symmetery/nonsymmetry of overdetermination  see causal nonsymmetry. Ayer, A. J.  background condition , –, , –, ,  as reasons for causal relations –





Bader Ralf  Balog, Katalin  Barker, Stephen , , , –, , –, –, –,  Baumgartner, Michael  Beall, J. C.  Beasley, N. A.  Beauchamp, Tom L.  Beebee, Helen , , , , , , , , –, , , – Bell Inequality – Bengson, John  Bennett, Jonathan , , , , , –, , –, – Bennett, Karen  Bernstein, Sara – best system analysis see laws, best system analysis biff role ,  big bang – Bigelow, John , ,  Billy and Suzy’s race  Billy and Suzy fighter-bomber cases see fighter-bomber cases Bird, Alexander , , –, , –, –, , ,  Bizet – Black, Robert – Block, Ned  bomb case , , , –, – Boyd, Richard  Braddon-Mitchell, David – Bradleian regress  brain in a vat , ,  Brand, Myles , –,  bridge bolts snapping case – Briggs, R , ,  Broad, C. D.  Bromberger, Sylvain  Brownstein, Donald  Bruckner, Cameron – brute see causation, brute one-off/singular see metaphysical necessity see properties, modal see relation of awareness Bunge, Mario  Butchard, William  Butterfield, Jeremy ,  Butterfill, Stephen  Camerer, Colin F. – Cameron, Ross , , ,  Campbell, Keith  cancellation and conversational implication  cancer, Bill’s failure to die of , , – Cappelen, Herman 

Cappelini, A.  Carroll, John ,  Cartwright, Nancy , , , , ,  Case A –, , ,  catalysts and anti-catalysts – categorical perception – catcher and the ball case  causability, loops of , , – causal asymmetry , , , , – see asymmetry of overdetermination; causal non-symmetry causal chain actual events account of completeness  complete , –, –, , , , –, , , –, , , , –, , , , , , ,  incomplete , , , –,  completeness at right time – see causation, pre-emption causal circumstances –, , , , –, , , –, –, –, –, , –, , –, , , , , , –, , –, , , , –, –, , , , , , , ,  causal closure of physics – accidental  cause condition – effect condition – causal connection –, ,  causal crescents – causal direction see causal asymmetry; causal non-symmetry causal field  see causal circumstances causal generalisations, belief in apparently resilient accidental generalisation – C-E belief regularity  commitments of  comparison with belief in universal generalisation (UG)  (UG)  (UG)  non-resilient causal generalisations  resiliency of causal generalisations – causal graphs/Bayesian networks approach ,  causal interaction (CI) –,  causal, loops of , ,  causal models ,  causal necessitation –, , –, , –, ,  causal necessity –, – (M), –, , – causal non-symmetry , , , , , –, , , , –, , –, , –, , , 

 independence condition , , , , , –, –, , , –, ,  non-symmetry of agency , , –, –, ,  non-symmetry of overdetermination –, , –,  realization of ,  time invariance of laws  see time, closed causal perspectivalism  causal phenomenal content thesis – causal pluralism –, , – causal potency – causal powers , , , , , –, , ,  causal priority  see causal asymmetry, causal non-symmetry causal profile , , –, , –, –, ,  causal relata , , , , , , , –, –, , , , –, , , ,  fundamental , , – causal relevance , –, , , , – causal role properties/causal role occupantcommitting properties , , , –, –, , , –,  capacities –, , ,  causal role characterisation, different interpretations – dispositions/dispositional property –, , –, , , –, –, –, , –, –, – functional properties , ,  incline but do not necessitate  Lewis on – powers see powers see also causally characterised properties/ causal properties; functionalism; powers net; powers ontology causal shell – causal sufficiency  (M), , – causally characterised properties/causal properties ,  backward commitment  forward commitment  causation action at a distance , –, , –, , –,  see causation, spatiotemporal contiguity/ proximity of agency theory of see agency theory of causation anthropocentric ,  backward , , , , , , , –, , , , , , –, 



binary , – brute one-off/singular , , , , , , , , –, ,  concept of/conceptual competence –, –, , , , , –, , –,  conception of causation  conditional probability analysis of causation see conditional probability analysis of causation context dependence/contextual/ contextualist , , , , ,  context sensitive contrastive relation , – contrastive , , , –, , –, –, , , , – counterfactual dependency , , , –, , , –, , , , , , , , , , , , –, , –, , , –, , –, , , , –, , , , , ,  counterfactual theory of see counterfactual theory of causation dependence  see causation, counterfactual dependency deterministic –, , , , –, , , , ,  distinct events , , , , , , , , , , , , , , , , , ,  distinct existences see distinct existences experience of , , , –, , , ,  fundamental –, , , – hindrance  Humean account ,  indeterministic –, , , –, ,  indeterministic causation, Lewis’s theory of see Lewis’s theory of indeterministic causation indicative features of (C)  (C*)  (C) ,  (C)  (C*)  (C) ,  (C)  (C*)  (C)  (C*)  (C)  (C*)  interlevel causation –





causation (cont.) intrinsic character of , –, , , –, , , , , –, , –, , –, –, ,  intrinsic, independent from competitors sense –,  intrinsic, nature of properties sense  involving chance-raising  iterated , ,  kinds of –, – law-based theories of see law based theories of causation mutual ,  mutual manifestation of disposition partners – natural kind –,  natural relation , , – necessitation/necessary connection , , , – see causal necessitation; necessary connections negative see negative causation non-relational –, – non-symmetric dependency relation , , , –, , , , , , ,  non-transitive , , , , , – normative dimension , , – of probability (CofP)  overlapping cases – (PC) negative causation condition  pragmatic factor ,  prevention see prevention process theories of see process theories of causation production  property see property causation realization of/variable realization , , , , , , , , – regularity theory of –, , ,  scepticism about – self-causation ,  sensitive/insensitive  spatiotemporal contiguity/proximity of , , –, , , –, , –, ,  superluminal , , –,  temporal direction of , , , , , , –,  token  transitive , –, , , , , , ,  see cause; chance, raising; regularity/ regularities

cause adequate for effect – analysis of , , ,  causal circumstances of see causal circumstances chance-lowering – chance-raising , , ,  chance of effect, timing of evaluation  circumstance-dependent sufficient condition –, –,  common , , , –, –, , , – complete cause (see total) ,  concept of, attribution of  conception of ,  conditions for effects  contra-normal conditions , , , , –, – definition, Hume’s  delayers , , , , –, , ,  see causing by preventing difference makers/making , , , – discouragers –, –,  disjunctive cause –,  effect driven  enabling conditions , –, , –,  encouragers –, –,  events see events explain their effects –, – facts see facts hasteners , , , , –, ,  immediate –, , ,  INUS condition , – means to ends , , , , , – mediate , , –, –,  negative cause see causation, negative; positive surrogate necessary in the circumstances –, , ,  object , –, –,  positive surrogate , –, – pragmatic explanation of –, , –, –,  precede effects (P), usually , , –, , , –, , –,  property see property causation proportional to effect ,  simple switcher –,  simultaneous , –,  sufficient condition –, –, , –, , –, 

 temporal difference between triggering and enabling conditions – total cause , – triggering , , –, , –, , –, , –, ,  two-way dependency of causes and causal circumstances  world driven  see causal non-symmetry, causal relata; causing and affecting; chance causing and affecting  causing by preventing  cement of the universe ,  centring assumption see possible worlds, centring assumption Chalmers, David , – chance background chance , , –, , –, , , , , , , ,  caused chance  humean supervenience of , – laws, determined by – mean chance of effect , , , –, , , , ,  (N₁)  (N₁*)  (N₂)  (N₂*)  non-Humean account of  see chance, propensities of decay  of effect –, –, –,  partition ,  propensities , –, –, – raising, chancesee cause, chance-raising relationship to frequencies , , , –, –, –, – semantically vague – undermining, problem of , –, –, –, –, – chance independence  (Chance-Might)  chance-raising competitor absent  conditional  counterfactual , , , ,  non-symmetric  primitive non-symmetric , , , , , –, –, , –, –, , –,  realisation of  Chatlosh, D. L.  Chernobyl nuclear power station accident  Child, William ,  Chisholm, Roderick 



Choi, Sungho – Chudnoff, Elijah  Clarke, Randolph –,  climate change  cognitive penetration  coin case  Cokely, Edward T.  colour –, –, –, , ,  common cause see cause, common common effect see effect, common competitor-absent chance raiser – see cause complete causal process, theories of absent event approaches , –,  cases of incompleteness without event absence – see counterfactual analysis of causation completeness of physics ,  compound X and critical time period – concept possession of –, –, ,  concept of causal necessitation , – concept of cause see cause, concept of concept of necessary connection a priori origin – origin in experience  possession of , – conception ,  concessive counterfactualism  concrete  existents  particulars  modal realism ,  non-actual worlds  concrete particularism , ,  conditional indicative ,  future directed indicative ,  might –,  would ,  Would-Will Correspondence  see counterfactuals conditional fallacy  conditional probability/probabilities , , –, , , , – causally homogenous circumstances – definition of  (CP) partition – conditional probability analysis of causation – circular  consciousness , , , – phenomenal 





consequent/consequents –, , , , , , , , , , –, , , , –, , , –, , –, –, ,  conservation laws –,  constitution see construction, constitution constitutional necessities , –,  construction constitution , ,  non-mereological composition  object formation  set membership  structural properties  see also properties, structural properties cotenability problem –,  circular  continuant –, –, , , – contrastive causal statements , – coronavirus  cosmic collusion  counterfactual invariance see laws, invariance, counterfactual counterfactual theory of causation , , , ,  actual events clause/condition –, –, , ,  basic idea  brute singular causation see causation brute one-off/singular causal necessity and sufficiency see also causal necessity, causal sufficiency causal properties, challenge from  circular , , , , , –,  compatible with different realizations  context sensitivity – see causation, context dependence/ contextual/contextualist; causation, context sensitive contrastive relation counterfactual dependency see causation, counterfactual dependency distinct existence, appeal to  see distinct existence/distinct existences essential properties of events see events, essential properties extra-linguistic – during time period T – Lewis’s theory – non-causal modal connections – non-symmetry see causal non-symmetry P probabilistic -dependence P seeP -probability conditions, probabilistic -dependence quantum entanglement, challenge from , – quasi-dependence –

(SC)  semantics for counterfactuals, reliance upon  see counterfactuals, semantics for supersets, the need to appeal to –, ,  theory advanced in book, statement of – P -dependence analysis – vertical necessitation relations, challenge from  see Humean supervenience; Humean world counterfactuals – analysis of ,  (C) antecedent see antecedent/antecedents backtracking –, , , –, , –, , , , , , , , –, –, , –,  causal modelling approaches  centring assumption, see centring assumption embedded ,  fit , , , , ,  fixity of laws – fixity of past – foretracking , , , , –, , , – future indicative conditionals, link to see conditionals, future indicative; conditionals, Would-Will Correspondence future similarity objection , , – indeterministic future similarity objection – intervention and semantics of – Lewis-Stalnaker analysis see possible worlds semantics, LewisStalnaker local miracles , ,  sub-regions of possible world match , , – metalinguistic –, – might see conditionals, might miracle , , , , , , – necessitarian accounts , – no widespread miracles condition , – perfect match see possible worlds, perfect match presumption of falsity of antecedent  quasi-miracle – semantics for , –, –, , , , , , –, , , , , , , , , ,  similarity weighting see possible worlds, similarity weighting subjunctive – transition period see transition period

 truth conditions/truth value, lack of – typicality , , – (WA)  (WB)  violations of law see law, violations of unexpressed antecedent , –,  widespread miracles , –, , ,  counterpart relation , , , –, –, , , , – Cover, J. A.  Craig, Edward  Crane, Tim  credence , , –, –, –, – Culpable Control Model – Damm, Vernon  Dardis, Anthony  Davidson, Donald , –, , –, ,  de facto dependence – decision-conducive states , –,  decision theory, subjective causal decision theory , –, –, , –,  evidential decision theory , –, , , –,  decision theory, objective , – defoliant case , , ,  deliberation , , , , , –, –, , – Demos, Raphael  denial of necessary connections between distinct existences see distinct existences principle; distinct existences, necessary connections between determinable-determinate relation  characterizing dimensions  determinable as higher order property of determinate  metaphysical necessitation  ways of being condition  determinism , , , , –, , , –, ,  directing qualities  dispositions see causal role properties, powers dissociation of experiences of causation from judgements of causation  distinct existence/distinct existences , –, –, , – conception of  distinct arrangement characterization , ,  modal characterisation –, –



necessary connections between , –, –, –, –, –, –, –, –,  numerical identity, denial of  spatial characterization –, –,  twins case  distinct existences principle , , , –, , , –, , , – Divers, John , – division of linguistic labour  doctor’s delaying – dog bite case –, , –, –, , ,  dogmatist responses to scepticism (D)  dome, Norton’s – Dorr, Cian – Dowe, Phil , , –, –, –, , , – Downing, P. B. ,  Dretske, Fred ,  drive, slicing  Driver, Julia  drumming my fingers case –,  drunken bad guys case –,  Ducasse, C. J.  Dummett, Michael  duplicate characterisation , , , – Eagle, Antony  Earman, John , , , , ,  Eddon, M.  Edgington’s devil case  Edgington, Dorothy , , –, , – Eells, Ellery –, ,  effects common effect , , , –, , ,  conditions for causes  see causal non-symmetry; causal relata egalitarianism –, –, , ,  two kinds  Egan, Andy ,  Ehring, Douglas , , , , , –, –, –, , , , –,  Einstein-Podolsky-Rosen experimental set-up – (EPR)  (EPR)  eleactic principle – eleactic stranger  electrofink  reverse electrofink ,  Elga, Adam , –, ,  Ellis, Brian , , , , ,  emergent , , , emphasis , , , –, , , 





encourager/discourger asymmetry  see hastener/delayer asymmetry endurantists  entropy –, , –, , ,  epiphenomenal emergentism  epistemic blur  ersatz modal realism  Esfeld, Michael  event/events –, –, , , , –,  absent see events, non-actual allomorph  and causal relevance , , , ,  see also property causation as changes  as cross-world entities  as fundamental causal relata , –, –, ,  as objects engaged in acts  as particulars  as truth-makers – Bennett on – coarsely individuated , , , – collision  constitutive objects –, ,  constitutive properties  constitutive time  Davidson on , – difference from objects  disjunctive events – duration of object  emphasis – essential properties –, –,  exemplification of properties by objects at times – exemplification of all those properties required for the exemplification of maximally determinate properties  Existence condition (Kim)  (F)  (F)  finely individuated , –, ,  identity condition (Kim)  imperfect nominals, named by  improbable – individuation by causes and effects  individuation of – Kim on – law-breaking  Lewis on , –,  micro-events , – missing  see events, non-actual negative , –, , , , , –, –, , , ,  non-actual , , , , , 

non-causal modal connections and efficacy ,  overdetermining events  perfect nominals, named by  positive , , –, –,  positive surrogate  possesses the properties anyway problem  possible events  properties of spatiotemporal regions  property instances , ,  property Plimited particulars ,  put in ,  reduction of – remarkable  sceptics about  P -set events –, ,  situations  target events see effects temporal parts  temporally limited particulars see particulars, temporally limited time of occurrence –,  token  , , ,  triggering causes see causes triggering types of (C, E)  evidence –, , , , , –, , , , – admissible/inadmissible see admissible information, inadmissible information canonical  expected value or utility –, , , – experience hallucinatory experience  illusion , ,  Newton’s Third Law  non-neutrality  non-subject committing  of agency  of causation, see causation, experience of of colour – of force  of meanings – of necessary connection, see necessary connection, experience of of ourselves  of necessitation  of necessitation-determiner  of pressure ,  of probabilification – of the past ,  of resistance  of will 

 perceptual, distinguished from judgement, thought and imagination – phenomenal content – relationist about  experience of causation, objections to – see causation, experience of experience of necessitation, failure to represent vs misrepresent  see experience, necessitation of experimental philosophy – expert analyst –, ,  data  expertise analysis , –, ,  calibration  philosophical –,  explanatory gap , – explanatory relevance as linguistic matter – explanatory virtues distinctive causal role/location in or unique contribution to a causal network , , – precision/exact non-redundant causal contribution , , – external independence/independent , , –, , , ,  Facts admissible – as causes , , , , –, –, , , – as ordered triples – as true sentences  as truth-makers – atomic  disjunctive causes – highlighting – imperfect nominals  modal , , ,  modal properties of  negative – partly linguistic  spatiotemporally coincident – totality , – see causal relata, truth-maker/truth-making failure to water the plants case , –,  Fair, David –, – Fales, Evan –,  fallback needs – Feltz, Adam  Fenton-Glynn, Luke ,  Fetzer, James , , – Fido – fighter-bomber cases , , –



figures . Conditions and Regularity Theories of Causation  . Approaches to Counterfactuals  . Options Regarding Necessary Connections Between Distinct Existences  . Launching  . Müller-Lyer Illusion  . Causal Crescents  . Barker’s Cylinder  . Kment’s Indeterministic Lottery  . Early Pre-emption , , ,  . Late Pre-emption , ,  . Frustration ,  . Hall and Paul’s doorbell case  . Sungho Choi’s case  . Ehring’s Case A  . Anti-catalyst  . Catalyst  . Vigorous Neurone Firing  . Mediate and Immediate Causation  . Options Regarding Transitivity of Causation  . Lewis’s Characterisation of Case Structure  . Drunken Bad Guys Detail  . Hall’s Double Prevention Case Structure  .a Dog bite Causal Graph (Hitchcock)  .b Dog bite Causal Graph (alternative)  .a Hiker and Boulder Causal Graph (Hitchcock)  .b Hiker and Boulder Causal Graph (alternative)  . Railway Tracks Case  . Railway Tracks Two Victim Case  . Theories of ‘the causes’  . Causes vs Total Causes  . Norm-Violation Model  . Culpable Control Model  . Theories of Causal Relata  . Counterexample to Davidson’s Theory of Event Identity  . Options Regarding Truth-making  . Challenge from Vertical Nomological Necessitation Relations  . Challenge from Vertical Metaphysical Necessitation Relations  . Physical Causation with Non-Physical Intermediary  . Physical Causation with Non-Physical Co-Cause  . Landing Heads and Tails  . Options Regarding Causal Role Properties  . Types of Process Theories 





figures (cont.) .a Lack of Prevention by Omission  .b Positive Prevention by Omission  .c Double Prevention  .d Double Prevention in the Bomber Mission ,  . Token Causation: Different Kinds or Different Concepts?  . Gun Mechanism  .a Light Circuit  .b Light Switch  . Overdetermination by Omission  . Overdetermination by Double Prevention  . Early Pre-emption Comparison Case  . Disturbing and Causing Condition  . Einstein-Podolsky-Rosen Experiemental Set-Up Options  . Hidden Source Feature in EPR Set-Up  . Bell Inequality and Backward Causation  . Circular Time and Symmetrical Causation  . Symmetrical Causation Via Two Paths  .a Relationship between Causal Nonsymmetry and Counterfactual Nonsymmetry  .b Proposed Variable Realization of Probabilistic Counterfactual Nonsymmetry  . Multiple Traces of a Cause  . Single Trace of an Effect  . Pebble Dropped in Pond  . States of a World and their Directional Reverses  . Independence Condition  . Common Causes, Common Effects and Probability Relations  . Cause to Effect: Many-One Relation  . Energy Distribution from Source to Wave Front  . Counterexample to Independence Condition as Sole Basis  . Barker’s Slabs  . Local Asymmetry Reversal in Nixon’s Brain  . A Simple Micro-Physical Case  . Tooley’s Inverse Universes  . Intention to Action of Window Opening  . Classic Newcomb Case  . Medical Newcomb Case  . Tickle Response to Medical Newcomb Case 

. Free Choice and the Perspective of the Agent  . The Psychopath Case  . Classic Newcomb Case Parallel with Psychopath Case  . Woodward’s Case for Interventionism  . Maudlin’s Game of Life  .a Carroll’s Mirror Argument: Particles Travelling Through Field  .b Carroll’s Mirror Argument: Particle Reflected  . Methane  .a Symmetric Simple Powers Net  .b Asymmetric Simple Powers Net  . Powers Net of Reflexive Potentialities  . Chance, Evidential Probability and Credence  . Types of Propensity Theory  . Varieties of Varieties  Fine, Kit , , , , – Fink, Charles E.  Fish, William  fist clenching case  fit see counterfactuals, fit fixing accounts see redundant causation, fixing accounts of flipper and reconnecter case – fluke , – Fodor, Jerry –, – foils –,  forest fire case (egalitarianism) –,  forest fire case (hasterner/delayer) , –,  Forrest, Peter  fortuitous non-causal recreation  Foster, John  four category ontology  Fox, John  Francescotti, Robert , –,  free will –, , , , , , ,  frequency limiting relative frequency , –, –, –, – long-run , , , –,  Frisch, Mathias , , –, – Funkhouser, Eric , – functional role see functionalism, functional role functionalism , , , , , –, , , – functional role ,  occupant  role 

 fundamental  horizontal , , –, , ,  vertical –, , ,  gambling addict , – Ganeri, Jonardon –, ,  Garb, Howard N.  Gasking, Douglas ,  Gemelli, A.  Gendler, Tamar Szabo  generalizations , , –, –, , , , –, –, , –, , –, , ,  genus  Ghiselin, Michael  Gibb, Sophie  Gibbard, Allan , , ,  Gibbons, John  Giere, Ronald N. , ,  Gillett, Carl , , –,  Glymour, Clark  God ,  Godfrey-Smith, Peter  Goldman, Alvin I. , , ,  golf  Good, I. J.  Goodman, Nelson , ,  Gonnerman, Chad – Greta’s egg case – Grice, H. P.  grounding , , , – Gruber, Howard E.  Grünbaum, Adolf , ,  Guglielmo, Steve  Gustafsson, Johan  Hacking, Ian ,  haecceittism , – Hájek, Alan  Hall, Ned , , –, , , –, –, –, , , –, ,  Halpin, John F.  hammer case –, , – Hampshire, Stuart  handedness, right/left – harmony, principle of , – Hart, H. L. A. ,  hastener/delayer asymmetry – Hausman, Daniel M. , –, , –,  Hawley, Katherine  Hawthorne, John , , ,  Heathcote, Adrian , ,  Heil, John ,  Hempel, Carl G. , ,  Hesslow, Germund  Higginbotham, James  hiker case –



Hinkfuss, Ian  Hirsch, Eli ,  Hitchcock, Christopher Read , , , , , , , –, , –, –, , , , ,  Hochberg, Herbert  hole in one  homogenous disc, rotating  Honderich, Ted  Honoré, Tony ,  Horgan, Terry ,  Hornsby, Jennifer  Horwich, Paul , –, – Huemer, Michael – Hume, David , , , –, , –, , ,  Humean Supervenience –, , –, , –, , , , , , , , , , , , , –, , , , – big bad bug  quality supervenience –, ,  modal supervenience ,  see distinct existences principle Humean World , –, –, – Humphreys, Paul – identity conditions , –, –, ,  ignorance approach  imagination/imagining , –, , – imperfect community, problem of –, – in virtue of –, , –, , –, , – inadmissible information , , ,  independence condition see causal non-symmetry, independence condition indeterminism , , –, , –, , , , , , , , , , , , –, ,  indeterministic lottery case – individudation conditions see identity conditions induction, problem of , , , , –, , , ,  scepticism about –,  inductive skepticism see induction, scepticism about infallible predictor/prediction ,  inference-base of causal statements  infinite alien properties – disjunction  energy  mass 





infinite (cont.) possible times and probabilities, number of  possible values and uninstantiated laws, number of  spacetime points, number of  worlds and quidditism, number of  worlds and probabilities, number of  sequence of events and probabilities , , , , –, –, – set of worlds  infinitesimal probabilities/chance , , , , ,  infinity, denumerable (Aleph₀)  informationally encapsulated  see processes, modular instantiation conditions –,  see properties instantiation, principle of – inter-virtue of – intervention/interventions , , , , , , –, , , –, , , –, ,  asymmetry of , – effective interventions and contra-normal conditions – intra-virtue of – intrinsic-making features , ,  see external independence; duplicate characterization; recombination, maximisation intrinsically typed entities  intuitions , –, , , –, , , , , –,  illusion ,  scepticism about ,  inviscerated state of affairs  Jack and Jim’s quarrel case  Jackson, Frank , , , , , ,  Jacobs, Jonathan D. –,  Jago, Mark –, , – Jeffrey, Richard C. ,  John Conway’s game of life world – Jonson, Erick J. – Joyce, James M. , , , – judgement , –,  of causation , –, , –, – of necessary connection  Kant, Immanuel  Kauppinen, Antti ,  Keeble, Stephanie – Kim, Jaegwon , , –, –, –, –, , , , ,  Kistler, Max , , 

Kment, Boris ,  Knobe effect – Knobe, Joshua , , – knowledge , , ,  asymmetry , – background ,  conceptual  empirical  everyday –, –,  infallible  of causal relations – of the past – safety  sensitivity  see a priori, a posteriori Kovitz, B. – Kripke, Saul ,  Kroedel, Thomas ,  Kukso, Boris –,  Kutach, Douglas ,  Kvart, Igal – Lange, Marc , –, , , , ,  Langford, C. H.  Langton, Rae –, , –,  LaPorte, Joseph  launching , –,  law-based theories of causation , – see pairing problem law of conditional excluded middle – law/laws , –, , , , , , , , , , , , , , ,  anthropocentric  association, of  best system analysis , , , , –, , , , , , –, –, , , –, –, , , , – causal , – ceteris paribus  classificatory  conception of ,  counterfactual supporting –, , – DTA account –, – dependent necessitation accounts of law  see powers ontology eternalism and  functional  governing , , , , , –, , – Humean accounts ,  see laws, best system analysis independent necessitation between properties , , , , ,  invariance, counterfactual , –, , , , , , ,  iron 

 lossy – N(F,G)  non-causal – non-Humean account  see independent necessitation between properties; powers ontology oaken  phenotypical  Platonist ,  potential patterns of causation , , ,  realization of/realisation base , , ,  regularity theory of , –, –, , –, –,  steel  uninstantiated –, , , – variable realization of , –, ,  violation of –, –, , –,  law of large numbers  layered picture of the world  Le Poidevin, Robin  Leboyer, Marion  Leibniz’s Law (LL)  Lemmon E. J.  Leslie, Alan M. – level generation causal level generation  conventional level generation  see metaphysical dependence, partial existential Levi, Isaac , – Lewis, David –, –, –, , , , –, –, , –, –, –, , –, , , –, , , –, , , –, , , –, –, , –, –, –, , , , , –, , , –, –, –, , , , , –, –, –, –, –, , , –, , –, –, , , , , , –, , –, , , –, –, , ,  Lewis-Stalnaker possible worlds semantics see possible worlds semantics, Lewis-Stalnaker Lewis’s theory of indeterministic causation – Menzies’ criticism – Menzies’ revision  light beam on wall , – limit assumption, see possible worlds, limit assumption Lipton, Peter  List, Christian –,  Loar, Brian  local matters of particular fact  see qualities



local multiworld properties  locality  see causation, action at a distance Loewer, Barry , , ,  logical entities  Lombard, Lawrence Brian , –, ,  loneliness –, ,  Lowe, E. J. , , –, , , , ,  Lyon, Ardon ,  MacBride, Fraser – MacBride’s challenge – Macdonald, Cynthia , , ,  Macdonald, Graham , , ,  Machery, Edouard –, ,  Mackie, J. L. , , , , , , –, , , , , , , –,  necessity₁  necessity₂  Mackie, Penelope –, ,  Macpherson, Fiona  macro-non-symmetries , –, –, , , ,  Malebranche, Nicolas  Malle, Bertram F.  Mallon, Ron – manipulability theory of causation see agency theory of causation Manley, David ,  Marshall, Dan ,  Martin, C. B. , –, , , , , , ,  Martin, M. G. F.  Martin, R. M.  masking cases see powers, masks Maslen, Cei – match striking case , ,  mathematical entities ,  (Matrix Hypothesis) – (PH)  (W)  Maudlin, Tim , , – maxim of be relevant and cooperative  maxim of quantity  maximal border sensitive entity  McDermott, Michael , , , , ,  McGinn, Colin  McGrath, Sarah  means to belief  Melia, Joseph , – Mellor, D. H. (Hugh) –, –, , , , , , , , , , , , , , , , –, –, , , –, , , –





mental causation , –, , – Menzies, Peter , , –, , –, , , –, , –,  mereological composition , ,  mereological simples ,  Merlin and Morgana , – Merricks, Trenton , , , ,  messy shopper  metal ball case, Davidson’s  metaphysical dependence disjunctive existential  existential  partial existential  partial disjunctive existential  metaphysically necessary existents  metaphysical necessity, brute  methane , –, , ,  method of agreement  method of cases  Michotte, Albert  micro-physical cases of causation ,  (might = not-would-not)  Mill, John Stuart , –, ,  Miller, Kristie  Millican, Peter  minimal duplicate –, , , – minimal mode of presentation strategy  minimal necessitation base –, , –, – and metaphysical necessitation  and metaphysical necessity  minimal necessitation condition  minimal supervenience-base –, , , –, –, , , ,  miracles see counterfactuals, miracle mirror argument – (L)  (G₁)  (SC*)  (SC’)  modal fictionalism  modal realism , ,  modal structure  modal supervenience see Humean supervenience, modal mode of presentation , , – moderate smoker case – modular see processes, modular modularity hypothesis – Moore, Michael , – Moran, Richard ,  Morgenbesser case –, , – Morris, Stephen  Morton, Adam 

Müller-Lyer illusion  Mulligan, Kevin  multigrade – Mumford, Stephen , – Nadelhoffer, Thomas  Nagel, Ernest  Nahmias, Eddy  Nakayama, Ken – natural kind –,  see causation natural kind natural necessities  and physical object talk  natural relation , – necessary connections  cognitive grasp of ,  concept of , – experience of necessary connection , , , , , , –, ,  see also experience of force, experience of pressure, experience of will horizontal  intra-world –, , , , , , , –,  metaphysical , ,  see also metaphysical necessitation nomological –, , ,  see also nomological necessitation scepticism about  vertical  see causal necessitation; causation, necessitation/necessary connection necessary connection phenomenal content thesis  necessitation base –, ,  causal –, , –, , , –, ,  horizontal ,  intrinsic necessitation base  macro-micro properties, necessitation of  nomological/nomic , , –, , –, –, –, –, –, , , , , , ,  metaphysical –, –, , , , ,  minimal metaphysical  property-independent , , , , –, –, , ,  property-dependent , –, , ,  vertical , , ,  necessitism  and distinct existences principle  negative causation , , , , , , , , –, –, –, , –,  analysis of 

 appeal to contra-normal conditions – (CG)  (PC)  problem of non-relationality  problem of profligacy  negative exemplification  negative ontological commitment – Neunaber, D. J.  neurone diagrams, introduction to  new Hume – Newcomb cases –, –, , , – medical , , , , – supernatural (or classic) –, , – news value –,  Newton-Smith, W. H.  Newtonian mechanics , , , , –,  Newton’s first law  Nichols, Shaun – Nixon case , , –, , –, –, – no interference condition , ,  Nolan, Daniel  non-physical emergent dualism  Noordhof, Paul , , , , , –, , , , , , –, –, –, , , , , –, , ,  norm-violation model – Norton, John  Nozick, Robert  Nute, Donald – O’Callaghan, Casey – O’Connor, Timothy – objects bundles of properties  causation necessary condition of identity – constitution of  constructions of possibilities of experience – cross-world entities  distinct existence of – duplicates , – gerrymandered – identity of – modal truths about – perfectly rigid – persistence of , – temporal extent of  temporal parts of – unrestricted mereological composition  see accidental intrinsics; cause, object; continuant; endurantists; perdure, terdurantists Oddie, Graham  omnipotence 



omissions –, – overdetermination and , – see events, negative; events, positive surrogate; events, possible; negative causation ontological categories , , , , – ontological commitment , – ontological dependence  see construction ontologically fundamental , ,  see construction, fundamental ontological layer/level  fundamental  grounding  see construction; fundamental; grounding ontological priority  see construction; fundamental; grounding open forks  open intervals  operative reason claim (A) – Ott, Walter  overdetermination , , , , , –, –, , –,  by omission – dependent and independent  prevention – systematic , ,  see causal asymmetry, asymmetry of overdetermination Owens, David  pairing problem  Papineau, David , , –,  Pargetter, Robert ,  Parsons, Josh , , ,  partial determinate  particular matters of fact –, –, –, – particulars – temporally limited , , , , ,  see events; objects; property instances parts, mereological –, ,  passion  past hypothesis – past perspectivalism  Paul, Laurie , –, ,  Peacocke, Christopher , –,  Pearl, Judea , , , , , ,  pebble dropped in the pond – Pendlebury, Michael ,  perception  perdure  Perry, John  phenomenal consciousness , –,  (P₁)  (P₂)  phenomenal concepts –





phenomenal concept strategy  phenomenal content or character , –,  auditory – necessitation  qualia  relationist  representationalist  phenomenal property – photons , –,  physicalism , , , , , –, , , , , , , –, ,  Kim’s argument against non-reductive physicalism – see phenomenal consciousness; phenomenal concepts strategy Plato’s heaven  plenitude, principle of , , , – (OAN)  polarity  polarization –,  Popper, Karl. R. , , ,  positive proxies  see cause, positive surrogates possible metaphysically , ,  nomologically/nomically , , –, , , , ,  see possible worlds positive surrogate see cause, positive surrogate possible worlds –, , –, , , –, , , , , , –, , –, –, –,  accessible –, ,  approximate match , –, , , –, , – centring assumption –, – closest –, , , , –, , , , , , , , , , –, –, ,  comparative similarity ordering – limit assumption – maximal sets of consistent propositions  necessity (N)  perfect match , –, –, , , , , , , –, –, –, –, , , , , , –,  perfect match condition, revised  perfect match at time of truth of antecedent  possibility (P)  semantics  semantics, Lewis-Stalnaker –,  similarity weighting of , –, , , , , , –, –, , , , , –, , , , –,

–, , –, –, , –, , , –, –, , , –, , ,  similarity weighting, first revised version  similarity weighting, implications of necessitarian accounts of law for – similarity weighting, second revised version  uninstantiated world properties  uniqueness assumption – potentiality –, , , ,  see powers powers , , –, , , , –, –, –, , , –, –, , , –, , – antidotes  Aristotelian – intrinsic  manifestations – masks ,  Platonist – trigger/triggering property  see causal role properties; electrofink; powers net, powers ontology powers net , –, , ,  powers ontology , , , –, , , –, , , –, , –, , , , , –, , , –, –, , ,  circular – identity of property with causal profile (R)  Janus-faced  non-relationality of causation – qualitative aspect ,  second order relation (R)  Powesland, Peter F.  pragmatic equivalence – pragmatic view of causes –, , – implications of Asperger’s/high functioning autistic subjects for – precognition ,  pre-decision state – pre-emption –, , –, , , –, , –, , , , , , , , , , ,  early pre-emption –, , –, , , –,  early pre-emption, indeterministic ,  late pre-emption – late pre-emption, indeterministic , –, ,  pre-emptive double prevention  see causation; overdetermination; redundant causation pre-empted event , –,  see events

 pre-empting cause , , , – omissions  see pre-emption pregnancy  prevention , , –, –, –, –, –, , –,  double , , –, –, –, ,  firing a gun ,  lack of, by omission  omission , –,  overdetermined , – positive  pre-emptive double prevention  turning on a light – see causation, action at a distance, causation, intrinsic character of; fighter-bomber cases, locality Price, Huw , , , –, –, , –, –, , , ,  primary intension – primitive counterfactualism  primitive non-symmetric chance-raising see chance-raising, primitive non-symmetric Principal Principle –, –, –, , – general  Htw  new principal principle , – pragmatic justification – special  Tw  Prior, Arthur  Prior, Elizabeth  priority monism , , – priority ordering of non-symmetries  probability of causation (PofC)  probabilistic-dependence – probabilistic independence of decision and actionP–, , –,  probabilistic -dependence P see -probability conditions P probabilistic -time-dependence P see -probability conditions P probabilistic -T-dependence P see -probability conditions probability, agent/probability, agent-generated fictional – role in similarity weighting for counterfactuals –,  probability evidential , , , – mean value of  relative – process theories of causation (CI) 



(CI*)  (CII)  conservation of a quantity , –, –, , , , ,  intuition of difference – non-necessary/empirical – (MT)  non gerrymandered objects and circularity  transfer/transmission of energy , –, –, , , , , ,  transmission of a mark –, – transmission of a quantity , –, ,  trope, persistence of ,  see causation; cause, chance-lowering; negative causation; prevention; processes processes –, –, –, , , , , , –, –, , , –, , , , , ,  competing/competitor , ,  complete , –, –, , , , –, , , –, , , , –, , , , , , ,  genuine , –, , , , , , , , –, –, –, –, , ,  incomplete , , , –,  independent  intrinsicality of – mechanical, see genuine modular – nomically characterized  non-causal – perceptual –,  pre-empted , – pseudo ,  substantial, see genuine thermodynamic  transitivity of causal processes – unbroken – propensities dispositions to have chances  disposition to produce a long-run frequency  disposition to have a relative limiting frequency  (L)  (L*)  primed dispositions  triggered dispositions – weight of physical possibility  see propensity theories propensity theories global supervenience 





propensity theories (cont.) Humphrey paradox  hybrid  long term or limiting relative frequency  single case  properties abundant  accidental intrinsics see accidental intrinsics broadly physical –, –, –,  determinable , –, , , , –, , –, , , –, , –, , – determinate , , –, , , –, , –, –, –, , , , , , , , – intrinsic , , , , , –, –, , ,  as best satisfier of intrinsic-making features in a world  see intrinsic-making features; properties, maximal recombination macro-properties , –, , , , , –,  maximal recombination – metaphysical relation between properties – micro-properties , –, , ,  minimal supervenience-base  modal , –, –, , , –, , , – modal, brute  narrowly physical , , , , –, , , ,  natural , –, , –, , –, , , , ,  see also natural relation; universals perfectly natural , ,  realized –, , , , –, , , –, –, – realising –, , , ,  relational , , –, , , , , , – sortal  sparse , –, ,  structural , , , , –, , ,  subvenient  supervenience-base –,  supervening –, , , , , , ,  symmetrically related – property causation , , , , ,  avoidance strategies  challenge from redundancy 

close world redundancy, different patterns of – (PAm)  (PAb)  emphasis  distinct from event causation  explanatory virtues , , – fundamental ,  generality condition , – inadequacy  laws –,  particularity condition – property instance causation , , –, , – realization of  response to challenge of efficacy of supervening properties  superfluity – trope solution – see trope metaphysics truth-makers of chances  unmotivated asymmetry – see causal relata; inference-base of causal statements property instances – as continuants , – coarsely individuated – distinct property instances strategy – identification conditions –,  instantiation and necessitation  moments  P  see property causation, property instance causation proposition explanation of truth distinctively relevant  general propositions  involving negative predications  negative existential propositions – set of possible worlds – truth depends on world  see truth supervenes on being truth explained  proto-probability/probabilification  Pruss, Alexander R. , , – Psillos, Stathis , ,  psychopath button case – pushing your head back case – Putnam, Hilary , , –, , , ,  qualitative , , , , , , ,  qualities –, , , , , –,  quality supervenience see Humean supervenience, quality supervenience

 quantum correlation as non-supervenient relation  quantum entanglement  quantum mechanics , , –,  Copenhagen Interpretation  quidditism , –,  distinctness without a difference objection  epistemological objection – semantic objection  Quine, Willard Van Orman , ,  radioactive decay ,  isotopes  Ramachandran, Murali , –, , , ,  Ramsey, Frank , ,  ratification, principle of  reality fundamentally conjunctive  infinitely decomposable  realization , , –, , ,  subset account of/thesis –, ,  recombination ,  maximisation , – principle of , , , , , , , –, – Redhead, Michael  reductive counterfactualism  redundant causation close-world redundant causation  fixing accounts of , , , , –, ,  overdetermination see overdetermination pre-emption see pre-emption subtracting/subtraction approach , –,  reference-fixing  RF – reflective equilibrium see analysis, reflective equilibrium regular succession ,  regularity/regularities –, , –, , , , , –, , , , –, , , , , –,  accidental , , , –, , ,  non-accidental –,  regularity-causation gap (R₁) – (R₂) – regularity theory see causation, regularity theory; laws, regularity theory



Reichenbach, Hans –, – Reid, Thomas ,  relation anti-symmetric  asymmetric  brute relation of awareness  intransitive  non-symmetric  non-transitive  symmetric  relativity, special theory of , –, – resemblance , , , –, , –, –, –,  resemblance nominalism – responsibility , , , , , – disjunctive account of – doing A intentionally – doing A knowingly  see Knobe effect Restall, Greg – Rives, Bradley , , –,  Robb, David , ,  Roberts, John T. , , – Robinson, Denis – Robinson, Howard  Rodriguez-Pereyra, Gonzalo –, ,  Rosen, Deborah  Rosen, Gideon , ,  Rosenberg, Alexander  Ruben, David-Hillel  Russell, Bertrand ,  Sainsbury, R. M. (Mark) – Salmon, Wesley C. , –, –, – Sanford, David H. , , ,  Sartorio, Carolina , , –, –,  Schaffer, Jonathan , , , , , –, , , , –, , , , , , , , , ,  Scheines, Richard  Schick, Frederic  Schiffer, Stephen  Schlick, Moritz  Schlottmann, Anne – Scholl, Brian J. – Schrenk, Markus ,  Schulz, Eric  screening-off ,  second law of thermodynamics ,  secondary intension – Segal, Gabriel , –,  semantically neutral concepts  Shanks, David R. –,  Shanteau, James  Shoemaker, Sydney , , , , , , 





Shope, Robert K.  Sider, Theodore , , , , ,  Siegel, Susanna ,  P -dependence condition – P -probability Pconditions make less -probable  P probabilistic -dependence – revised account of because of hasterners/ delayersP –, –,  probabilistic P-T dependence  probabilistic -time-dependence  P -probabilistic independence  P -set membership restriction , – Simons, Peter M.  simplicity , , – Skiles, Alexander  Skow, Bradford –, –,  Skyrms, Brian , , , , ,  Slote, Michael  Smart, J. J. C.  Smith, Barry  Snowdon, Paul ,  Sober, Elliot , –,  social cognition – see pragmatic view of causes Socrates and hemlock – (S)  (S)  (S)  (S)  (S)  (S)  (SC)  (SC)  (SC)  Socrates and Xantippe –, – {Socrates} ,  soprano case  space-time  density of  spatial extent –,  spatial parts ,  spatial region –, ,  special sciences, causation in ,  see property causation species ,  capacity for additional properties  independently special differentiating feature  speech perception  spin up/spin down, see angular momentum Spirtes, Peter  Stalnaker, Robert –, ,  states , –,  states of affairs , , –, , –, , –, , ,  see facts Stern, Cindy D.  Stevenson, Charles L. 

Steward, Helen , –,  Stich, Stephen – Stoljar, Daniel –, ,  Strawson, Galen , –, ,  Strawson, P. F. , ,  strength laws , – propensities , , ,  Strevens, Michael , , ,  structure –, –, –,  Sturgeon, Scott ,  subpoena case –,  subtracting/subtraction approach see redundant causation, substracting/ subtraction approach sunburn case – Suppes, Patrick –,  subjunctive conditional see counterfactuals, subjunctive conditional subset thesis see realization, subset account of/thesis superluminal causation, see causation, superluminal superluminal signalling – supervenience , , , ,  grounding see grounding of causal relationships –, , ,  see also causal relata; property, property instance causation of truth see truth supervenes on being supervenience-base –, , ,  see Humean supervenience; properties, subvenient; properties, subveniencebase; properties, supervening; swamp probabilities ,  Suzy’s cramp  Swain, Marshall  Swoyer, Chris , ,  Tables . Types of Counterfactualism  . Tooley’s case  . Imperfect Community  . Dowe on Negative Causation  . Loneliness and Accompaniment  . Egg Cracking and Cooking Sequence  . Classic Newcomb Problem  . Psychopath Case  . Psychopath Case with Illustrative Pay-offs  Taylor, Barry  Taylor, Richard , ,  temporal direction , , –, , , , ,  preponderant causal direction –,  temporal extent , , , –

 temporal parts , , , – temporal precedence, causal theory of , – terdurantist  theoretical identification ,  things in themselves  thought experiment ,  Tichy, Pavel  tickle identification claim (A)  tickle response , – time , –, , – asymmetry, de facto  closed – direction of – see temporal direction entropy  loops  time invariance of laws  time reverse , – time symmetry of laws ,  see temporal precedence, causal theory of Tooley, Michael , , , , , –, –, , , , –, , , ,  Tooley’s inverse universes – Tooley’s simple  particle world – transition period , –, , , , , –,  cable cutters and the holocaust – graceful transition –, ,  Hausman’s reactor case – substantial miracle  thief and the stolen coat – Tooley’s case of backward causation – transitivity of causation distinct property instances strategy  contrastive approach  transmission of causality principle  Tremoulet, Patrice  triggered dispositions see propensities, triggered dispositions Trogdon, Kelly – trope metaphysics –, , , –,  tropes as indicative of causal relations –, –,  see process theories, trope, persistence of tropes as truthmakers  trope identity – trumping cases ,  truth supervenes on being , , , ,  truth-base/truth-basing , –, , ,  truth-making/truth-maker , , , –, , –, –, , , –,  and events  being fundamental as a truth-maker  conjunctive –



maximalism  necessitation –, –, , , –,  negative  particulars qua F – (T) see truth-making/truth-maker, necessitation see propositions two conceptions response  two slabs case – two way causal interaction – two-dimensional semantics  two-way positive dependency account – Tugby, Matthew  Turner, Jason  Tye, Michael  undermining future , –, –,  Fu  unigrade – uninterfered-with potence  uniqueness assumption see possible worlds, uniqueness assumption universal generalisation belief in  universals –, –,  and laws –, – Aristotelian  platonic , ,  numerical identity of  structural , , –, – wholly present , , –, –,  vagueness, supervaluationist  Vallentyne, Peter  Van Fraassen, Bas C. ,  variable realisation , –,  mental states  see causal non-symmetry, realisation of; causation, realization of; laws, variable realisation vase cases –, –, –, ,  Velleman, J. David  Verdi – vertical necessitation relations, challenge from – avoidance strategies – Vihvelin, Kadri  void, the deadly ,  Von Wright, Georg Henrik – Vranas, Peter B. M.  Ward, Barry  Wasserman, E.A.  Wasserman, Ryan  wave front/segment –,  weak counterfactualism  Weatherson, Brian 





Weinberg, Jonathan M. , – White, Peter A. ,  Williams, J. Robert G. (Robbie) – Williamson, Timothy –,  Wilson, Jessica , –, , , ,  Wilson, N. L.  Witmer, D. Gene  Wittgenstein, Ludwig  Wolterstorff, Nicholas  Woodward, James , , , , , , – worlds

essential properties of – essentially total  most extensive entities  Wright, John P.  Yablo, Stephen , , –, –, , , , ,  Yagisawa, Takashi  Zalla, Tiziana  zombies , 